Stories From My Classroom: Using Powerful Problems to Build Mathematical Reasoning Bushra Makiya, CIS 303, The Leadership and Community Service Academy, NY Suzanne Alejandre, The Math Forum, Philadelphia, PA

Introductions  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:  started experimenting  school-wide initiative  deeper problem solving  process: o read problems together o whole-class discussion o work together: pairs or groups of 3 o individual write-up for HW o class presentations

Scholars’ 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 1

Write-up:  Step One: What I Know  Step Two: What I Need to Know  Step Three: Process and Thinking  Step Four: Solution adapted from what was learned in a visit to the Urban Assembly for Arts and Letters

Student Sample 2

Scholars’ Challenge B

Student Sample 3

Scholars’ Challenge 13

Student Sample 4

Student 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: NAEP Tasks: The Math Forum: Other Interesting Problems

Online Resources

Rubrics (free PDFs)  Primary  Math Fundamentals  Pre-Algebra  Algebra  Geometry  Trig & Calculus  Discrete Math

Opportunity