Almost halfway through Mathematical Mindsets by Jo Boaler. So much mathematical information to process and think about. Starting to tuck away ideas to implement next school year, which is not so far away. Let's take a look at Chapter 4, Creating Mathematical Mindsets: The Importance of Flexibility with Numbers.
Mathematics is a conceptual domain. It is not, as many people think, a list of facts and methods to be remembered. ~Jo Boaler (36)
Key Takeaway: Math facts are best learned through the use of numbers in different ways and different situations. The goal is to help students develop number sense where they can think about numbers flexibly using different combinations. Timed math tests should be replaced with conceptual mathematical activities. Activities where students play with numbers and begin to see relationships and patterns of numbers. Check out "Fluency without Fear" for some ideas to implement in the classroom and grow students understanding of math facts. The point that really resonated with me in this chapter was when Boaler explained that readers do indeed need to memorize the meaning of many words (41), but it is not the fast memorization and recall of words. Math facts is a hot topic that can be a mind shift for some teachers and some parents alike.
Classroom Connection:
- In the area of math practice, more is not always better. Synapses fire when learning takes place, not when doing the repetitive practice of isolated methods in their simplest form. When having students practice math, reduce the number of problems to practice. A whole page of practice is not necessary.
- Students need to be introduced to math beyond its simplest form that is often seen in textbooks. For example, when identifying geometric shapes, students need to see many, varied examples, not just regular polygons that are the "perfect" example of each shape. Students should see different examples and non-examples. Jo Boaler mentioned how perfect examples can lead to misconceptions. I recall a time when learning about types of angles. Rather than draw a right angle opening to the right, I drew a right angle that opened to the left. Some students did not think it was a right angle and even questioned, "Why isn't that a left angle?" From that point forward, I now draw angles that open to the right, left, up, and down.
- With the integration of technology into more and more classrooms, it is important to think about choosing apps and games that develop a conceptual approach to math. I visited the website, Youcubed, and followed the link for math apps and games. There are a handful of games to view. This is a great starting point for building a bank of more conceptually based apps and games that do not rely on computation and speed.
