A recent study published in the *Philosophy of Mathematics Education Journal* confirms that teachers’ images of mathematics and their mathematics history knowledge are interlinked. According to the study’s lead author, Danielle Goodwin of the Institute for Mathematics and Computer Science (IMACS), "By and large, the teachers with low history scores in this study were the teachers who exhibited narrow, negative views of mathematics."

*Key findings from the study include:*

- Respondents with low history scores
- were more likely to indicate that they believed mathematics overall was like "cooking a meal" or "a tool for use in everyday life."
- were more likely to believe that mathematics is a disjointed collection of facts, rules and skills than respondents with high history scores.
- appeared to be more likely to agree with the statement that "the process of doing mathematics is predictable" than those with higher history scores.

- Respondents with high history scores
- exhibited more favorable views of mathematics.
- were more likely to indicate that they believed mathematics overall is like "doing a dance" or "an art, a creative activity, the product of the imagination."
- disagreed more often with the statement "everything important about mathematics is already known" than did their low-scoring counterparts.

**Attitudes Influence Decisions that Affect Students**

Why does this matter? Because educators’ views of mathematics affect student learning experiences in a variety of ways, from daily classroom instruction to curriculum selection and development to far-reaching proposals for national math education reform.

Teachers’ images of math are typically based on their own limited experiences as young students, and so teacher education programs should incorporate mathematics history into their curriculum as a way of reshaping attitudes, the study suggests. Doing so would help future teachers develop an appreciation for and understanding of math as a subject that is alive and fundamentally creative. Fostering this viewpoint could help teachers help their students understand that mathematics is a natural place for inventive problem-solving where questioning and investigating are highly valued.

"Teachers who have rule-oriented images of mathematics can weaken student learning by representing mathematics in misleading ways," says Goodwin. Instead of conveying as healthy the struggle of intellectual discovery that naturally takes place in mathematics when new ideas are explored, "struggle" in US K-12 math classrooms has come to mean being "bad at math." This unfortunate association has left generations of Americans hating math and believing in the myth that they are not "math people."

Current teachers and pre-service teachers who want to improve their ability to teach math don’t have to wait for curriculum changes at schools of education. There are wonderful and accessible resources that provide a willing and curious mind with a deeper understanding of mathematics in the context of its rich history.

**Recommended Reading and Viewing**

If you’re still looking for a holiday gift for your child’s math teacher, perhaps one of the recommended books below would be appreciated. For the visually-inclined,

the videos and movies that follow provide many hours of awe-inspiring and sometimes humorous enlightenment.

*Books:**Journey through Genius: The Great Theorems of Mathematics*by William Dunham*The Man Who Loved Only Numbers: The Story of Paul Erdos and the Search for Mathematical Truth*by Paul Hoffman*e: The Story of a Number*by Eli Maor*Women in Mathematics*by Lynn M. Osen*The Joy of Pi*by David Blatner*Gödel, Escher, Bach: An Eternal Golden Braid*by Douglas R. Hofstadter

*Videos and Movies:**Mathematics: Making the Invisible Visible*, a five-lecture survey course by Stanford mathematics professor Keith Devlin*A Mathematical Mystery Tour*, BBC documentary looking at some of the greatest problems in the history of mathematics, some of which have since been solved*Fermat’s Last Theorem*, BBC documentary about mathematician Andrew Wiles’ proof of Fermat’s Last Theorem*The Story of 1*, BBC documentary about the history of numbers*A Beautiful Mind*starring Russell Crowe as mathematician John Nash (PG-13)*The Imitation Game*starring Benedict Cumberbatch as mathematician and computer scientist Alan Turing (PG-13)

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Thank you to a friend of IMACS who recommended “How Not to Be Wrong: The Power of Mathematical Thinking” by Jordan Ellenberg as another thought-provoking book.

Yes! a) Teachers who have a wide range of interests are more interesting and students learn more regardless of subject and b) Pi did not fall from the sky. I always tell my kiddies (ages 5-25) – imagine the awe when the ancient mathematicians could easily draw/construct pi or sqrt(2), but could not measure it exactly. (P.S. I also love decimals and approximations and think math teachers should teach some recipes, some exact/symbolic and some approximate/numerical maths at every level.)