Quite a bit of time ago, I posted my intentions to review families of functions using Mary Bourassa's Which One Doesn't Belong format. This is a follow-up to that post.
First, I feel overly proud of myself right now. I have all sorts of grandiose ideas I never follow through on. I did this one!
Originally, I planned for this:
First, I feel overly proud of myself right now. I have all sorts of grandiose ideas I never follow through on. I did this one!
Originally, I planned for this:
- Groups of 3 or 4
- Big honking whiteboards and classroom set of graphing TI-84s (not a one-to-one school)
- Handouts for notes with simple directions.
- Do a quick little wodb based on shapes. It doesn't really matter--just pick one. The idea here is to prime the pump for compare and contrast ideas.
- In groups, students pick 3 of the five types of families of functions we've looked at this year and create their own wodb for each family of function. Each of the four boxes needs both a graph and an equation. I need to know students can make connections between representations.
Here's what happened.
1. Groups of 4 worked really well. I had to help a couple of groups with their 'dynamics'. All groups were able to make progress without my help. I did have to give some clarification about what I wanted but I didn't have to help with the math.
1. Groups of 4 worked really well. I had to help a couple of groups with their 'dynamics'. All groups were able to make progress without my help. I did have to give some clarification about what I wanted but I didn't have to help with the math.
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2. No groups wanted to use the whiteboards. They wanted to sketch the options on the handouts or in their notes. I didn't expect that. Normally, they jump at the chance to do some white-boarding. I'll have to ask them about that. I also pulled in a chromebook cart into my classroom for the activity so students could choose to use graphing calculators or Desmos. Here the students surprised me again. Most chose calculators instead of chromebooks.
3. Handout needs some slight tweaking. See #5.
4. Rather than doing a w.o.d.b. on shapes, we did one on rational functions. I shot myself in the foot a bit here. I wanted students to compare and contrast within a family of functions not between the families of functions. The example I chose had one function that wasn't a rational function. I should have caught that. Next year.
5. Students did an impressive job making connections between representations. Next year, I plan to change the directions regarding the graphs. This year, I said "sketches of graphs" were okay. Turns out, they were in no way okay. Apparently, my concept of "sketch" is different than almost all of my students' concepts of "sketch". Next time, I plan to require an "accurate" graph and put a grid inside the 4 boxes. Hopefully, that fixes the differences in expectations. While I'm at it, I probably should require that all the graphs have the same window.
Here's a quick selection of student work. I'll talk a bit more about how the days went after the picture show.
3. Handout needs some slight tweaking. See #5.
4. Rather than doing a w.o.d.b. on shapes, we did one on rational functions. I shot myself in the foot a bit here. I wanted students to compare and contrast within a family of functions not between the families of functions. The example I chose had one function that wasn't a rational function. I should have caught that. Next year.
5. Students did an impressive job making connections between representations. Next year, I plan to change the directions regarding the graphs. This year, I said "sketches of graphs" were okay. Turns out, they were in no way okay. Apparently, my concept of "sketch" is different than almost all of my students' concepts of "sketch". Next time, I plan to require an "accurate" graph and put a grid inside the 4 boxes. Hopefully, that fixes the differences in expectations. While I'm at it, I probably should require that all the graphs have the same window.
Here's a quick selection of student work. I'll talk a bit more about how the days went after the picture show.
Day 1: I didn't know what to expect. As it turns out, this task was easier for them than I thought it was going to be. After groups rocked out a quick w.o.d.b. on lines without a whole lot of effort, I did ask them to make the distinctions more interesting. For example, when making a w.o.d.b for lines, please don't use 1) positive slope, 2) negative slope, 3) zero slope, and 4) no slope. That works, but it's a little too basic for end of the year Algebra students. Most groups finished one of the families of functions on this day.
Day 2: Most groups finished their other two families of functions. Those that didn't finish needed to finish at home.
Day 3: Peer revisions! Students worked collaboratively to create the w.o.d.b. for all three families. Mostly this worked well. However, in some groups there was a feedback loop of bad advice and/or misconceptions. The logical voice didn't always win out over the loud voice in the groups. I took a play from our English and History departments and decided to spend a day doing peer revisions. I shifted the groups, so that every member of the group was now with a different group. (Group 1 Student 1, Group 2 Student 1, Group 3 Student 1, and Group 4 Student 1 are now all in a group together.) Students gave each other great feedback. Afterwards, students went back to their original groups and shared the criticisms. Then groups had a chance to revise their work before handing it in to me the next day.
Day 2: Most groups finished their other two families of functions. Those that didn't finish needed to finish at home.
Day 3: Peer revisions! Students worked collaboratively to create the w.o.d.b. for all three families. Mostly this worked well. However, in some groups there was a feedback loop of bad advice and/or misconceptions. The logical voice didn't always win out over the loud voice in the groups. I took a play from our English and History departments and decided to spend a day doing peer revisions. I shifted the groups, so that every member of the group was now with a different group. (Group 1 Student 1, Group 2 Student 1, Group 3 Student 1, and Group 4 Student 1 are now all in a group together.) Students gave each other great feedback. Afterwards, students went back to their original groups and shared the criticisms. Then groups had a chance to revise their work before handing it in to me the next day.
| 14_project_-_families_of_functions_-_which_one_doesnt_belong.docx |
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