Error Analysis Case Study

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Mathematics

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Feb 20, 2024

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1 ERROR ANALYSIS CASE STUDY Error Analysis Case Study Alyson Crosby Liberty University, EDLC 530 School of Education Author Note Alyson Crosby I have no known conflict of interest to disclose. Correspondence concerning this article should be addressed to: Alyson Crosby. Email: aacrosby@liberty.edu

2 ERROR ANALYSIS CASE STUDY Case Study Level A, Case 1 – Dalton Dalton, age 12, attends Mrs. Moreno’s math lesson in the seventh grade. According to Mrs. Moreno, Dalton has consistently demonstrated high achievement in her math class. Dalton’s academic performance declined after the introduction to multiplying decimals which caused him to struggle with his schoolwork. Mrs. Moreno plans to analyze his most recent homework assignment for common errors with the goal to better understand where he is going wrong. To conduct an error analysis for mathematics, the teacher must first collect data. They can do so by utilizing homework, assuming that the teacher is confident that the student can complete the assignment independently. (Brown, 2016). Dalton made several practical mistakes while performing multiplication with decimals, as seen in his most recent homework assignment. When trying to solve to problem, the decimal point is being misplaced during multiplication. It is also possible that this misunderstanding stems from an incorrect understanding of the concept of place value. A discussion with Dalton would help the teacher understand his thought process and the context of his mistakes. When conducting a conversation with the student, the teacher is essentially asking them to describe how they came up with the solution to the problem. The conversation might be conducted by asking the student broad questions like “How did you come up with that solution?” Teachers can assess whether or not their students have the necessary background knowledge for resolving the problem by utilizing one-on-one discussions with the student. The teacher could also use another method, which is to simply watch the learner. It is essential to observe the students because they might have difficulty expressing their concepts verbally. Teachers could tell which component of the problem is causing

3 ERROR ANALYSIS CASE STUDY difficulty by looking for indications of frustration, such as the student starting to slow down or begin to mumble to themselves. By doing so, Mrs. Moreno may be able to pinpoint the step in the process at which Dalton loses his direction and makes a decimal point error. Case Study Level A, Case 2 – Madison Madison, a second-grade student in Mis. Brooks class, is a vibrant and intelligent young lady. Madison has a specific learning disability in math. The class recently completed a lesson focused on money skills. Ms. Brooks used play money to teach the lesson and she feels that Madison did a good job demonstrating the basics of money. In her IEP, Madison’s team noted that she benefits from visual representations of abstract ideas. The next lesson Ms. Brooks taught was focused on telling time. While the rest of Madison’s class has mastered the basics of telling time, she is still exhibiting some difficulties with the concept. According to Maddison’s homework assignment, it appears she is encountering a logical mistake. Madison has difficulties understating specific math vocabulary. The vocabulary she struggles with understanding is the term “quarter” or “quarter past.” Madison could benefit from recognizing mistake patterns as a means of overcoming these difficulties. Following Madison’s inspection of her assignments, the instructor can explain the origin of the mistake and how the two of them will proceed to correct it in a collaborative effort. Ms. Brooks could also provide Madison with visual definitions of math terms to assist her with the assignments until she gains a full understanding of what the vocabulary means. For example, Ms. Brooks can give Madison laminated cards displaying a terms such as “a quarter after – 15 minutes after.” Case Study Level B, case 2 – Elias

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4 ERROR ANALYSIS CASE STUDY Mrs. Gustafson has been administering extensive interventions to second grader Elias who has a learning disability, for the past six weeks. The data indicates that Elias is not making adequate progress to meet his end-of-year goals. (Brown, 2016). Mrs. Gustafson uses an error analysis on Elias’s progress monitoring data to figure out where he is having trouble and what kind of individualized education he will require. Elias is having difficulty with a procedural error, as shown by the data from his progress monitoring. Elias has trouble with addition and specifically disregards the action of regrouping, which is when the numbers are carried over. When Elias encounters an instance requiring regrouping, he fails to shift the number into the tens’ column. This misunderstanding may be a direct outcome of Elias’s learning disability, for which he receives the appropriate interventions and extra assistance. Before introducing double-digit addition with regrouping, make sure the students have a firm grasp on the idea of place value. This is an essential groundwork that will facilitate much deeper comprehension of the concept. Breaking numbers down into their associated values can help struggling learners be more flexible with their addition strategies and helps promote computational fluency. (Rebecca, 2022). Once the student understands place value, the teacher can utilize graphic organizers. Research findings have shown that using graphic organizers helps students understand topics through visualization, reduces complexity and streamlines organization. Students can use regrouping boxes, as a type of visually assisted organizer, to break down and solve double-digit problems. Case Study Level C, Case 1 – Wyatt Mr. Goldberg is now in the final stages of a fraction lesson. He was proud of how quickly his students picked up the ability to add and subtract fractions. Unfortunately, when Mr.

5 ERROR ANALYSIS CASE STUDY Goldberg introduced the concept of multiplying fractions, a few students struggled to understand the material. However, it seems that after brief guidance, only a few students still struggled to grasp the concepts necessary to find the correct solution. Wyatt appears to be among the students having the most trouble. Mr. Goldberg concludes that he requires additional information to identify the root cause of the error Wyatt is encountering. After assessing the context of Wyatts assignment, he is committing a procedural error. Procedural errors are errors due to the incorrect performance of steps in a mathematical process. (Brown, 2016). In attempt to multiply the fractions, the student made a common mistake by no inverting the numbers first. When multiplying fractions, Wyatt transfers the same denominator, which only partially resolves the problem. Mr. Goldberg can assist Wyatt by identifying precisely when the mistake occurs. After identifying where Wyatt begins to get confused, Mr. Goldberg can model the correct way to solve the problem and work with him one-on-one so that he gets the practice he needs. It is recommended to focus on the specific areas that need improvement rather than reteach the entire lesson. When Wyatt gains a better understanding of how to multiply fractions the correct way, Mr. Goldberg can provide him with an opportunity to play online math games. Online activities and games allow students to learn concepts from a different medium than human instruction. Teachers can use online activities and games in small groups for centers or as part of group instruction. (Garrett-Hatfield, 2016). Online practice should be utilized because most students have access to this at home as well. This will also keep students engaged and enjoy learning new math concepts.

6 ERROR ANALYSIS CASE STUDY References Brown, J. (2016). Mathematics: Identifying and addressing student errors . IRIS Center. Retrieved April 23, 2023, from https://iris.peabody.vanderbilt.edu/standards/mathematics- identifying-and-addressing-student-errors/ Garrett-Hatfield, L. (2016, September 29). Innovative strategies for teaching the multiplication of fractions . Education. Retrieved April 23, 2023, from https://education.seattlepi.com/innovative-strategies-teaching-multiplication-fractions- 4496.html Rebecca. (2022, August 20). How to simplify addition with regrouping to help struggling learners . Differentiated Teaching. Retrieved April 23, 2023, from https://www.differentiatedteaching.com/addition-with-regrouping/

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