Debunking the Myth that Math Practices Don’t Matter
Featuring a White Paper by John SanGiovanni, M.Ed.
What Are Math Practices?
Mathematics isn’t just about getting the right answer. Math is about adopting a way of thinking, understanding, exploring, and problem-solving. Math is a habit of mind, and a corresponding set of behaviors, that can propel students on a track to success throughout school and career. Teachers can help instill this way of thinking and encourage students to adopt these behaviors by focusing instruction on the Standards for Mathematical Practice.
The Standards for Mathematical Practice (Council of Chief State School Officers [CCSSO], 2010) identify eight practices that reflect a deep conceptual and procedural understanding of math.
Here’s a bit of history on the practices from math education expert John SanGiovanni:
“These practices have had long-standing importance in mathematics (CCSCO, 2012), and they are not new. The predecessor of today’s practices appeared in the National Council of Teachers of Mathematics (NCTM, 2000) landmark publication, “Principles and Standards for School Mathematics.” That work organized elementary mathematics learning into content and process. The National Research Council’s (NRC, 2001) report, “Adding It Up,” described the strands of mathematical proficiency. These strands outlined behaviors of mathematically proficient students including adaptive reasoning, strategic competence, conceptual understanding, procedural fluency, and productive disposition. The NCTM process standards and strands of mathematical proficiency were used to establish the eight MPs (CCSCO, 2012).”
For more from John SanGiovanni, see his full white paper here.
Here are all eight practices:
- Make sense of problems and persevere in solving them.
- Reason abstractly and quantitatively.
- Construct viable arguments and critique the reasoning of others.
- Model with mathematics.
- Use appropriate tools strategically.
- Attend to precision.
- Look for and make sense of structure.
- Look for and make use of repeated reasoning.
You may notice that none of the practices reference specific math content, and none are limited to a grade range. The practices are designed to support students’ development from primary grades to high school, because, for example, throughout their academic careers, students make sense of problems and persevere in solving them (SMP 1). The practices are designed to be nurtured by the teacher, empowering students to explore the “what, why, and how” of math as they engage more deeply and thoughtfully with content every passing year.
Why Do Math Practices Matter?
For some, the abstract, fluid nature of the math practices makes them seem less important than math content, fueling the myth that math practices don’t matter. But this is simply a false dichotomy. In carefully designed curriculum and instruction, math practices and content are equally important, building on and supporting one another. Math practices are transferrable skills that will allow students to make use of mathematical content knowledge in any application, particularly in a rapidly evolving college and career landscape.
John SanGiovanni puts it this way:
“The need for critical-thinking, problem-solving, and communication skills, as well as abilities to use tools effectively, seek evidence, and make sense of patterns, has never been greater. Evidence of this need is reflected in other disciplines. The Next Generation Science Standards Lead States (2013) outline practices that embody similar behaviors. Language arts also calls for practices or habits of mind outlined in “student capacities” (CCSSO, 2010). Today, learning to do mathematics is more than a set of procedures that one learns and uses without deep thinking. Instead, students learn mathematics content and mathematics practices so that they are armed with skills to prepare them for their future.”
Here are a few key reasons why the math practices are so important:
They foster resilience and adaptability. Students need resilience to navigate challenging problems to grow as mathematicians (and, importantly, as humans!) The first practice, “Make sense of problems and persevere in solving them,” is a skill that will serve students far beyond the math classroom. Teachers can nurture this skill by building a classroom culture that doesn’t put “answer-getting” first, encouraging and celebrating productive struggle, and providing students with the rigorous instruction they need to succeed in solving challenging math problems.
They create space for curiosity and sensemaking. The practices emphasize the ability to make sense of mathematical ideas. Sensemaking encourages students to explain and justify their problem-solving, developing a deeper understanding of math concepts. That conceptual understanding is necessary for students to translate mathematical principles across applications and construct or interact with mathematical arguments. Teachers can nurture sensemaking abilities by giving students room to be curious, ask questions, and explore through open-ended challenges.
They bridge the gap between theoretical knowledge and real-life application. Resilience, adaptability, curiosity, critical thinking, and creativity all contribute to a student’s ability to apply math in real-world scenarios, from higher education to career to everyday life. Math content knowledge is (of course) necessary, but the practices give students the conceptual knowledge and skill capacity to apply procedures in any context. Teachers can nurture these connections by presenting real-world, authentic problems that engage students in meaningful contexts that foster a deeper understanding of how math is used in the world.
They prepare them for the jobs of tomorrow. In his white paper, John SanGiovanni writes:
“It is difficult to imagine that people once thought that elevator operators and telephone operators were irreplaceable. Changes are greatly influenced by technology, and in today’s world of ever-advancing technology, thinking may be the most important skill we can develop in our students. MPs are mathematical habits of mind. They are the behaviors of mathematicians and thinkers.”
The math practices are precisely the type of transferrable, flexible, uniquely human intellectual skills that will give students the upper hand in a rapidly changing workforce.
They unlock student potential. Finally, math practices unlock every student’s potential to be competent, confident, high-achieving thinkers and doers of mathematics. Mastering skills like abstract reasoning and mathematical modeling while demonstrating that they can persevere through problems will prove to every student — despite whatever preconceived notions they may carry about their own abilities — that they are, in fact, a math person.
Why are the Standards for Mathematical Practice important for California math teachers?
For California teachers, the math practices present clear ties to the state’s new framework for mathematics, which is student-centered, inquiry-based, and focused on “Big Idea” instruction that uses open and engaging tasks to invite students to ask questions and think critically about math. According to the California Department of Education Math Framework:
“The SMPs embed the habits of mind and habits of interaction that form the basis of math learning — for example, reasoning, persevering in problem solving, and explaining one’s thinking. To teach mathematics for understanding, it is essential to actively and intentionally cultivate students’ use of the SMPs.” (Chapter 1, p. 23)
Our TK-12 math program for California teachers, California Reveal Math, leverages the math practices to help teachers address important elements of the state’s framework.
Mathematical practices are a central component of the California Reveal Math instructional design. California Reveal Math features Standards for Mathematical Practice discussion prompts embedded at the center of daily instruction. These discussion prompts, thoughtfully positioned throughout each lesson, encourage productive conversations around approaches to problem-solving, helping students to develop mathematical thinking habits, connect Big Ideas, cultivate curiosity, and develop mathematical language. As students engage with their peers through learning activities and rich discussions, they are encouraged to ask questions, try strategies, fail, and try again. This allows them to see the continuous process of learning and understand that their thinking drives their learning.
To learn more about California Reveal Math, our TK-12 program that offers a balanced approach to Standards for Mathematical Practices by thoughtfully weaving together the why, how, and what of mathematics, click here:
For more on the math practices, from why they matter and how to nurture them in the classroom, read John SanGiovanni’s white paper, here.
Finally, learn more about our national PreK-12 math program, Reveal Math, below. The math practices are a central component of Reveal Math’s instructional design.
