What Do Mathematicians Do? Expanding Visions through the SMP
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This document discusses the standards for mathematical practice and how teachers can develop these practices in students. It begins by posing questions about what math is and what it means to do math. It then outlines the session which will explore how math tasks can develop students' understanding of what mathematicians do if set up and implemented properly. It describes the standards for mathematical practice and provides an example penny jar task that fourth graders worked on, noting the teacher's moves to support the practices. It closes by reflecting on ensuring all students regularly engage in tasks promoting the practices and how teacher educators can better equip teachers to implement the standards.
What Do Mathematicians Do? Expanding Visions through the SMP
- 1. What is math? What does it mean to do math?
- 2. What Do Mathematicians Do? Expanding Students’ Visions through the Standards for Mathematical Practice Nicole Rigelman Portland State University Teachers of Teachers of Mathematics Annual Meeting Friday, September 9, 2011
- 3. Session Overview We will: Consider key questions: What is math? What does it mean to do math? and how they relate to the standards for mathematical practice. Explore how the tasks we pose and the moves we make during implementation of those tasks develop students’ visions of what mathematicians do.
- 4. TASKS as they appear in curricular/instructional materials TASKS as set up by the teacher TASKS as implemented by the students Student Learning Mathematics Tasks Framework Student Learning Henningsen& Stein, 1997; Stein & Smith, 1998; Stein, Smith, Henningsen, &Silver, 2000, 2009
- 5. Standards for Mathematical Practice The Standards for Mathematical Practice describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. - CCSS, 2010
- 6. Standards for 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.
- 8. Penny Jar Situation Start with 4 pennies in the jar. Add 5 pennies each day. Create a table and graph for the first seven days. Predict how fourth graders might reason about the total number of pennies for the 14th day without determining the number of pennies for all the days in between.
- 9. 45 40 •39 Number of Days Number of Pennies start 1 2 3 4 5 6 7 4 9 14 19 24 29 34 39 n Number of Pennies 35 • 34 30 • 29 25 • 24 20 • 19 15 • 14 10 5 •9 •4 0 0star 1 t 2 3 4 5 Number of Days 6 7
- 10. Video case: A non-proportional linear relationship 4th graders Penny Jar Situation Start with 4 pennies Add 5 pennies each round Consider the following as you take notes; What mathematical thinking do the students offer?
- 11. Video case: A non-proportional linear relationship What specific moves did this teacher make to support the development of the mathematical practices in her students?
- 12. TASKS as they appear in curricular/instructional materials TASKS as set up by the teacher TASKS as implemented by the students Student Learning Mathematics Tasks Framework Student Learning Henningsen& Stein, 1997; Stein & Smith, 1998; Stein, Smith, Henningsen, &Silver, 2000, 2009
- 13. What is math? What does it mean to do math?
- 14. Reflecting on Our Practice Do all students have the opportunity to engage in mathematical tasks that promote students’ attainment of the mathematical practices on a regular basis? How are we, as teacher educators, equipping teachers (preservice and inservice) for implementing the standards for mathematical practice?
Editor's Notes
- #14: According to Stein and Smith (1998, p. 269), “the day-in and day-out cumulative effect of classroom-based tasks leads to the development of students’ implicit ideas about the nature of mathematics – about whether mathematics is something about which they can personally make sense and about how long and how hard they should have to work to do so.” Further, as tasks pass through the phases shown in the Mathematics Tasks Framework, the nature of the tasks may change and, hence, influence what mathematics students learn.