ECE 353 Cognitive Development of Infants & Young Children/ week 4 discussion 1 and 2, and journal

What is Special Education? 1

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Pre-Test

1. 1. You can use the terms disability and handicap interchangeably. T/F 2. 2. The history of special education began in Europe. T/F 3. 3. The first American legislation that protected students with disabilities was passed in the 1950s.

T/F 4. 4. All students with disabilities should be educated in special education classrooms. T/F 5. 5. Special education law is constantly reinterpreted. T/F

6. Answers can be found at the end of the chapter.

8Problem Solving and Reasoning

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Learning Objectives By the end of this chapter, you should be able to:

• Analyze the nature of problem solving and its emergence in infants and toddlers.

• Explain how analogical reasoning is used to solve problems in different contexts.

• Describe the nature of planning and factors that facilitate the development and use of the skill.

• Relate divergent thinking to effective tool use in the context of problem solving.

• Analyze how children discover and use rules to solve problems.

• Outline the differences between intuitive and analytical processes of reasoning in children, including the development of those processes.

• Summarize the foundations of scientific thinking and the evidence that those foundations are present in young children.

Pretest Questions

Pretest Questions

1. By age 2, infants can anticipate the consequences of their problem-solving efforts and adjust accordingly. T/F

2. Four- and 5-year-olds cannot explicitly detect analogies between one relationship and another because they cannot think abstractly. T/F

3. Individual differences at age 4 in the executive functions predict differences in children’s planning skills even into the grade school years. T/F

4. Sometimes knowing too much about an object’s function is counterproductive, such as when it interferes with one’s ability to see how the object might serve in a novel way. T/F

5. Asking children to explain why they tried to solve a task the way they did is a counterproductive distraction that negatively impacts their ability to eventually find a solution. T/F

6. Instructing children to “pretend” or “make believe” improves their ability to reason logically. T/F

7. When grade school children are free to investigate on their own in learning how to conduct scientific experiments, they experience greater and longer lasting gains than when they receive explicit instruction. T/F

Maria is a sixth-grade student who has just arrived home from school. Her mom, Mrs. Garcia, asks Maria about her day. Maria had quite a busy day and shares her experiences. Maria says her history teacher asked her to write an essay about what would have happened to the civil rights movement in the United States if Martin Luther King Jr. had not been assassinated. Then in math class, her teacher worked out a few example problems on the board and gave her a math worksheet to complete during class. Maria tells her mom all about how she collaborated with her biology partner to record and evaluate data on an experiment examining the effect of acid rain on plant growth. Finally, Maria tells her mother that the chain on her bike came loose dur- ing her ride home. She did not have any tools, so she improvised a solution, drawing on a similar situation she experienced last month.

These scenarios, which are part of a fairly typical school day for a busy student, highlight the importance of reasoning and problem solving. Her mother is impressed with Maria, since the history class assignment required her to reason about consequences that follow from a hypo- thetical premise. Her mother thinks that in math class, Maria used effective problem-solving skills that required her to detect relationships between the example problems and the new prob- lems on the worksheet. Garcia tells Maria that she did a great job in her biology class, since the assignment required her to think scientifically about what she can and cannot conclude from her evidence.

Finally, Garcia points out that repairing the loose chain required all of the skills previously men- tioned. During her day, Maria engaged in (a) the type of careful analysis found in scientific thinking, (b) problem solving as she generated a solution, and (c) reasoning. Maria smiles and is proud of her accomplishments. She then starts to wonder how best to construct a rational argu- ment to convince her parents that she needs a new bicycle!

Introduction

Questions to Think About

1. Maria’s essay assignment requires her to imagine events that differ from what actu- ally happened. How is the assignment similar and different from designing a scien- tific experiment?

2. Maria’s math teacher presented examples before assigning students problems to solve on their own. Do you think children would learn more if they relied less on examples and instead simply worked out the problems on their own, using trial and error to discover solutions? Why or why not?

3. In science class, if Maria’s predicted outcome was not supported by the data, how would you help her to systematically figure out if the unexpected result was due to a design flaw in the experiment? What reasoning skills would you nurture to help Maria think through the problematic results of the study?

Introduction The topic of this chapter is one that underlies a significant portion of our lives. When we reflect for a moment, we can see that numerous everyday activities draw on sophisticated rea- soning and problem-solving skills. Whether we are following a recipe, maneuvering through traffic, figuring out bus or subway schedules, or navigating the Internet to find a reasonable hotel price, we are engaging in a series of decisions that require reasoning and deliberation. We compare and contrast information, consider possible consequences (both intended and unintended), and engage in trial-and-error efforts to arrive at the best outcome.

The wide-ranging impacts of reasoning and problem-solving skills are, of course, not restricted to adulthood. As we saw in the case study, reasoning and problem-solving skills influence children’s schoolwork in a variety of subjects. Those skills are also necessary for everyday challenges like fixing a bicycle or constructing a convincing argument for a new bicycle. In sum, the focus of this chapter—the development of reasoning and problem-solving skills— involves a topic that is central to our lives.

Core Themes, Reasoning, and Problem Solving In this chapter, we will look at the development of reasoning and problem solving in the con- text of the four overarching themes of the book. The themes broadly apply because they frame our understanding of how children approach and solve problems in a wide range of contexts.

Nature and nurture. Early competency in infancy suggests innate capabilities (nature) in areas of reasoning and problem solving. However, we will encounter evidence that suggests that experiences like practice and instruction advance the development of problem-solving skills and scientific thinking, which indicates an important role for nurture as well.

Continuity and discontinuity. This chapter’s discussion of Piaget’s theory and IP theory high- lights the continuity–discontinuity theme. We will examine whether children’s reasoning develops in distinct stages (discontinuity) or instead varies in sophistication depending on the task (continuity).

Section 8.1Problem Solving

Domain general and domain specific. We will see that children acquire general principles, such as inferring cause and effect or drawing a logical conclusion, that apply across domains. In this sense, the abilities we discuss are domain general (Markman & Gentner, 2001). However, we will also see how children’s reasoning depends on the specific content and context of the problem they are solving. In this sense, the processes are domain specific (Markman & Gentner, 2001).

Performance and competence. Recall that the performance–competence theme involves the challenge of sensitively measuring children’s knowledge without over- or underestimating their competence (knowledge). A sensitive measurement minimizes performance demands that may be taxing to children. Performance demands involve the length of time of the testing, the com- plexity of the instructions, and so forth. As we describe performance demands that impact the quality of children’s reasoning, we will be illustrating the performance–competence theme.

8.1 Problem Solving Adults do not always realize that, just like them, infants and children are confronted with obstacles on a daily basis. Simple goals like figuring out how to reach a toy or drink from a sippy cup require cognitive processes to find a solution. Effective problem solving is a skill that broadly impacts children’s lives. Given the number and range of possible problems chil- dren face on any given day, it is helpful to ask if there are cognitive processes that are common to problem solving in general. If so, those abilities would be especially important to target in instruction because they would have a broad and domain-general impact on development.

In this section, we define the fundamental components of problem solving and describe its early emergence in infancy. In the next few sections, we examine the development of three cognitive processes—analogical reasoning, planning, and tool use—that generally underlie effective problem solving.

Problem solving is often viewed from an IP theory perspective. Recall that IP theory places an emphasis on detailed observations that allow us to see up close the process of developmental change. In that context, we take an extended look at children’s attempts to solve a classic phys- ics problem concerning the qualities of density and volume. Detailed observations can provide general insights into how instruction can effectively promote the discovery of solutions.

In the News: Common Core Standards The Common Core state standards are academic standards adopted by many states. The stan- dards are intended to ensure that all students possess sufficient knowledge and skill to succeed after high school. The introduction of Common Core has engaged proponents and critics in a debate over reasonable and effective goals for children’s learning. Follow the link to the Com- mon Core standards website below. How many times are problem-solving skills referenced?

http://www.corestandards.org/read-the-standards

Critical-Thinking Question

Why do you think problem-solving skills are given such prominence within the new standards?

Section 8.1Problem Solving

Problem solving consists of (a) identifying a goal, (b) developing and enacting a solution, and (c) monitoring the attempted solution’s effects and making corrections as necessary (Friedman & Scholnick, 1997; Keen, 2011). To illustrate some foundational features of prob- lem solving, we consider a problem typically faced in the infant or toddler stage of childhood: how to eat with a spoon. We see each component of problem solving in this effort. Success first involves identifying the goal—getting food in the mouth. The second step is to develop a solution. This involves identifying that the spoon is a useful tool for attaining the goal and then trying to eat with it. The third step is monitoring the success of the attempted solution and making modifications when necessary.

How effectively do infants and toddlers solve the problem of feeding themselves with a spoon? Three different age groups (9-, 14-, and 19-month-olds) were studied to investigate this ques- tion (McCarty, Clifton, & Collard, 1999). Each child was seated in front of a bowl of applesauce and a small spoon. The children typically grabbed the spoon with one of three grips (see Figure 8.1).

Figure 8.1: Infants’ and toddlers’ grip of a spoon in a problem-solving task

Infants and toddlers were presented with a spoon that was next to either their dominant or nondominant hand. When the spoon was placed next to their nonpreferred hand, developmental differences in problem solving emerged.

Source: Adapted from Keen, R. (2011). The development of problem solving in young children: A critical cognitive skill. Annual Review of Psychology, 62, 1–21. Modified from McCarty, M. E., Clifton, R. K., & Collard, R. R. (1999). Problem solving in infancy: The emergence of an action plan. Developmental Psychology, 35(4), 1091–1101.

Developmental differences in problem solving emerged when the handle of the spoon pointed toward the infant or toddler’s nonpreferred hand. To appreciate the problem this arrange- ment poses, place a spoon (or some other object as a stand-in) with its handle pointing toward your nondominant hand. Infants reach for the spoon over the top rather than underneath it. If using your dominant hand, you will see that the easiest maneuver when reaching over the top is simply grabbing the bowl of the spoon (bowl-end grip, see Figure 8.1). The 19-month-olds often avoided this outcome by reaching for the spoon with their nonpreferred hand, which allowed them to use the more effective radial grip.

Section 8.2Analogical Reasoning

The younger infants tended to pick up the spoon with their dominant hand by using a bowl- end or ulnar grasp grip. They were not, evidently, monitoring their attempted solution and did not make corrections until after the spoon handle (and no food) was in their mouths. The 14-month-olds were more likely to anticipate the handle would end up in their mouths and made corrections. For example, after gripping the spoon they would place it back on the table and turn it around until it was successfully reoriented so that they could get the bowl of the spoon into their mouths (Keen, 2011).

These differences reveal a lot about the early development of problem solving (Keen, 2011). The oldest children were capable of formulating a plan before acting. The children in the sec- ond oldest age group were not as plan oriented but were able to closely monitor their action and correct their ineffective grip. The youngest infants were not particularly plan oriented or careful in their monitoring. Sometimes they adjusted and manipulated the spoon only after their failure to get food into their mouth. We see a series of successful intermediate steps before the problem is most effectively solved.

