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Standards for Mathematical Practice
Central to the Common Core are the Standards for Mathematical Practice. These practices reflect the most advanced and innovative thinking on how all students should interact with math content to master essential skills and their underlying concepts.
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Facilitate a classroom conversation around a grade appropriate yet challenging problem. Dialogue like this engages students and allows them to explore new ideas and strategies while creating a community of shared experience.
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Let Students Explore!
If they have adequate background to figure out how to make progress on a problem, then let them sort through how to tackle it. It's not about a right answer here—it's about letting students think about how they could solve a problem with what they know. This useful skill will help round out their problem-solving toolbox, connecting it to more advanced math and real-world applications for years to come.
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Provide students with a grade appropriate, open ended opportunity to consider how a problem can be deconstructed. For example, “The answer is 45. What equation(s) results in this answer?”
There are many answers—(5+10+20+10), (15x3), (60-15), etc. By leaving the question open ended, students are forced to think about the actual number 45, and consider how that quantity breaks apart and comes back together.
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Construct & Deconstruct!
The goal is to help students to understand the relationship between part and whole. In this case, by encouraging students to truly grasp the meaning of quantities and how to represent them in multiple ways we are helping them to understand the relationship between the quantities and the solutions and even between the quantities themselves.
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The role of the teacher as facilitator and questioner is crucial to develop this proficiency. Students may understand the difference between correct and incorrect logic, but they may lack the verbal skills to put their words in context. Requiring students to "narrate" problem solutions—without teacher influence—will help them develop the skills to formulate sound reasoning, and to determine the flaws or validity in the mathematical arguments of others.
It is important to create an environment that will help students feel safe enough to open up an honest mathematical discourse, discuss thinking processes aloud, and develop the capacity to effectively critique the logic of others. It comes down to Math Talk and creating opportunities to talk through concepts, processes, and strategies.
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 Educators need to walk a fine line when introducing this practice into the classroom; we cannot lead students toward one tool over another based on our own experiences. Let students experiment with different tools to determine what works and what does not. If they are able to solve a problem with a protractor instead of a compass, assuming the same level of time and effort, then who's to say only one way is "correct?"
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Because this may be an unfamiliar approach to students, they may require some coaching to become comfortable and proficient with looking for and making use of structure. Try these strategies out in the classroom:
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The teacher’s role in implementing this standard is less instructor and more facilitator. You can lead a horse to water, but you can’t make him have "aha moments" in the classroom. Below are some tips for moving students closer to identifying more efficient solutions:
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Bring Math Solutions to Your School or District!
Math Solutions looks forward to partnering with you to help you improve math instruction and student outcomes. Our consulting, courses, and coaching are offered on-site at your school or in your district based on a schedule convenient to you and your team.
Contact us today to speak with one of our Education Consultants:
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