ERROR ANALYSIS CASE STUDY 1
Error Analysis Case Study Assignment
Lakesha McInnis
School of Education, Liberty University
Introduction
This paper analyzes the cases of Dalton, Madison, Elias, and Wyatt, following the STAR
sheet model to diagnose each student’s mathematical difficulties and recommend instructional
strategies. All recommendations are grounded in positive, supportive, and student-centered
instructional practices. These cases and strategies are based on the Mathematics: Identifying
and
Addressing Student Errors Case Study Unit developed by Brown and Skow (2016).
Level A- Case 1: Dalton
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Identifying Dalton’s Error Pattern
Dalton demonstrates consistent difficulty placing the decimal correctly when multiplying
decimal numbers (Brown and Skow, 2016). Although he performs the multiplication correctly, he
incorrectly positions the decimal in the product. This indicates a procedural error because he
misunderstands or inconsistently applies the algorithm used to determine decimal placement.
According to the IRIS guidance, procedural errors occur when a student partially understands a
process but lacks the mastery of all required steps.
Dalton’s error suggest that he may have memorized a multiplication procedure without
understanding why decimal places must be counted and matched in the final product (Brown &
Skow, 2016). He might also be overgeneralizing whole-number multiplication rules, assuming
that decimal placement is arbitrary. The teacher can clarify this by asking Dalton to explain how
he decided where to place the decimal, prompting a think-aloud, or having him model the
problem with place-value tools. Similar errors include misplacing decimals when diving by
powers of ten, incorrectly converting decimals to fractions, or shifting decimals in the wrong
direction when multiplying by tenths.
Strategies to Address Dalton’s Errors
Explicit instruction is a great strategy to use, it offers clear, sequential modeling of
decimal multiplication, including direct explanation of why decimal places must be counted. The
teacher models each step, highlights common errors, and provides immediate corrective
feedback. This strategy supports Dalton by ensuring he received guided practice that isolates
the specific step he struggles with.
Another strategy would be to use manipulatives or visuals such as base-ten blocks or decimal
grids to help Dalton visualize tenths and hundreds. He can see, for example that 0.3 x 0.4 equals
0.12 because three tenths groups of four tenths creates twelve hundredths. Concrete
representations deepen conceptual understanding so that procedural steps make sense and are
retained. The last strategy would be guided practice with feedback. Dalton would benefit from
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repeated practice with immediate feedback, allowing him to internalize the rule that the total
number of decimal places in the product must equal the sum of decimal places in the factors.
This strategy helps prevent recurring procedural errors.
Level A- Case 2: Madison
Identifying Madison’s Error Pattern
Madison has difficulty telling time on and analog clock, misreading the minute-hand and
associating numbers incorrectly with their minute values (Brown & Skow, 2016). Her errors
reflect both factual and conceptual misunderstandings. Factually, she does not consistently
know that each number on the clock equals five minutes. Conceptually, she appears unsure how
the hour hand moves as minutes pass and how the two hands relate.
Madison’s IEP states that she learns best using concrete materials, and telling time is a
skill that requires interpreting spatial relationships. She may not have had enough exposure to
analog clocks or may confuse the numeric values with minute intervals. A teacher could ask
Madison to demonstrate how she reads a clock to determine where her confusion begins.
Similar errors include confusing the hour and minute hand, counting by ones instead of fives, or
misunderstanding time phrases such as “quarter past.”
Strategies to Address Madison’s Errors
Collecting data with Additional examples of Madison’s time-telling attempts is one
strategy that would allow the teacher to identify whether the errors are consistent across
quarter hours, half past times, or hour transitions. Collecting data helps in tailoring instruction
rather than making general assumptions. Another strategy would be the use of manipulatives
such as a movable-hand clock, which allows Madison to physically adjust time and observe how
both hands move. This concrete experience supports her learning style and reinforces minute
counting by fives. Manipulatives bridge the gap between abstract time concepts and hands-on
exploration. Another strategy would be explicit instruction. Explicit modeling of counting by
fives around the clock, identifying hand positions, and using time vocabulary supports Madison
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in learning procedures systematically. With clear demonstrations and repetition, she gains
confidence in interpreting analog clocks. The last strategy would be to use visual supports.
