error analysis 530
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Liberty University *
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530
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Mathematics
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Feb 20, 2024
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docx
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Error Analysis 1
Error Analysis Case Study Assignment
Catherine V. Long
School Of Education. Liberty University
EDLC 530- Teaching Mathematics
Dr. Holter
Author Note
Catherine V. Long
I have no known conflict of interest to disclose .
Correspondence concerning this article should be addressed to Catherine V. Long. Email:cvlong@liberty.edu
Error Analysis 2
Case Study Level A, Case 1-Dalton
Dalton is a 12 year old boy in grade 7. Mrs. Moreno, his math teacher, has concerns about his performance. Mrs. Moreno believes that Dalton has strong foundational math skills, but
he has been performing poorly on multiplying decimals since the beginning of the lesson. After conducting an error analysis on Daltons homework, it can be seen that he is making a procedural error and he is not placing decimals in appropriate place when multiplying numbers. Dalton is making this error because he did not count and the number of decimal places in each factor to determine the number of decimal places in the product. (Brown et al, 2016) Some other types of procedural errors with decimals occur when the student does not align the decimal points to show digits in like places during adding or subtracting decimals. Dalton does not seem to have a problem with place value as evident by him getting the correct number answer apart from decimals being in the wrong place. For example, on number one .78 x 9.6 Dalton was able to get 7488 number but answered 74.88 instead of 7.488 the correct number with decimal in correct place. I would determine the reason Dalton is making this error by looking for exceptions to the error pattern. Looking for exceptions to an error in the problem is when the teacher looks to see when the student does not make the same error on the same types of problems. This strategy would be useful because Dalton was able to get the correct answer on number 11 where he only had one number with a decimal place. Seeing this exception
to error could show the teacher that Dalton understands place value because he gets the decimal place correct when there is only one number with decimal in a problem. I would also interview Dalton as a strategy to get an idea his thought process and reasoning on how he decides on where
to place the decimal in the answer. By interviewing and asking Dalton how he reaches his
Error Analysis 3
answer I can discuss with Dalton how he is deciding where to place his decimal in his answer numbers.
Case Study Level A, Case 2- Madison
Madison is a third-grade student with a specific learning disability in math. Madisons class just finished a chapter on money. Madison did well during the math chapter due to being able to use manipulatives to understand the concept. In Madisons IEP it states that she easily grasps concepts when using concrete objects. Madisons teacher used concrete objects such as cardboard clocks with moveable hands for the time chapter, but Madison continues to struggle with the concept. Based on Madisons recent error analysis she seems to be having trouble with conceptual errors. Conceptual knowledge is an understanding of underlying ideas and principles and a recognition of when to apply them. Conceptual errors occur when a student holds a misconception or lacks understanding of the relationship between numbers. (Brown et al., 2016).
Madison shows that she understands the relationship between the numbers on the clock and time being asked except when she is asked “ What is a quarter past __?” It appears that Madison thinks a quarter past the given hour is fifteen minutes after the hour. Maddison is making this error because she has a misunderstanding of the ideas connected to the meaning of “a quarter past” time problems. Another example of conceptual relationship error is over specialization: Because of a lack of understanding, the student develops an overly narrow definition of a given concept or of when to apply a rule or algorithm. (Brown et al .,2016) One strategy I could use to determine the reason for Maddison time error would be by Interviewing her. Interviewing a student is when the teacher ask detailed questions to see how to they are arriving at their answer This strategy would be used to help Madison because I would be
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Error Analysis 4
able to talk with Madison to see how she is counting time and what she believes is being asked when she is asked “ What is a quarter past __?” I would ask Maddison how much time she perceives has passed when asked what is a “quarter past” and also ask her to verbally walk me through how she would find a quarter past 6 on the cardboard clock. . I would ask Madison to verbalize the minutes portion of finding time when looking for a “quarter past”. Case Study Level B, Case 2- Elias
Elias is a special education student in the 7
th
grade who has a learning disability. Elias’ teacher has been providing him with intensive intervention. Elias teacher has been collecting progress monitoring data for the past 6 weeks. His data indicated that he is not making adequate progress to meet his end-of-year goals. As a part of the diagnostic assessment to identify areas of difficulty and to determine specific instructional needs, Elias’ teacher also conducts an error analysis. When Elias teacher scores the probe she finds two possible explanations, One is that he is making a conceptual error and the other is that he is not applying the correct procedure due to lack of understanding. Elias could possibly be making a procedural error due to his incorrect performance of steps in the mathematical process. (Brown et al. 2016). It appears that Elias is able to add correctly but is making a procedural area because he is not carrying the one. For problem number 1. 18+22 ,I can see that when given the problem vertically Elias added 8 plus2 and wrote 10 and then added one plus 2 and wrote 3 giving him 310 instead of writing zero in the ones place carrying the one and adding 2+1+1 and getting the correct answer of 40. Elias got the correct answer of subtraction problems that did not require regrouping. Elias appears to have necessary prerequisite skills of addition and subtraction because he is computing the right number but he is not regrouping correctly.
Error Analysis 5
Conceptual errors occur when student does not understand place value. Elias does not seem to struggle with place value because he had correct answers and place value setting on problems that do not require regrouping. Some other examples of conceptual errors are overgeneralization and over specialization which I do not see according to Elias’ error analysis. One strategy that could be employed while addressing Elia’s error pattern would be to look for exceptions to the pattern. This strategy would be informative because it would show how much of a basic understanding he has of the concept. (Brown et al., 2016) If Elias’ teacher looked to see instances where he does not make the error she would see that Elias’ answers subtraction and
addition problems correctly showing that he understands the concept overall .
Case Study Level C, Case 1- Wyatt
Wyatts teacher has been teaching a unit on fractions. Wyatt seemed to do well with adding and subtracting fractions, but his teacher noticed that he struggled with multiplying fractions. After reviewing the information through a quick mini lesson Wyatt continued to struggle. After evaluating Wyatts most recent classroom assignment you can see that Wyatt partially understands the concept because he got all of the questions correct except the one where
the bottom denominator is the same for both fractions in which he just uses that denominator as the denominator in the answer. On question 1. ½ x ¼ you can see that the Wyatt got the correct answer on 1/8. Ethans teacher will have to interview him to see if Wyatt understands that they answer is 1/8 because 1x1 = one and not because you just take the common numerator or denominator and use it as your answer. Wyatt needs to understand that all number have to be multiplied even the if the numerators or denominators are the same for example 2/3 x 2/3 would be 4/9 instead of 2/3. I would determine that Wyatt is making a procedural fraction error. Wyatt is making this error because he is failing to change to denominator or numerator when they are
Error Analysis 6
the same and he is multiplying. Some other examples of procedural fraction error are when students fail to find common denominator when adding or subtracting fractions. The strategy I would use to identify error would be looking for exceptions to an error pattern. Looking for exceptions to error patterns requires going over the assignment and seeing what instances the student did not make the error. Looking for exceptions you would see that Wyatt only got incorrect answer when denominators where the same. I would interview Wyatt to get a verbal understanding of how of he is getting answer when numerator or denominator is that same. I would be looking to see if he is skipping the step where the numbers still have to be multiplied even if they are the same. Interviewing the student will make it clear why the errors are being because you will be able to hear the student go through the computation step by step..
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Error Analysis 7
References
Brown, J. & Skow., (2016) Mathematics: Identifying and Addressing Student Errors. IRIS Center