I took the time to watch the first Math video, about estimation. Even though it focuses on elementary students, the thinking behind the presentation is solid, that when teaching a strategy such as estimation in multiplication, if we want the students to comprehend the concept, it means more than just telling them how to do something, it involves multiple solutions and rich discussion of the thought process of each solution.
Think about the Standards of Mathematical Practice and how many apply in such instruction.
- Make sense of problems and persevere in solving them. Estimation begs the very questions, "Does my answer make sense?" While many a students goal is to simply provide an answer, our desire should be that students come up with a reasonable answer.
- Reason abstractly and quantitatively. We want our students to think about numbers in a variety of ways. Multiplication can be a rather abstract concept to many students, even as time goes on. Presenting multiplication as "times" (abstract) and "groups of" (quantitative) helps students make stronger connections to the processes involved.
- Construct viable arguments and critique the reasoning of others. Did you see in the video the way he presented 2 thought processes and discussed their reasoning?
- Model with mathematics. Manipulatives, drawings, diagrams, that promote the understanding. An area model is especially appropriate for multiplication.
- Use appropriate tools strategically.
- Attend to precision. Notice that this is paired with #1 in the diagram above. It's not just about getting an answer, it's about getting the best answer.
- Look for and make use of structure. Patterns!
- Look for and express regularity in repeated reasoning. More patterns. Critical thinking!
