Chapter 9 is basically a recap of what was discussed throughout the book. In this chapter, Boaler discussed ways for parents to make a difference in mathematics teaching and learning. This chapter also listed other books about teaching math for parents and elementary teachers to read.

This chapter and book and general were helpful to me and made me realize there are several different ways a teacher can teach math. It also taught me that the traditional way of teaching math is not necessarily the way to go if I want my students to be successful. Hopefully, this book will help me become a better elementary teacher and maybe I can use some of these methods discussed in the book in the future.
Chapter 8 is called, "Giving Children the Best Mathematical Start". The title of this chapter pretty much describes what the chapter is all about. This chapter explains how it is important to start children off on the right foot with mathematics. There are several different examples of word problems and puzzles for children in this chapter.

I think it is very important to introduce mathematics to children in an enjoyable way with puzzles and different word problems. If a child starts off liking math then maybe they will enjoy it through out their life times. 
In chapter 7, Boaler talked about the time she taught summer school in California. The students in her summer class had struggled in their math classes during the school year. When Boaler taught them over the summer she used different strategies that would help the students individually. She had the students journal, and discuss math with one another in groups. The students were successful in her summer class. Once they went back to their math classes during the regular school year they went back to a traditional math classroom and were again, unsuccessful.

I think that it is crazy that students do so much better in mathematics when they are taught it in a different way. I surprises me that math classes are still taught traditionally and some students are still unsuccessful, when teachers could be engaging the students more and teaching them math differently. I would think teachers would all teach non-traditionally since it is proven that it has a higher success rate. 
Chapter 6 is about girls and women being discouraged to study mathematics and science. This chapter explains how girls and women want to know how things work while boys and men just do the work and do not ask questions about what they are doing. The chapter also suggested that women do not go into math or science because of societal stereotypes. This chapter's purpose was to help encourage girls to enjoy math and science and to encourage them to make a career out of them.

Honestly, I did not completely agree with chapter. Being a girl, I was never afraid to ask questions in my math classes and was never intimidated by the males in my math classes. I just did not find math interesting at all. I feel like I never would have enjoyed math no matter how many different ways it was presented to me. English and Social Studies were always my favorite subjects. I know several women that are math or science majors, including my own mother who is a high school AP Biology teacher. This chapter felt to me like it was stereotyping all women. I agree that we should encourage all students to go into math or science and enjoy these subjects, but if a student really is not interested in the subject, then they are just not interested. 
Chapter 5 discusses whether or not students should be grouped together based on prior attainment, which is sorting students into different groups based on their ability level. In the United States we group students later on in their years into different level classes, while in Japan every type of student is placed together because they believe it allows students, "to help each other, to learn from each other, to get along and grow together-mentally, physically and intellectually" (108). I personally agree with Japan's way of thinking. 

I believe that placing the same type of students together is unnecessary. Placing all different kinds of students together makes a classroom more diverse and this can help the different types of students learn from each other. I believe that lower achieving students can learn from higher achieving students. Clearly, mixed-ability classrooms are working out very well for Japanese students. 
Chapter 4 is entitled, "Taming the Monster". The monster being, assessments. This chapter discussed what is wrong with the American testing system. America uses multiple choice exams, which does not really assess understanding. Also, standardized assessments give questions involving unfamiliar scenarios and does not focus on the mathematics part of the question. Giving students an unfamiliar situation confuses students and makes it hard for them to visualize the situation.  

Assessments should be able to show a students understanding and assess them on what they have learned. I personally remember struggling with multiple choice exams when I was younger, and would do a lot better if an exam was a short answer assessment. I think it is important to make assessments with questions that are familiar to the students, yet challenging. This way, students will be able to show what they have learned about the subject area. 
Chapter 3 discussed three different types of mathematical teaching approaches in three different schools. The first school Boaler visited was Railside High School which used a communicative approach in teaching. Students would need to explain their work to other students. Students were also placed in different groups to discuss mathematical problems. The students of this school described math as being language instead of being a "set of rules". This way of teaching appeared to be very effective. 

I have experienced both a traditional way of being taught math and I have experienced the "communicative approach" Personally, I did not enjoy either of these methods. Though, the communicative approach seems to work at Railside. In high school, we were sat in different groups and we would be forced to work together. The problem was, it was high school, and a lot of people (at least at my high school) did not get along. I found myself a lot of the time not being able to discuss math because someone in my group thought they were "too cool" to talk to me. Another issue was the students that did not care about their education whatsoever. Those students would not do any work and I found myself doing their work for them, since they would just copy me. Using groups like this in high school is difficult because of these situations. For this method to work, I believe that it really depends on the class and their motivation to be successful in school. 

The other two approaches Boaler explored were the "Project-Based Approach" and the "Typical Traditional Approach". With a project-based approach there is a lot less organization, but this approach seemed to be very effective. This approach allows students to explore and choose what they want about mathematics. It allows students to be creative with math and makes it enjoyable. With the traditional approach the classroom was more controlled, but was a lot less creative and was very traditional. The Project Based students ended up doing better on examinations than the traditional mathematics students. This shows that creativity in the classroom, especially a math classroom, helps students be more successful.  
Chapter 2 is entitled, "What's Going Wrong in Classrooms?". This chapter introduced the phenomenon of "math wars" which is described as, "a series of unproductive and heated exchanges between advocates of different mathematics approaches" (Boaler 31). The war in a California classroom was between the "traditional curriculum" and a "reformed curriculum". Groups of people are trying to save the traditional math curriculum which consists of students sitting in isolation, doing math problems from their books. In a reform curriculum students would discuss math and teachers would try to make math more meaningful to the students. 

I believe that discussion in a mathematics classroom is essential. Going through traditional math classes when I was younger was very unhelpful for me. I remember sitting at my desk, in silence, and not doing anything because I had no idea how to do the problems. Getting all of the students engaged and discussing math I feel would definitely benefit all of the students. I believe that more students would understand the math better and it would be more meaningful to them. Educators need to realize math is not just memorization and just repeating problems and skills. There is so much more to math. I believe that getting students more engaged in math classrooms is essential for success of all students. 
In chapter one of, What's Math got to Do with It?, Jo Boaler discussed what math really is. I thought this chapter was interesting because I have never thought of math as being more than just sitting and doing math problems. Boaler showed in chapter one that math is not just sitting isolated doing math problems, but math has so much more to it. She discussed that math really applies to a lot in life. Boaler mentioned the best selling novel, The Da Vinci Code, by Dan Brown. This novel involves a lot of math and introduces readers to the "divine proportion". I thought it was interesting that Boaler brought up this book, because I personally liked this book, but always have hated math. If I learned math by applying it to things such as The Da Vinci Code, then I feel like math would have been way more interesting to me. 

Another thing Boaler shows in chapter one is that math also applies to nature. She has a picture of a flower and maps the spirals in the flower. After reading this chapter I realized math applies to a lot of interesting things in the world. Math applies to science, music, history, and almost every other subject in school. An interesting quote I found in chapter one was, "Mathematics is a performance, a living act, a way of interpreting the world" (Boaler 29). As a teacher this made me think that it is necessary to teach mathematics this way instead of forcing my students to sit and do endless amounts of math problems, I should apply math to the world and other subjects. I feel that students would really enjoy math more if teachers treated math just like any other subject such as English or Science and let them explore and discover different theories. Math definitely needs to be more creative in schools.