As Paula and I continue to learn about our new role as math coaches for an entire district, we get the rare opportunity to talk about math. Not only solving tricky problems from time to time, but also the direction of mathematics and how we might be able to help the progress that many teachers are yearning to see in their students, their classes, and themselves. Truth be told, it's an overwhelming thing to think about and the majority of the work is not exciting. One of our recent conversations, though, was about the fact that we would start a new unit that built off something from a previous year and hear this:
"I never learned that. Nope. Nevahhhhh. Haven't seen it."
We're getting ready to use the Distance Formula, so a natural refresher is to ask students about the Pythagorean Theorem. From there, we can launch straight into Distance and get dee... wait, you've never been taught Pythagorean Theorem? A squared plus B squared equals C squared? NEVER?!
Geez, those 8th grade teachers don't do anything anymore.
After marching down the hall and preparing to confront last year's teacher for completely cutting out Pythagoras and his super-useful theorem, you realize that she did teach it, and spent two weeks on it. Damn.
Look, this happens for a lot of things in math class. Part of the blame is on the kids for not remembering; part of the blame is on the teachers for not creating an experience worth remembering; a bigger part of the blame, though, is that we don't spiral nearly enough. I mean, how can we? With all the standards to teach, things to cover, tests to administer...
It came to us that we can help by building a natural progression series. Take this handout:
Geez, those 8th grade teachers don't do anything anymore.
After marching down the hall and preparing to confront last year's teacher for completely cutting out Pythagoras and his super-useful theorem, you realize that she did teach it, and spent two weeks on it. Damn.
Look, this happens for a lot of things in math class. Part of the blame is on the kids for not remembering; part of the blame is on the teachers for not creating an experience worth remembering; a bigger part of the blame, though, is that we don't spiral nearly enough. I mean, how can we? With all the standards to teach, things to cover, tests to administer...
It came to us that we can help by building a natural progression series. Take this handout:
Here's how this would all work:
In Integrated Math I, the students would be handed this sheet of paper. As a group, or in teams, they would complete the function table. This would help them practice completing the table, apply the Order of Operations, and it would also allow them to see what will be coming up next in their academic career. Because, after they are done and the class has gone over correct answers, the teacher collects the handouts and sets them aside.
At the end of the year, the Integrated Math I teacher hands over a giant stack of student papers to the Integrated Math II teacher. When they get to their unit on graphing quadratics, the teacher hands out the document that students completed section 1 for from last year. This way, they will be reminded through student work that they completed function tables last year. Even if it isn't their own writing on the page, our hope is that it will trigger a memory. The students work as a group or in teams to complete the bottom section of the handout, then go over the correct answers before having the teacher collect all handouts and set them aside, handing them off to the Integrated Math III teacher for the following year.
On the other side of the handout is this:
In Integrated Math I, the students would be handed this sheet of paper. As a group, or in teams, they would complete the function table. This would help them practice completing the table, apply the Order of Operations, and it would also allow them to see what will be coming up next in their academic career. Because, after they are done and the class has gone over correct answers, the teacher collects the handouts and sets them aside.
At the end of the year, the Integrated Math I teacher hands over a giant stack of student papers to the Integrated Math II teacher. When they get to their unit on graphing quadratics, the teacher hands out the document that students completed section 1 for from last year. This way, they will be reminded through student work that they completed function tables last year. Even if it isn't their own writing on the page, our hope is that it will trigger a memory. The students work as a group or in teams to complete the bottom section of the handout, then go over the correct answers before having the teacher collect all handouts and set them aside, handing them off to the Integrated Math III teacher for the following year.
On the other side of the handout is this:
To start the lesson in Integrated Math III, the teacher would allow the students to review the previous two students' work on the "front" side of the document. This would again refresh their memory that they completed a function table, then graphed quadratics. Next, we want the students to use the concept of function transformations on quadratics, but the review is sitting on the front of the page.
Students would work through the examples at the top of the page as a group or in small teams, then work on the bottom piece of the second half as a way of tying it all together.
This is the first example that we have come up with, and we want to make more. Ideally, we have one for each unit and students get accustomed to creating something that they know will serve as a bridge to something else, either forward, backward, or both. Also ideally, the students would have a place in their folder or notebook to keep all of these, then use them from year to year so that the teacher doesn't need to hold on to work for extended periods of time.
If that doesn't sit well, you could also take your favorite 35 (or however many students you have) and make copies of them for the following year. Either way, the goal is for students to see that they have seen this stuff before and get them to the content quicker than we currently do.
So now, my question to you: How do you see this being used in your grade level, if at all? How can I make this better?
Happy "Progress" Fishing
Students would work through the examples at the top of the page as a group or in small teams, then work on the bottom piece of the second half as a way of tying it all together.
This is the first example that we have come up with, and we want to make more. Ideally, we have one for each unit and students get accustomed to creating something that they know will serve as a bridge to something else, either forward, backward, or both. Also ideally, the students would have a place in their folder or notebook to keep all of these, then use them from year to year so that the teacher doesn't need to hold on to work for extended periods of time.
If that doesn't sit well, you could also take your favorite 35 (or however many students you have) and make copies of them for the following year. Either way, the goal is for students to see that they have seen this stuff before and get them to the content quicker than we currently do.
So now, my question to you: How do you see this being used in your grade level, if at all? How can I make this better?
Happy "Progress" Fishing
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