Notice that the outlines of this developmental progression reflect some of the qualities Piaget described in his theory of infant cognitive development (see Chapter 2). Infants dis- play means–end understanding during the sensorimotor period in Piaget’s theory (8 to 12 months). In solving the problem of feeding oneself, means–end understanding was demon- strated as 9-month-olds used the spoon as a tool to achieve their goal.

Later, in sensorimotor development, the mastery of object permanence involves solving prob- lems mentally by keeping track of hidden objects in order to find them. Older infants and tod- dlers became increasingly sophisticated in their ability to mentally devise plans and solutions to the problem of eating with a spoon. The oldest age group figured out the problem of reach- ing for the spoon with their dominant hand and mentally devised a solution before acting.

In the next sections, we will see how the skills evident in learning to eat with a spoon (plan- ning and tool use) continue to develop. We will also see that older children have something in common with infants when problem solving. Specifically, learning to eat with a spoon is a

trial-and-error process. Generally speaking, children’s errors during problem solving should not surprise us. Nor should they necessarily discourage children from making further attempts. Errors provide feedback that children can use to make progress. From infants’ exam- ple, we can see the value of allowing children to actively engage with a problem and attempt to solve it. Progress can emerge through active attempts and failures along the way.

8.2 Analogical Reasoning Once a problem’s solution is discovered, the knowledge can be transferred to new situations. This is a key component of learning. This is evident, for instance, when teachers and parents instruct with examples and expect children to extrapolate what they learned to new situations and related problems. As they approach their first birthday, infants appear capable of learning from examples. That is, they are capable of observing how an adult solves a problem—such

Question to Consider

Can you think of other everyday problems that infants and toddlers try to solve? What developmental differences between a 12- and 18-month-old might arise when solving those problems?

Section 8.2Analogical Reasoning

as obtaining an out-of-reach toy by pulling a string—and then applying what they saw to new, related problems that involve getting an object on their own (Chen, Sanchez, & Campbell, 1997).

Generalizing a solution to a new problem is a form of analogical reasoning. Analogical rea- soning involves detecting a relationship between two entities and then extending that rela- tionship to other pairings (Goswami, 2013). For instance, the relationship between hammer and nail is analogous to saw and wood because both pairings share the underlying relational structure of tool-to-use.

Analogies are crucial for transferring knowledge one already possesses to new situations and encounters. For instance, once 3-year-olds are taught that the solution for one problem involves stacking bales of hay to reach the top of a tractor, they transfer this knowledge to another problem in which the solution involves stacking telephone books to reach a jar (Brown, Kane, & Long, 1989). For older children, thinking analogically is helpful when learning how to read (Goswami, 1993). If a beginning reader learns the vowel a is silent when it directly follows the vowel o (for example, soap), knowing that the second vowel is silent transfers when the child encounters other words with two consecutive vowels (for example, leap and treat).

The cognitive capacity to solve analogy problems with familiar entities (like dogs and birds), even when incorrect options serve as distractors, is evident around ages 4 to 5 (Goswami & Brown, 1990). For instance, when told “Bird is to nest as dog is to ?,” 4- and 5-year-olds chose doghouse to complete the analogy even though they were given other options like bone that were associated with dogs (see Figure 8.2). As we saw in Chapter 5, young children pos- sess a relatively sophisticated store of knowledge about, and interest in, living things. Their early familiarity with animals likely contributes to their success at detecting such relation- ships (Vosniadou, 1989).

Figure 8.2: Analogical reasoning in preschoolers

A test of analogical reasoning for 4- and 5-year-olds.

Source: Adapted from Goswami, U., & Brown, A. L. (1990). Higher-order structure and relational reasoning: Contrasting analogical and thematic relations. Cognition, 36(3), 207–226.

Section 8.3Planning

Rather than following a stage-like development, children’s ability to solve analogies is highly variable across tasks. In particular, children’s analogical reasoning depends on their general knowledge of information relevant to the relationships they are trying to infer (Goswami, 2013). A child unfamiliar with world geography will find it difficult to infer that Europe is the correct answer in the analogical relationship Andes: South America :: Alps: ? As children’s gen- eral knowledge base increases, their analogical reasoning improves (Goswami, 1991. Thus, although the capacity for analogical reasoning may be present in early childhood, subsequent detection of analogies is dependent on learning.

Development of the EFs also influences analogical reasoning. For instance, analogical reason- ing can be complicated when two objects look similar but are otherwise unrelated. If given the analogy tree: apple :: vine: ?, children might be tempted to complete the analogy by choos- ing a picture of a red circle instead of a grape because the circle looks like the apple.

The development of inhibitory control (introduced in Chapter 3) helps children ignore irrel- evant superficial similarities between stimuli when inferring analogical relationships (Rich- land, Morrison, & Holyoak, 2006; Thibaut, French, & Vezneva, 2010). In a longitudinal study, individual differences in inhibitory control at age 4 predicted successful analogical reasoning at age 15 (Richland & Burchinal, 2013). This finding illustrates continuity in development and the domain-general impact of inhibitory control on cognitive development.

Analogical reasoning involves comparing relationships; that is, determining how the relation- ship between A and B compares to the relationship between C and D. When a child says, “I know how to solve this problem, it is like one I did before,” he or she is detecting an analogous correspondence—a relationship between two sets of problems (Richland, 2011). In our case study, the math examples presented by the teacher offered an opportunity for Maria to detect relationships in the examples and find corresponding relationships in new problems. Prompt- ing children to look for comparisons during coursework positively impacts their learning in the classroom (Rittle-Johnson & Star, 2011).

To illustrate, consider how a teacher used analogy as an instructional technique for eighth graders when prompting them to compare how two geometry problems were solved: “Do you remember how we found the perimeter and area of polygons last week? This time it is the same concept but we are going to use similar formulas to solve for circumference and area of

a circle” (Richland, Holyoak, & Stigler, 2004, p. 45).

In this example, the teacher is helping children detect generalizations of knowledge they have already learned and apply them to new math problems (Richland, Zur, & Holyoak, 2007).

8.3 Planning Problems are usually challenging because they do not have an immediate, obvious solution. Whether a young child is building an elaborate toy house with blocks or an older child is trying to determine which equation to use when solving a math word problem, it is usually necessary to formulate a plan before actually tackling the problem. Planning is deciding on a course of action prior to attempting a solution (Friedman & Scholnick, 1997). Notice that

Question to Consider

In what ways could analogies prove useful for teaching in a preschool classroom?

Section 8.3Planning

planning requires identifying a goal—thinking ahead—before acting. Planning also involves figuring out the step(s) necessary to reach the goal.

An illustration of planning in everyday contexts is the end-state comfort effect. This refers to adopting an initial awkward posture to efficiently ensure a comfortable end posture when manipulating objects (Adalbjornsson, Fischman, & Rudisill, 2008). To illustrate, place a cup upside down and reach for it with the plan of turning it upright to fill it with water. When you first reach for the cup your thumb is most likely pointing downward. Inverting your hand is a temporary awkward movement, but you do it because it ensures a comfortable end-state because the thumb faces upward when the cup is upturned.

Close observations of young children grasping an upside-down cup revealed a very different approach. Children ages 2 to 6 often reached for the cup with their thumb up. Consequently, children often placed the cup against their chest or on the table as they regrasped it in order to comfortably hold it. They did not incorporate an intermediate plan—thumb down—in ser- vice of the overall goal of comfortably holding the upturned cup (Adalbjornsson et al., 2008).

Planning, of course, extends beyond tasks that require manipulating objects. We see a similar developmental pattern of ignoring intermediate steps when planning how to solve cognitive tasks. The Tower of London is a common cognitive assessment of planning in which children have to vertically arrange a set of discs to match a model; it requires them to move the discs among pegs in as few moves as possible (see Figure 8.3). Successful planning on the Tower of London and on similar tower tasks is measured by whether children complete the task in the minimum number of moves.

Notice in Figure 8.3 that a variant of the three-move problem for the Tower of London requires planning ahead and making an intermediate move. We see again the challenge of making a temporary counterintuitive move in order to obtain a goal. This means children have to move one ball to a temporarily “wrong” position before ultimately placing it on the correct peg.

Figure 8.3: Tower of London Task

The initial state (far left) and goal (far right) in the three-move version of the Tower of London. Note that in (a), the white ball has to be moved to a temporary location (first move) before its correct placement at the top of the tower. In the easier task, (b), the balls are stacked one at a time without the need of an intermediate step.

(a)

(b)

Source: Adapted from McCormack, T., & Atance, C. M. (2011). Planning in young children: A review and synthesis. Developmental Review, 31(1), 1-31. Reprinted with permission from Elsevier.

Section 8.3Planning

In one study, although 4-year-olds were very accurate on problems that did not require an intermediate step, they struggled when they had to generate the intermediate step (a sub- goal) in service of obtaining the overall goal (Kaller, Rahm, Spreer, Mader, & Unterrainer, 2008). Five-year-olds, in contrast, were significantly better at planning the intermediate step (Kaller et al., 2008). More complicated tower tasks requiring a greater number of moves reveal gradual improvement between ages 6 and 13 in planning and making the minimum number of moves (Unterrainer et al., 2014).

Evidence is somewhat mixed, but overall, individual differences in inhibitory control appear to be a contributing factor to successful planning on tower tasks for young children (McCor- mack & Atance, 2011). Inhibitory control presumably facilitates children’s ability to resist jumping into a problem without first planning its solution.

For instance, for relatively complex tower tasks requiring five or more moves to solve, there was a significant increase from childhood (ages 10 to 15) to later adolescence (ages 16 to 17) in the amount of time individuals waited before making their first move (Steinberg et al., 2008). The extra waiting time presumably reflects inhibitory control and careful planning compared to younger children, who instead tend to begin trying to solve complex problems more quickly (Luciana, Collins, Olson, & Schissel, 2009). Related, a tendency toward impul- sivity may contribute to the deficits in planning on tower tasks among children with ADHD (Aguiar, Eubig, & Schantz, 2010; Sarkis, Sarkis, Marshall, & Archer, 2005).

The importance of planning is evident in how children solve problems in school. For instance, inefficient planning on the Tower of London is also linked to arithmetic difficulties in children ages 7 to 18 years (Sikora, Haley, Edwards, & Butler, 2002).

Consider how math problems can have multiple, counterintuitive steps that draw on effec- tive planning skills. When adding fractions, the denominators must be the same. However, children have learned to add whole numbers by simply summing them; consequently, the new intermediate step of finding a common denominator for fractions is counterintuitive and a source of error (Siegler, Fazio, Bailey, & Zhou, 2013). Thus, when given a problem such as 1/3 + 1/6, children have to plan ahead by finding the common denominator rather than erro- neously summing the denominators. We discuss the development of math skills further in Chapter 11.

