So many variables to consider! I would weigh the benefit of the inquiry to students (math identity, engagement, problem solving skills, curiosity) vs the cost (usually just time). And sometimes students benefit from explicit teaching after inquiry or vice versa so it's not one or the other!

I also provide Khan Academy links as resources for extra practice, but that's for students to use independently, not during class. I think the skill of using digital resources independently is a good one to pick up in middle/high school.

If you don't tell the students who is correct, just that they have different answers and should talk to each other and figure out why, you end up stimulating really productive and interesting conversations between kids. This would be much harder to orchestrate without the dashboard.

As others have said, Desmos is one of the better online platforms for structuring digital investigations. I have students working in pairs and find the teacher dashboard helpful - common use case is to identify a pair with an incorrect answer and have them chat with a pair who has the right answer.

Love this! I may tweak this into a jigsaw type thing so that each member of the original group presents to a small group of peers who haven't done that topic. Trickier to assess with a rubric, but maybe more engaging??

Oooh wish I'd been that smart. Maybe next year.

I do include a few review problems on almost every homework assignment, so I've got that going for me, which is nice.

Nothing like desperately making review worksheets at 10 pm on a school night to bring out people's helpful sides!

Follow up question - ideas for fun or creative ways to review? #iteachmath

I'd love to see your materials! This is a weird Alg2 class I'll be teaching again next year for a few very advanced 8th graders. It only meets 3 times per week and has to fit IB specifications so I'm always looking for projects and other ways to hit multiple content objectives while still being fun.

Dope! Thank you!!

Both were super helpful - thank you!!

Cool format! Love the emphasis on justification, not answers.

Can you use a goal-setting structure where one of the goals come from them and one from you? Sounds like they may also need coaching to make their goals more quantifiable and actionable (or at least connected to actions under their control).

I limit critique by connecting feedback to the areas that they've identified they want to improve or grow in. Do you find that PSTs that are really confident in their practice are still able to identify areas for growth?

I would show it just to see their reactions... These are 7th and 8th graders so probably can't pump them full of caffeine, unfortunately.

Thank you for the help - you rock!

Oh, I wasn't as smart as you. I just wrote out the expression for C(n,2) and generated the first few terms of v_4 and saw they were the same. Your way is better :)

Totally makes sense now! And now I see how you get from f = e - v + 1 to the final formula n C 0 + n C 1 + n C 2. This is very cool - thank you so much!