Reflection on Teach Correct Errors
Learning based on my work on student work
I learned that no matter how you teach a lesson, there may be misconceptions. If you teach it using manipulative tools, it will give students an opportunity to see how each number, fraction, or mixed number is represented. Additionally, making real-world connections is crucial. This is one factor I missed in mine because I did not connect it to any story problems or make it applicable to situations in the real world. I could have included it in the problem given to the students when they did the partner activities. I think that not including this portion took away from how realistic the concept can be in daily life.
One thing I did try to incorporate is allowing students to critique one another. I saw if they agreed or disagreed with one another and why. I had one student explain why they agreed with the other and had them explain the process used. I asked a lot of questions throughout the lesson to see what they understood and I allowed them to do majority of the computing without much more explanation than modeling one problem on the board.
I learned that sometimes students will need more guidance and other times they have more knowledge on a topic than expected. Just because one student has a misconception does not mean that all of them do, but sometimes when there is one there are multiple. Another thing I could have done to add to the lesson and the students' understanding is ask them what they think the student did wrong in the example problem instead of explaining it myself. In previous articles, we discussed how showing an answer completely incorrect and working up to one that is correct can show different examples of what to do and what not to do in a given problem, and this could have also enhanced my lesson.
During the making of my lesson, I think I made it too scripted. You suggested to not have a scripted lesson and for lessons in some classes it may be necessary, but in math it is subjective because students may not catch on to the trend of a concept as quickly as planned or they may understand it sooner than anticipated. Additionally, I think I planned well for engaging students with the manipulatives and recognizing repeated reasoning because I planned for students to have multiple chances to use the manipulative tools and explain their thinking/ show an example as to why one rule carries over to other fractions.
Reflection based on the tasks and questions from others in my group
In my group, Rachel had subtracting and Kayla had multiplying fractions. Rachel had great questions to engage the students and she also showed the problem she was correcting in another way, which was changing the 6 to 5 and 4/4 to subtract from 1 1/4. This was another good way to show that subtracting a mixed number from a whole number can be simpler on paper. The manipulatives she chose to use can allow students to put the ones being taken away on top of the ones being subtracted from then count how many are left. I also learned from her to allow students to correct the problem themselves if it is incorrect. I knew the importance of this from previous articles and class discussions, but seeing it in action in a lesson made me realize how important it is for students to express any knowledge on the subject they already have.
Kayla used an incredible real-life situation when she showed us a picture of a Kit Kat bar. It was split into 4 pieces and she colored 1 of the pieces on the bar. Then she split it into 1/2 down the middle and colored one of the sides in, representing the one half. Then, she asked us how many were shaded by both and that was the answer (1/8). This was not something I learned in grade school and a representation like that was never shown to me to show what the answer is when multiplying fractions, and it is definitely a strategy I will use in my classroom. Then, she did another problem with us and finally let us do one on our own and I understood it better when she explained it than any time I tried to follow a recipe in grade school when I learned how to multiply fractions.
My learning based on the videos presented
Throughout the class, we all had different approaches to teaching the lesson, but included using manipulatives and correcting a specific error students made in their work. One video that stood out to me had the teacher have the students explain the error and critique the work. I liked this because the students could explain their understanding this way instead of being told what was wrong in the process of answering the question. Simple questions such as "do we agree with a student and why" are acceptable when teaching a new concept or when we want to know what students understand. Others asked many "how" questions to gauge if the student understood how to get to a certain point in answering a question.
There are a lot of different manipulative tools different people used and I found some more useful than others in the videos. It was common among the people who had multiplying and dividing to use the bars and cubes to express the place values and amounts. They explained to students different ways to group the numbers and allowed the students to figure out how to break each block down to get down to the next value (hundreds to tens, tens to ones) and continue grouping. I would use these in my classroom because it can show students that the 3 in 345 represents 300, the 4 represents 40, and the 5 is 5 ones; something I was not taught but I think is important for students to know as they learn to add, subtract, multiply, and divide.