Facilitating Planning in Children Various factors can facilitate planning in childhood. For young children in preschool and kin- dergarten (roughly ages 3 to 6 years), strategies for helping them learn to plan can take place in the context of play (Bodrova & Leong, 2007). Children might draw who they will pretend to be during a game (for example, a police officer) and then draw some things they plan to do while playing that role. As children are learning to write, they might first create an outline before writing a story. More generally, adults can collaboratively involve children in planning processes (for example, planning a trip to the beach) and in doing so perhaps facilitate the development of strategic, efficient planning (Gauvain & Rogoff, 1989).

A possible contributor to successful planning in children is self-talk or private speech (dis- cussed in Chapter 7). Recall that Vygotsky believed private speech helps children regulate and guide behavior. It occurs among some children as they attempt the Tower of London

Section 8.4Divergent Thinking and Tools

task, when they utter self-directed statements like “This one’s in the way” and “This isn’t right” (Lidstone, Meins, & Fernyhough, 2011, p. 208). The occurrence of task-relevant private speech while working on the Tower of London task was predictive of successful planning in 5- and 6-year-olds (Fernyhough & Fradley, 2005). This finding is consistent with social constructivist theories that emphasize the role of language in cognitive development (see Chapter 7).

Similarly, encouraging children to outwardly verbalize if–then plans—such as, “If I am in the middle of doing my homework, then I will ignore incoming text messages” (Wieber, von Suchodoletz, Heikamp, Trommsdorff, & Gollwitzer, 2011, p. 40)—can significantly improve school-aged children’s performance on cognitive tasks (see also Gawrilow, Gollwitzer, & Oet- tingen, 2011a, 2011b). In general, when children have difficulty sustaining attention, con- crete reminders—such as a small set of written if–then statements placed in front of them while they work—may be helpful reminders of goals and plans.

Individual differences in children’s EF skills at age 4 predict differences in planning skills (assessed with a variant of the Tower of London task) in the grade school years (Friedman et al., 2014). Consequently, the EF training and intervention efforts discussed in Chapter 3 are relevant for improving children’s planning. Practice on tasks that require planning can also be helpful. To illustrate, practice on computerized games that involved planning moves ahead of making them helped improve third graders’ planning skills (Goldin et al., 2013).

For children who have difficulty organizing and plan- ning their homework and other activities, tools such as planners can help them prioritize activities and manage time more effectively (Rief, 2013). Similarly, notebooks that contain assignments that are color coded (perhaps into categories such as “doing” and “not started”) can also help in planning activities (Rief, 2013).

8.4 Divergent Thinking and Tools Adults can readily attest that many jobs—from professional work to activities such as gar- dening, building a bird house, or preparing a gourmet dinner at home—are made easier with tools. As we will see in this section, tool use can be observed in children very early in devel- opment. A challenge occurs when the tool we need for a task is not immediately available or obvious. Such instances pose a problem and often require a creative, insightful, improvised solution. In this section, we examine how children solve problems in the context of their abil- ity to recognize or create tools.

Tool use is overcoming physical limitations by using an instrument as a means to attain a goal (Lockman, 2000). From a nativist perspective, tool use is an adaptation, an inborn capacity, that confers a selective advantage for a variety of species (Biro, Haslam, & Rutz, 2013). Chim- panzees can use a stick to manipulate obstacles and obtain food that is otherwise out of reach (Whiten, Horner, & De Waal, 2005). Other primates also use percussive tools like stones to crack open objects such as nuts (Inoue-Nakamura & Matsuzawa, 1997).

Question to Consider

In this section, we talked about how EFs can support the development of planning. How might providing a child with concrete planning aids help compensate for some limitations in executive functioning?

Section 8.4Divergent Thinking and Tools

Humans’ motor skills, along with cognitive capacities such as reasoning and the EFs, enable complex, creative tool use that greatly exceeds the capacities found in nonhuman primates (Vaesen, 2012). This developmental process begins in infancy. Recall that infants can use simple tools like spoons or strings to solve problems. By age 2 toddlers possess the motor capability to use their wrist when hammering (with a toy hammer!). Hammering with a wrist enables a precision that is not found in other species, where hammering is more reliant on more gross motor movements of the shoulder and elbow (Kahrs, Jung, & Lockman, 2014).

Children have a developmental lag between successfully using and successfully creating tools. For instance, in one study, children had to figure out how to lift a tiny bucket out of a small test tube (see Figure 8.4). Children were given a pipe cleaner and a string (a distractor item) and encouraged to solve the problem (Cutting, Apperly, & Beck, 2011).

Although most children touched the pipe cleaner and investigated it, fewer than 10% of the 4- and 5-year-olds used it to make a hook that would latch onto the bucket and lift it out of the tube. In fact, only 30% of the 6- and 7-year-olds spontaneously generated a solution by creating a tool with the pipe cleaner.

Figure 8.4: Tool use in problem solving

Children are given a potential tool, in the form of a pipe cleaner (left) and a distractor item, a piece of string (right), for lifting the bucket out of the test tube.

Test tube 

Bucket

Pipe cleaner

Distractor item

Source: Adapted from Cutting, N., Apperly, I. A., & Beck, S. R. (2011). Why do children lack the flexibility to innovate tools? Journal of Experimental Child Psychology, 109(4), 497–511.

In Chapter 7 we learned about the importance of observation and imitation in devising solu- tions. Similarly, when young children observed someone transforming a pipe cleaner into a hook-like shape, they readily transferred the lesson and created a hook when confronted with the test tube problem (Cutting, Apperly, Chappelli, & Beck, 2014). Thus, with hints, young children can accurately identify an effective tool and use it when prompted to do so. Examples that serve as hints are a way in which adults can build a scaffold to facilitate and advance chil- dren’s thinking about a problem. Learning about tools from observation can also take place in other species (Tomasello, Davis-Dasilva, Camak, & Bard, 1987).

Section 8.4Divergent Thinking and Tools

If infants and children can use tools, why do they experience difficulty creating one on their own? One analysis concludes that creating a tool is an open-ended problem (Cutting et al., 2011). Open-ended problems are like essay questions on an exam in that solutions have to be generated by the individual. The open-endedness of a problem—its lack of a concrete, well- defined solution— appears to be problematic for children.

Divergent thinking flexibly generates multiple and original possibilities (Charles & Runco, 2001). This type of thinking is particularly useful for open-ended problems. In the context of tools, it involves thinking about the different ways everyday objects can be transformed and used. Rather than seeing the pipe cleaner as simply a pipe cleaner, for instance, divergent thinking produces new possibilities to investigate. Such thinking could promote the insight needed to fashion a new tool out of everyday materials.

A longitudinal analysis revealed a slight increase in divergent thinking between fourth and ninth grade (Claxton, Pannells, & Rhoads, 2005). In another study that measured divergent thinking by asking individuals to generate as many uses as possible for a brick, adolescents and adults articulated a comparable number of uses, but adolescents’ uses were less original than adults’ ideas (Kleibeuker, De Dreu, & Crone, 2013). One possible explanation for the improved quality of ideas is the greater amount of experience and knowledge adults can draw on compared to adolescents (Kleibeuker et al., 2013).

In contrast to divergent thinking, functional fixedness occurs when knowledge of an object’s typical function poses an obstacle to imagining its alternative use to solve a problem (Duncker, 1945; German & Defeyter, 2000). Functional fixedness is a curious case in which well-learned, established knowledge about an object is a potential disadvantage.

For example, in one study, 5- to 7-year-olds were asked to help a toy bear reach an object on a shelf (German & Defeyter, 2000). Among the objects that could be used to solve the problem was a container. The conventional function of the container is, of course, to secure and hold things. If overturned, however, it could also be used as a support on which a block tower could be placed, allowing the bear to reach the object.

After being reminded of the container’s conventional function, 5-year-olds were significantly faster than 7-year-olds at overcoming functional fixedness and using the container, unconventionally, as a support. The greater susceptibility of older children to functional fixedness was subsequently replicated for other problem-solving tasks (Defeyter & German, 2003).

Spotlight on Research: Preschoolers Outsmart College Students in Figuring Out Gadgets http://www.npr.org/blogs/health/2014/06/30/325230618/ preschoolers-outsmart-college-students-in-figuring-out-gadgets

This article discusses a study in which young children’s cognitive flexibility allowed them to solve a problem better than adults. How might pretend play promote the type of problem solv- ing preschoolers display in the article?

Question to Consider

How might analogical reasoning support divergent thinking?

Section 8.5Rule Use and Problem Solving

8.5 Rule Use and Problem Solving In this section, we take a closer look at how children approach a problem. Close scrutiny of children’s trial-to-trial efforts provides insight that generalizes to a broader understanding of how children approach problems. This understanding, in turn, informs how adults might effectively guide children toward achieving greater insight into finding solutions.

Examining the development of problem solving through detailed observations of children’s ongoing efforts is consistent with IP theory. Recall that IP theory views the computer as a metaphor for understanding how the mind works. Computer programs operate by following programming rules (if–then statements) designed to achieve a goal (Anderson, 1993; Munak- ata, 2006). In problem solving, rules are strategies systematically followed when carrying out a solution (Jansen & Van der Maas, 2002).

Rule use is evident when children consistently apply a particular approach to a problem set (Siegler & Chen, 2002). For instance, when solving multidigit addition problems, a rule for when to carry a number (“if the sum is greater than 10”) guides the solution of the problem (Ander- son, 1993). Errors result when children employ a less advanced rule that is ill suited for a rela- tively complex problem. For example, a child’s (relatively simple) rule for subtraction may be to always subtract the smaller number from the larger one. This rule would result in characteristic errors for multidigit problems that require “borrowing” (Young & O’Shea, 1981).

Theoretically, with practice, children are expected to sequentially progress from using less effective to more effective rules when problem solving (Siegler, 1985). To illustrate, first through fourth graders’ use of rules to solve a water displacement problem was measured over a series of trials. In the water displacement problem, children predicted which of two objects varying in weight, size (volume), and material (such as metal or wood) would cause a higher water level when dropped into a beaker of water (Siegler & Chen, 2008).

The study consisted of pretest, training, and posttest phases. During a pretest, children made their predictions about which of two objects would cause a greater level of water displace- ment. They typically adopted a rule-based approach (see Table 8.1).

Table 8.1: Examples of rules children used to predict water displacement

Rule Description

More-is-more rule No differentiation or integration: Weight and volume were not differentiated; for instance, if weight was unequal between two objects, the heavier was chosen as more likely to cause a higher water level. In contrast, if volume was unequal, the bigger object was chosen.

Weight and volume rule Differentiation but no integration: Reliance on just one dimension, weight, or volume to predict water displacement.

Correct rule Differentiation and integration: For floating objects the heavier object was pre- dicted as causing greater water displacement, and for sinking objects the larger object was predicted as causing greater water displacement.

Source: Siegler, R. S., & Chen, Z. (2008). Differentiation and integration: Guiding principles for analyzing cognitive change. Developmental Science, 11(4), 433–448.

