1. Error Analysis in Algebra Identification and classification of common errors using metacognitive learning strategies 1 Copyright © 2010 Lynda Greene Aguirre

2. Why Metacognition? What is it? How a person’s thinking affects what and how they are able to learn. Why is it important? Identifying what the thought process is and classifying the types of errors made will help the student know exactly what they did wrong and what they need to study to fix the problem Minor or careless errors can cause a student to make the same low grades as a student who has no clue what they are doing, damaging the self-confidence of both types of students and possibly creating math anxiety. 2Copyright © 2010 Lynda Greene Aguirre

3. Types of Metacognitive Errors Type I (wrong tool): Using the wrong tool or procedure. Type II (procedural errors): Using the correct procedure, but making errors within the process itself. Type III (concept errors): The student has no idea what to do so they make an obvious guess or leave the answer space blank. 3Copyright © 2010 Lynda Greene Aguirre

4. How can I use this information? Instead of focusing solely on whether you got the correct answer, analyze the work closely to determine what type of errors you are making. Classify the types of errors in order to proceed on a suitable course of study to correct specific errors. Analyze and classify your own errors and design your own study plan. 4Copyright © 2010 Lynda Greene Aguirre

5. Classification and Correction Type I Error (wrong tool) – Using the wrong tool implies that the student is either not reading the instructions or they don’t know which situations are appropriate for each tool or procedure. The Fix: – The student does not need practice working problems, they need practice looking for the “clues” within different types of problems that indicate the use of a particular tool. 5Copyright © 2010 Lynda Greene Aguirre

6. Classification and Correction Type II (procedural) – This student uses the correct tool but makes mistakes within the process. This indicates errors in: The thinking process- the student is using faulty logic Holes in their knowledge- there is a mathematical property or lower-level math skill that the student does not know how to do. Careless errors- the student rushed through the problem or copied something wrong The Fix: -- This student needs to review the individual steps within the procedure, review lower-level rules or properties they missed, and/or slow down and double-check their work. – Prescription: Give the student more practice problems to do, include extra problems of the type that they missed. 6Copyright © 2010 Lynda Greene Aguirre

7. Classification and Correction Type III (concept) – Guessing or leaving the answer blank indicates: The student may not know how to do the problem at all The student may have an idea of what to do but may lack the confidence to attempt it or may try to make up a “new” procedure. – The student needs to review the lecture and/or meet with the teacher to learn the procedure from scratch. It is important for the student to be reassured that when you are unsure, guessing is better than leaving the answer blank. 7Copyright © 2010 Lynda Greene Aguirre

8. Error Analysis Exercise Each of the following problems include errors made by a student. Using your error analysis chart, do the following 1.Write the problem in it’s original (wrong form) 2.Highlight the error 3.Identify the type (Type I, II, or III) 4.Explain (in words) what was done wrong and how it should have been done. 5.Work the problem correctly. 8Copyright © 2010 Lynda Greene Aguirre

9. Error Analysis Practice Simplify 1) 9Copyright © 2010 Lynda Greene Aguirre

10. Error Analysis Practice Simplify 2) 10Copyright © 2010 Lynda Greene Aguirre

11. Error Analysis Practice Simplify 3) 11Copyright © 2010 Lynda Greene Aguirre

12. Error Analysis Practice Simplify 4) 12Copyright © 2010 Lynda Greene Aguirre

13. Error Analysis Practice Factor Completely 5) 13Copyright © 2010 Lynda Greene Aguirre

14. Error Analysis Practice Simplify 6) 14Copyright © 2010 Lynda Greene Aguirre