I learned that no matter how you teach a lesson, there may be misconceptions. If you teach it using manipulative tools, it will give students an opportunity to see how each number, fraction, or mixed number is represented. Additionally, making real-world connections is crucial. This is one factor I missed in mine because I did not connect it to any story problems or make it applicable to situations in the real world. I could have included it in the problem given to the students when they did the partner activities. I think that not including this portion took away from how realistic the concept can be in daily life.
One thing I did try to incorporate is allowing students to critique one another. I saw if they agreed or disagreed with one another and why. I had one student explain why they agreed with the other and had them explain the process used. I asked a lot of questions throughout the lesson to see what they understood and I allowed them to do majority of the computing without much more explanation than modeling one problem on the board.
I learned that sometimes students will need more guidance and other times they have more knowledge on a topic than expected. Just because one student has a misconception does not mean that all of them do, but sometimes when there is one there are multiple. Another thing I could have done to add to the lesson and the students' understanding is ask them what they think the student did wrong in the example problem instead of explaining it myself. In previous articles, we discussed how showing an answer completely incorrect and working up to one that is correct can show different examples of what to do and what not to do in a given problem, and this could have also enhanced my lesson.
During the making of my lesson, I think I made it too scripted. You suggested to not have a scripted lesson and for lessons in some classes it may be necessary, but in math it is subjective because students may not catch on to the trend of a concept as quickly as planned or they may understand it sooner than anticipated. Additionally, I think I planned well for engaging students with the manipulatives and recognizing repeated reasoning because I planned for students to have multiple chances to use the manipulative tools and explain their thinking/ show an example as to why one rule carries over to other fractions.
Reflection based on the tasks and questions from others in my group
In my group, Rachel had subtracting and Kayla had multiplying fractions. Rachel had great questions to engage the students and she also showed the problem she was correcting in another way, which was changing the 6 to 5 and 4/4 to subtract from 1 1/4. This was another good way to show that subtracting a mixed number from a whole number can be simpler on paper. The manipulatives she chose to use can allow students to put the ones being taken away on top of the ones being subtracted from then count how many are left. I also learned from her to allow students to correct the problem themselves if it is incorrect. I knew the importance of this from previous articles and class discussions, but seeing it in action in a lesson made me realize how important it is for students to express any knowledge on the subject they already have.
Kayla used an incredible real-life situation when she showed us a picture of a Kit Kat bar. It was split into 4 pieces and she colored 1 of the pieces on the bar. Then she split it into 1/2 down the middle and colored one of the sides in, representing the one half. Then, she asked us how many were shaded by both and that was the answer (1/8). This was not something I learned in grade school and a representation like that was never shown to me to show what the answer is when multiplying fractions, and it is definitely a strategy I will use in my classroom. Then, she did another problem with us and finally let us do one on our own and I understood it better when she explained it than any time I tried to follow a recipe in grade school when I learned how to multiply fractions.
My learning based on the videos presented
Throughout the class, we all had different approaches to teaching the lesson, but included using manipulatives and correcting a specific error students made in their work. One video that stood out to me had the teacher have the students explain the error and critique the work. I liked this because the students could explain their understanding this way instead of being told what was wrong in the process of answering the question. Simple questions such as "do we agree with a student and why" are acceptable when teaching a new concept or when we want to know what students understand. Others asked many "how" questions to gauge if the student understood how to get to a certain point in answering a question.
There are a lot of different manipulative tools different people used and I found some more useful than others in the videos. It was common among the people who had multiplying and dividing to use the bars and cubes to express the place values and amounts. They explained to students different ways to group the numbers and allowed the students to figure out how to break each block down to get down to the next value (hundreds to tens, tens to ones) and continue grouping. I would use these in my classroom because it can show students that the 3 in 345 represents 300, the 4 represents 40, and the 5 is 5 ones; something I was not taught but I think is important for students to know as they learn to add, subtract, multiply, and divide.
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