2. The Power of Mistakes and Struggle

• The premise here is that every time a student makes a mistake in math, they grow a synapse. Research shows that mistakes generate stronger brain signals than correct answers and this leads to brain growth. Brain signals are also stronger in people with growth mindsets. It’s key that teachers tell students that making mistakes is useful and they show that learning is taking place. They should also avoid only giving students work that they are likely to get correct. We know that successful people: feel comfortable being wrong, try wild ideas, are open to different experiences, play with ideas without judging them, are willing to go against traditional ideas, and keep going though difficulties. In order to generate mistakes we need to give students ambiguous challenging work. It is also vital that students become comfortable sharing mistakes in class.

3. The Creativity and Beauty in Mathematics

• Math classrooms typically feature too much answer time and not enough learning time. It should be a subject full of uncertainty about explanations, conjectures, and interpretations rather than definite answers. At it’s core it’s about patterns. Students spend thousands of hours learning procedures and rules that they will never use. Real working math involves posing a question, going from the real world to a mathematical model, calculating, and checking to see if the question was answered. Unfortunately, 80% of school math is spent on calculating and this is the one thing that no one does at work! Mathematicians engage in a great deal of collaboration, which you seldom see in math class. Math tests also tend to be timed while real mathematics takes as long as necessary. Real math is a lively subject while school math seems mostly dead.

4. Creating Mathematical Mindsets: The Importance of Flexibility with Numbers

• The dry methods used in most schools rob students of joy and fascination in math. Starting too soon could be a problem. Formal math isn’t taught in Finland until kids are seven. Young students should be playing with numbers and shapes. They should also not move forward until something makes intuitive sense. The subject should be approached with flexibility and number sense. Drilling students on formal procedures is a bad idea. Here Jo focuses on concepts and how methods should be used to promote conceptual understanding. Math facts should be encountered as students explore concepts and not be drilled in isolation. Timed testing is also a great way to promote math anxiety. DON’T DO IT! This chapter ends with sample activities and apps that children can use to understand concepts and gain proficiency with math facts.

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