Section 8.5Rule Use and Problem Solving

Next, during training, children again made predictions; however, unlike the pretest, this time children received feedback by witnessing whether their predictions were accurate. In one condition, after seeing the results on each trial, children were asked to explain why one pre- diction was correct and another prediction incorrect.

None of the children used the correct rule to solve the problems during pretest. During the training phase, children tended to advance from a lower level to a higher level. At posttest, older children (third and fourth graders) tended to have adopted the correct rule more fre- quently than the younger children.

An additional observation at posttest is especially relevant for children in instructional con- texts. Asking children during training to explain both correct and incorrect answers increased the likelihood they would eventually adopt the correct rule. Asking children to explain the various ways of answering a problem encourages them to think about why the observed out- come occurred and also why other possible outcomes did not occur (Lin, Siegler, & Sullivan, 2010). Children were, in other words, thinking about the problem from different perspec- tives, which apparently prompted a deeper understanding of it.

A number of related instructional strategies may facilitate grade school children’s learning as they attempt to discover solutions. We briefly outline three that are supported by empirical evidence (Honomichl & Chen, 2012; Lee & Anderson, 2013).

First, two children who might otherwise appear comparable will differ in how they benefit from the same experience because of the different assumptions each child holds (Honomi- chl & Chen, 2012). Recall Vygotsky’s concept of scaffolding (discussed in Chapter 7), which involves adapting the amount and type of guidance to provide challenges just above the child’s current level of understanding. In the context of problem solving, knowing the child’s underlying rules (that is, preexisting assumptions) can be very informative for revealing the partial knowledge the child brings to the task and the additional learning the child needs to discover.

Second, children’s learning is often facilitated when they receive feedback on the accuracy of their predictions and attempted solutions. Recall that in the water displacement study children saw the results of their predictions during training, and this feedback facilitated acquisition of the correct rule. Sometimes feedback consists of simply viewing the results of a predic- tion. Other times it may need to be more direct and explicit if a child’s ini- tial understanding is limited.

Third, prompting children to explain answers helps them elaborate on and articulate their understanding of a problem. Recall the greater success in

Comstock Images/Stockbyte/Thinkstock Providing feedback and asking children to explain their reasoning are some instructional strategies that can help children improve their problem- solving abilities.

Section 8.6The Development of Deductive Reasoning

the water displacement task that was associated with prompting the child to explain why predictions were correct or incorrect.

Asking questions like “Tell me why you think it’s not working?” or “When you did that, why did this happen?” prompts children to become aware of faulty assump- tions and gaps in their reasoning (Chi, de Leeuw, Chiu, & LaVancher, 1994). Prompts for specific explanations can also draw children’s attention to aspects of a prob- lem they may otherwise overlook (Legare, 2014). Prompting can help children progress through the zone of proximal development as their answers promote reflection, refinement, and progress.

8.6 The Development of Deductive Reasoning It is an understatement to say that parents can find it challenging to reason with toddlers. Toddlers seem unconvinced by logical arguments for why eating as many cookies as they please before dinner is a bad idea. What the 2-year-old perceives as an injustice is understood by parents as best for the child’s welfare. Rather than helping the child see the hypothetical consequences of doing as he or she pleases, the parents’ rationale may seem beyond the grasp of a 2-year-old. What does it mean for a child to be “reasonable” or “logical”? What cogni- tive characteristics help children think through possibilities and consequences, and when do these characteristics develop? We address such questions in the following section.

We begin with a focus on Piaget’s theory. Piaget, as we will see, was interested in the devel- opment of the ability to think systematically about possibilities. This includes questioning one’s own assumptions, supposing something is true even if it is not, and then systematically considering the consequences of those hypothetical thoughts. These cognitive features are considered by many today to be essential to college and career readiness.

Real-World Application: Logic as an Essential Skill http://www.achieve.org/adp-english-benchmarks

Achieve is one of many nonprofit organizations working with states to create new educational standards and graduation requirements. Its American Diploma Project English benchmarks for career and workplace readiness include the ability to think logically and objectively among the English skills that high school graduates should possess. How would you go about con- structing an argument against that claim? Would it be easier if you were asked to argue in support of the claim? Why or why not?

Question to Consider

Do you think prompting explanations would be as effective at helping children discover solutions in topics other than physics (for example, problems posed in history or literature)? Why or why not?

Section 8.6The Development of Deductive Reasoning

Piaget’s Theory and Reasoning Piaget’s theory proposed that the mind becomes structured during development so that thought becomes increasingly logical and abstract (Inhelder & Piaget, 1958). This theoretical claim places logical reasoning at the center of cognitive development—a claim that generated a considerable amount of interest and follow-up research among investigators in subsequent years (Beilin, 1992).

Recall from Chapter 1 that Piaget’s final three stages of cognitive development are the preop- erational (2 to about 6 years), concrete operational (about 7 to 12 years), and formal opera- tional (12 years to adulthood) stages. Notice that the concept of an operation is so funda- mental to Piaget’s theory that it appears in the title of each of these stages. Operations, as we indicated in Chapter 1, are mental representations of actions that obey logical rules.

A preoperational thinker is, therefore, someone whose thinking is not yet characterized by logic, according to Piaget’s theory. The concreteness associated with the next stage means children are capable of engaging in logical reasoning about problems with observable and/or factual content. An example of the difference between the two stages is the conservation task.

Chapter 1 described the conservation of liquid task. In the number conservation task, children are shown two rows that each contain the same number of objects. In one row, the objects are placed farther apart, making the row longer than the other (see Figure 8.5). Children are asked whether the rows have the same number of objects or whether one row contains more objects.

Figure 8.5: Number conservation task

After one row is transformed to look bigger (right) children are asked if both rows are the same or if one row contains more objects. Children acknowledge the two rows are equivalent (left).

Equivalent in the number of objects and spacing

To answer the question if both rows are the same or if one row has more objects, children need to differentiate between length of rows and number of objects in the rows.

Transformed rows with different spacing

According to Piaget, children do not pass conservation tasks until they enter the concrete- operational stage of cognitive development (see Piaget, 1970, for an overview of his theory). The concrete-operational child can reverse the series of steps in the conservation task, logi- cally reasoning that if the two rows were initially the same number, and nothing was added or subtracted, then they remain the same (see Chapter 1). Note that this logical reasoning occurs in the context of real, physically present objects and materials. At the formal- operational stage, logical reasoning is not bound to concrete content but extends to content that is hypo- thetical and abstract.

Section 8.6The Development of Deductive Reasoning

Formal-operational thinking in Piaget’s theory is closely tied to deductive reasoning. Deduc- tive reasoning is the process of determining when a conclusion necessarily follows from premises (Moshman, 2004). By premise, we mean a statement that is assumed to be true, for the sake of the argument, and forms the basis for a conclusion.

When psychologists study deductive reasoning, they are typically assessing whether a par- ticipant distinguishes between a valid and invalid argument (Johnson-Laird, 1999). An argu- ment is valid when, assuming the truth of the premises, the conclusion must follow from them. An argument is invalid if the conclusion does not necessarily follow from the premises.

For instance, a syllogism is a deductive argument that consists of two premises and a con- clusion. An example of a syllogism with a valid conclusion begins with the two premises all swans are white and the bird is a swan. The only possible conclusion is the bird is white. It would be impossible to conclude the bird is not white assuming the truth of the premises.

Piaget argued that a formal-operational thinker would appreciate the necessity of the conclu- sion; that is, the conclusion has to follow from the premises (Miller, 1986). As we will see in the next section, this means accepting that a conclusion is valid (necessarily true) even when we know that in the real world the conclusion is inaccurate or inconsistent with our beliefs.

Belief-Inconsistent Content and Reasoning Referring to an argument as valid can be confusing, because in everyday language we usually associate that term with accuracy. In actuality, a conclusion’s validity is not judged by whether it is empirically accurate (that is, factual). We will refer to a belief-inconsistent argument as one in which the conclusion of a valid argument is empirically false and a belief-consistent argument as one in which the conclusion of a valid argument is accurate.

Notice that the belief-inconsistent examples in Table 8.2 have conclusions and premises that are not factual; however, the belief-consistent and belief-inconsistent arguments have exactly the same form (that is, structure). The validity of a deductive conclusion is determined by the form of the argument and not by its content. Understandably, children’s performance on reasoning problems improves when they receive instruction about logical analysis (Daniel & Klaczynski, 2006).

Table 8.2: Examples of deductive reasoning and valid conclusions

Belief- consistent argument Belief-inconsistent argument

Premise If it is raining, the pavement is wet. If ice forms, the temperature is above freezing.

Premise It is raining. Ice forms.

Valid conclusion The pavement is wet. The temperature is above freezing.

Belief-consistent argument Belief-inconsistent argument

Premise All humans are mammals. All birds are reptiles.

Premise Billy is a human. A sparrow is a bird.

Valid conclusion Billy is a mammal. A sparrow is a reptile.

Section 8.6The Development of Deductive Reasoning

Generally speaking, however, even with instructions, reasoning problems with belief- consistent material are easier than problems with belief-inconsistent content and purely abstract content (Markovits, 2014). In fact, even adults sometimes incorrectly categorize valid, belief-inconsistent arguments as invalid (Moshman, 2004; 2010; Moshman & Franks, 1986). Adults’ failure to reason in a manner consistent with formal-operational thinking is, of course, inconsistent with Piaget’s theory.

Equally problematic for Piaget’s stage theory is the fact that under some circumstances, young children exhibit what appear to be deductive-reasoning capabilities well before they reach the concrete- or formal-operational stages. For instance, placing reasoning problems in a fantasy context is particularly helpful in facilitating young children’s ability to reason (Dias & Harris, 1990).

In one study, children ages 2 to 4 were encouraged to pretend they were on another planet, one very different from their own (Richards & Sanderson, 1999). They were then given syl- logisms with belief-inconsistent content. In one problem they were told, “All sheep ride bicy- cles. Bill is a sheep. In the pretend story did Bill walk or ride a bicycle?” Children correctly accepted the logical, but belief-inconsistent, conclusion substantially more often than when similar problems were presented without a pretend context. Reality is suspended in a make- believe context. According to one theory, this lessens the likelihood that factuality will intrude on judgments of belief-inconsistent conclusions (Markovits et al., 1996).

Hypothetico-Deductive Reasoning Hypothetico-deductive reasoning is a hallmark of formal-operational thinking (Inhel- der & Piaget, 1958). It is the ability to systematically think about possibilities and logically infer whether those possibilities are confirmed in reality. When adolescents create their high school class schedule, they might begin by listing all of the possible classes they would like to take, rank order them, note the times they are offered, and then, step-by-step, form an optimized schedule. This process illustrates hypothetico-deductive reasoning. Note, in particular, that it starts with all of the possibilities and then deductively reaches an actual conclusion.

