The book begins in the classroom of math teacher Emily Moskam. The writer observes the class, and watches the way that Moskam teaches in ways that are far from traditional, but get the students actually excited and participating in math. The students work together to solve the problems, questioning one another, and in the end coming up with a solution they agree upon. This is very different from the classrooms where teachers stand in the front of class lecturing the students and teaching them rules. Here the students are actively involved in their learning, and in helping their fellow classmates understand the concepts. The author then goes on to express that the problem with teaching mathematics today is that from early on students are taught to hate math. In 2005, an AOL news poll showed that "four out of ten adults said that they hated math in school" (p. 5). The problem is in the way that math is portrayed in the media, compared to the way it is being taught to students. Students are often taught math out of context, and begin to believe that math has nothing to do with their lives outside of school. With so many students hating math, it is unfortunate because they grow up into adults that hate math, and math is a necessary skill required for everyday life. On page 10 it says "the math of the world is so different from the math taught in most classrooms that young people often leave school ill prepared for the demands of their work and lives". Through this book, Jo Boaler hopes to inspire people who "have been wounded by math experiences and have hated math ever since" to take a new look at math, and to think about the ways that math can be taught differently in classrooms so that students will not learn to despise it so intently (p. 14). 

Boaler begins this chapter by discussing the distorted view of math held by young students today. She asks students what math is, and gets responses such as "lots of rules" and "numbers" (p. 15). This is different from what professors in the math field have to say about it. However, in other subjects such as English, the descriptions of the subject told by students are much more similar to the descriptions told by professors. This shows that students have a much more distorted view of what math is from early on than other subjects. Boaler then goes on to discuss what math really is. She references another author, Reuben Hersh, who wrote a book titled, What is Mathematics, Really?. In Hersh's book, he talks about the different patterns in math and how all math is basically focused around patterns. Boaler then goes on to clarify what mathematics is really, and begins to highlight the different areas of math and how it can be exciting. Schools go wrong in math when they revolve their teachings around numbers and rules, instead of empowering students to find the patterns in math and begin to use them to explore the subject. 

This chapter begins by addressing the idea of math wars---"unproductive and heated exchanges between advocates of different mathematics approaches" (p. 31). Boaler highlights that often the outcome of these math wars is that it discourages good teachers and eventually drives them out of the teaching profession. The subject of the math wars is what is being taught in the classrooms, the curricula. However, the problem is that the focus is too much on what book to teach from, when in reality "a good teacher can make mathematics exciting even with a dreary textbook...and bad teachers do not become good just because a book is written well" (p. 32). The problem in many American schools is that students are constantly being bombarded with rigid rules out of context that make no sense to them, and it makes students frustrated which in turn leads them to hate math. Talking about math concepts in a way that students are allowed to share their ideas, bouncing back and forth, is essential to teaching math in a way that will be effective for students. Students should not be forced to work alone on problems, as this is setting them up for failure. There has to be collaboration that requires students to actually think and share their ideas. Instead of students being taught rules as straight up, no question laws, they should be allowed to question and wonder. Boaler also goes on to talk about how the context of math is important, and students should be taught math in a way that they see how problems relate to their actual lives. This helps them to get a better grasp on what is really going on in math, and they are able to practice and relate it to their everyday lives. Students should be given the opportunity to "realize they are learning an important subject that helps them make sense of the world, rather than a subject that is all about mystification and nonsense" (p. 55). 

Boaler discusses in this chapter different approaches that can lead students to become more excited about math. Parents play a critical role in supporting the child in each approach. One of the approaches is called "The Communicative Approach". This form of teaching is supported by words and how one can describe math in different various ways. One school that used this approach was the Railside School, and it was highly effective for their students. They used the approach in various ways, ranging from drawing to graphing and calculating. Another approach that was talked about in this chapter was "The Project Based Approach". This form of teaching used in Phoenix Park school had "a lot less order and control than in traditional methods...instead of teaching procedures the teachers gave students projects that needed mathematics methods" (p. 69). This approach is similar to the approach used by Emily Moskam talked about in the introduction of this book. With this approach, students are given freedom to explore their learning possibilities and branch out from the prompting they are given. While this approach has less control over what is learned, students are able to actually be excited about math and learn more about things that spark their interest. Compared to the traditional method, these alternative methods ranked higher. However, over all the Project Based Approach got the highest score on exams. I wonder, how would it be possible to get students more involved in their student's learning, especially if the idea is to not give homework?

