Error Analysis Case Study - EDUC 530

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ERROR ANALYSIS CASE STUDY ASSIGNMENT 1 Error Analysis Case Study Michelle A. Towles School of Education, Liberty University Author Note Michelle Annette Towles I have no known conflict of interest to disclose. Correspondence concerning this article should be addressed to Michelle Annette Towles Email: More1@liberty.edu

ERROR ANALYSIS CASE STUDY ASSIGNMENT 2 Error Analysis Case Study Teaching a student and making sure they are progressing well is a crucial aspect of being a teacher. If teachers are not aware of what or where their students are struggling from, then they will not be able to alter lesson plans or offer the correct differentiation for those students. This is where teachers need error analyses. An error analysis is a type of diagnostic assessment that can help a teacher determine what types of errors a student is making and why [ CITATION Jan16 \l 1033 ]. With an error analysis, you are able to see if there is a pattern to the errors in an assignment. If there is a pattern, it helps teachers decide what to do to help their students. There are steps you should follow when conducting an error analysis: collect data, identify error patterns, determine reasons for errors, and to use the data to address error patterns [ CITATION Jan16 \l 1033 ]. Case Study Level A: Case 1 – Dalton Dalton is a 12-year-old boy who is in the 7 th grade. Mrs. Moreno, Dalton’s teacher is concerned about his performance. He usually does very well in Math class, but since beginning lessons on multiplying decimals, he has struggled greatly on his classroom assignments; however, Mrs. Moreno feels he has strong foundational mathematics skills [ CITATION Jan16 \l 1033 ]. He was given a worksheet consisting of 12 problems of multiplying decimal numbers. This included one word problem, and one finding the area problem. Dalton got 11 out of 12 problems incorrect with the same error on each of them. He simply placed the decimal in the wrong place in each problem. Types of Errors The type of errors that Dalton had on his analysis were procedural errors. Procedural knowledge is an understanding of what steps or procedures are required to solve a problem. These errors occur when a student incorrectly applies a rule or algorithm [ CITATION Jan16 \l

ERROR ANALYSIS CASE STUDY ASSIGNMENT 3 1033 ]. More specifically within procedural errors are decimal errors. This type of error is identified when the student does not count and add the number of decimal places in each factor to determine the number of decimal places in the product. Dalton had difficulty placing the decimal in the appropriate place when multiplying or dividing the problems. Determining Why the Errors Were Made This error can be made for a variety of reasons. The first step to determining why the error was made is to observe the student as he is doing the problems. This will help figuring out exactly when Dalton is having the issue knowing where to put the decimal. Strategies to Improve There are some ways to help the student improve or overcome errors in their work. The first thing a teacher can do in general is to discuss the error with the student. The teacher should describe the error that has occurred to the student, and explain how they will work together to correct it. Dalton could benefit from some explicit, systematic instruction. This involves teaching a specific skill or concept in a highly structured environment using clear, direct language, and incorporating components such as modeling, guided practice, and independent practice [ CITATION Jan16 \l 1033 ]. I feel Dalton would benefit mostly from modeling, and guided practice. With modeling the teacher can think aloud and demonstrate how to complete the problem, and with guided the practice the teacher, or other peers could complete the problems with him. After working on some strategies to improve his errors, Dalton should be given another assessment to see if he has understood what has been taught and to see if he has figured out the correct way of the decimal placing in the problems. Case Study Level A: Case 2 – Madison Madison is an 8-year-old girl with a specific learning disability in Math. Her teacher Mrs. Brooks just finished a chapter on money with the class and was very pleased with Madison’s