In Piaget’s theory, in contrast, concrete-operational children are limited to deductive reason- ing about actual events rather than about possibilities (Inhelder & Piaget, 1958). They experi- ence difficulty reasoning with what if questions, as illustrated in this interview excerpt:

If you could touch the sun, would he feel it?

You can’t touch him.

Yes, but if you could manage to, would he feel it?

He is too high up.

Yes, but if…, etc. (Piaget, 1928, pp. 68–69)

Section 8.6The Development of Deductive Reasoning

Questions to Consider

Witnesses in judicial proceedings are nearly always expected to take an oath to tell the truth (Lyon, 2011). Consider the following questions a judge asked a 4-year- old in an attempt to establish the child’s competency to testify (Commonwealth v. Corbett, 1989):

Q. If you tell a lie, will you get into trouble? A. No. Q. You won’t get into trouble? A. But I am not going to tell a lie. Q. Have you ever told a lie? A. No. Q. If you don’t tell the truth, do you know what will happen to you? A. What? Q. You have to tell me. A. Okay. Q. Can you? A. Yes. Q. What would happen to you? A. Well, I can tell you just what happened. (adapted from Lyon, 2013)

1. How do the child’s answers ref lect a focus on concrete reality rather than on what would happen if, hypothetically, the child lied?

2. Given what we know about young children’s strengths and limitations in reason- ing, what are more effective ways to phrase questions about the consequences of lying and telling the truth?

Section 8.6The Development of Deductive Reasoning

Spotlight on Research: Is Reasoning an Innate Capacity? Piaget (1970) believed that preoperational children are semilogical and incapable of logical reasoning. Yet as we just saw, under some circumstances preoperational children can rea- son and reach logically valid conclusions. Does reasoning ability extend in some form even to infants?

Sixteen-month-olds witnessed an actor demonstrate a preference by reaching for a red ball (A) instead of a yellow ball (B)—both objects were equidistant from the actor (Mou, Province, & Luo, 2014). Next, the yellow ball (B) and a green ball (C) were placed on either side of the actor. The actor reached for the yellow ball (B). Lastly, the red balls (A) and green balls (C) were placed on either side of the actor. The question of interest asked if infants would make a transitive inference and form a correct expectation of which ball the actor would prefer.

A transitive inference occurs when the relationship between two variables necessarily fol- lows from how they relate to another variable. For instance, if we already know that Amy is taller than Ben and Ben is taller than Carl, we can infer with certainty that Amy is taller than Carl. The same logical relationship underlies this study. If infants formed an expectation based on the transitive properties of the problem, they should expect the actor to prefer and reach for the red ball (A). Put another way: If A > B and B > C, then we can infer A > C.

Evidence indicated this was, in fact, infants’ expectation. They were surprised and looked significantly longer when the actor unexpectedly chose the green ball (C) instead of the red ball (A). Infants seemed to be reasoning, implicitly, “If you like red over green, and if you like green over yellow, then you will like red more than yellow.” The authors of the study point out that other species like fish and rats also make transitive inferences. They argue that transitive reasoning is an innate capacity that is revealed early in development under sensitive testing conditions. In the context of the performance–competence theme of our text, this innate com- petency is evident in infants when performance demands are minimized.

Critical-Thinking Questions

1. How does the ability to make transitive inferences underlie Piaget’s conservation task?

2. What props and games might promote making transitive inferences in early childhood (before age 7)?

Variability and EFs in Reasoning In Chapter 3 we discussed evidence that the EFs have a broad (domain-general) influence on cognition and therefore may be improved through training. In this section, we explore the extent of that influence by examining how executive functioning impacts reasoning in chil- dren. To the extent reasoning is dependent on the EFs, we will have clues about how to facili- tate children’s ability to reason. Modifying tasks and situations—whether in the classroom or in the school as a whole—in a way that lessens EF demands should improve reasoning if the two concepts are related.

For instance, belief-inconsistent reasoning involves inhibiting what one knows to be true in order to recognize the validity of a conclusion (Beck, Riggs, & Gorniak, 2009). Consequently, simplifying the inhibitory demands of reasoning tasks can improve reasoning performance even for children as young as 3 to 5 years old (Beck, Carroll, Brunsdon, & Gryg, 2011). For

Section 8.6The Development of Deductive Reasoning

older children, accuracy on a belief-inconsistent deductive-reasoning task increased from 19% for 12-year-olds to 55% for 16- to 17-year-olds and was linked to their ability to inhibit the factual beliefs that cued incorrect responding (Steegen & De Neys, 2012).

Differences in working-memory capacity are also related to individual differences in chil- dren’s deductive reasoning (Handley, Capon, Beveridge, Dennis, & Evans, 2004). Reasoning problems require keeping in mind comparisons and contrasts among premises (for example, “the first part of the argument said ‘A > B,’ the second part said ‘B > C,’” and so on). Also in working memory, one must manipulate all of the premise information in order to reach a valid conclusion (Handley et al., 2004).

In sum, building a scaffold for learning how to reason could involve first providing reason- ing problems in contexts that facilitate performance (such as pretend play or minimal EF demands). One could then gradually pose more complicated problems to help children gener- alize the mastery they attained under the highly facilitative conditions.

Questions to Consider

The developmental disorder dyscalculia, mentioned in Chapter 2, is characterized by severe deficits in mathematical ability. In one study, 10-year-old children diagnosed with dyscalculia performed poorly on belief-inconsistent deductive-reasoning problems compared to controls, even though the two groups were matched for IQ (Morsanyi, Devine, Nobes, & Szűcs, 2013).

1. How might struggling with deductive-reasoning skills affect a child’s ability to learn math?

2. What other subject areas might be affected, and how?

3. Do you believe this evidence indicates that deficiencies associated with dyscalculia are caused by domain-general or domain-specific processes? Explain your answer.

Reasoning: Dual Processes Consider the following problem: A bat and a ball cost $1.10 in total. The bat costs $1 more than the ball. How much does the ball cost? (Evans, 2011; Fredrick, 2005). The intuitive, quick answer adults most often give is “10 cents” (Fredrick, 2005). A more considered, analytical response, however, holds that impulse in check.

If the ball costs 10 cents and the bat costs one dollar more than the bat, the total cost would be $1.20 (10 cents for the ball and $1.10 for the bat). Recall the problem states that $1.10 is the total cost. Taking a few moments and thinking about the problem step-by-step leads to the correct answer of 5 cents (the bat is $1.05 and the ball is 5 cents for a total of $1.10).

Two different ways of thinking about the problem (each of which lead to two different con- clusions) appear to be in competition in determining the cost of the ball. According to dual process theory, cognitive tasks can be processed by two different ways of thinking: type 1

Section 8.6The Development of Deductive Reasoning

thinking is (a) automatic, intuitive, fast, and biased by preexisting beliefs and assumptions, while type 2 thinking is (b) analytical, deliberate, rational, and effortful (Evans, 2011; Evans & Stanovich, 2013).

The type of formal-operational thinking Piaget envisioned—deductive reasoning that differ- entiates the form of an argument from its belief-inconsistent content—illustrates type 2 pro- cessing. Judging the quality of a conclusion by its believability is, in contrast, a type 1 process. These processes are relatively independent, with effort and inhibitory control required for type 2 to override type 1 when the processes lead to conflicting responses (Evans & Stanov- ich, 2013).

Type 1 judgments, it should be pointed out, do not always lead to incorrect responding (Evans & Stanovich, 2013). Many times a quick and intuitive judgment is useful and accurate (Todd & Gigerenzer, 2000). Type 1 thinking is often plausible in situations in which individuals have incomplete information. When a beginning reader encounters a new word (for example, fea- ture), he may automatically infer, based on past experience, that only the first of the two con- secutive vowels is sounded out and then proceed to correctly pronounce the new word.

Type 2 reasoning is ideally called on in situations that call for deliberation and in which a full range of probabilities and possibilities should be accounted for in order to arrive at a correct answer. Figuring out whether the statement “If two things happen at the same time then one caused the other” is true or false would draw on type 2 reasoning because evaluating the truth of the sentence involves carefully generating examples and counterexamples related to the question.

Table 8.3 illustrates four reasoning problems that can be solved intuitively (type 1) or ana- lytically (type 2). Note that in each problem, type 2 thinking accounts for all of the relevant information and leads to a more reasonable and more plausible response than type 1 think- ing. Thus, each problem assesses whether children can draw on type 2 processing when warranted.

Table 8.3: Reasoning problems presented to second through ninth graders

Reasoning problem Example

Base rate neglect. When judgments about the likelihood of an event are overly influ- enced by a personal experience instead of the statistical probability of the event occurring.

Erica wants to go to a baseball game to try to catch a fly ball. She calls the main office and learns that almost all fly balls have been caught in Section 43. Just before she chooses her seats, she learns that her friend Jimmy caught two fly balls last week sit- ting in Section 10. Which section is most likely to give Erica the best chance to catch a fly ball?

a. definitely section 43 b. probably section 43 c. probably section 10 d. definitely section 10

Belief bias (belief-inconsistent) syllogisms. When the believability of a syllogism con- flicts with the validity of its conclusion.

All mammals walk. Whales are mammals. Whales walk.

Logically valid? Yes or No

(continued)

Section 8.6The Development of Deductive Reasoning

Reasoning problem Example

Denominator neglect. When numerators are overemphasized relative to denomi- nators when evaluating probability.

From which container are you more likely to draw a white marble? One with 1 white marble and 9 blue marbles (1 in 10 chance) or one with 9 white and 91 blue (9 in 100 chance)?

Myside bias. A tendency to generate evidence and arguments consistent with one’s own beliefs as opposed to open-minded consideration of counterarguments.

Q: “Should kids have cell phones?” Participants are first asked their opinion about this issue. Then, no matter what they personally believe, they are asked to generate as many arguments as possible both in support of children having cell phones and against it. Responses are coded for the total number of arguments generated either consistent or inconsistent with the participant’s belief. A myside bias occurs when a participant produces a dispropor- tionate number of arguments in support of his or her own belief. A type 2 response considers both sides of a position and therefore also considers alternative views. One’s argu- ment can be strengthened by considering how it compares and contrasts with alternative viewpoints.

Note. The answers in bold are the correct answers to the problems, which are reached through type 2 thinking overriding type 1 thinking.

Source: Adapted from Kokis, J. V., Macpherson, R., Toplak, M. E., West, R. F., & Stanovich, K. E. (2002). Heuristic and analytic processing: Age trends and associations with cognitive ability and cognitive styles. Journal of Experimental Child Psychology, 83(1), 26–52; and Toplak, M. E., West, R. F., & Stanovich, K. E. (2014). Rational thinking and cognitive sophistication: Development, cognitive abilities, and thinking dispositions. Developmental Psychology, 50(4), 1037–1048.

