8 Mathematical Practices: Not a Mile Wide, But a Mile Deep

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Web_Samulski_8 Mathematical Practices 3-5_blog1We ran across a disturbing article. It described a study a few years ago that followed thousands of undergraduates for four years. It found that large numbers of these students did not know how to think critically or reason—two higher-order thinking skills that we, as teachers, are very aware of now that the Common Core has focused our attention on building them.

No one in K–12 education can ignore these findings. Virtually every one of us would agree that critical thinking is of the utmost importance. And not just because the Common Core says so. Our students need to see both sides of an issue, be able to reason, back up their claims with evidence, deduce and infer conclusions from facts. And the power of these skills is never as obvious as in the math classroom.

Students who think critically, reason, and solve math problems independently are excited. They are verbal. They are engaged.  They listen, collaborate, explore. They enjoy math and they are successful at it. They are empowered.

We all want that for our students. And for ourselves. But, as every teacher knows, critical thinking is one of the most difficult skills to teach and  acquire, especially in the early grades.  If we want to succeed at teaching critical thinking, we must be willing to go the extra mile. We must create a new classroom environment where higher-level thinking and reasoning occur naturally.

Thankfully, we have the 8 Mathematical Practices. They will become your most valuable tool in this vital endeavor.  Too often we see teachers focus all their energy on the content standards and forget about the Mathematical Practices. Consequently, students gain only a surface-level understanding of the math taught. But the Mathematical Practices are just as important as the content standards—only they outline how students are to go about doing the math.

Transforming your classroom doesn’t just entail work. It entails the right kind of work. The Mathematical Practices will help you address the problem of a curriculum that is a mile wide and an inch deep. They will help your students go deeper.

Don’t make the mistake of looking at the Mathematical Practices as just one more thing to add to your plate. When implemented correctly, they will not create more work for you. They’re not supposed to. What they will do is help you bring critical thinking into your everyday classroom. That way, you’ll know you’ve done all you could to make sure your students think, reason, and succeed in your classroom, future grades, college, and life.
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For more insight on the 8 Mathematical Practices and how to implement them at your grade level, check out SDE’s webinar 8 Mathematical Practices: Addressing the Higher Standards (Grades 3–5) by author and intervention expert Shannon Samulski.


No one ever said teaching students to think critically is easy. We’d love to hear about your struggles and successes as you take on this big responsibility.

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