The goal is for students to take charge of their own learning and work on the problem for themselves, with their own strategies. Then for them to reflect, revise, and improve.
The common traps are telling students what to do or leading them step by step.
Here are some video clips showing good techniques at different moments in the problem-solving process. The "student" and "leader" roles are played by different Drexel students... use the context to help you figure out who is leading in each clip.
Once you've accessed this video: http://rmcp.dcollege.net/playlists/19216/218948.html view the timed segments noted below to observe an example of what Max has noted. Note that the time clips are also availabe as .flv files to play online or download and view locally on your computer.
- In this clip watch how the leaders get the students started problem-solving:
(in the third clip, notice how the leader clarifies the student's noticing without correcting)
- 14:15 - 14:50
- 23:55 - 24:55
- 35:20 - 37:14
- access the three clips all in one .flv file: [play] or [download] (16.6 MB)
- In this clip, watch how the leader listens to and makes use of the student's idea (and helps them formalize it when appropriate)
- 25:30 - 28:40
- access the clip in one .flv file: [play] [download] (14.5 MB)
- Your students might ask, "why are we doing this?" This clip shows one way to answer that.
- 38:00 - 40:00
- access the clip in one .flv file: [play] [download] (10.0 MB)
- Watch how the leader celebrates the students' ideas! Inviting students to estimate or say what they can about the answer before solving is also a really good habit:
- 39:49 - 40:59
- access the clip in one .flv file: [play] [download] (5.8 MB)
- Get a peek behind the scenes in this clip as Max explains how he thought about leading/mentoring his "students":
- 44:42 - 45:44
- access the clip in one .flv file: [play] [download (5.1 MB)
- In this clip Max explains and invites the Drexel students to reflect on why we're leading small-group problem solving the way we are (and goes into more detail about how we recommend leading small groups):
- 53:20 - 57:15
- access the clip in one .flv file: [play] [download] (5.1 MB)
- In this clip we explore some ways to handle the common situation in which one student has solved the problem and been asked to explain it to the others:
- 81:35 - 85:55
- access the clip in one .flv file: [play] [download] (20.3 MB)
- This clip models ending a problem-solving session with reflection:
- 106:00 - 106:50
- access the clip in one .flv file: [play] [download] (4.1 MB)
- Watch these clips to see the Drexel students recover from the trap of telling the students what to do:
- 66:27 - 68:30
- 90:13 - 96:00
- access the two clips all in one .flv file: [play] [download] (36.0 MB)
- Max and the Drexel students discuss, "When is it good to have students explaining things?"
- 72:45 - 74:40
- access the clip in one .flv file: [play] [download] (10.5 MB)
- Max and the Drexel students discuss, "When is it good for the leader to make suggestions?"
- 102:35 - 103:57
- access the clip in one .flv file: [play] [download] (6.6 MB)
- Max and the Drexel students discuss, "How do you know what the students' math level is to not make it too challenging?"
- 105:05 - 106:00
- access the clip in one .flv file: [play] [download] (4.4 MB)
- Max and the Drexel students discuss some of the ways that the roleplays don't reflect the real small-group problem-solving sessions:
- 75:20 - 75:52
- access the clip in one .flv file: [play] [download] (3.2 MB)
Notes from the board: These are the leaders' take-aways about the traps or pitfalls in leading the sessions (what's hard) and what some best practices are for really building students' independence and problem-solving ability.
- hard to listen as a leader
- hard for students to listen
people hear and remember what they think, not what you said
- hard to remember what you wanted to say/thought about the problem
What's good to do:
- listen to what the student understands
- use their language and ideas
- let the students lead with their ideas
- repeat ideas and questions back to show you're listening
- value their ideas (even crazy guesses)
- build on their ideas and use them, don't ignore or dismiss them
- have them draw
- have them write key info (not a sentence)
- use your strategies as a last resort; build off of what they have
- train students in labeling
- don't let students get lost/confused by organizing your thoughts
beforehand, do the question your way and ways that students might
- be organized enough that you can listen to and understand their ideas
- be open to yourself and with your scholars that you are learning how
to get good at this, and it's not easy
Please email us with any questions.
Max Ray and Suzanne Alejandre
Video editing developed by Drexel University, Office of Information Resources and Technology. Third-party content listed on this page retain their original copyright status.
© 1994- Drexel University. All rights reserved.
Home || The Math Library || Quick Reference || Search || Help
The Math Forum is a research and educational enterprise of the Drexel University School of Education.