Reasoning problems like those in Table 8.3 were presented to children in grades 2 through 9 (Toplak et al., 2014). Accuracy was moderately correlated with age. This means older chil- dren were more likely than younger ones to provide responses that were consistent with the analytical process of type 2 thinking. Children’s improvement does not mean they eventually mature to the point where reasoning biases are finally overcome. Adults routinely use type 1 thinking even when situations call for type 2 (Kahneman, 2011).

Returning to a theme of our book, overall, improvement was gradual and not stage-like. There was also evidence of idiographic development (see Chapter 1). The frequency of type 2 think- ing was linked to individual differences in IQ and executive functioning. Consider, for instance, the role of inhibition and memory in overcoming the myside bias. The ability to suppress one’s own point of view and remember disconfirming information would facilitate generating arguments counter to one’s own belief (type 2 thinking).

Type 1 processing is heavily influenced by factors that are familiar, stereotypic, and perceptu- ally obvious (Stanovich & Evans, 2013). Personal experiences and biases disproportionately influence judgments compared to more objective and statistically reliable information. As children acquire knowledge about stereotypes and other biasing information, they are sus- ceptible to type 1 reasoning (Denison & Xu, 2014; De Neys & Vanderputte, 2011).

Asking children to identify the preconceptions they bring to a problem and providing instruc- tion in logic may be useful tools for encouraging type 2 thinking (Abrami et al., 2008). Never- theless, we see that a strictly analytical approach to problems is more work than the quicker, intuitive, and even biased cognitive process that leads to favoring information consistent with

Section 8.7Scientific Thinking

one’s preexisting beliefs. We will see the challenge of overcoming biases in the next section that examines scientific thinking.

Questions to Consider

Think of some topics that would be controversial or emotional for junior high and high school students.

1. What is an advantage of teaching reasoning skills in the context of these emotion- ally important topics?

2. What would be a disadvantage?

8.7 Scientific Thinking In response to national goals of increasing the number of children pursuing careers in science, in 2013 President Barack Obama announced that training science teachers should become a national priority:

One of the things that I’ve been focused on as President is how we create an all-hands-on-deck approach to science, technology, engineering, and math. We need to make this a priority to train an army of new teachers in these subject areas, and to make sure that all of us as a country are lifting up these subjects for the respect that they deserve. (as cited in Committee on STEM Education , 2013, p. vi)

Science education involves teaching the subject matter found within scientific disciplines. It also advances children’s ability to reason about the process of scientific investigation (Klahr, Zimmerman, & Jirout, 2011). We refer to this reasoning process as scientific thinking, and it is the focus of this section. Scientific thinking is purposefully acquiring knowledge by forming and designing tests of theories and evaluating evidence derived from such tests (Klahr et al., 2011; Kuhn, 2011). In this section, we examine the development of cognitive abilities funda- mental for children’s scientific thinking. We also explore how those abilities are nurtured, particularly in educational settings.

There are three reasons for focusing on scientific thinking in this chapter. First, Piaget’s investigations on the development of scientific thinking inspired a long-standing interest in developmental psychology in investigating the emergence of, and changes in, the processes by which children acquire scientific knowledge (Inhelder & Piaget, 1958; Zimmerman, 2007). Second, the study of scientific thinking is related to our earlier discussions of reasoning and problem solving. Like those processes, scientific thinking involves using evidence to draw conclusions and find solutions. Third, national educational curriculum standards emphasize the advancement of children’s scientific thinking as a major educational goal (Duschl, 2008).

Section 8.7Scientific Thinking

Foundations of Scientific Thinking In general, scientific investigations test theories by (a) changing one variable while keeping everything else the same and (b) interpreting how the results were impacted when the vari- able of interest was changed. Such investigations, and the skills associated with them, are not restricted to the laboratory or science classroom.

Consider, for instance, an adolescent who experiments with different recipes for making cookies (Cook, Goodman, & Schulz, 2011). He might predict (theorize) that butter is a key ingredient that causes cookies to vary in taste. Testing the theory would involve making two or more sets of cookies with exactly the same ingredients except for the amount of butter included in each batch. The evidence (how the cookies taste) would refute or support the adolescent’s theory.

In this example two foundations of scientific thinking are evident. First, one must be capable of inferring cause–effect relationships based on whether the results vary with changes to the ingredient. Note that all of the ingredients between conditions were the same except for the butter. If two variables had been changed at the same time (perhaps more butter and a dif- ferent quality of flour in one recipe), it would be impossible to conclude with certainty that butter alone was responsible for the difference in taste.

A confound occurs when two or more factors are varied between experimental conditions. When confounds occur, the ability to infer with certainty a cause–effect relationship is com- promised. For instance, in our example, the difference in taste could have been due to dif- ferences in the amount of butter, the quality of the flour, or the combination of both factors working in tandem.

A careful evaluation of evidence is the second foundation of scientific thinking found in our example. In particular, to properly evaluate the evidence, one must be capable of understand- ing that theories may need to be revised because of disconfirming evidence. Evidence and theory are distinct. If the initial tests disconfirmed the theory and showed no difference in taste when the butter was varied, further exploration of other variables (ingredients) should follow.

At what age do children begin exhibiting these foundations of scientific thinking? The answer will inform how early in schooling science education might begin. Many national and state cur- ricula now provide guidance and expectations for science learning in preschools (Brenneman, 2011). We will look now at what research says about whether these expectations are realistic.

Causal Inference From Data Scientific investigations determine whether one factor causes changes in another factor. Causal inference in science occurs when a pattern of evidence indicates one variable is impacting another variable. Particularly relevant is a pattern of evidence known as covaria- tion. Covariation refers to the frequency with which two events do or do not co-occur (see Table 8.4, top row). For instance, if students are more likely to pass an exam under instruc- tional method A compared to instructional method B, then strong exam performance and the type A instructional method are covarying. This pattern of evidence indicates that differences in instructional methods cause differences in exam performance.

Section 8.7Scientific Thinking

Table 8.4: Example of covariation and confounding

Perfect covariation indicating that A causes X

Outcome A is present; B is not. B is present; A is not.

X X occurs 100% of the time. X occurs 0% of the time.

Confounded study—cannot infer if A causes X

Outcome A and B are both present. A and B are not present.

X X occurs 100% of the time. X occurs 0% of the time.

Note. A and B are factors manipulated by an investigator to examine their effect on X.

Do preschoolers pay attention to covariation between variables and, on that basis, infer that one variable is affecting the other one? To investigate this question, young children were familiarized with a machine that turned on or off depending on the number and type of blocks placed on it (Gopnik, Sobel, Schulz, & Glymour, 2001; see Figure 8.6).

Figure 8.6: A covariation task

Most 3- and 4-year-olds correctly understood which block needed to be removed to turn off the machine. This indicates that they recognized that the activation of the machine more consistently covaried with A rather than B.

Source: Adapted from Gopnik, A. (2012). Scientific thinking in young children: Theoretical advances, empirical research, and policy implications. Science, 337(6102), 1623–1627.

In addition to the type of understanding shown in Figure 8.6, preschoolers (ages 3 to 5 years) can also spontaneously vary factors with the aim of acquiring cause–effect information. In one study, 4-year-olds were shown a demonstration in which some beads activated a machine but other beads did not (Cook et al., 2011). Next, children were shown a pair of beads that were stuck together but could be pulled apart. The experimenter then placed the paired beads

Section 8.7Scientific Thinking

on the machine and activated it. Next, children were encouraged to play with the machine and beads.

Many of the preschoolers experimented by detaching the beads and placing a bead one at a time onto the machine. Presumably, they were recalling the earlier demonstration that only some beads were effective. By pulling them apart and testing them one at a time, children were experimenting to see which bead specifically caused the machine to activate. Young children’s exploratory play served as a training ground for their early scientific inquiry (Legare, 2014).

In fact, playtime can be an effective context for engaging in aspects of scientific thinking. For example, a child playing with various objects and water might observe that some objects float and others sink (Hamlin & Wisneski, 2012). A parent or educator could prompt the child to observe differences among the objects and make predictions about whether they would sink or float. A child playing with a magnet could be prompted to figure out which type of objects are attracted or not attracted to the magnet. Similar experiments could be carried out to determine why different-sized toy cars travel different distances when pushed.

We have examined evidence that preschoolers possess early competency in designing a study. Of course, all studies do not yield expected results. When unexpected results occur, a hypoth- esis needs to be revised. By age 5 children understand that beliefs can be false (see Chapter 6). This understanding is a foundation of scientific thinking because it underlies the realiza- tion that a prediction (hypothesis or theory) can be false (Koerber, Sodian, Thoermer, & Nett, 2005). Preschoolers have a beginning awareness that evidence can lead to changes in a belief (hypothesis). That is, when a prediction is falsified they have some awareness the prediction should be revised (Gropen, Clark-Chiarelli, Hoisington, & Ehrlich, 2011).

Questions to Consider

The processes by which knowledge is socially constructed, detailed in Chapter 7, apply to the development of scientific thinking. After all, the scientific process is generally a social, shared pursuit. Scientists share findings in journals and at conferences and collaborate with one another to design and conduct studies. For children, an important social source of engagement in scientific thinking comes from interaction and conversation with parents (Haden, 2010).

1. What shared activities between parent and child lend themselves to encourage scientific thinking in young children?

2. Choosing one of those activities, list some questions and prompts that would direct children to think scientifically about evidence and variables.

Scientific Thinking After Age 5 Aspects of scientific thinking such as forming a hypothesis, isolating variables, and interpret- ing evidence are domain-general reasoning abilities (Bao et al., 2009). Their development can deepen children’s understanding when applied to a wide variety of subject matter. For

Section 8.7Scientific Thinking

instance, virtually any time one is searching for clues to understand how something works (such as a toy, a machine, or a magic trick), scientific thinking is a systematic and effective approach to ruling out alternatives and establishing cause–effect relationships.

However, the skill with which children apply these general processes is specific to task and content. For instance, in some domains children may have entrenched beliefs that impair their ability to objectively interpret evidence they generate from experimentation (Penner & Klahr, 1996). To illustrate, young adolescents tend to overrate the quality of a flawed study when the conclusion favors their religious beliefs (Klaczynski, 2000).

Whereas the precursors of scientific thinking are in place by early childhood, developmental challenges continue throughout childhood and into adolescence. Although children can dis- tinguish between theory and evidence for simple problems possessing perfect covariation, there is nevertheless a strong tendency to favor preexisting beliefs and ignore data when evaluating evidence (Feist, 2011). Generally speaking, children (Amsel & Brock, 1996; Kuhn, Amsel, & O’Loughlin, 1988) and even adults (Bastardi, Uhlmann, & Ross, 2011) are suscep- tible to bias by selectively evaluating evidence based on whether it fits with their prior beliefs and assumptions. Such biases are consistent with type 1 thinking.

In one study, children in grades 3, 6, and 9, and adults, evaluated patterns of evidence that var- ied from trial to trial (Kuhn et al., 1988). Whereas children gradually improved in their ability to separate theory and evidence, even the oldest group (and some adults) exhibited a ten- dency to view theory and evidence interchangeably (Kuhn, 1989). Many children appealed to their beliefs as evidence, simply restating their theory when prompted to reexamine evi- dence. Other times they ignored evidence inconsistent with their theory.

