Debates over math standards, whether they are the NCTM Standards or the Common Core Math Standards, often spill into the question, “What do they mean for struggling students?” There are many issues behind this question, not the least of which is the exceedingly heterogeneous group of students frequently called “struggling.” Unpacking that issue alone is an essay in itself. For our purposes, what standards mean for struggling students can be distilled into at least two basic questions:

• Are high standards appropriate for struggling students?
• If they are not appropriate, are they even relevant?

Part 8 of 8, Strategies for Integrating the Mathematical Practices into Instruction

By Dr. Michele Douglass

Last but definitely not least in this series on Integrating the Mathematical Practices into Instruction is MP#6: Attend to Precision, which often impacts a solution more than any other practice. This practice is generally understood to be about accuracy of solutions and good estimations. While these ideas are certainly part of the practice, it includes so much more.

“Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.” —Common Core State Standards (CCSS), MP#6: Attend to Precision

Make Sense of Problems and Persevere in Solving Them

Part 7 of 8, Strategies for Integrating the Mathematical Practices into Instruction

By Dr. Michele Douglass

This mathematical practice involves the ways students can explain to themselves the meaning of a problem and the ways they find to enter into solving it. It might feel like being a detective who is looking for clues or evidence on how to solve a problem. Students proficient with this practice believe they are mathematicians and try several methods to come to a solution. 

This blog series will conclude by examining Practice #1 in this post and Practice #6 in the final post. These two practices can be thought of as overarching habits of mind that productive thinkers use as they work with mathematics.

Look for and Express Regularity in Repeated Reasoning

Part 6 of 8, Strategies for Integrating the Mathematical Practices into Instruction

By Dr. Michele Douglass

Of all the mathematical practices, I find this one hardest to implement. It is probably from my years of being taught how to just manipulate numbers versus how to use patterns to generalize.

This practice reverses the thinking of the previous practice (MP#7). For this practice, we want students to use patterns that we might give them to generalize a situation. For example, instead of teaching rules for adding integers, how could students look at patterns to generalize or come up with the rule? Think about a lesson that has students examining graphs and matching equations in order to generalize the slope-intercept equation.

Part 5 of 8, Strategies for Integrating the Mathematical Practices into Instruction

Use Appropriate Tools Strategically

Part 3 of 8, Strategies for Integrating the Mathematical Practices into Instruction

Part 2 of 8, Strategies for Integrating the Mathematical Practices into Instruction

Part 1 of 8, Strategies for Integrating the Mathematical Practices into Instruction