High Impact Instruction
Making Math Count in WHPS
Fundamentals of Great Teaching in Math
Plan for instruction that supports students to achieve math goals.
- Ask deep questions
- Build conceptual understanding before focusing on procedural fluency
- Make connections between math ideas
- Connect math concepts to real situations
- Teach problem solving and integrate problems into daily lessons
- Use multiple representations of mathematics
- Encourage students talk and writing
Let's zoom in and focus on the first four of these strategies today.
Ask Deep Questions
On page 23 in Math in Practice: A Guide for Teachers, Susan O'Connell identifies the types of questions we should be asking:
- We ask why. We expect students to justify their answers, defend their choices, and construct arguments to prove their thinking.
- We ask how. We expect students to explain how they solve problems or arrive at answers, knowing not just what steps they took, but why each one made sense.
- We ask what. Rather than having students copy definitions of math concepts, we expect them to define and describe key math concepts in their own words.
- We ask for insights. We expect students to be able to observe data, notice patterns or repetition, make conjectures, and explain their insights.
The goal is to shift students from doing math, to thinking about and understanding math.
Build Conceptual Understanding Before Focusing on Procedural Fluency
We have many tools available to help students build conceptual understanding:
Show multiple strategies. When students develop a toolbox of strategies, they develop a deeper understanding of the mathematics. It is powerful when students see the connections between strategies and the mathematics.
Explain and defend your answers. While a right answer is necessary, it is not sufficient to show conceptual understanding. When students explain their thinking and defend the answers, then they can show their true understanding of the math.
Be flexible and nix the tricks. Susan O'Connell says, "There is nothing wrong with shortcuts, rules, and algorithms...Telling [students] how it all works robs them of the opportunity to make sense of the math they are learning." (p.14) Let students use strategies and solve problems in a way that values their understanding of the mathematics rather than follows a prescribed procedure that has little connection to their own understanding.
Arouse discovery. Develop lessons that are grounded in understanding mathematical processes. Give students opportunities to look for rules and patterns in the work through models, so they can discover the math ideas and shortcuts or rules. Then connect their understanding and rules to procedures that lead to efficiency. Susan O'Connell says," We want students to be involved in finding the shortcuts, not just using them." (p. 14) Go to www.heinemann.com and register Math in Practice: A Guide for Teachers (See page 12 of your guide for the registration code) to see video examples of guiding students to make discoveries and develop understanding in math (Chapter 1).
Make Connections Between Math Ideas
Connect Math Concepts to Real World Situations
Examining context helps students really understand the operations. Having students visualize the story or context and see the action of the story helps builds students' understanding in order to apply and connect the mathematical operations to their real experiences. Understanding operations is a cornerstone in developing mathematical understanding and context helps students lay this foundation.