This book review examines Jo Boaler's What's Math Got to Do With It? (2008), in which Boaler argues that traditional mathematics education — centered on rote memorization and abstract procedures — fails students by disconnecting math from real-world application. The review summarizes Boaler's key claims: that problem-solving and creative reasoning produce deeper mathematical understanding; that tracking students by ability and over-reliance on standardized testing are counterproductive; and that math is fundamentally a social, human activity relevant to all areas of life. The review also notes Boaler's longitudinal research supporting nontraditional teaching methods and her concern about declining U.S. mathematics proficiency.
Very often, students will whine in math class: "When will we ever use this in real life?" This question 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 applied to everyday questions.
As Boaler writes, "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). Students are taught to find the area of a square rather than being asked: when might you want to find the area of a square room? The answer, of course, is when you want to buy a new carpet. This distinction — between delivering answers and posing meaningful questions — is central to Boaler's educational philosophy.
Boaler delineates two approaches to mathematical education: the traditional approach, which emphasizes abstract methods and procedures applied 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 earn 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 life?
Boaler's book recounts a number of different observational classroom experiences. One of the most positive involves adolescent boys solving a geometric problem related to a skateboard's arc. They laugh; they are excited — and this, Boaler stresses, is how math class should be. Students should not leave the classroom feeling as though they will never use the math they have learned. After all, an English teacher would not feel satisfied if students could only read the assigned course material but had never learned to apply those skills to reading outside the classroom.
This overview makes clear which side of the "math wars" Boaler stands on — that of an emphasis on application. The National Council of Teachers of Mathematics (NCTM) lists communication, connections, representation, and problem-solving as critical standards for mathematics education, giving these standards equal weight alongside knowledge of numbers, algebra, geometry, measurement, data analysis, and probability. But how much time do teachers really spend helping students represent mathematical concepts or communicate mathematical thinking coherently? How many students genuinely perceive connections between mathematics and other subjects — despite math's vital place in philosophy, science, architecture, and even sports? Not enough time, Boaler would contend.
To those who argue that her approach would fail to prepare students for standardized mathematics curricula, Boaler points out that even individuals who use mathematics professionally — such as engineers — cannot rely on a purely formulaic approach to learning. She writes: "Structural engineers … 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).
"Positive feedback and mixed-ability classrooms improve learning"
"Math as social, creative, and culturally embedded practice"
"Testing culture harms teachers, students, and learning quality"
Mathematics is not a series of bubbles to be filled in on a scantron — it is part of life, and should be taught as such. Finding patterns, making connections, and coping with open-ended questions are skills that will shape the next generation of scientists and computer engineers. An excessive commitment to the idea that mathematics must be difficult, and that quantitative subjects are more rigorous when taught "traditionally," serves only to hold students back. Traditional methods strive to make students fit into a traditional world that is rapidly ceasing to exist.
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