DUE MONDAY 7 AM EST

PART 1

· As classrooms become more inclusive and more diverse, the number of students needing special attention increases, as do the pressures on their teachers to provide for their needs. If a teacher has a standard, one-size-fits-all-learning-levels textbook as the tool with which to teach the curriculum to every student, the onus for differentiation falls squarely on the shoulders of the teacher. This need for differentiation means that when teachers are planning they need to move away from planning for the class as a whole and think more about planning for students with specific needs. It may mean thinking and planning mathematics centers where at each center rigorous mathematics is presented using various open-ended problems or tasks requiring multiple representation, modeling using appropriate manipulatives, extensions to the basic problem or task for gifted or talented student, and supportive strategies for those students in need of that support.

When we think in terms of learning, universal design means the design of instructional materials and activities that allows the learning goals to be achievable by individuals with wide differences in their abilities to see, hear, speak, move, read, write, understand English, attend, organize, engage, and remember. Universal design for learning is achieved by means of flexible curricular materials and activities that provide alternatives for students with disparities in abilities and backgrounds. This is similar to the iPhones and Zunes problem we examined last week. The differentiation was built into the activity…it was not added on to the problem.

Universal design for learning stresses the importance of using clear, precise, mathematical language. One of the reasons students have so much trouble with mathematics is because the language teachers use or allow students to use is vague and often misleading. Clear explanations are often not enough to ensure learning but unclear explanations often result in misconceptions incorrect learning.

What Universal design is not is a series of shortcuts, mnemonics, or naked computations for students who struggle. It is not a watering down of the curriculum. It is not the lowering of expectations for some students. Since Universal design for learning builds in access and opportunity for all students it is important that appropriate and precise mathematical language is used by the teacher and expected of all the students. Examine the following list of phrases or shortcuts commonly used in mathematics classrooms across the country.

Commonly Heard Short Cuts

· You cannot take a smaller number from a larger number. (What about...'You cannot take a larger number from a smaller number.')

· When you multiply the number gets bigger and when you divide the number gets smaller.

· Two negatives make a positive.

· Always reduce fractions to lowest terms.

· Always change an improper fraction to a mixed number.

· When solving a proportion cross-multiply first.

· To multiply mixed numbers always convert them to improper fractions first.

· To multiply binomials always use FOIL.

· When solving an equation first, always bring the variable to one side of the equation.

· Always do the operation inside the parenthesis first.

· When adding numbers always line up the digits starting at the right.

For each bullet in the list above, explain why it is not a good tip to give to students. Be sure to offer a counter example to support your reason the short cut is not empowering students but rather can actually stunt a student’s understanding of important conceptual ideas in mathematics.

Post your reasons

PART 2

· Applications

As teachers we need to focus on teaching to our district or state learning targets. We need to clearly articulate the learning targets to our students and listen very carefully to our students' oral and written communication to understand the logic behind their oral or written work.

post your solution to the following problem and justify your answer. How do you think your students would solve this problem?

3 more than 5 times 6

Examine the following student solutions.

1. Classify each solution as either correct or incorrect.

2. What does each solution indicate about the student's understanding?

3. What feedback would you provide each student?

How might you take the following problem and adapt it for all students in a diverse class? Consider how you would address this concept with students with disabilities. Gifted and talented students.

The number of speeding tickets in Quincy have dropped from 210 tickets in October to 190 tickets in November. What is the percent of decrease? a. 5% b. 10% c. 20% d. 90%

Each foil/mistake (the term for each answer choice) represents an error in student thinking. Identify the misconception represented by each. What are some strategies or representations that can effectively be used to solve the Speeding Ticket problem. Include at least three different ways in which the problem can be represented. Share your strategies with your peers. Respond or react to the postings of at least two of your peers. In her book Math for All: Differentiating Instruction, Linda Dacey uses the following model illustrating the range of readiness that can be met when a teacher takes the time to adapt a task.