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ERROR ANALYSIS CASE STUDY ASSIGNMENT 4 performance. She used a lot of concrete objects such as manipulatives during her lesson to assist as this was noted in Madison’s IEP. She seems to easily grasp concept when there are concrete objects. Mrs. Brooks used more concrete objects during her new lesson on telling time. She used cardboard clocks with moveable hands; however, was disappointed when she saw Madison was struggling with the concept of telling time [ CITATION Jan16 \l 1033 ]. An error analysis was conducted by giving a work sheet using the different concepts of telling time. Included was reading a clock and drawing lines on the clock after reading the time in word form, and number form. Types of Errors Madison seemed to do well with telling time except when it came to the wording “quarter past” and “quarter till”. She got every question correct on the analysis except for the ones containing those words. It seemed she did not understand the wording. The types of errors Madison seems to have ae factual and conceptual errors. Factual errors are errors related to the lack of factual information [ CITATION Jan16 \l 1033 ]. Conceptual errors are found in a misunderstanding of the underlying principles. This is seen with Madison’s misunderstanding of the meaning of “quarter till” and “quarter past”. Why Did Madison Have These Errors? In this study, observations and interviews can be used to figure out why Madison is making this error. In this particular case, she only had an error with the problems including the wording “quarter past” and “quarter till”. First, try to observe Madison to see where the misunderstanding is with the wording, then she can be interviewed to determine the exact point of time she misunderstands, so you can work together to fix it. Strategies to Help

ERROR ANALYSIS CASE STUDY ASSIGNMENT 5 Some strategies that could help Madison are data collection, error pattern identification, and providing some effective instruction to help address the error Madison is showing. The data collection will confirm for sure that Madison is struggling with the “quarter past” and “quarter till” problems. The identification of error patterns can help determine the pattern in Madison’s error. Madison has a very consistent error pattern. She confuses the quarter thinking it references 25 minutes, instead of 15. This would be a great opportunity to provide some specific instruction to Madison to address her confusion. Case Study Level B: Case 1 – Shayla Shayla is a 10-year-old girl who just began a new school. Her teacher Mr. Holden is concerned because Shayla seems to be having great difficulty during their current lesson about adding and subtracting fractions with unlike denominators. Mr. Holden has decided to do an Error Analysis to see exactly where her issue is and how to fix it. Types of Error Shayla is Experiencing Shayla is given a worksheet with eight number problems on it where she has to add or subtract the fraction with like and unlike denominators. She is also given five word problems where she has to figure out if she needs to add or subtract. The word problems is where she is struggling. The types of errors Shayla is experiencing is procedural errors (more specifically fraction errors) and conceptual errors. Conceptual errors are due to misconeptions or faulty understanding of the underlying principals and ideas connected with the mathematical problem [ CITATION Jan16 \l 1033 ]. Shayla also suffers from some factual errors. These are due to lack of factual information. In Shayla’s case, she does not understand the wording used to help her know she needs to subtract instead of add. Determining the Errors

ERROR ANALYSIS CASE STUDY ASSIGNMENT 6 In order to determine how to help Shayla, the teacher needs to determine where the errors are taking place. This is where collecting data is most beneficial. Observing Shayla work out the problems would allow her teacher to see exactly where in the problem she is getting confused. One common difficulty associated with solving word problems is poor vocabulary knowledge. Shayla seems to not understand the correct vocabulary that will tell you to subtract or add. Another common difficulty Shayna is experiencing is the inability to translate the information from the word problem into a mathematical equation. This happens when the student is not able to determine the correct operation to use [ CITATION Jan16 \l 1033 ] Strategies to Address Shayna’s Errors The best way to address Shayna’s errors is to first, discuss the error with her. After observing and figuring out exactly where she is getting confused, sit down with her, read through the problem, and help her understand the wording that will help her know if she needs to add or subtract. Another way is to have explicit, systematic instruction. This can be in the form of modeling and guided practice. This could go hand in hand with reading through the problem together. Once Shayna is more confident, give her another analysis to see if she has overcome the confusion and see if she still makes the same error. Case Study Level B: Case 2 – Elias Elias is a 7-year-old boy with a learning disability in the 2 nd grade at Bordeaux Elementary School. He has been working with the special education teacher, Mrs. Gustafson who has been providing him with intensive intervention. Mrs. Gustafson has became concerned with Elias’s progress to meet his end of the year goals. For this reason, Mrs. Gustafson has decided to do an error analysis using Elias’s progress monitoring data [ CITATION Jan16 \l 1033 ]. Types of Errors