Why do children find it difficult to fully distinguish theory from evidence (Kuhn, 2011)? One possibility is that children, and even adults, have a confirmation bias. This is a tendency to seek evidence that supports, rather than disconfirms, theory and belief (Mercier, 2011; Nickerson, 1998). The development of the analytical, type 2 thinking we described earlier may help children overcome biases and increase the likelihood they will instead reason about evidence with objectivity (Amsel et al., 2008). The presence of a confirmation bias means that educators and parents may need to be direct in pointing out alternative explanations to chil- dren when the findings of flawed designs are consistent with the child’s prior expectations.

Designing Studies and Avoiding Confounds Science fairs engage children in the process of designing experiments and presenting results to the community. Criteria for judging the projects account for factors such as topic, original- ity, and quality of presentation; however, perhaps the most foundational criterion is whether the experimental design is adequate. Without an adequate experimental design, the results will be very difficult to interpret. An inadequate experimental design leaves everyone guess- ing whether the effect occurred for the reasons that were hypothesized.

Effective scientific experimental designs employ the control-of-variables (COV) procedure. The COV procedure ensures that all variables are held constant except the one being tested. As we saw earlier, a confound occurs when two or more variables in an experiment change at the same time (see Table 8.5, bottom row), making it impossible to tell if just one is actually responsible for causing an outcome.

Section 8.7Scientific Thinking

In general, children often find it difficult to design studies that avoid confounds, failing to realize that confounds make it impossible to interpret a study’s results (Siler & Klahr, 2012). A relatively common misconception among grade school and middle school students is that the goal of scientific experiments is to “engineer” the desired outcome (Schauble, Klopfer, & Raghavan, 1991; Siler & Klahr, 2012). This means they design an experiment to see which combination of variables will produce the biggest effect, rather than isolating variables to see which variable produces an effect.

Piaget theorized that children in the concrete-operational stage do not engage in hypothetico- deductive reasoning and thus do not systematically consider all possible combinations of vari- ables and test them one-by-one (Inhelder & Piaget, 1958). Instead of systematically isolating variables, they are prone to design experiments with confounds. Are the failures of grade school children to employ the COV procedure the result of cognitive unreadiness, as Piaget predicted? Or are grade school children cognitively capable of learning to design scientific experiments if they receive facilitative experiences? In the next section, we examine teaching methods that attempt to promote scientific thinking in grade school children.

Discovery Learning and Direct Instruction A heavily researched question concerns whether children are more likely to discover and apply the COV procedure through direct guidance or on their own through a trial-and-error process (see Table 8.5). Discovery learning posits that development and learning advance when children actively explore and investigate on their own. Direct instruction, in contrast, includes explicit instruction and examples to help children learn. Direct instruction is not rote memorization, but instead provides information, strategies, and examples that support the acquisition of concepts and procedures (Kirschner, Sweller, & Clark, 2006).

Table 8.5: Comparison between direct and discovery methods of science instruction

Phase Task Direct instruction Discovery learning

1 Establish goal of the experiments

Teacher Teacher

2

Design experiments with materials

Teacher Student

Probe questions about experiments

Yes No

Explain good and bad designs

Yes No

3 Assessment: design an experiment

Student Student

Source: Adapted from Klahr, D., Zimmerman, C., & Jirout, J. (2011). Educational interventions to advance children’s scientific thinking. Science, 333(6045), 971–975; and Klahr, D., & Nigam, M. (2004). The equivalence of learning paths in early science instruction effects of direct instruction and discovery learning. Psychological Science, 15(10), 661–667.

Section 8.7Scientific Thinking

We can see reflections of Piaget’s theory and of social constructivist theories within these two instructional methods. From a Piagetian perspective, children acquire a deep understanding of the physical world through active trial-and-error experimentation on their own (see Chap- ter 1). There is some consistency between this view and instructional methods that emphasize discovery learning. From a social-constructivist (Vygotskian) perspective, cognitive develop- ment occurs when children are guided by a more knowledgeable peer or adult (Chapter 1). Guidance takes the form of demonstrations accompanied by questions that prompt reflection, and explanations that illuminate the principles underlying the demonstrations.

Research has compared both methods and assessed whether one better promotes scientific thinking and long-lasting change in children. In one study, third- and fourth-grade children were randomly assigned to either a direct instruction or discovery learning condition (Klahr & Nigam, 2004). In the exploration phase at the outset of the study, children in both conditions were given the goal of investigating which factor(s) influenced the distance a ball rolled after it was released on a downhill ramp. Children were given a number of materials that served as variables that potentially impacted distance (for example, type of ball, surface of the ramp).

In the next phase of the experiment, children in the direct instruction condition observed a teacher design sample experiments. Some experiments were deliberately confounded whereas others were not confounded. Children were asked whether they could know for sure whether a variable impacted the outcome.

The experimenter then explained why each confounded experiment did not allow for cause– effect conclusions and why each unconfounded experimenter permitted drawing conclusions. Prompts and questions were posed during this period. In contrast, children in the discovery condition were instructed to design experiments on their own to test the effects of particular variables on the distance the ball rolled.

In the final phase of the experiment, children in both groups were given identical experimen- tal goals such as determining the effect of ramp surface on distance. Children did not receive feedback during this period. The adequacy of children’s research designs was measured by whether their designs employed the COV procedure.

In the initial exploration phase of the study, children generally designed confounded experi- ments (see Figure 8.7). However, during the assessment phase of the study, children who received direct instruction were significantly more likely to use the COV procedure than those in the discovery condition. Employing the COV procedure means all of the variables between Condition A and B were the same except the one being tested for its effect. Moreover, the gains from the direct instruction method transferred to other science-related assessments testing children’s ability to identify confounds in other experiments. Additional research indicates such gains may extend for months and even years (Klahr, 2013).

Section 8.7Scientific Thinking

Figure 8.7: A confounded experiment

Third and fourth graders designed experiments with ramps (Condition A and B) to determine how variables impacted the distance a ball rolled upon release. The figure shows a confounded experiment because many variables are different between each condition, making it impossible to isolate how particular variables impacted the distance the balls rolled.

Source: Adapted from Klahr, D., & Nigam, M. (2004). The equivalence of learning paths in early science instruction effects of direct instruction and discovery learning. Psychological Science, 15(10), 661–667.

More generally, there is an extensive body of evidence indicating that direct instruction is an important factor in helping children acquire new insights and discoveries in problem- solving activities (Lee & Anderson, 2013; Mayer, 2004). Pure discovery learning—in which children are given materials and largely left to explore and find solutions on their own— has not received substantial empirical support (Alfieri, Brooks, Aldrich, & Tenenbaum, 2011; Kirschner et al., 2006; Mayer, 2004). This evidence indicates an answer to the question we posed in our own case study asking whether Maria’s teacher should have encouraged her to discover solutions on her own rather than first providing example solutions.

Overall, these results suggest that grade school children can design effective scientific experi- ments by accounting for confounds and alternative explanations. They apparently possess cognitive readiness to design unconfounded scientific experiments, but they typically require direct instruction to actually employ the COV procedure.

Summary and Resources

Questions to Consider

In the case study at the outset of the chapter, we asked how you might instruct the child, Maria, to evaluate her experimental design if her hypothesis was not confirmed.

1. How does your answer at the beginning of the chapter compare with your answer at the end of this section (and chapter)?

2. How does what we have learned about type 1 reasoning and scientific thinking specifically alert you to particular points you will need to make when helping Maria evaluate her study?

Summary and Resources

Chapter Summary

• Problem solving involves enacting a solution to attain a goal and monitoring the progress of the attempted solution. Problem solving is evident in infancy.

• Analogical reasoning is evident before grade school, since 4- and 5-year-olds can complete analogies if the content of a problem is familiar to them. Analogical reason- ing serves problem solving in everyday and educational contexts.

• Some evidence indicates language and the EFs support the ability to carefully plan during problem solving.

• Divergent thinking supports the creation of tools for problem solving. Functional fixedness, in contrast, constrains finding novel uses for objects.

• Children’s rule-based problem solving becomes increasingly sophisticated and accurate with practice and feedback, and when accompanied by prompts to explain predictions and attempted solutions.

• Children and adolescents exhibit variability in their performance on deductive- reasoning tasks. Competency is influenced by factors such as instructions, believabil- ity of logical conclusions, and executive functioning.

• In Piaget’s theory, concrete-operational thought is logical when the contents are real, whereas formal-operational thought is logical when dealing with hypothetical content.

• There are two processes of reasoning: Type 1 is intuitive, and type 2 is analytical. During childhood and into adolescence, there is gradual development in relying on analytical reasoning when it conflicts with intuitive reasoning.

• Distinguishing between theory and evidence and making causal inferences from evidence are two foundations of scientific thinking. Evidence indicates both founda- tions begin to emerge in early childhood.

• With direct instruction and practice, grade school children can learn to effectively design experiments.

Summary and Resources

Posttest Questions

1. When 9-month-olds are first learning to eat with a spoon, which of the following statements about problem solving is FALSE?

a. Nine-month-olds generally recognize the spoon as a tool. b. Nine-month-olds are often sufficiently motivated to eat with a spoon. c. Nine-month-olds monitor the effects of attempts to eat with a spoon. d. Nine-month-olds are capable of lifting the spoon.

2. Means–end understanding in Piaget’s sensorimotor stage is MOST closely associated with the emergence of which feature of problem solving?

a. successfully solving the problem b. identifying a goal and a tool to help attain it c. mentally devising a series of intermediate steps to solve the problem d. identifying analogies to help solve the problem

3. Which statement about analogical reasoning is FALSE?

a. The development of analogical reasoning is stage-like. b. Analogical reasoning is influenced by the development of inhibitory control. c. Features of analogical reasoning are evident during infancy. d. Analogical reasoning improves as children’s factual knowledge base increases.

4. involves detecting a relationship between two things and then inferring a similar relationship between two other things.

a. A categorical syllogism b. Analogical reasoning c. The end-state comfort effect d. The more-is-more rule

5. Which statement is most accurate about performance on tasks like the Tower of London, which assesses the development of planning?

a. For complex problems, adults take longer to plan their solution than children. b. Private speech does not help children plan. c. Four- and 5-year-olds are equally likely to include intermediate steps in their

planning. d. Inhibitory control is unrelated to successful planning.

6. Motor planning that involves adopting an intermediate, awkward position is known as .

a. functional fixedness b. the end-state comfort effect c. transitive inference d. the ulnar grip grasp

Summary and Resources

7. Solving an open-ended and novel problem requires __________.

a. divergent thinking b. functional fixedness c. end-state comfort effect d. confirmation bias

8. Which statement about the development of tool use is FALSE?

a. Nonhuman primates other than humans use tools. b. Functional fixedness can limit recognition of how an object might serve as a tool. c. There is generally a developmental lag between using and creating tools. d. There is no evidence of tool use in infants and toddlers.

