Our video series on the Mathematical Practices is wrapping up today as we share our video for Mathematical Practice #8. If you’ve missed any of this video series, you can catch up with our previous posts:
• Mathematical Practice #1: Make sense of problems and persevere in solving them.
• Mathematical Practice #2: Reason abstractly and quantitatively.
• Mathematical Practice #3: Construct viable arguments and critique the reasoning of others.
• Mathematical Practice #4: Model with mathematics.
• Mathematical Practice #5: Use appropriate tools strategically.
• Mathematical Practice #6: Attend to precision.
• Mathematical Practice #7: Look for and make use of structure.
There are multiple parts to each practice. The parts help students develop the habit of mind that is the main practice. Remember that the practices are defined as ways to help students become mathematically proficient. As we look at each practice, think of ways we can help students to take ownership of these practices.
In the eighth video, students are learning how to describe an equation. The Essential Question asks: “How do you describe the equation y=mx+b?”
Notice how the teacher probes the students rather than supplying the students with answers. What questions does she ask? Students are making sense of the problem and planning a solution pathway. When they begin to work on problems in their groups, they will be able to use these strategies, thereby building their proficiency.
Mathematical Practice #8: Look for and express regularity in repeated reasoning.
• Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts.
• By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y – 2)/(x – 1) = 3.
• As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details.
• Mathematically proficient students continually evaluate the reasonableness of their intermediate results.
As you look at your classroom, you probably see students with varying degrees of expertise in this practice. Our job, as educators, is to help students develop a habit of mind that helps them naturally think before they begin, make sense of what they are doing and persevere in their work. Ask yourself:
Do your students notice patterns in mathematics?
Are your students able to use patterns to formulate a solution?
Do they evaluate the reasonableness of their solution?
As students take ownership of their learning and develop expertise using the mathematical practices, the content standards (knowledge, skills and understandings, procedural skills and fluency, and application and problem solving) will make sense, allowing students to achieve success in mathematics.