Errors Reflection
I have learned that errors can either be conceptual misunderstandings or calculation errors. Most errors depend on what the question is asking and if applicable, what the rubric states. If there is a rubric and the student fails to meet or exceed what the higher categories are asking but they are able to answer the question, they still may have some errors in their answer. Errors in calculation may be because the teacher expects students to follow a specific formula or recipe to get an answer so they do not understand the concept. This is one of the most important lessons I learned this semester. If students do not understand the concept as a whole, it is likely they will make computation errors when trying to fill out a formula and follow a recipe to get an answer. Rather, if they understand the concept they will be able to make connections from problem to problem and make the connections to the real-world examples they are given.
The first errors we learned were from NAEP. I learned that students can make simple calculation errors or not understand in full what the question is asking. For example, the question with the busses could have been up in the air because if students were previously taught to round down and the answer was 21.4, they may round down and assume another method of transportation for students. Or, they may understand that they need a bus so they can round up. It depends on the perspective the student takes. Other NAEP questions included errors that the students could not detect when answering. One of the examples in my group included a student who got a correct answer but had no other explanation other than "I punched in the numbers and got the answer." Had they explained themselves, per the rubric they would have gotten more points but because it was holistic, I realized the maximum points they could get were low- in the minimal/ off task category. I realize we worked on solving these errors and grading them ourselves with the rubric because it made us more familiar with the rubrics as well as what errors students make. It opened my eyes to seeing there are many different ways to looking at problems and interpreting them when you are unfamiliar with a concept as a whole. This taught me to make sure I teach concepts to my students instead of just the formula to get an answer.
It is important to look at errors before becoming a teacher because it is important for us to know any common errors among computations in different mathematical operations as well as more complex ones. The biggest take-away from looking and evaluating different errors is becoming familiar with and being able to identify the errors that need small adjustments and those that make reteaching the entire lesson and concept necessary, and that is where fair, equitable assessment comes into play. If we do not assess our students fairly over what the content we taught in class was, we cannot expect them to answer the questions accurately with no errors. If they do not know the concept, they will make errors. The errors we assessed this semester were important to look at because there were different ways of assessing them. Some were based on whether or not they were right or wrong, and others were based on how in-depth their answer was. Those that required a more in-depth answer included answers that could easily be identified if students understood the concept or not. Looking at errors students have when they are given a rubric is a sign of whether or not the concept needs to be taught in another way or if it should be revisited.
The first errors we learned were from NAEP. I learned that students can make simple calculation errors or not understand in full what the question is asking. For example, the question with the busses could have been up in the air because if students were previously taught to round down and the answer was 21.4, they may round down and assume another method of transportation for students. Or, they may understand that they need a bus so they can round up. It depends on the perspective the student takes. Other NAEP questions included errors that the students could not detect when answering. One of the examples in my group included a student who got a correct answer but had no other explanation other than "I punched in the numbers and got the answer." Had they explained themselves, per the rubric they would have gotten more points but because it was holistic, I realized the maximum points they could get were low- in the minimal/ off task category. I realize we worked on solving these errors and grading them ourselves with the rubric because it made us more familiar with the rubrics as well as what errors students make. It opened my eyes to seeing there are many different ways to looking at problems and interpreting them when you are unfamiliar with a concept as a whole. This taught me to make sure I teach concepts to my students instead of just the formula to get an answer.
It is important to look at errors before becoming a teacher because it is important for us to know any common errors among computations in different mathematical operations as well as more complex ones. The biggest take-away from looking and evaluating different errors is becoming familiar with and being able to identify the errors that need small adjustments and those that make reteaching the entire lesson and concept necessary, and that is where fair, equitable assessment comes into play. If we do not assess our students fairly over what the content we taught in class was, we cannot expect them to answer the questions accurately with no errors. If they do not know the concept, they will make errors. The errors we assessed this semester were important to look at because there were different ways of assessing them. Some were based on whether or not they were right or wrong, and others were based on how in-depth their answer was. Those that required a more in-depth answer included answers that could easily be identified if students understood the concept or not. Looking at errors students have when they are given a rubric is a sign of whether or not the concept needs to be taught in another way or if it should be revisited.
And it is important to know the concepts - so that students focus on the concept - as much or more than the answer.
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