We are continuing with Mathematical Practice #5 in our video series on the Standards for Mathematical Practice. 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.
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 fifth video, students are learning how to determine the sum of integers. The Essential Question asks: “Are the sum of two integers positive, negative or zero and how can you tell?”
Observe how the teacher immediately makes a real life connection for the students giving meaning to the mathematics. What questions does she ask? Students are using multiple representations to display the mathematics. When they begin to work on problems in their groups, they will be able to use these strategies, thereby building their proficiency.
Mathematical Practice #5. Use appropriate tools strategically.
• Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software.
• Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations.
• Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
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 use manipulatives to assist them in making sense of a problem?
Are students aware that there may be more than one way to find a solution?
Are students given time to discover the rules of integers rather than just being told?
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.