EDUC 504 LIBERTY UNIVERSITY ERROR ANALYSIS CASE STUDY 2025.docx

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ERROR ANALYSIS CASE STUDY

Jaquita Pratt

School of Education, Liberty University

ERROR ANALYSIS CASE STUDY ASSIGNMENT

As an educator, understanding and analyzing student errors is a crucial component of

effective instructor. Being able to identify the nature and root causes of these mistakes enables

educators to tailor their instructional strategies and better support student learning. This case

study examines a range of mathematical errors made by students at various grade levels,

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Level A, Case 1

contribute to poorer performance among students of Dalton’s age. This analysis explores the

nature of Dalton’s errors, their possible causes, and instructional strategies to address them.

The most evident error Dalton exhibits is a procedural error. As Brown and Skow explain,

procedural knowledge refers to understanding the steps and methods required to solve a

problem. Procedural errors occur when a student incorrectly applies a rule or algorithm; in

Dalton’s case, this relates specifically to decimal placement in multiplication (Brown &

Skow,2016). Other common procedural errors include mistakes with regrouping, errors involving

fractions, or misaligning decimals during addition or subtraction.

For Dalton, the main issue is failing to count and add the number of decimal places in

each factor to determine the correct decimal placement in the answer. Although the numerical

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the underlying principle. In this case, there is a misconception of where to place the decimal

point when multiplying decimals. Not to dig too deep, but at the surface level, there may also

be some factual errors simply because the mistakes Dalton made were simple (nothing further

than that).

There are several effective strategies for addressing Dalton’s error patterns. First, it is

helpful to discuss the error with Dalton after completing an analysis of his work. By clearly

explaining his mistake and assuring him that you will work together to correct it, this approach

can boost Dalton’s confidence, help him recognize his errors, and reassure him that he is not

alone in facing such challenges.

Instruction should focus specifically on the identified error rather than reteaching the

entire lesson. Explicit instruction is an appropriate strategy in this case, as structured, targeted

“Math think-aloud” can further benefit Dalton. When students verbalize their

problemsolving process, it makes their thinking visible to both them and the teacher. This can

uncover misconceptions and enable the teacher to provide immediate, targeted feedback.

Additionally, error correction exercises, where Dalton is presented with incorrect solutions

to analyze and correct, can foster higher-level thinking skills. Through these exercises, Dalton

learns to identify and understand errors, including those in his own work.

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Each of these strategies actively engages Dalton in the learning process, promotes

selfawareness and the development of correct mathematical habits, and ensures he builds a

solid foundation before moving on to more advanced concepts.

Case Study Level A, Case 2 - Madison

Madison is exhibiting more of the conceptual and vocabulary errors. She seems to have

the telling time down pack. She seems to struggle to understand the meaning of the terms

underlying ideas and principles, a recognition of when to apply them, and an understanding of

the relationships among ideas and principles (Brown & Skow, 2016). The conceptual errors occur

when a student holds misconceptions of the underlying principles and ideas related to a given

mathematical problem(Brown & Skow, 2016). These errors include, but are not limited to,

misunderstanding place value, overgeneralizing, and Overspecializing. In this case, I would

venture to say that it’s more so overspecializing, because the lack of conceptual understanding,

the student develops an overly narrow definition of a given concept or of when to apply a rule

or algorithm. Madison seems not to fully understand the relationship between the numbers on

the clock and the concepts of “quarter past” and “quarter ‘til. Her difficulty with the phases

shows a misunderstanding of mathematical or time-based terms.

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To determine the reason, the teacher should examine Madison’s work to identify specific

patterns, such as repeated difficulty with quarter-related terms, and then discuss the error with

her to understand her thought process. Other errors could include misunderstanding the

difference between the minute hand and hour hand, or confusing am/pm with telling time.

grasp the relationship between the number of minutes and their position on the clock. Guided

practice with word problems provides practice using time-related word problems that

incorporate the target vocabulary and concepts. This strategy allows Madison to apply her new

vocabulary and conceptual understanding in a practical context, reinforcing her learning and

providing opportunities for the teacher to monitor and address misconceptions as they arise.

