Implementing the Standards for Mathematical Practice
Math Content Standards Series #3: Student-Driven Discovery
One of the most important elements of classroom instruction is ensuring students develop expertise in mathematics in a variety of ways. The Standards for Mathematical Practice (SMP) can help establish a student-driven learning environment in the classroom. Practical mathematics — the skills students can carry with them into higher education and the workforce — are not just about finding the right answer. They’re about establishing foundational, conceptual understandings of numerical, spatial, and logical problem solving. By modeling the SMP, educators are actually training their students to be independent thinkers, problem solvers, and discoverers. Here are three key advantages your math students will gain when they successfully learn to apply the SMP:
1. Students will deepen their conceptual understanding of mathematics.
Verbal communication of math problems through mathematical discourse is an excellent way to help students delve into conceptual understanding. Mathematical discourse is a multi-faceted, constructive discussion wherein students solve math problems by verbally expressing their thinking through mathematical language. To engage in these discussions, students draw on previous knowledge, use analytical reasoning, and listen with an open (but critical) ear to the reasoning of others. Engaging in mathematical discourse helps place students in a cross-disciplinary intersection of learning: they will practice verbal, communicative, and investigative skills while developing critical mathematical competencies. Better yet, by “talking through” the math problem — step-by-step, taking the time to ask “why” and “how” — students will begin to establish a thorough understanding of the problem before they even begin to solve it.
2. Students learn how to think independently and work collaboratively.
Some students may look to the teacher for the answer when it doesn’t come to them immediately. Instead, imagine a classroom in which students take two steps when a math problem is difficult: they run through their own knowledge bank, or collaborate with peers to talk through potential strategies. This approach helps students learn to be resourceful, pulling from both an internal and a communal toolbox. Through collaborative problem solving, students will glean new mathematical insights from their classmates, while practicing group work skills that will translate to college or career, such as listening to the opinions of others, clearly communicating their own ideas, and arriving at consensus.
3. Students learn that it’s OK to be wrong the first time around.
When students fully grasp the Standards for Mathematical Practice, they learn to accept that sometimes, it’s OK to be wrong! Throughout the critical thinking process, students will find themselves trying out different approaches, adjusting reasoning in the face of new information or insights, and trying again until all the components of the scenario begin to fall into place. Whether working independently or as a group, odds are, they will be wrong — at least once — in their first few attempts to apply what they know to a mathematical situation. The key for student success is to develop a classroom environment where revising an approach is OK, and perseverance in logical thinking is valued over the answer itself. By putting emphasis on the process, independent reasoning, and conceptual understanding, students will leave your math classroom with the tools to excel in higher education and the workplace.Our new eBook, “Successful Strategies to Meet the Mathematical Content Standards”, highlights the key advantages of making students responsible for mathematical modeling, and provides examples of helpful modeling tools.
eBook Sneak Peek // The End Result of Implementing the SMP:
“Students are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts, and formulas.”
Click below to download the eBook, “Successful Math Strategies to Meet the Mathematical Content Standards”:
Meeting the rigor of the mathematical content standards. More questions than answers? Find strategies to help.