ERROR ANALYSIS 1
Error Analysis Case Study
School of Education, Liberty University
Author Note
I have no known conflict of interest to disclose.
Correspondence concerning this article should be addressed to
Error Analysis Case Study
Case Study Level A, Case 1- Dalton
Dalton can fluently multiply whole numbers. He is a grade level reader, demonstrating
knowledge of a dozen meaning the number 12 and the area of a rectangle without the aid of
the formula. Dalton understands how to set up the multiplication problem, as seen by fluently
changing the multiplication problem from horizontal to vertical and correctly setting up
ERROR ANALYSIS 2
equations from text (word problem) and picture. He correctly answered a word problem dealing
with money, when there was only one decimal number and a whole number.
Dalton makes conceptual errors when multiplying decimals. Conceptional errors are
errors made due to not fully understanding the principles or ideas in a math problem (Brown &
Skown, 2016). Dalton struggles with decimal placement in multiplication. It appears that he
does not know how to count the places after the decimal and add the places for final decimal
placement in the product (Brown & Skown, 2016). That is when given the multiplication
problem .78 x 9.6, Dalton answered 74.88, as if he just brought the decimal point straight down,
rather that adding the decimal places and correctly answering 7.488. Dalton is using what he
knows about the addition of decimals and applying that to knowledge to multiplication with
decimals.
A strategy that will work with Dalton, as he has solid multiplication skills and will not
need the whole lesson retaught, is for Mrs. Moreno to discuss with Dalton the decimal
placement in multiplication and how it is different than addition. For a concrete model, Mrs.
Moreno can make a small anchor chart or note sheet that is color coded that displays the steps
to multiply decimal numbers. For example, one column has the problem (5.45 x 6.2); the other
column would say step 1. Count and add the decimal places (3 places) 2. Mark below the equals
sign the decimal places (_. _ _ _) 3. Solve the problem like normal. Once Mrs. Moreno has
discussed Dalton’s multiplication error and addressing specific examples, pinpointing Dalton’s
error and correcting it. Once the error has been pinpointed, Dalton will need to correct the
remaining problems so that Mrs. Moreno can confirm that error has been corrected and that
Dalton is no longer making the same errors with decimal multiplication.
Case Study Level A, Case 2- Madison
Madson appears to have a grasp on the minute and hour hands of an analog clock, as
well as the concept of half past. Madison demonstrated knowledge of when given a clock and
time, she can identify the hour (3:00), she can tell time to the twenty-five (9:25) and to the
ERROR ANALYSIS 3
fifteen (7:15). She struggles with when given the time as in quarter past, drawing hands to show
the correct time. For example, when asked to draw a quarter past one, Madison drew the time
as 1:25. Demonstrating she reads adequately for the problem and has the background
knowledge to know that quarter means 25, as in with money. Madison demonstrated her lack of
understanding of the term quarter when referencing time in not properly labeling quarter ‘till
four, she drew 4:35, identifying a time before 4 and after the half.
The errors that Madison is making are factual errors. That is, she is making errors due to
lack of understanding of the vocabulary (Brown & Skown, 2016). To correct this error, Ms.
Brooks will need to discuss and review the vocabulary for telling time, that the term quarter
when discussing time means fifteen (15) as in quarter after 3 means 3:15 or 3:45 is a quarter ‘till
4, pinpointing the error on Madison’s assessment. Since Madison understands concepts when
given concrete manipulatives, Ms. Brooks should label the sides of the minutes of the clock.
Madison’s clock should be labeled at the 1 :05- five after, at the 2 :10 – ten after, at the 3 :15 -
quarter after, at the 4 :20- twenty past, at the 5 :25 past – twenty-five past, etc. all the way
around the clock. This way Madison has a clear concrete manipulative to help bridge the gap
between the vocabulary terms. Ms. Brooks will then need to have Madison practice a few time
problems, either by retaking the assessment or by correcting her assessment is enough practice
to confirm that Madison did not understand the vocabulary of quarter has having two different
meanings and not a different skill.
Case Study Level B, Case 2- Elias
Elias is making are procedural and conceptual in his double digit by double digit addition.
A procedural error means that Elias struggles with the procedure of how to complete the steps
to solve the problem, while a conceptual error means that he does not fully understand the
ideas of the math problem (Brown & Skown, 2016). That is, he does not seem to understand the
procedure of carrying in addition and the concept of place value.
ERROR ANALYSIS 4
Elias has a strong grasp of adding single digit numbers, such as 2+8 equaling 10 and 3+9
equaling 13. Elias is also very good with subtraction with zero, as in 20-15 equaling 5. However,
he struggles with carrying in addition. When given the problem, 18+22 Elias answered 310.
Meaning that he added the ones place 8+2 and wrote 10 and then added the tens place 1+2
and wrote 3, rather than carrying the 1 (from the tens place of 10) to make 1+1+2. The errors
that
While counting rods will help to solidify Elias’s understanding of place values and
carrying in addition, Mrs. Gustafson can do a brief review of addition and carrying. This strategy
of review will be enough to help Elias, as he has a solid understanding of single digit addition. In
a brief review, Mrs. Gustafson can use the math problem 18+22 from Elias’s assessment and
discuss with Elias when and why to carry the tens place. Targeting this skill will build his
understanding of the addition of double digits. To practice and confirm that he understands
carrying in addition and place value, Elias should be allowed to correct the four problems he
answered incorrectly. After the corrections have been made, Mrs. Gustafson will be able to
analyze the other 15 questions for additional skills that Elias may not fully understand.
Case Study Level C, Case 1- Wyatt
Wyatt has a solid grasp of multiplication with a model and had adequate reading skills to
create an equal and model from a given world problem. Wyatt does appear to understand that
when multiplying fractions he needs to multiply across, an example of this 1/2 x 1/4 he correctly
answered 1/8 demonstrating that he understands how to multiply numerators and
denominators. However, in the problem 1/3 x 2/3, Wyatt incorrectly answered 2/3,
demonstrating that he does not appear to know his doubles facts or that he is overspecialized
errors. The errors that Wyatt is making are called procedural errors, in that he does not know
how to multiply the denominators of the same value which may be due in part to lack of
doubles fact knowledge. To help determine what skill Wyatt is missing, doubles fact knowledge
or not knowing to multiply denominators of the same value, Mr. Goldberg should do a quick
ERROR ANALYSIS 5
pinpoint review addressing problems 5 x 5 and 3/5 x 4/5; since Wyatt correctly answered 12 for
the numerator and incorrectly answered 5 for the denominator. After reviewing those two
problems Mr. Goldberg will be able to identify where Wyatt is struggling and review fractional
multiplication, addressing if Wyatt is also making conceptual errors, specifically in
overspecialization.
If Wyatt is making overspecialization, that implies that he has difficulties transferring
knowledge of doubles multiplication to fraction multiplication. Then Mr. Goldberg can review
with Wyatt that multiplication of the denominators is the same process as if the denominators
were different. A fraction multiplication chart may help Wyatt for a quick reference, especially if
he struggles with doubles facts, however, Wyatt has solid multiplication skills so the chart will
not be needed for very long. Wyatt should correct his test because he only missed three
problems. That will be enough practice to demonstrate mastery of skill.
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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
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