# Research Paper: What's Math Got to Do With it by Jo Boaler

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¶ … Math Got to Do With it? By Jo Boaler

Boaler, Jo. What's Math Got to Do With It? Helping Children Learn to Love Their Least

Favorite Subject -- and Why It's Important for America. New York: Viking, 2008.

Very often, students will whine in math class: 'when will we ever use this in real life?' This explains the title of Jo Boaler's book: What's Math Got to Do With It? Her answer: everything. Math is used everywhere in real life. However, the students' question underlines the abstract nature of what is taught in most math classes, despite the fact that math is a very practical discipline. Teachers must make students understand that math did not arise as a subject to torment children: it organically arose from a need to engage in real and productive problem-solving efforts to everyday questions. "All the mathematical methods and relationships that are now known and taught to schoolchildren started as questions, yet students do not see the questions. Instead, they are taught content that often appears as a long list of answers to questions that nobody has ever asked" (Boaler 27). They are taught to find the area of a square rather than asked -- when might you want to find the area of a square room? (Answer: when you want to buy a new carpet!)

Boaler delineates two approaches to mathematical education -- the traditional approach which emphasizes abstract methods and approaches to numbers, versus what she sees as the superior approach which emphasizes creative reasoning, problem-solving and "flexibly applying methods in new situations" (Boaler 7). If a student can manipulate numbers and get good grades on a standardized test, what use is this if he or she does not understand the applicability of numbers to his or her own existence? Boaler's book recounts a number of different observational classroom experiences, and one of the most positive is that of adolescent boys solving a geometric problem involving a skateboard's arc. They laugh, they are excited -- this is how math class should be, stresses Boaler. Students should not leave the classroom feeling as if they will never use the math they learn. After all, an English teacher would not feel as if he or she had done a good job teaching, if students only knew how to read the course material, but had not learned to apply those skills to reading outside literature!

This overview indicates very clearly what side of the 'math wars' Boaler stands on -- that of an emphasis on application. The National Council of Mathematics Teachers, after all, lists communication, connections, representation, and problem-solving as critical standards for mathematics education, and gives these standards equal weight as knowledge of numbers, algebra, geometry, measurement, data analysis, and probability. But how much time do teachers really spend on representing math concepts or the ability to communicate mathematical thinking coherently to others? How many students really perceive connections between mathematics and other subjects, despite its vital place in philosophy, science, architecture -- even sports? Not enough time, Boaler would contend.

To those who would argue that her approach would not prepare students for standardized mathematics curricula in the future, she points out that even individuals who use mathematics in their profession, like engineers, cannot take a formulaic approach to learning: "structural engineers & #8230;rarely used standard methods and procedures. Typically, the engineers needed to interpret the problems they were asked to solve (such as the design of a parking lot or the support of a wall) and form a simplified model to which they could apply mathematical methods. They would then select and adapt methods that could be applied to their models, run calculations (using various representations -- graphs, words, equations, pictures, and tables -- as they worked), and justify and communicate their methods and results. Thus, the engineers engaged in flexible problem solving, adapting and using mathematics. Although they occasionally faced situations when they could simply use standard mathematical formulas, this was rare and the problems they worked on were usually ill-structured and open-ended" (Boaler 7). Too much emphasis is given to the specific standards of content, such as algebra, geometry, and numbers, and too little is given to how to use these tools in an effective fashion. And if students do not feel they can use these tools, they will forget them upon moving to the next grade level, like many students forget the fact they had to memorize all of the state capitals in 7th grade.

One of the most radical suggestions Boaler gives is not to tell students that they are 'wrong.' She gives the example of one Swarthmore professor, for example, who is well-known on campus for always finding something 'right' about even a wildly inaccurate guess (Boaler 183). He reasons back from the student's incorrect answer, understands the student's thinking, and then shows the reasoning behind the correct answer. The student understands, fully and deeply, the mathematical processes and rationale through this method. They student does not feel stupid for trying to grapple with a difficult problem and the teacher remains engaged and excited with the educational process.

This anecdote and the positive tone with which it is recounted underlines how passionately Boaler feels about the misguided nature of 'tracking' students based upon their ability. Boaler believes that students should teach one another -- a core idea behind the mathematical educational standard of 'communication' that is so seldom reinforced within the classroom. Also, the class can move at the same pace conceptually, while more advanced students can use the concepts in higher-level applications while their fellow students catch up. Getting to the 'end' of the textbook the fastest should not be the main objective of the class. Additionally, this creates a false idea that mathematics can be mastered, when of course all textbooks are artificial constructions.

We have forgotten, Boaler says, what mathematics truly is -- it is sad to hear students define math merely as sets of rules, which is an impoverished notion of how math functions for those who love the subject (Boaler 15). "Mathematics is a human activity, social phenomena," she says (Boaler 16). Without it, where would we be -- we would not have measurement, our money system, or even sports statistics! There is a kind of mathematics even in poetry, music, and the symmetrical beauty of nature. Boaler thus views mathematics in an interdisciplinary and holistic fashion -- as part of life, rather than separate or even fundamentally different than life.

The stakes are great, she stresses -- the U.S. is rapidly falling behind the rest of the world in mathematics proficiency. As the world grows increasingly technologically sophisticated, this is dangerous. Boaler demonstrates how her longitudinal studies reveal how students taught math in a nontraditional, problem-solving fashion show higher level mastery of the subject and enjoy math more, eschewing the 'math phobia' that plagues so many students. What is truly tragic, however, is that many parents, perhaps remembering their own painful math education believe that math has to be 'traditional' -- that is, not fun, and with an emphasis on rote manipulation of equations. In one school district that adopted a problem-solving approach that the students responded to well, the parents actually insisted that the school return to its previous approach, because it was deemed more valid in their eyes. This may be more for emotional reasons than any demonstrable, practical reasons -- even based upon standardized test performance -- parents believe that math should be hard and unpleasant and feel that their children are not learning math unless they are miserable!

Unsurprisingly Boaler is not a fan of standardized tests. She criticizes them for encouraging teachers to 'teach the test,' even to cheat and give 'hints' (answers) to students, because of their fears that if their students do…
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