By Derek Pipkorn, posted August 17, 2015 –

In my latest post, I discussed the need for providing opportunities for productive struggle in math classes. Students need to experience both failure and success in the mathematics classroom to become mathematically proficient. Using the Standards for Mathematical Practice, we will explore what it takes to develop these skills and habits with our students.

In May, I was asked to present an award to our top math student at the eight-grade promotion ceremony. I quickly realized that this was simply based on the student’s grades. Luckily, the student I had in mind also had the top grade in the class, so I wouldn’t have to worry about explaining my choice to someone who wasn’t chosen.

As I began my speech, I shared not only that the occasion was the 50th anniversary for this award but also a rousing rendition of the Standards for Mathematical Practice. Although I may not have received the standing ovation I was hoping for, I did expose 400+ parents, faculty, and students to these Standards.

Mathematically proficient students—

• explain to themselves the meaning of a problem and look for entry points to its solution.

• make sense of quantities and their relationships in problem situations.

• use assumptions, definitions, and previously established results to construct arguments.

• apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.

• consider all available tools when solving a mathematical problem.

• communicate precisely to others.

• look closely to discern a pattern or structure.

• notice if calculations are repeated and look for general methods and shortcuts.

Zach, the student who won this award, truly embodied a mathematically proficient student. He’s the type of student who thanked me at the end of every lesson and would exclaim to his classmates how much fun he was having using the Law of Sines on nonright triangles.

So what’s the trick? Well, I’m not sure there is a perfect algorithm for creating mathematically proficient students, but I can share one secret. Take a look through the Standards for Mathematical Practice one more time and see if you notice a pattern.

Mathematically proficient students—

• explain to themselves the meaning of a problem and look for entry points to its solution.

• make sense of quantities and their relationships in problem situations.

• use assumptions, definitions, and previously established results in constructing arguments.

• apply the mathematics they know to solve problems arising in everyday life, society, and the workplace.

• consider all available tools when solving a mathematical problem.

• communicate precisely to others.

• look closely to discern a pattern or structure.

• notice if calculations are repeated and look for general methods and shortcuts.

Did you notice how the Standards are completely student-centered? Instead of teacher-led instruction for a majority of the class period, I facilitated meaningful discussions in my classroom and allowed my students to drive the conversations. I provided tasks like the one in my last post and motivated my students to attack each task from their own angle. I allowed them to explore, discuss, and disagree with one another. They failed, succeeded, and failed some more, but in the end the vast majority of my class became mathematically proficient.

Mathematically proficient students do not strictly—

• listen while the teacher provides direct instruction for the entire class period.

• copy notes word for word from the board.

• memorize procedures for solving problems and duplicate exact replicas for homework and assessments.

• sit quietly throughout the entire lesson with minimal peer interaction.

All students can be mathematically proficient. As teachers, we must offer them the opportunity to realize this potential in our classrooms. It’s okay to step back and allow students to explore mathematics collaboratively. Eventually they’ll thank you, and you can rest assured that you’ve passed a class of mathematically proficient students.

In my final post, I will share my plans for the upcoming school year and how I plan to shock my students from day 1 with an opportunity to fail.

Derek Pipkorn, dpipkorn@mtsd.k12.wi.us, is the middle school math specialist for the Mequon-Thiensville School District in Mequon, Wisconsin. He is a member of NCTM’s Classroom Resources Committee and a Board Member on the Wisconsin Math Council. Pipkorn can be found tweeting at @mrpipkorn.