I have been teaching exponents to freshman and sophomores for the last week and a half. I had a carefully planned graphic organizer. I planned on spending 1 or 2 days per exponent property and moving on with the year without too much difficulty...
Little did I know what I was up against. Apparently, exponents are not as simple as I had always thought they were. I don't think I really cared in high school why the properties worked. I was great at memorizing things that I needed to know, and so I never had a problem or a need to know, "Why." I was a grade-chaser all the way.
Well after teaching every exponent property in the unit and giving a 5-question lesson quiz, I learned that perhaps some of my students had learned nothing over the last week and a half... That's not really true. They had partially learned the properties in isolation, but putting everything together was just too overwhelming. I agree, the students need more practice, but if I had sent them home that night with more homework problems like their lesson quiz, even if they had actually tried every single problem, they probably would have gotten more of them wrong than right.
I brainstormed and felt frustrated and wondered, and I ended up coming up with a 4-page packet that took the kids back to the very beginning. I made them expand EVERYTHING. (They were thrilled...) I made them write things in their own words to help them remember the different rules and when to use them. I made them take the time to re-see the, "Why," and then had them practice multiple additional problems to just get more comfortable with using the property.
I was worried about this activity because there was absolutely nothing fun or entertaining about it. In most of the classes, I was able to return the lesson quizzes and show the students that they did indeed evidence that they needed additional learning and practice in some areas. Most of my students have been amazing about actually working their way through the packet. Some students finished all 4 pages a day. I have other students that are working diligently, but still have about 1/3 of the packet still to go.
Learning doesn't happen at the same pace for everyone, and for most people, it happens slowly!
Students are having an easier time with the problems this time around. They are some of the same problems I showed them last week, but now they are getting an additional exposure and learning experience with that type of problem, and it is helping their brain make better connections. It's helping them fix misconceptions they had the first time around. Even the students that got 9/10 and 10/10 on their packet have told me they don't think the packet is a waste of time.
One student was actually able to articulate to me today (after getting 5/10 and 6/10 on his previous lesson quizzes on the topic) that when you have a whole number, you multiply it by itself, but when you have an exponent, you just do regular multiplication. His use of vocabulary isn't perfect, but he's able to talk about the problems, and generalize how to solve them which is a HUGE step for him!
Another student has gotten a high A on every single test and quiz he's ever taken for my class, and he's done maybe 2 homework assignments all year. He got a 9/10 on the most recent lesson quiz over exponents. I made sure to ask him if he thought the packet was useful or a waste of time, and he told me he thought it was useful because he was able to figure out what he missed that one point on the lesson quiz on, and he was able to fix it and practice it. (I thought for sure he would tell me it was a waste of time because he already knew how to do it!)
My whole point is that learning is so different for everyone. For many students, it does just take time. I suspect that some kids act lazy and don't try homework because they already know they're not going to know how to do it, but our traditional schedules and lesson plans don't allow time for that student to get what they need to learn it. I know there is a time restraint and we can't just infinitely slow down and there is going to be some outside of class work required for some students, but I feel like a bully when I expect the same achievement out of all students at the same time.
Little did I know what I was up against. Apparently, exponents are not as simple as I had always thought they were. I don't think I really cared in high school why the properties worked. I was great at memorizing things that I needed to know, and so I never had a problem or a need to know, "Why." I was a grade-chaser all the way.
Well after teaching every exponent property in the unit and giving a 5-question lesson quiz, I learned that perhaps some of my students had learned nothing over the last week and a half... That's not really true. They had partially learned the properties in isolation, but putting everything together was just too overwhelming. I agree, the students need more practice, but if I had sent them home that night with more homework problems like their lesson quiz, even if they had actually tried every single problem, they probably would have gotten more of them wrong than right.
I brainstormed and felt frustrated and wondered, and I ended up coming up with a 4-page packet that took the kids back to the very beginning. I made them expand EVERYTHING. (They were thrilled...) I made them write things in their own words to help them remember the different rules and when to use them. I made them take the time to re-see the, "Why," and then had them practice multiple additional problems to just get more comfortable with using the property.
I was worried about this activity because there was absolutely nothing fun or entertaining about it. In most of the classes, I was able to return the lesson quizzes and show the students that they did indeed evidence that they needed additional learning and practice in some areas. Most of my students have been amazing about actually working their way through the packet. Some students finished all 4 pages a day. I have other students that are working diligently, but still have about 1/3 of the packet still to go.
Learning doesn't happen at the same pace for everyone, and for most people, it happens slowly!
Students are having an easier time with the problems this time around. They are some of the same problems I showed them last week, but now they are getting an additional exposure and learning experience with that type of problem, and it is helping their brain make better connections. It's helping them fix misconceptions they had the first time around. Even the students that got 9/10 and 10/10 on their packet have told me they don't think the packet is a waste of time.
One student was actually able to articulate to me today (after getting 5/10 and 6/10 on his previous lesson quizzes on the topic) that when you have a whole number, you multiply it by itself, but when you have an exponent, you just do regular multiplication. His use of vocabulary isn't perfect, but he's able to talk about the problems, and generalize how to solve them which is a HUGE step for him!
Another student has gotten a high A on every single test and quiz he's ever taken for my class, and he's done maybe 2 homework assignments all year. He got a 9/10 on the most recent lesson quiz over exponents. I made sure to ask him if he thought the packet was useful or a waste of time, and he told me he thought it was useful because he was able to figure out what he missed that one point on the lesson quiz on, and he was able to fix it and practice it. (I thought for sure he would tell me it was a waste of time because he already knew how to do it!)
My whole point is that learning is so different for everyone. For many students, it does just take time. I suspect that some kids act lazy and don't try homework because they already know they're not going to know how to do it, but our traditional schedules and lesson plans don't allow time for that student to get what they need to learn it. I know there is a time restraint and we can't just infinitely slow down and there is going to be some outside of class work required for some students, but I feel like a bully when I expect the same achievement out of all students at the same time.
Wow, absolutely fantastic blog.
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