Upon looking at Elias’s work, it is evident that he has the basic knowledge of adding and

subtracting. Elias seems to be portraying a combination of conceptual and procedural errors.

Brown and Skow point out on page 9 that, “Conceptual knowledge is an understanding of

underlying ideas and principles and a recognition of when to apply them and understanding the

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instance, overgeneralization, where rules are improperly applied, is a more specific type of

conceptual error observed in Elias’s addition problems, such as adding numbers without

carrying over the tens column (regrouping).

solve a problem(Brown & Skow, 2016). Procedural errors are shown by difficulties in following

the correct steps or algorithms in math. Elias’ mistake here is that he forgets to regroup, which

is known as the regrouping error. Some other examples of procedural errors are making

computational mistakes during addition, subtraction, multiplication, or division, or incorrectly

applying steps in a multi-step problem, such as not regrouping correctly in subtraction.

Determining the reason for Elias’s errors can be determined through direct questioning,

using manipulatives, and administering a diagnostic test. Direct questioning allows Elias to be

asked to explain his thought process for solving the specific problems, which in turn would

reveal whether conceptual understanding or procedural application is the primary challenge.

Providing manipulatives, such as number lines, counters, and base ten blocks, allows for an

assessment of his concrete understanding of concepts like place value and addition strategies.

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Error analysis involves presenting Elias with solved problems containing intentional errors

thinking skills and deepen conceptual understanding by directly engaging with common

misconceptions. By identifying and correcting both conceptual and procedural errors in his work

or in sample problems, Elias can gain insight into why certain steps are incorrect and how to

apply the correct procedures, particularly in areas such as carrying over in addition.

Direct Instruction with Explicit Modeling is characterized by clear explanations of concepts

and procedures, followed by step-by-step demonstration of correct methods. It is especially

helpful for addressing procedural errors. For Elias, explicit modeling of processes like regrouping

in addition or subtraction provides clear guidance, helping him internalize the correct

algorithms and perform them independently.

Manipulatives and Visual Aids include incorporating concrete materials and visual

timely feedback allows for immediate correction of mistakes and consolidation of learning.

Each of these strategies is designed to deepen conceptual understanding, clarify

procedural steps, and provide opportunities for reinforced learning and error correction,

thereby helping Elias build a stronger mathematical foundation.

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reviewing Wyatt’s assignment, he only got 3 wrong out of 12. Wyatt demonstrates both

Procedural knowledge is when there is an understanding of the steps and procedures

that are required to solve a problem. Procedural errors occur when a student incorrectly applies

a rule or algorithm(Brown & Skow, 2016).. Wyatt makes the mistake of executing the correct

steps, such as multiplying numerators and denominators or confusing operations. For instance,

he might add denominators (as in addition) rather than multiplying them.

The conceptual errors occur when a student holds misconceptions of the underlying

misunderstand the underlying concept of fraction multiplication, perhaps believing common

denominators are required, which is not the case for multiplication. Which again was very

minute, as it shows in the other 9 problems that he knows how to multiply fractions; he was

thrown off with the same denominator.

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There are many strategies to address the error patterns: Error analysis, explicit

instruction, and scaffolding. Error Analysis involves careful examination of a student’s mistakes

to identify misunderstandings and misconceptions. The purpose is to reveal exactly where the

students’ thinking diverges from the expected process. By looking at Wyatt’s work closely, his

Explicit instruction involves direct, step-by-step teaching of mathematical procedures

and rules, including modeling and demonstration. Its purpose is to solidify Wyatt’s accurate

understanding of both the procedure and the concept. Wyatt will therefore benefit from clear,

structured lessons differentiating between addition and multiplication rules for fractions.

Explicit instruction also corrects misunderstandings and sets him on the right path.

charts, or guided practice, to help Wyatt master the concept. The support is gradually removed

as proficiency increases. Wyatt benefits from using manipulatives and a multiplication fraction