We are continuing with our video series on The Standards for Mathematical Practice. So far, we’ve looked at Mathematical Practice #1 and Mathematical Practice #2, and today we are sharing our video for Mathematical Practice #3.
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 third video, students are learning how to determine whether or not figures are similar to each other. The Essential Question asks: “What information do you need to know to find the dimensions of a figure that is similar to another figure?”
Observe how the teacher engages the students in demonstrating similar figures. Notice how she incorporates previous knowledge and mathematical terminology as she instructs students to form similar right triangles. Students are justifying their conjectures and providing valid arguments. When they begin to work on problems in their groups, they will be able to use these strategies, thereby building their proficiency.
Mathematical Practice #3: Construct viable arguments and critique the reasoning of others.
• Mathematically proficient (MP) students understand and use stated assumptions, definitions, and previously established results in constructing arguments.
• MP students make conjectures and build a logical progression of statements to explore the truth of their conjectures.
• MP students are able to analyze situations by breaking them into cases, and can recognize and use counterexamples.
• MP students justify their conclusions, communicate them to others, and respond to the arguments of others.
• MP students reason inductively about data, making plausible arguments that take into account the context from which the data arose.
• MP students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is.
• Students learn to determine domains to which an argument applies. They can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.
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 to construct viable arguments and critique others. Ask yourself:
Do you give students opportunities to rely on previous knowledge?
Are students given enough time to explain their thought processes?
Do they validate the conclusions of others?
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.