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ERROR ANALYSIS CASE STUDY ASSIGNMENT 7 The error most visible in Elias’s case analysis is a procedural error. A procedural error is usually due to the incorrect performance of steps in a mathematical process [ CITATION Jan16 \l 1033 ]. The issue that Elias is having is regrouping. This is considered a factual error. Elias does well with the first step of adding two digits; however, if the answer is more than one digit, for example the 8+2 in the first problem, that equals 10. Elias did not seem to understand how to carry the one. He simply wrote the entire number under the equal line. This type of error is very consistent through his problems he was given. Any problem that required regrouping was incorrect. Another possible error that is visible for Elias is a conceptual error. These occur when a student holds misconceptions or lacks understanding of the underlying principles and ideas related to a given mathematical problem [ CITATION Jan16 \l 1033 ]. Elias does not seem to understand or fully comprehend the place value position of the said numbers. Determining Reasons for the Errors One way to determine the reason for these errors is to observe Elias. Watch him closely and see exactly where he begins to get confused or make the errors. It is important to monitor Elias when he is doing the regrouping part and notice where the error is coming from. This will help in recognizing the exact source of the issue. If you look and find the exemptions in the error pattern, it will make it easier to determine the reasoning for making the error. Strategies for Addressing Error Patterns There are a few ways to address student errors. One way to do this would be to discuss the error with Elias. Sit down with him, and explain to him how he made the error and work together to solve the problem until he completely understands the steps and can do it correctly. Another strategy is to provide effective instruction to address the specific error for Elias. If the

ERROR ANALYSIS CASE STUDY ASSIGNMENT 8 teacher targets the specific error instead of reteaching how to work the type of problem in general, the student will have an easier time understanding how to overcome the error. Case Study Level C: Case 1 – Wyatt Wyatt is a 12-year-old boy in the 6 th grade. Wyatt’s teacher Mr. Goldberg has been teaching a unit on fractions where all students were doing well with adding and subtracting fractions; however, when they began to multiply fractions, not all students did well. Wyatt in particular was really struggling therefore Mr. Goldberg chose to do an analysis to find out what errors Wyatt is making and how to help him overcome them. Types of Errors Wyatt made both procedural and conceptual errors. The type of procedural errors that Wyatt makes are fraction errors. Wyatt fails to change the denominator in multiplying fractions. He does not do this with all problems. The only ones he seems to struggle with are the ones he has to multiply with like denominators [ CITATION Jan16 \l 1033 ]. For example: 1 3 × 2 3 = 2 3 . Wyatt did not multiply the bottom numbers, he left them the same. He probably thought since they were already the same denominators, he did not have to change them since when you add or subtract, you leave the denominator the same. Wyatt also has conceptual errors, because he is challenged and struggles with word problems. He seemed to not understand the relationship between equivalent fractions and to place the final fraction into simplest form. Determining Why the Errors Were Made The best way to determine why Wyatt made these errors is through observation and interview. Observe him while he is completing the analysis worksheet to see where he gets

ERROR ANALYSIS CASE STUDY ASSIGNMENT 9 confused or makes the error. Then sit with him one on one and discuss what you saw, and try to talk together to find out why he gets confused or things the way he does. Once you have this information, it will be easier to work together for Wyatt to overcome these errors. Wyatt’s teacher should also look for exemptions in his error patter. Find out which problems Wyatt is not making the errors. For example: he does not make this error when he multiplies fractions with unlike denominators. Strategies to Address the Error Pattern The best strategy to use to address Wyatt’s error patterns is to first identify the exemptions in his error pattern and discuss them with him. You can also collect data, and when doing these two you will be able to see that the error pattern is occurring only when he is multiplying fractions with like denominators. If you sit down and talk with him, you can come up with some techniques together to help him. You can work together to help figure out what is best to help him overcome his confusion and issues so he can ne stronger.

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ERROR ANALYSIS CASE STUDY ASSIGNMENT 10 References Janice Brown, P. V., Kim Skow, M. V., & Center, I. (2016). Mathematics: Identifying and Addressing Student Errors. Retrieved from https://canvas.liberty.edu/courses/225013/modules/items/24389142

Error Analysis Case Study - EDUC 530

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