This summer, I finally got around to reading Mathematical Mindsets by Jo Boaler. This book really needs to be required reading for anyone (elementary or secondary) that is teaching math. If you haven't read it yet, there are a ton of summaries on other blogs. (I have been avoiding them like the plague while reading the book for myself, but now I'm excited to read them.) Keeping that in mind, today I'm blogging about the changes that I will make in my instruction as a result of this book.

- "When we teach students that mistakes are positive, it has an incredibly liberating effect on them." (page 15) - Jo Boaler suggested highlighting your favorite mistakes that students make. The focus should be on conceptual errors. What you do is share the mistake with the class and discuss where it came from and why it's a mistake. You can also ask students to share their mistakes on the board. I love this idea! It reinforces a growth mindset, and changes the negative connotation of mistakes by valuing them as an additional learning experience.
- "I strongly believe that if school math classrooms presented the true nature of the discipline, we would not have this nationwide dislike of math and widespread math underachievement." (page 22) - Students need to discuss mathematics together. I now see it as a critical component of math instruction, and not as an additive. I really want to make discussions a daily practice.
- Teach definitions with examples and non-examples. There is so much new vocabulary in Geometry that this tip needs to used. Jo Boaler says to give multiple examples, including some that barely meet the criteria, and to include non-examples so students have a more thorough understanding of the word. The first instance where I can see using this method is teaching angles formed by parallel lines. The diagram always looks the same, and then when it doesn't, students are lost.
- "One of the very best things we can do for students is to help them develop mathematical mindsets, whereby they believe that mathematics is about thinking, sense making, big ideas, and connections - not about the memorization of methods." (page 47) - I always gave students homework that included a challenge question, but this question was rarely completed or even attempted beyond reading the problem. One suggestion (if you give homework at all) is to assign reflection questions for homework. I will definitely be incorporating this. I also plan on assigning 1 - 3 basic questions each night (depending on the type of homework assignment it could be more - for example if I was doing a matching assignment it would have to be more than 3 questions). So after answering the questions, students will have a reflection question to answer about the day's work.
- I want to incorporate the number talks that Jo Boaler described into my Do Now repertoire. I think it will be especially beneficial for my SAT Prep class because we need to develop our mental math skills and number sense for the no-calculator section of the exam.
- I'm excited to give students an applied problem to work on before we learn the method. I'm hoping that students will be intrinsically motivated to learn. I have done this once or twice before, but it was not as intentional.
*(Hey Geometry teachers, where do you find your applied problems?)* - "No one is good at all of these ways of working, but everyone is good at some of them." (page 121) - This year, I am going to have students sitting in groups. I like the suggestion for group roles on page 132. I want to incorporate these into my student groups. I would also like to read "Designing Groupwork" as Sarah has suggested, but I think that will have to wait until after the school year has begun.

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