Exploring the Richness of Math
By Mr. Glenn Stevenson, Supervisor of STEM
When people find out that I supervise our math department, their reactions and comments orient around two poles… “I loved math, I was really fast,” or “Oh, I hated math, I’m just not a math person.” Related to these responses is a general belief that math is a gift that you are either born with, or you will just not get. My fear is that the WAY we teach math creates this duality among peoples’ view of their math capability. Inspired by the work of Carol Dweck and Jo Boaler, the teachers and administrators of the Verona Public Schools have begun to explore the teaching of mathematics in new ways.
Carol Dweck is a professor of Psychology at Stanford University who is best known for her work on mindset. In 2006 Dweck published the book Mindset: The New Psychology of Success . This work lays out how success is heavily influenced by our beliefs about our talents and abilities. The basic dichotomy of mindset is there are those with a fixed mindset, the belief that abilities are fixed and unchangeable, and there are those with a growth mindset, the belief that abilities are malleable and can be developed. Dweck has found in numerous studies that those with a growth mindset outperform those with a fixed mindset. A key feature of a growth mindset is learning from mistakes and treating mistakes as opportunities to grow.
In 2014 the New York Times Magazine ran an article called Why Do Americans Stink at Math?
The article spells out the typical, traditional pattern at play in many, many math classes across the country.
“Most American math classes follow the same pattern, a ritualistic series of steps so ingrained that one researcher termed it a cultural script.” This pattern is frequently identified as “I, We, You,” and is also labeled as the gradual release of control.
The usual math class will follow a script like this:
1) Check and review homework.
2) Present a new procedure (the I).
3) Lead the class in 2-3 sample problems (We).
4) And then assign a series of problems on a worksheet or from the textbook (You).
This pattern emphasizes standard algorithms, places students in the role of calculator, and removes the student from the sense making process. Worst is that it can also produce the fixed mindsets that Dweck describes. The responses, “I loved math, I was really fast,” or “Oh, I hated math, I’m just not a math person,” are the end result of the repetitious script.
How do you flip the script and end with students who love math because it makes sense? Jo Boaler, a professor of Mathematics Education, also at Stanford, has taken Dweck’s ideas and applied them specifically to mathematics learning. In her book Mathematical Mindsets Boaler makes the case for emphasizing growth mindsets related to mathematics learning and Boaler’s answer for flipping the script is the rich math task. Rich math tasks have multiple methods, pathways, and representations. They place the students in the role of a sensemaker and take them out of the role of calculator. Rich tasks “make the difference between happy, inspired students and disengaged, unmotivated students.” Combined with rich math tasks is the approach that one teacher, Magdalene Lampert, labels as “You, Y’all, We.” This sequence deemphasizes “answer finding” and places the emphasis squarely on the sense-making process. Students engage in mathematical discourse and arrive at mathematical understanding by learning from their own mistakes and from the perspectives of other students.
Verona Public Schools teachers and administrators have been exploring these ideas in various ways. We have established book clubs, one amongst the administration and another with our teachers, where we are reading and discussing Boaler’s book. Discussions have been interesting and engaging. Teachers have begun to try Boaler’s ideas and report back favorably each meeting with victories both large and small. Chris Cunningham reported favorably on having his students write and solve their own homework problems. Cindy Graves spoke proudly of her students developing more ideas for understanding the multiples of five when presented the task as a You and Y’all than when confronted and tackled as a We in years past.
In October we began working with Bill Jackson of Math Demystified . Bill has a long pedigree as a math teacher and coach. He taught 8th grade math for many years and then went on to be a math coach in Scarsdale, NY, eventually leading as a Director of Math in New York City. He is an author and math education consultant. Bill has been helping Verona with a technique called lesson study. Lesson study is a Japanese technique for community sourced professional development. Teachers form lesson study groups of 3-7 people and then begin a systematic process of dissecting the pertinent learning standards, curriculum materials, and resources. Once a topic and materials are chosen, teachers work collaboratively to plan a lesson which will be taught by one member and observed by the other group participants. The observers focus on the sense-making work completed by students. All members of the group reflect on the lesson and provide feedback for improving the lesson, often times with the lesson being taught a second time, to a different group of students, using the reflections and suggestions provided to grow and improve as teachers.
We established two lesson study groups for the 2017-18 school year. One group is comprised of kindergarten, first, and second grade teachers. The second group is composed of third, fourth, and fifth grade teachers. The focus in our lesson study sessions have been the rich math tasks that are recommended by Boaler. The classrooms have been a buzz with student energy and conversations as they explore mathematics. Our teachers have learned a great deal from our students and from one another. Our goal moving forward is to support our staff in finding and implementing rich math tasks in their instruction and to expand our lesson study efforts to include more teachers.
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