As per my MO, I ran right through the bell in Friday’s lesson. I spent way too long talking about homework, but it was a necessary evil. I love new classes and meeting new students, but I really don’t like having to set procedures and guidelines in the first few days of school. I know spending time at the beginning pays dividends later, but I really wish they could just read my mind…
Here are my thoughts on homework:
- Students should never work on exactly what they worked on in class that day. They just learned how to do it 5 minutes ago, and yet we expect them to now be able to do it perfectly? Practice doesn’t make perfect, it makes permanent, and students with shaky understanding will now permanently do it wrong. Homework should be practice with concepts and procedures they are already comfortable doing.
- If students already feel comfortable doing their homework, parents won’t feel the need to step in and teach their child, reducing home anxiety surrounding homework. AND maybe we can avoid some of the tricks and shortcuts that parents and tutors often teach. Double win!
- Homework should be mixed practice. When students get 20 of the same problem, they become robots and stop thinking about what they’re doing. My go-to example of this is when we’re graphing quadratics and I throw in a linear function to graph, they graph a parabola because they’re not thinking. We’ve got to mix it up so they don’t get complacent… I need my students always questioning.
- Practice should be spaced out over time. I figure if they’ve really learned it, then it’s fair game. I throw in all kinds of stuff for them to practice.
- Students need some kind of feedback on homework. This is close to impossible to get right, I think. On the suggestion of another teacher in my district, I’ve started making complete, detailed solutions for each assignment and doing in-class corrections (5 minute time limit). She said that this was the single most effective thing she’s done to improve the quality of work turned in by students. I really hope it has the same positive effect in my class!
This year, all of my homework assignments are divided into three parts: Ready, Set, Go (thanks MVP!). Ready problems are intended to get students ready for the content in the next unit, Set problems are intended to employ the concepts in the current unit, and Go problems are all content that has been previously mastered. I try to build complexity and conceptual understanding over time. I really like where this is going so far; it’s a ton of work, but it’s totally worth it for my students and if it helps other teachers in my district.
(Can you see why I can never manage to finish a class period on time?!? I could go on about this for days…)
On with the lesson. I needed a quick way for my students to see multiple visual patterns in multiple representations without having to spend a lot of time; a simultaneous roundtable sounded like the perfect way to achieve this.
In teams of 4, each student was given the first three terms of a quadratic pattern (all different), for which they drew the fourth term and explained how they figured it out. Then they rotated their papers so that they had a different pattern, for which they created a table based on the four terms and description their teammate came up with. Then they rotated again, so now they had a different pattern and had to create a graph based on the table their teammate completed before them. Finally, they rotated one more time to find the number of squares in the 30th term of the pattern and explain how they figured it out. Each rotation was timed at 3 minutes. When they were finished, each team had four completed patterns, and each teammate had completed a different portion of each pattern.
I gave them 3 minutes as a team to look for similarities between all four patterns and connections between representations within the same pattern, then two minutes independently to write it all down. Then we shared out one observation from each table: the second differences were constant, they all had similar curves when graphed, they all had a degree of 2, …
I wanted to focus in on the second differences and writing the explicit equations. We were able to do this for two patterns before I ran out of time. 😦 That’s ok, it gave me time to make this. In a simultaneous roundtable, each student still only has one paper in the end, and thus keeps only part of the team product; this summary page will allow them to record their observations for all four patterns. It’s not perfect, but it will get to the points I want to make on Monday.
I, Kristie Donavan, do solemnly swear to finish my lesson on time on Monday! (I bought a new timer… no excuses!)