9. Strategies systematically followed when carrying out a solution are known as .

a. rules b. type 1 (intuitive) thinking c. analogical reasoning d. belief-consistent reasoning

10. To solve the water displacement task, grade schoolers must .

a. rely on one dimension (weight or volume) and disregard the other b. treat weight and volume as interchangeable c. distinguish between the two dimensions of weight and volume and test each

separately d. adopt the more-is-more rule with no differentiation or integration

11. Two rows each contain an equal number of coins. In one row, the coins are spread apart, making the row look much longer than the other row. According to Piaget, the first stage at which children consistently say the two rows contain equal numbers is

.

a. formal-operational stage b. preoperational stage c. sensorimotor stage d. concrete-operational stage

12. A child is asked to think of reasons why school recess time should be shortened as well reasons why it should be lengthened. The child believes strongly that recess time should be lengthened and proceeds to list only the reasons for her belief, with- out consideration for alternative viewpoints. The child’s approach to the problem is typical of .

a. deductive reasoning b. type 2 thinking (analytical) c. type 1 thinking (intuitive) d. scientific thinking

Summary and Resources

13. Which factor is MOST likely to facilitate deductive reasoning in young children?

a. placing the reasoning problem in a make-believe context b. beginning the argument with a hypothetical statement c. instructing children to focus on the content of the statements rather than on their

validity d. arranging the problem so that the conclusion has belief-inconsistent content

14. Which statement about the development of scientific thinking is FALSE?

a. Children do not necessarily have to be in Piaget’s formal-operational stage to learn how to effectively design an experiment.

b. An experiment has a confound when two or more variables change at the same time.

c. Preschoolers are not yet capable of using covariation to make causal inferences. d. Sometimes high school students and even adults do not distinguish theory and

evidence.

15. A child is investigating which plant food promotes the best growth. She takes three seeds and places them in soil possessing identical nutrients. Each day the plants receive the same amount of sunlight and water. The only difference among the plants is the type of food placed in the soil. The child’s activities are BEST described as

.

a. divergent thinking b. analogical reasoning c. the control-of-variables procedure d. type 1 (intuitive) reasoning

Critical-Thinking Questions

1. How might certain computer games potentially facilitate the development of chil- dren’s problem-solving skills? In particular, what features of the games would be important for enhancing problem-solving development in light of the skills dis- cussed in this chapter? In contrast, is there anything about computer games that could hinder or pose an obstacle to facilitating children’s problem-solving skills? Explain.

2. Competency to stand trial, Dusky v. United States (1960), requires the ability to consult with a lawyer “with a reasonable degree of rational understanding” and “a rational as well as factual understanding” of the court’s proceedings. How would you define and assess “rational understanding” in children? Given what you now know about the development of reasoning, is there a particular age or stage at which you can say a juvenile possesses rational understanding? Why or why not?

3. Recall your grade school and middle school science classes. After reading this chap- ter, is there anything you would do differently if you were responsible for teaching scientific thinking in those science classes? Why or why not? How do your answers relate to the national goal of increasing the number of individuals pursuing careers in science?

Summary and Resources

Key Terms

analogical reasoning The idea that a rela- tionship between two things generalizes to a relationship between two other things.

belief-consistent argument A valid argu- ment in which the conclusion is accurate.

belief-inconsistent argument A valid argument in which the conclusion is empiri- cally false.

causal inference The process of determin- ing that a cause–effect relationship exists when evidence indicates that changes in one variable impact a second variable.

confirmation bias A tendency to seek evi- dence consistent with one’s own preexisting assumptions.

confound The phenomenon of two or more variables in an experiment changing together; this prevents the experimenter from determining whether only one of them is actually affecting the experiment’s results.

control of variables (COV) The proce- dure of making sure that all variables in an experiment remain the same except for the one being tested by the experimenter.

covariation The extent to which changes in one variable are associated with changes in another variable.

deductive reasoning The process of assuming that the premises in an argument are true and then determining whether the conclusion of the argument necessarily fol- lows from those premises.

direct instruction A teaching method that includes worked examples and explicit guid- ance to help children learn how to eventu- ally solve problems on their own.

discovery learning A teaching method in which children are expected to acquire knowledge and skills through their own active exploration and interaction with the environment.

divergent thinking The generation of mul- tiple, nonobvious possibilities for solving a problem.

dual process theory The idea that one can process a cognitive task by using two different ways of thinking. Type 1 thinking is intuitive and automatic and may reach conclusions in conflict with type 2 thinking, which is analytical and rational.

end-state comfort effect Motor planning by using an initial awkward posture in order to ensure a comfortable end posture when handling objects.

functional fixedness A tendency to use something only for the purpose for which it was originally designed, thus potentially preventing one from manipulating it to solve a problem.

hypothetico-deductive reasoning The systematic analysis of all of the possibili- ties of a problem and deducing the concrete realities that follow when those possibilities are tested.

planning The process of determining an action or series of actions to solve a problem before one solves the problem.

problem solving The process of identify- ing a solution for overcoming an obstacle and then monitoring the effectiveness of the attempted solution.

rules  The strategies and assumptions that guide predictions and solutions when solv- ing a problem.

Summary and Resources

Additional Resources Web Resources

Nurturing Reasoning in Young Children http://eclkc.ohs.acf.hhs.gov/hslc/hs/sr/approach/cdelf/l_reason.html This site provides strategies from Head Start for facilitating reasoning and problem solving in children.

Planning It Out in Words http://www.psychologytoday.com/blog/the-child-in-time/201105/planning-it-out-in- words This article for general readers is about the role of private speech in planning, illus- trating how social-constructivist theory contributes to our understanding of cognitive development.

10 Tips to Support Children’s Science Learning http://families.naeyc.org/learning-and-development/child-development/10-tips- support-children%E2%80%99s-science-learning The National Association for the Education of Young Children offers everyday activities and simple questions to promote scientific thinking in young children.

Further Reading

Gopnik, A. (2012). Scientific thinking in young children: Theoretical advances, empirical research, and policy implications. Science, 337(6102), 1623–1627. The author details research findings related to promoting scientific thinking even in the preschool years.

Keen, R. (2011). The development of problem solving in young children: A critical cognitive skill. Annual Review of Psychology, 62, 1–21. This article discusses the foundations and importance of problem solving in childhood.

Siegler, R. S. (2005). Children’s learning. American Psychologist, 60, 769–778. This article provides an overview of strategies, problem solving, and learning in children.

Stanovich, K. E. (2009). The thinking that IQ tests miss. Scientific American Mind, 20(6), 34–39. The author discusses IQ tests and the questionable extent to which they assess type 2 reasoning.

scientific thinking The process of acquir- ing knowledge by designing tests of theories and then inferring whether the evidence supports or disconfirms those theories.

syllogism  An argument in which a conclu- sion follows from two premises.

tool use The act of using an object to over- come physical limitations that would other- wise prevent attainment of a goal.

transitive inference The process of deter- mining how two things are related based on their relationship to other things; for instance, if A > B and B > C, then A > C.

Summary and Resources

Answers and Rejoinders to Chapter Pretest

1. True. Beginning in infancy, the foundations of problem solving are evident. We can see infant problem-solving capacities, such as monitoring solutions, in everyday tasks like eating with a spoon.

2. False. During infancy the beginnings of the capacity to detect analogous relation- ships is evident. As long as the content of an analogy is familiar, children can explic- itly solve analogies by age 4 or 5.

3. True. Evidence indicates continuity between EF skills and later planning skills. The development of planning skills is associated with general processes like language and the EFs.

4. True. Young children (age 5) may actually be able to see a novel way to use an object more quickly than older children (age 7). The older child’s problem solving is more constrained by his or her knowledge of the object’s conventional function.

5. False. Children’s discovery of solutions is facilitated when they are prompted to explain their attempts to figure out a solution to a problem.

6. True. When being overly literal leads to an incorrect conclusion, placing problems in a pretend context helps preschoolers reason and come to correct conclusions.

7. False. Evidence indicates that explicit instruction more effectively promotes scien- tific thinking in children than methods that rely on self-discovery.

Answers and Rejoinders to Chapter Posttest

1. c. Nine-month-olds monitor the effects of attempts to eat with a spoon. Nine-month-olds can typically attempt to use a spoon for eating. They have difficulty monitoring their efforts, which sometimes leads to the wrong end of the spoon end- ing up in the infant’s mouth.

2. b. identifying a goal and a tool to help attain it Problem solving involves identifying a goal (solution) and the means to attain it. In infancy means–end understanding was demonstrated as 9-month-olds used the spoon as a tool to achieve their goal.

3. a. The development of analogical reasoning is stage-like. Children’s analogical reasoning skills develop gradually as content knowledge and executive functioning capabilities increase.

4. b. Analogical reasoning Analogical reasoning is the process of inferring a relationship between two stimuli based on a similar relationship discovered in two other stimuli.

5. a. For complex problems, adults take longer to plan their solution than children. With development, individuals take longer to plan how to solve complex problems compared to younger children, who tend to respond more impulsively.

6. b. the end-state comfort effect When grasping an upturned cup, the end-state comfort effect involves first handling the cup with the thumb downturned. Children instead tend to grasp an upturned cup with thumb up, resulting in an awkward grasp when it is turned upright. This illustrates a more general tendency in children’s planning to overlook intermediate, counterintuitive steps.

7. a. divergent thinking Divergent thinking is flexible thinking that generates novel possibilities. It is evident when children find an unconventional but effective use for an object as a tool.

Summary and Resources

8. d. There is no evidence of tool use in infants and toddlers. The capacity for tool use is evident in infants and toddlers. Toddlers’ motor skills enable tool use that exceeds capabilities found in nonhuman primates.

9. a. rules Rules are evident through close observation of trial-by-trial attempts at problem solving. Through practice and feedback, children’s rules tend to become more sophisticated and effective.

10. c. distinguish between the two dimensions of weight and volume and test each separately Progress in solving the task comes from differentiating between the two dimensions. Distinguishing between them allows children to separately test how each might con- tribute to water displacement.

11. d. concrete-operational stage Piaget theorized that concrete-operational children use logical reasoning to solve the conservation task and other problems with observable content.

12. c. type 1 thinking (intuitive) The myside bias, type 1 thinking, is a bias toward considering only one’s own belief when asked to look at both sides of an argument.

13. a. placing the reasoning problem in a make-believe context A make-believe context appears to help young children distinguish the form of an argument from its content, making it easier to accept false, but valid, conclusions.

14. c. Preschoolers are not yet capable of using covariation to make causal inferences. When given concrete objects to explore, preschoolers notice patterns of evidence that indicate one factor, but not another, is responsible for causing an effect.

15. c. the control-of-variables procedure The control-of-variables procedure holds all factors constant and manipulates the variable of interest to see the effect.