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ERROR ANALYSIS CASE STUDY
Error Analysis Case Study
Thuy Nguyen
EDLC:530 Teaching Mathematics
Dr. John Squires
July 25, 2025
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ERROR ANALYSIS CASE STUDY
Introduction
Good teaching requires, among other things, dealing with the mistakes students make, especially
about the concepts students find the hardest in mathematics. Four students, Dalton, Wyatt,
Madison, and Elias, each have their specific learning challenges, which require the use of
tailored approaches to foster their mathematics skills.
Case Study Level A, Case 1- Dalton
Dalton, a seventh-grade student, is 12 years old and has an interest in learning whenever he can.
He is having some issues with multiplying and understanding decimals. His teacher, Mrs.
Moreno, is aware that he struggles with the basic understanding of decimal place value. This is a
crucial issue because it affects the child's understanding of the fundamental concepts of
multiplication or even of addition and subtraction related to it. Mrs. Moreno is aware that these
issues need to be treated archically, the same as any other, based on the needs of the case.
Focused interventions. The patterns in the lack of understanding of arithmetic place the issues at
the foundational core of arithmetic, in this case, with the basic decimal place value and inability
to determine the decimal point's position. This is a form of procedural error. There is a lack of
applying appropriate techniques in other mathematical disciplines, for example, in the addition
and subtraction of decimals, where the identification of the position of decimal points is crucial
to the accuracy of the answer.
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ERROR ANALYSIS CASE STUDY
Mrs. Moreno aims to find out the reason for Dalton’s mistakes by collecting comprehensive data
on his understanding and practice of multiplication with decimals. To help Mrs. Moreno
understand Dalton’s thinking processes and to identify recurring themes in his mistakes, she can
watch how he tackles problems during class work and tests. In addition, reviewing some of
Dalton’s earlier work may reveal recurring themes, which may be a contributing factor to his
ongoing challenges with multiplying decimals. Through a careful analysis of his various tasks,
Mrs. Moreno can pinpoint the exact areas in which Dalton needs more customized instructional
intervention.
To address Dalton’s persistent problematic behavior, one intervention Mrs. Moreno can
implement is integrating personalized education strategies aligned with intensive progress
monitoring. Tracking Dalton’s progress on his development milestones, such as grasping
decimal multiplication and proficient problem-solving, enables Mrs. Moreno to tailor her
instruction to his specific challenges. She can provide focused intervention solutions such as
guided practice and direct instruction to correct Dalton’s procedural misconceptions and
reinforce essential concepts. Moreover, Mrs. Moreno can analyze Dalton’s assignments to
diagnose patterns and recurring errors to modify her instructional approaches. For instance, to
address recurrent errors with decimal placement, Mrs. Moreno could draw a U-shaped line as a
visual aid to help him see where decimal points should be placed. This hands-on approach
enhances Dalton’s understanding of decimal place value and provides him with concrete
strategies to improve his skills.
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Also, Mrs. Moreno might give Dalton specific tasks and give him focused practice to help
deepen his understanding and improve his accuracy in multiplying decimals. Mrs. Moreno
fosters a growth mindset to boost Dalton’s self-confidence and allows him to own his learning by
pointing out his errors, and motivates him to analyze his work. Moreover, in his problem-solving
and other related activities, Dalton applies his understanding of decimal multiplication, which in
turn deepens his understanding and enhances his skills.
As we have seen, Dalton’s challenges with multiplication of decimals can be resolved with a
thoughtful approach that includes data evaluation, personalized educational plans, targeted
strategies, and mapping out a comprehensive plan of action. Mrs. Moreno can foster mastery and
success through diagnosis and the application of appropriate strategies and techniques to resolve
his multiplicative errors. With the right continuous evaluation, constructive feedback, and
consistent practice, he will master the skills of decimal place value and foster a deeper
understanding, which will build his mathematical confidence and proficiency.
Case Study Level A, Case 2-Madison
An 8-year-old second-grade student, Madison, has a specific learning disability in mathematics,
which means that she requires specialized methods for instruction. Madison’s teacher, Ms.
Brooks, has noted that she does well with learning through manipulatives, which was evident
when she learned about money with toy money. Madison has also been taught with moving hand
cardboard clocks, but she struggles with reading the time. Ms. Brooks knows that she has to
assist Madison with her learning challenges through manipulatives and visual strategies because
also she needs to grasp more abstract concepts like the concept of time.
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ERROR ANALYSIS CASE STUDY
Examining Madison’s latest quiz, it seems she mostly struggles with identifying the clock hands
and telling the time. This shows an error understanding and applying mathematical concepts
using time phrases such as “half-past” and “quarter before.” To support Madison, Ms. Brooks
designs specific strategies aimed at overcoming these challenges by strengthening her
understanding of time concepts and vocabulary.
To help Madison understand time intervals, Ms. Brooks could resume the lesson on money
where Madison showed proficiency and attempt to draw parallels on how both money and time
are segmented into quarters. Ms. Brooks can emphasize parallels to help Madison with time
intervals and enhance her ability to read clocks accurately. Madison can also be individually
tutored by Ms. Brooks with a cardboard clock where she will be prompted to verbalize the time
displayed by the clock hands. This way, Madison is able to engage with the notion of time
through a hands-on, multisensory approach, which strengthens her grasp of the concept.