Testing differences often pose a problem to American students more than they do to students in other countries. This is because of the way that testing is set up here in America. Often times, the wrong type of assessment is being used and teachers maybe aren't considering what they are actually trying to assess when they make up tests. Multiple choice tests are often used, although they are proved to be unreliable and inaccurate. Instead of being tested on their own knowledge, students are being given broad standardized tests that rank them in comparison to other students. When ranked based on their their test scores, students often have their confidence and self esteem damaged because the tests are used in the wrong way. This discourages students from wanting to continue in math, and it is much easier for students to write off math altogether. From this chapter I learned that America over tests compared to other countries.

In this chapter, Boaler discusses how students divided based on skill level can impact them, as well as the impact that testing and scoring in math classes has on students and their self esteem. She discusses how often students are grouped based on skill level, and that ability grouping negatively affects learning. Some problems with teaching groups with a wide range of students would be that some may think the material is too difficult, while others too easy. This would cause some students to be left behind, and some would be stuck in a spot where they were ready to learn more but not given the opportunity. Grouping students based on skill puts unnecessary pressure on students of all age levels. Some of the questions that would arise from being against grouping, and putting them all together, are:

• With a mixed classroom, how could you keep higher achieving students from doing all the work?    
• Why should we give struggling students more practice? How is that supposed to help them more? Will they actually achieve if given more time? What would this look like in a classroom where everyone is at different levels?
• How could you accurately assess the students to find out who's falling through the cracks? Tests don't seem to always work, but often they are valuable to determine where students are at.
  
• Is it fair to even assess students at all? Where is the line drawn between checking for understanding and progress, and labeling students based on their abilities?

This chapter was mostly about gender equality. It questioned the way that we look at boys and girls differently in terms of their abilities, and how women are often encouraged less to become good at math than men are. Often in our society it is impressed upon women from a young age that they are not as good at math or as smart just because they are women. This carries throughout learning, into adulthood. The traditional method of teaching math supports this divide between genders. Female and male thinking has been proven to differ. In math, women and girls often question how and why things are the way that they are, while men and boys tend to be more focused on just getting the answer. Females are more concerned with the how and why, while males are more concerned with the what and don't get hung up in questioning. Often because of this, girls tend to acquire lower test results than boys do. There are chemical differences in the male versus female brain that cause these differences to occur. Some questions I have with this are how does it relate to the topics of transgender and gay students? If it makes sense to sort students into classes based on their gender, how would students who associate with neither gender be placed? How could that impact the social problems between genders?

Math is a series of connected parts, and different strategies exist in math. Many times when students struggle in math with a certain part, it is because they struggled with something else earlier on and didn't fully understand it. The cone versus ladder idea was discussed in this chapter. It is better for a student to be like a cone, with a wide range of understanding that can be funneled down into a point, than to be like a ladder, which is a student trying to memorize every rule and stay on the narrow track. 

Children are interested in math right from the beginning. When given the opportunity, children will become apt at counting, sorting, and grouping blocks based on pattern even from a very young age. Puzzles and mental problems are fun for young children, and they also help to create a good association with math. Students should be given the opportunities to make these connections early on in the classroom, realizing these connections exist and that puzzles and games like Sudoku do involve math. This not only makes math more interesting to students, it also builds their confidence and requires them to think. This chapter also talked about the importance of how the teacher talks to students about their answers to problems, if they are incorrect. Approaching a wrong answer by simply stating that the student is wrong will not help them to explore further, but instead it will discourage the student. However, if a teacher takes the time to look at the work the student did with the student, and have them explain their reasoning, the teacher can relate to the student's thinking and look at it from their perspective, helping the student to realize their ideas have value. Students having confidence in themselves is important to help them expand their learning. Starting early at home in a child's education can often help to build that confidence up before they even start school.

If any real change towards success is going to happen in the schools, parents and teachers alike are going to be a part of that change. It cannot be done by just teachers or just parents, the learning of students involves effort on both parts. Parent teacher conferences are important for this, and cooperation is necessary to accurately develop a curriculum that will be effective. Students also need support outside of the classroom, in their home environments. 

I will create a reading schedule as soon as I get the book. Unfortunately, there have been issues with shipping and it hasn't come in the mail yet!