Error Analysis Case Study
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Jan 9, 2024
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CASE STUDY
1
Error Analysis Case Study
Courtney Peyton
School of Education, Liberty University
Author Note
Courtney Peyton
I have no known conflict of interest to disclose.
Correspondence concerning this article should be addressed to Courtney Peyton. Email:
clpeyton@liberty.edu
CASE STUDY
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Error Analysis Case Study
Case Study Level A, Case 1 - Dalton
This case study revolves around Dalton, a seventh-grade student named Dalton who has
been facing challenges in his math class, particularly when it comes to multiplying decimals.
Despite Dalton's initial success in Mrs. Moreno's class, his recent independent assignments have
shown a decline in performance. Recognizing this, Mrs. Moreno, Dalton's math teacher, aims to
conduct an error analysis on his most recent homework assignment. By investigating the specific
mistakes Dalton made, Mrs. Moreno hopes to identify the specific type of error he consistently
commits. This analysis will enable Mrs. Moreno to develop a tailored plan to enhance Dalton's
understanding and proficiency in multiplying decimals.
Based on the information provided with Dalton’s example work, it is evident that Dalton
is making errors related to placing the decimal in the wrong position when performing
multiplication calculations. These errors can be categorized as procedural errors specifically
related to decimal placement. To determine the reasons behind this student making this kind of
error, the teacher can employ the strategy of identifying error patterns. By analyzing other
examples of similar errors made by students, the teacher can gain insights into common
misconceptions or misunderstandings that lead to these mistakes. This could involve reviewing
past assignments or assessments to identify recurring patterns in decimal placement errors.
When addressing these error patterns, several strategies can be employed:
1.
Direct Instruction: The teacher can provide explicit instruction on the correct procedure for
decimal placement during multiplication. This strategy aims to clarify the proper steps and
CASE STUDY
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reinforce the correct approach. Direct instruction provides clear and explicit guidance on the
correct procedure for decimal placement during multiplication.
2.
Models and Visuals: Utilizing visual representations, such as grids or place value charts, can
help students visualize the process of multiplying decimals and correctly place the decimal
point. This strategy provides a concrete and visual representation to support understanding.
Models and Visuals enhance understanding and visualization of decimal multiplication,
helping students grasp the concept of decimal placement.
3.
Error Analysis: By analyzing Dalton's work and pointing out the specific errors in decimal
placement, the teacher can draw attention to the mistakes and prompt Dalton to self-correct.
This strategy helps students become more aware of their errors and encourages them to
develop a habit of double-checking their work. Error Analysis draws attention to specific
errors made by Dalton, promoting self-correction and self-awareness.
4.
Guided Practice: The teacher can provide guided practice opportunities for Dalton to
reinforce the correct procedure for decimal placement. This strategy allows for targeted
feedback and support while gradually increasing Dalton's independence in applying the
correct method. Guided Practice provides opportunities for Dalton to practice the correct
procedure with support and feedback, gradually building his confidence and independence in
applying the correct method.
These strategies are beneficial for Dalton's improvement as they address his specific error pattern
by providing clear guidance, visual support, error awareness, and opportunities for practice and
reinforcement.
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CASE STUDY
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Case Study Level A, Case 2 - Madison
Madison is a bright and enthusiastic third-grade student who has a specific learning
disability in math. Recently, her class completed a unit on money, and Madison's teacher, Ms.
Brooks, was pleased with her performance. Ms. Brooks believes that Madison's success can be
attributed to the use of play money as a teaching tool, which aligns with Madison's
individualized education program (IEP) that states she learns best with hands-on materials. To
build on this success, Ms. Brooks incorporated concrete objects, such as cardboard clocks with
movable hands, to teach the concept of telling time. However, halfway through the chapter, Ms.
Brooks noticed that Madison is struggling with this topic. As a result, Ms. Brooks decides to
analyze Madison's most recent quiz to understand the errors she might have made.
Based on Madison's quiz answers, it is evident that she does not understand the concept
of a quarter of an hour. The incorrect answers she provided were related to the phrasing of
"quarter past" and "quarter till" in relation to an hour. By analyzing Madison's errors, we can
determine that there is a consistent pattern of mistakes involving the word "quarter." It seems that
Madison lacks information, particularly in understanding the vocabulary associated with the
word "quarter" in the context of time.
To address these error patterns, several strategies can be employed:
1.
Explicit Vocabulary Instruction: This strategy involves explicitly teaching Madison the
meaning and usage of vocabulary words related to time, specifically focusing on the word
"quarter." The purpose of this strategy is to ensure that Madison comprehends the concept of
a quarter in relation to time and can accurately interpret phrases like "quarter past" and
"quarter till."
CASE STUDY
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2.
Visual Representations: Utilizing visual aids, such as diagrams or pictures, can help Madison
visualize and understand the concept of a quarter of an hour. By depicting the passage of time
and highlighting the specific intervals represented by a quarter, Madison can develop a
clearer understanding of the concept.
3.
Manipulatives and Hands-on Activities: Like the successful use of manipulatives like play
money in the money unit, incorporating hands-on activities can be beneficial in teaching time
concepts to Madison. For example, using a physical clock with movable hands or interactive
time-telling games can engage Madison and provide her with tangible experiences to
reinforce her understanding of quarters in time.
These strategies are designed to help Madison improve by addressing her specific
difficulties with the concept of a quarter of an hour and the associated vocabulary. Explicit
vocabulary instruction aims to ensure she comprehends the terminology, while visual
representations and hands-on activities provide her with concrete experiences to enhance her
understanding. By using these strategies, Madison can develop a solid foundation of knowledge
and overcome her errors in relation to time concepts.
