Error Analysis Reflection

Error Analysis Reflection:

 

            The error analysis reminded me a lot of the NAEP analysis of student work. In both activities, we had to look at student samples, find what (if any) errors the student made, and how we could provide further support/meaningful feedback (i.e. through verbalization, learning tasks, guided questions) that focus on helping them better understand the area where they were having trouble. With both of these activities (error analysis and NAEP analysis), I learned that if students continue making the same errors without anyone correcting them, they are being set up for failure in the future. This may sound tough, but it is true because if students keep progressing in math while making those same errors, they are going to continually have a misunderstanding of the concept, have difficulty understanding future concepts that build off of the prior concept, and likely get the answer wrong. Therefore, it is vital that teachers step in and guide the students in the proper direction so they understand their error and how to correct it.

In the error analysis (“finding errors”) activity, Sarah, Kaitlin, and I each analyzed the student errors prior to class. It was interesting to jump into a student’s mind and think the way they were thinking. For example, I noticed one student subtracted the smaller digit from the larger digit no matter which digit was on top (and didn’t borrow). Or, for instance, I noticed a student did not get the common denominator when adding fractions. Some students made errors in solving the problems, some students just had an incorrect answer, or in many cases, some students made an error in solving the problem, which resulted in an incorrect answer. I went through each sample student’s problem, discovered where they were making an error, and how they were thinking about the concept (i.e. adding left to right instead of right to left). Then, using the student’s errors, I tried solving similar problems in the same way that the student would. It was tricky to think like a student would and use that student’s error when solving similar problems! Since I will constantly be analyzing, interpreting, and understanding my student’s mathematical work, I hope that as I get more practice with analyzing errors, the easier it will be for me to detect student’s errors. Also, in a real-world classroom, I could always talk one-on-one with a student and have them explain their thought process to me. After analyzing all these errors, it showed me that each student might think about a concept differently from each other as well as differently from the teacher. It’s important to consider various ideas/methods/strategies because what works for one student may not work for another (one strategy may make sense to one student but not to someone else). I think encouraging various strategies in the classroom is great (as long as the student is not making repeated errors with their strategy). Also, this error analysis caused me to realize that when I am teaching math to my students, I need to be aware of the methods I use. In other words, I might teach a strategy that makes sense to me but that doesn’t work or make sense for a student. Therefore, offering different ways to solve a problem may be beneficial so all students can find the best strategy that works for them and so they can be more successful in math.

Looking at students’ errors provides teachers valuable information about what area/concept a student is misunderstanding and aids in helping teachers know what information they need to review/reteach. Sometimes students’ work shows a clear pattern of their errors. For example, if a teacher analyzed a student’s addition work they may recognize a pattern in that the student consistently added from left to right instead of right to left. This information would help the teacher know they need to work on the concept of place values when adding. Furthermore, I learned that some student errors are easy to detect whereas others are less obvious (sometimes at first glance, a student may appear to understand the concept but when the teacher looks more closely at the student’s work, he or she realizes that the student made several errors and/or doesn’t have a true understanding of the material). Also, I learned that there could be a wide range of student error. In other words, some students may make a simple error that could be easily corrected (i.e. added two numbers wrong) whereas some students’ errors are more significant and indicate that they don’t understand the concept (i.e. adding left to right or carrying a number over the ones place rather than the tens place). Additionally, I learned that some students might make one error whereas other students may make multiple errors. It is understandable that students make errors, especially when first exploring a concept, but it is key that the teacher works with the students to understand why their error was wrong and how to correctly solve a problem. In other words, the teacher needs to provide meaningful feedback to the students. The teacher should think about what the students know and are able to do and what they struggle with and use that knowledge to plan the next steps in instruction. The teacher can use guiding questions to help the student understand why their way was wrong and have the student explain what the correct way is and how they know that. Also, the teacher could provide learning tasks that focus on the area where the student was making mistakes. Through guided questions and learning tasks, the student will hopefully better understand the concept and be less likely to perform those errors in the future. After analyzing these errors, I learned that it is crucial as a teacher to take the time to evaluate students’ work because it helps you gauge the students’ level of understanding.

            In class, for the reteach error assignment, Sarah, Kaitlin, and I decided to focus on finding errors problem #1 (Gary). We decided we wanted to stick with math content related to our grade band (K-2). Gary was working on adding with single digit numbers. We discussed that Gary’s error was that he was double counting a number when counting on, which was resulting in him finding an incorrect answer (his answers were always one less than the number they should have been). Therefore, we decided it was appropriate to address this error by having Gary focus on mastering counting on (specifically focusing on counting on when adding numbers one to ten). We separated the learning task for Gary into different areas (guided instruction, independent instruction, further independent practice (critique), and extended instruction). We decided to use base ten units to help Gary practice counting on. Using the base ten units, the teacher would model counting on for Gary explaining the process/verbalizing what he or she is doing (guided instruction). Then, Gary would model what the teacher did in a similar problem using base ten units (guided practice). Next, Gary would pick two cards (single digit cards only) and use the base-ten units to show the addition of the two cards he picked demonstrating counting on (independent instruction). After that, Gary will critique an imaginary peer’s work (further independent practice). Gary will be presented a problem that a student did incorrectly and then a problem that a student did correctly. In the incorrect problem, he will have to show the correct way of doing it (using base ten units blocks), demonstrate counting on, indicate the correct answer, discuss what the student may have done wrong, and discuss why his answer is correct. In the correct problem, Gary will verify the student’s correct answer (using base ten blocks and counting on) and discuss how he knew (prove) that answer was correct. Lastly, the teacher and Gary will practice counting on without the base ten units (extended instruction).

            I think we created a great learning task to help Gary practice counting on. Gary clearly had trouble adding because he was counting a number twice. Therefore, we knew we had to develop a rich and meaningful activity with various modes of instruction to help Gary learn from his error and correct it. We made sure to have guiding questions, think about how we will engage the student, and consider tools we could use (i.e. base ten units). I could actually picture using this learning task to help Gary improve his counting on abilities. I think it is effective, practical, and meaningful and would allow Gary to gain a deep understanding for counting on. After analyzing Gary, I learned the significance of making sure teachers provide further instruction so students do not repeat their errors. I also learned that students need to learn WHY. They need to learn what their errors were, WHY their errors were wrong, the correct way to fix their error, and WHY it is the correct way. For example, critiquing a student’s work is meaningful for Gary because he can understand his own error, why it was wrong, what the correct way is, and understand why that way is correct. Although easier and less time-consuming, if students are simply told the correct answer they are not going to have a good grasp/understanding on the math concept and will probably continue making those same errors. Teachers must have conversations, guided questions, and/or plan learning tasks to help students understand their errors and learn the correct strategies for solving the problem!