Stories From My Stories From My Classroom: Classroom:

Using Powerful Problems Using Powerful Problems to to

Build Mathematical Build Mathematical ReasoningReasoning

Bushra Makiya, CIS 303, The Leadership and Community Service Academy, NY

Suzanne Alejandre, The Math Forum, Philadelphia, PA

IntroductionsIntroductions Bushra Makiya

7th and 8th grade math teacher since 2004

Math for America Master Teacher Bank Street Math Leadership Program

2014

Suzanne Alejandre middle school mathematics and

computer teacher 1973–1977, 1988–2000

Math Forum Staff 2000–present

Audience ?

The Common Core demands that students engage in much higher level problem solving than many have experienced before.

The Standards for Mathematical Practice (SMPs) are the heart of the Common Core and all our activities should move towards working thoroughly with them.

In my classroom:In my classroom: started experimenting school-wide initiative deeper problem solving process:

o read problems togethero whole-class discussiono work together: pairs or groups

of 3o individual write-up for HWo class presentations

Scholars’ Challenge AScholars’ Challenge A

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.

Student Sample 1Student Sample 1

Write-up:

Step One: What I KnowStep Two: What I Need to KnowStep Three: Process and ThinkingStep Four: Solution

adapted from what was learned in a visit to theadapted from what was learned in a visit to theUrban Assembly for Arts and LettersUrban Assembly for Arts and Letters

https://vimeo.com/29610959

Student Sample 2Student Sample 2

Scholars’ Challenge BScholars’ Challenge B

Student Sample 3Student Sample 3

Scholars’ Challenge 13Scholars’ Challenge 13

Student Student Sample 4Sample 4

Student Sample 5Student Sample 5

Lessons and Results• Our test scores as a school improved on the open-

response section of the state test.

• While students initially had a hard time, they became much more comfortable with the process over the course of the year.

• Students felt great satisfaction when they did well on problems.

• It is important that all students have an entry point to the problem. Students shut down when problems were too hard.

• This year, I am focusing on using more open-ended problems that will allow students to develop strategies for reasoning and proof.

Sources for Problems

The Math Forum: http://mathforum.org/problems_puzzles_landing.html

NAEP Tasks: http://nces.ed.gov/nationsreportcard/itmrlsx/search.aspx?subject=mathematics

The Math Forum: Other Interesting Problems http://mathforum.org/pow/other.html

Online Online ResourcesResources

Rubrics (free PDFs)Rubrics (free PDFs)PrimaryPrimaryMath FundamentalsMath FundamentalsPre-AlgebraPre-AlgebraAlgebraAlgebraGeometryGeometryTrig & CalculusTrig & CalculusDiscrete MathDiscrete Math

http://mathforum.org/pows/http://mathforum.org/pows/teacher/teacher/

http://mathforum.org/workshops/http://mathforum.org/workshops/amtnys2012/amtnys2012/

OpportunityOpportunity