Jamalee Stone, Rhonda Airheart, Sean Bialas, Jeremy Elsom, Jennifer Johnson, Becca Myers, Jinhua Tan

Promoting Reflective Inquiry in Mathematics

Mathematical thinkers with well-developed

“Habits of Mind” *

1. Understands which tools are appropriate when solving a problem

2. Is flexible in his or her thinking

3. Uses precise mathematical definitions

4. Understands there exist multiple paths to a solution

5. Is able to make connections between what one knows and the problem

6. Knows what information in the

problem is crucial to its being solved

7. Is able to develop strategies to solve a problem

8. Is able to explain solutions to others

9. Knows the effectiveness of algorithms within the context of the problem

10. Is persistent in his or her pursuit of a solution

11. Displays self‐efficacy while doing problems

12. Engages in meta‐cognition by monitoring and reflecting on the processes of conjecturing, reasoning, proving, and problem solving

CCSSM Standards of Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics. 5. Use appropriate tools

strategically. 6. Attend to precision. 7. Look for and make use of

structure. 8. Look for and express

regularity in repeated reasoning.

*This definition was developed by Dr. Jim Lewis (UNL) and Mark Driscoll’s book, Fostering Algebraic Thinking: A Guide for Teachers Grades 6-10.

• On the index isosceles right triangle

provided, please write down 1-2 of your

favorite “habits of mind” problems that

you may have used in your teaching.

• Please share with one of the persons

sitting in your proximity.

• As a table, share the problems that came

to mind.

Thank you Google!

• Will This Boat Float? -> Crossing the River

• Shapes of 4 Triangles -> Ninja Star Boomerang

• The DVD Bandit Dilemma -> Coconut Problem

• The Pool Tiling Problem ->The Border Problem

• A Peachy Problem -> The Mango Problem

• An Open and Shut Case -> The Locker Problem

• Donovan’s Donut Dilemma -> Golden Apples

• To work with material aligned with the age group we

will teach

• More experience teaching content to others.

• Gives us experience getting up in front of the class and

practice asking questions.

• Gives us a chance to work the problems and present

them.

• So we can learn to differentiate instruction.

• Helps us think in different ways

• To get different perspectives on how other people think

and also teach…

• GoogleDocs spreadsheet used for HOM sign-up.

– Partner and date

• Problems were posted in D2L content area for

students to review and select.

• Partners met with me at least four days in

advance to review the HOM problem, discuss

the solution(s) found, and provide an overview

of how they planned to facilitate the lesson.

• HOM lesson was videotaped (by me, not a

professional )

• Peers used an index card to indicate what went

well with the lesson, and at least one

suggestion for improvement. Comments typed

and shared.

• Students scheduled a time where they could

both watch the video in my office.

• While watching the video, partners took notes

of what they noticed while watching

themselves.

• Between peer reflections and the video

viewing, noticeable issues are addressed…

Peer Review Comments

•What kind of things would you offer students with less

experience in math to help guide them along?

•More interaction with groups would be beneficial.

•I think that you could do better on not correcting right away.

Lead us to it, not show us.

•Be more sure of the equations and what you are saying so you

don’t have to start over.

•Too long to work on the experiment and not enough time for the

proof.

•When walking around and seeing how everyone is doing, make

sure to ask everyone what they are thinking.

I was never asked a question.

• I mentioned that I wanted online

discussion to include Jordy, but what

other reasons do you think I use online

discussion with a face-to-face class?

• Why do you think I respond to your

discussion posts via email rather than

posting to the discussion board?

Jami.Stone@bhsu.edu

(402) 613-0136