In the introduction to What's Math Got to Do With It, Boaler notes interesting trends - many adults say they hated math in school, but like math in their work. Many adults enjoy activities like Sudoku, that require logical thinking, but they did not enjoy their math experiences in school.
The math that is needed for working situations is logical thinking, comparing numbers,
analyzing and reasoning. People need to be able to reason, problem
solve and apply methods to new situations. An official report examining math needed in the workplace revealed that estimation is the most useful math activity.
Boaler references Conrad Wolfram's TED talk in
which he talks about math as a four-step process: posing a question,
constructing a model to help answer the question, performing a
calculation, and converting the model back to the real-world solution by
seeing if it answers the question.
Boaler shares that her book will identify the problems that American students encounter and will share some solutions.
In Chapter 1, Boaler talks about the difference between how students view math and how mathematicians view math: students see math as "numbers" and "rules," but mathematicians see math as "the study of patterns" or a "set of connected ideas."
According to Boaler, math is a "set of methods used to help illuminate the world." She discusses the Fibonacci sequence and the golden ratio, which many middle and high school students have never heard of.
Boaler discusses quite a few differences between "school math" and "mathematician math." Mathematicians work on long and complicated problems that involve combining many areas of math, while school children spend hours answering short questions that address the repetition of isolated procedures. Long, complicated problems encourage persistence, and an important part of "real math" is the posing of problems. According to Boaler, mathematics involves going from answer to question, while computation goes from question to answer.
The work of mathematicians is collaboratory. Mathematicians do not work in isolation - when interviewed, mathematicians have stated that they collaborate to learn from one another, increase the quality of ideas, and share the "euphoria" of problem solving. However, Boaler states, there are still many silent math classrooms where students work in isolation.
I enjoyed reading about the "meaning" of math, and I will pose the question to my students this week - "What is math?"
Reading this chapter has inspired me to create a couple posters that reflect what math really is.