Moreover, Ms. Brooks applies the Madison case study to understand her unique educational
needs by employing evidence-based approaches to instruction for her. Analyzing Madison’s
work systematically allows Ms. Brooks to identify problem areas, such as the pattern of clock
misreading, which will help her understand the student and strengthen her problem-solving
approaches. This enables her to devise targeted instructional strategies that address Madison’s
unique misconceptions and enhance her grasp of abstract math concepts.
In her structured plan for Madison, Ms. Brooks intends to help her with time-telling skills,
advancing her understanding in other areas of mathematics, and integrates methods informed by
her data and insights. To support Madison, Ms. Brooks employs a mix of direct teaching, hands-
on learning, and formative evaluation to foster her development and engagement in mathematics.
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ERROR ANALYSIS CASE STUDY
Case Study Level B, Case 2- Elias
Mrs. Gustafson, a special education teacher, is working with 7-year-old second grader Elias, who
is struggling in math. As part of her special education teaching, Elias is dealing with some
evidence-based interventions. Elias’s goal setting progress monitoring indicates a lack of
sufficient progress towards his year-end goals, despite his baseline and Mrs. Gustafson’s
interventions over the past six weeks. Mrs. Gustafson’s diagnostic evaluation reveals
considerable gaps in strategy use, which suggest difficulties with core mathematical concepts
and the problem-solving processes involved in mathematics.
Elias's procedural errors such as regrouping without carrying over digits illustrate problems he
may encounter during the execution of any given stage in mathematics. These errors may stem
from his learning difficulties, underscoring the need for a more tailored and focused intervention.
To address the complexities of difficulties, Mrs. Gustafson archives meticulous records of Elias’s
work, analyzes the patterns of his errors, and classifies them as either conceptual or procedural,
using them to formulate a targeted strategy.
By doing data collection and error analysis, Mrs. Gustafson knows what to help Elias with and
what his preferences are, allowing her to offer appropriate help and guidance. Step by step, Mrs.
Gustafson goes over the regrouping lesson with Elias, correcting his procedural errors with
visual aids to help improve his comprehension. In addition, Mrs. Gustafson has worked with
Elias to help him articulate the solution processes, and this has helped him remember and
understand some mathematical concepts.
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ERROR ANALYSIS CASE STUDY
The consistent positive learning environment that Mrs. Gustafson provides has helped build
Elias’s confidence and ability to solve mathematical problems independently. Mrs. Gustafson’s
focus on specific, measurable, attainable, relevant and time-bound goals combined with the
fostering of a positive self-image serves to help him advance his mathematical skills and achieve
his academic goals.
Through focused instruction, constant assessment, and supportive oversight, Mrs. Gustafson
strives to help Elias overcome his challenges with comprehending and mastering mathematical
concepts.
CASE STUDY LEVEL C, CASE 1-Wyatt
Wyatt, a twelve-year-old student in the sixth grade, struggles to understand the multiplication of
fractions and, as a result, possessed a poor score on his recent independent class assignment. A
brief lesson on the topic was given, and as Mr. Goldberg, the class teacher, mentions, “Most
students understand the basics of multiplication and are able to apply it effectively, with the
exception of Wyatt.” Further assessment reveals that Wyatt has the tendency to commit errors
when attempting to multiply fractions and subsequently simplify the fractions to their simplest
forms. This points to a greater lack of understanding of multiplication and the simplification of
fractions.
To uncover the specific challenges, misconceptions, and knowledge gaps that Wyatt has, Mr.
Goldberg intends to analyze his students’ work, documenting specific error patterns as they
relate to a given problem and collating detailed information about his problem-solving strategies.
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ERROR ANALYSIS CASE STUDY
Mr. Goldberg hopes to understand Wyatt's challenges in a more detailed manner by unearthing
methodically and tailoring strategies that address Wyatt’s needs. Wyatt has a tendency to
incorrectly simplify fractions with like denominators and inappropriately simplify by dropping
the denominator without performing a multiplication.
As focused forms of teaching, Mr. Goldberg help Wyatt understand the processes of
multiplication of fractions and address his practical errors. He plans to put Wyatt through
participatory instructions wherein the instructor and the student reflect on their ideas. This will
help him precisely know what he needs to help him with and provide specific suggestions. Using
participatory problem solving, Mr. Goldberg will be able to clarify misunderstandings Wyatt has
concerning multiplication of fractions and model appropriate problem solving behavior.
Also Mr. Goldberg explains to Wyatt the importance of repetition of the concept of
multiplication of fractions and the explanation of the problem solving processes. Mr. Goldberg
attempts to help strengthen Wyatt’s understanding of multiplication and impart appropriate
problem solving strategies through modeling and explicit teaching. Mr. Goldberg further
describes the expectation of Wyatt working on his solitary practice problems, which he attends to
giving guidance and instruction as needed to help the student to become confident and
independent in solving the mathematical problems.
Using targeted teaching strategies and empathy, Mr. Goldberg helps Wyatt overcome his
challenges with fraction multiplication and conceptual understanding of deeper mathematical
topics. Mr. Goldberg aims to enhance Wyatt's academic progression and develop his
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mathematical competencies through direct teaching and collaborative solving of complex
problems.
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