Visual anchors such as labeling minute increments on her personal clock model or color-coding
hands, reinforce connections between numbers and minutes.
Level B- Case 2: Elias
Identifying Elias’s Error Pattern
Elias struggles with comparing, reducing, and operating with fractions, demonstrating
errors consistent with conceptual misunderstanding (Brown & Skow, 2016). He appears to reply
on whole-number reasoning, assuming, for example, that fractions with larger denominators
represent large values. This reflects a common misconception among students who have not yet
internalized fraction magnitude. Elias likely sees fractions as two unrelated whole numbers
rather than parts of a whole. He may not understand that larger denominators divide a whole
into smaller pieces. Interviewing Elias or asking him to represent fractions using drawings would
help determine whether he grasps fractional size conceptually. Examples of similar errors
include believing 1/8 is larger than ¼ because “eight is bigger than 4,” incorrectly simplifying
fractions or adding numerators and denominators separately.
Strategies to Address Elias’s Errors
One strategy to use is Fraction strips, circles, or bars. This would allow Elias to compare
fractional sizes physically. These tools would help him observe that as denominators increase,
the size of each part decreases. Another strategy is to provide visual models. This would
strengthen foundational number sense. Explicit modeling is also a strategy that would help
clarify processes such as finding common denominators or reducing fractions. Including
nonexamples such as showing why adding denominators is incorrect, prevents misconceptions
and reinforces accurate reasoning. The last strategy guided practice would give Elias targeted
support as he applies new fraction strategies. Immediate feedback corrects misconceptions
before they become habits, helping him internalize correct procedures. Situations involving
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pizza slices, measuring cups, or shaded regions help Elias see fractions as meaningful quantities
rather than abstract symbols.
Level C- Case 1: Wyatt
Identifying Wyatt’s Error Pattern
Wyatt struggles with integer operations and multi-step algebraic reasoning. His errors
reflect both conceptual misunderstandings and procedural gaps (Brown & Skow 2016). He
sometimes apples incorrect rules for adding or multiplying integers and loses steps track steps in
multi-step problems. Wyatt may misunderstand why negative numbers behave the way they do
or confuse rules such as “a negative times a negative equals a positive.” Multi-step tasks may
overwhelm him, leading to errors in sequencing. Interviews, think-alouds, or having him model
problems using integer chips can help clarify his thinking. Common related errors include
subtracting incorrectly when negative numbers are involved, reversing operations, or dropping
signs in multi-step work.
Strategies to Address Wyatt’s Errors
Strategies to address Wyatt’s errors include concrete manipulatives (integer chips),
integer chips allow Wyatt to model positive and negative values physically. He can see how
adding a negative removes a positive, supporting conceptual understanding of integer
operations. Another strategy would be explicit instruction and scaffolding. Breaking problems
into smaller manageable steps reduces cognitive load. Explicit modeling and guided examples
would help Wyatt understand each part of a multi-step problem, preventing procedural
mistakes. Providing visual models is also another strategy to use. The use of number lines help’s
Wyatt visualizes integer movement. Moving left for negative values and right for positive values
reinforces directionality and magnitude. The last strategy is repeated practice with feedback.
Frequent practice with diverse problems helps Wyatt generalize rules and build confidence.
Immediate feedback corrects recurring misconceptions.
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Conclusion
Across all four cases, error analysis provides insight into whether students mistakes stem
from factual, procedural, or conceptual misunderstandings. By collecting data, identifying
patterns, determining causes, and applying targeted strategies, teachers can tailor instruction to
each student’s unique needs. Strategies such explicit instruction, manipulatives, guided practice,
visuals, and feedback support deep understanding and long-term skill development.
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References
Brown, J., & Skow, K. (2016). Mathematics: Identifying and Addressing Student Errors CASE
STUDY UNIT IRIS@CGU Technical Assistance and Training Mathematics: Identifying and
Addressing Student Errors.
https://iris.peabody.vanderbilt.edu/wp-content/uploads/pdf_case_studies/
ics_matherr.pdf
ERROR ANALYSIS CASE STUDY 8
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