End of Linear Relations - Mixed Results

I've now finished the first unit (Linear Relations) while trying to create a culture of thinking. It's time to reflect.

Changing how Students Work

I've been successful having students work in random groups, standing, on vertical surfaces. They now fully accept working in random groups at whiteboards. And my whiteboard alternatives are working very well. After 3 weeks of daily use, there is virtually no ghosting. I'd say they're as good or better than "regular" whiteboards.

Starting the Semester with Non-Curricular Thinking Questions

I did this for 6 days, and the students enjoyed those problems much more than the curriculum-related problems :-).

No More Answering Stop-Thinking Questions

I've gotten very good at not answering stop-thinking questions, and instead either directing them to other students/groups, or just asking probing questions to get them to think carefully about their work. Students now expect to justify their solutions, and rarely ask stop-thinking questions.

Use Upside-Down Lessons

Starting class with group work using questions from the end of textbook lessons worked well, although progress was slow and often took much of the class. However as I noted in an earlier post, the success of groups masked the inabilities of the individual students. In the future I will reduce the amount of group work so there will be more time for individuals to practice the concepts/skills encountered in the group work questions.

Leverage the Collaborative Environment


I wrote about stopping leveling or leveling to the bottom. I found this difficult to do because of the wide range of abilities and math knowledge. Sometimes I tried to wait until all groups were at a level I was comfortable with (so I could level to the bottom), however that left the stronger groups with little to do towards the end of that process.

Stop Giving Traditional Notes

I was pretty religious about this. After each group problem, I would discuss the important points from different group's work. Then I would encourage them to make there own exemplar, including page numbers in the workbook that provide a good discussion of the material at hand.

Use It or Lose It

I had mentioned that Peter said you'll lose the culture of thinking if you teach traditionally too much (if anything I didn't teach that way enough), or if you give problems directly from the textbook. Interestingly, there seemed to be no decrease in thinking when I assigned questions from the book.


This is the negative part of my analysis. They had their unit exam today and the results were much lower than I was expecting. Although I know I can improve a lot, student apathy definitely played a role.

Here's how I plan to improve for the next unit:

  • Reserve group work for challenging problems that will hopefully generate an "aha" moment or highlight a significantly new concept or skill. That will leave more room for direct teaching and individual practice time. For the first unit I used group work for virtually everything, at the expense of direct teaching and individual practice time. I think there's definitely room for direct teaching when students have such weak math backgrounds, and the individual practice time is important since groups are usually more capable than individuals.
  • Put more thought into the questions I give for group work so I can level to the bottom without having the faster groups sitting around with little to do.
  • Put more emphasis on figuring out what a word problem is actually saying and on basic algebra skills, as those were the main difficulties students had on the exam.
  • Encourage students to share their summaries/exemplars to hopefully provide better notes for them.

I'll start the next unit, Limits to Measurement, on Monday.

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