Case Study Level B, Case 2 – Elias
Elías, a 7-year-old student in 2nd grade with a learning disability, has been receiving
intensive intervention from his special education teacher, Mrs. Gustafson, at Bordeaux
Elementary School. After six weeks of progress monitoring, it is evident that Elías is not making
sufficient progress to meet his end-of-year goals. To identify his areas of difficulty and determine
his specific instructional needs, Mrs. Gustafson decides to conduct a diagnostic assessment. As
part of this assessment, she analyzes Elías' progress monitoring data by conducting an error
analysis.
CASE STUDY
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The identified error pattern in Elías' answers on the diagnostic assessment is a procedural
error related to regrouping when adding. Specifically, Elías consistently forgets to regroup when
adding numbers that require carrying over to the next column of tens or hundreds. To determine
the reasons behind these errors, Mrs. Gustafson can employ various strategies:
1. Interview the student: Mrs. Gustafson can have a conversation with Elías to understand his
thought process and determine if there are any misconceptions or gaps in understanding that are
causing the regrouping errors. This strategy allows for direct communication and insight into
Elías' thinking.
2. Observe the student: By observing Elías during math activities or while solving similar
problems, Mrs. Gustafson can gain further understanding of his approach and identify any
specific areas of struggle. This strategy provides visual cues and real-time feedback on Elías'
problem-solving strategies.
3. Look for exceptions to the error pattern: Mrs. Gustafson should also analyze Elías' work to
identify any instances where he successfully applied the regrouping concept correctly. These
exceptions can provide clues about when and why Elías is making errors and help pinpoint
specific areas that require additional focus and practice.
The purpose of these strategies is to gain insight into Elías' understanding of regrouping
and identify the root causes of his procedural errors. By understanding why Elías is making these
errors, Mrs. Gustafson can tailor her instructional approach to address his specific needs and help
him improve. In this case, using these strategies would help Mrs. Gustafson determine if Elías is
struggling with the concept of regrouping or if there are specific circumstances or types of
problems where he consistently forgets to apply the regrouping process. This information would
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CASE STUDY
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guide Mrs. Gustafson in developing targeted interventions and providing additional practice
opportunities to help Elías improve his regrouping skills.
Case Study Level C, Case 1 - Wyatt
Mr. Goldberg recently taught a unit on fractions. While most of his six grade students
quickly grasped the concept of adding and subtracting two fractions, a few struggled when it
came to multiplying fractions. After a brief mini lesson, all but three students demonstrated
understanding of how to solve the problems. However, twelve-year-old, Wyatt, a continues to
struggle, prompting Mr. Goldberg to collect data from Wyatt's recent independent classroom
assignment. Mr. Goldberg aims to determine the type of error Wyatt is making to provide
appropriate instruction and support to help Wyatt succeed in understanding and solving
multiplying fractions problems.
It appears that Wyatt is making errors when multiplying fractions with the same
denominator. Instead of correctly multiplying the numerators, he is keeping the denominator the
same. This indicates a specific error pattern related to fractions with identical denominators. To
determine the reason for this type of error and to identify other examples, Mr. Goldberg can
employ several strategies:
1. Error Analysis: Mr. Goldberg can analyze Wyatt's work and identify specific instances where
he made the error. By examining multiple examples, Mr. Goldberg can identify any patterns or
common mistakes Wyatt is making.
2. One-on-One Discussion: Mr. Goldberg can have a conversation with Wyatt to understand his
thought process and reasoning behind the incorrect answers. This will help uncover any
misconceptions or gaps in understanding that may be contributing to the error.
CASE STUDY
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3. Explicit Instruction: Mr. Goldberg can provide explicit instruction to address Wyatt's error.
This can include modeling the correct method of multiplying fractions with the same
denominator, providing guided practice with similar problems, and giving Wyatt independent
practice to reinforce the correct approach.
4. Reassessment: After providing instruction and practice, Mr. Goldberg should reassess Wyatt's
skills by giving him similar problems to solve. This will allow Mr. Goldberg to gauge Wyatt's
progress and determine if further instruction or support is needed.
Each strategy serves a specific purpose in helping Wyatt improve:
1. Error Analysis: This strategy helps Mr. Goldberg identify the specific error pattern Wyatt is
making and any common mistakes he consistently commits.
2. One-on-One Discussion: By having a conversation with Wyatt, Mr. Goldberg can gain insight
into Wyatt's thinking and reasoning process. This will allow him to address any misconceptions
or gaps in understanding that are contributing to the error.
3. Explicit Instruction: Providing explicit instruction helps Wyatt understand the correct method
of multiplying fractions with identical denominators. Through modeling, guided practice, and
independent practice, Wyatt can reinforce the correct approach and develop a deeper
understanding.
4. Reassessment: Reassessing Wyatt's skills allows Mr. Goldberg to determine if the instruction
and practice have been effective in addressing the error pattern. It helps Mr. Goldberg monitor
Wyatt's progress and identify any further areas of improvement or support needed. By employing
these strategies, Mr. Goldberg can help Wyatt overcome his error pattern and improve his ability
to correctly multiply fractions with the same denominator.
CASE STUDY
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References
Brown, J., & Skow, K. (2022, March 24).
Mathematics: Identifying and Addressing Student
Errors
. iris. Peabody. Vanderbilt .edu. https://iris.peabody.vanderbilt.edu/wp-
content/uploads/pdf_case_studies/ics_matherr.pdf
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