**There is a free iPad app from IBM called Minds of Modern Mathematics. It is a beautiful timeline of the history of mathematics and world events, and there are 9 vintage videos to watch as well. Charles and Ray Eames, a famous, husband-and-wife design team created the original interactive mathematics exhibit back in 1961, which provided the content for this app. The Eameses films are wonderful, simple, short. I enjoyed Something About Functions, and the non-verbal Exponents.**

I also happened upon a great blog called MathMunch. MathMunch calls itself “a weekly digest of the mathematical internet”. They posted something about Minds of Modern Mathematics, and have a fabulous page of math videos. If you miss the old Schoolhouse Rock videos and you know a young person who could use some work on counting by 5s, MathMunch has the link. Their video collection is exhaustive, and includes videos about solving a Rubik’s Cube, paperfolding, Pi, M.C. Escher, and more.
**When I arrived at work last week, several people were excitedly talking about the NPR piece they’d heard on the radio during their drive in. Here is a link to the Morning Edition show, Teachers’ Expectations Can Influence How Students Perform, which aired September 17. **

I recommend listening to the audio, but you can also read the transcript. Back in 1964, Harvard professor Robert Rosenthal began studying how teachers’ expectations influence student achievement.

**[Rosenthal] found that expectations affect teachers' moment-to-moment interactions with the children they teach in a thousand almost invisible ways. Teachers give the students that they expect to succeed more time to answer questions, more specific feedback, and more approval: They consistently touch, nod and smile at those kids more.**

"It's not magic, it's not mental telepathy," Rosenthal says. "It's very likely these thousands of different ways of treating people in small ways every day."

It is difficult to truly change our beliefs, but there is a way. Recent studies have shown that teachers who actively worked on their teaching through videotape analysis and targeted work with coaches in their classrooms to change their behavior also experienced a significant shift their beliefs about students.

**A man is on a diet and goes into a shop to buy some ham slices. He is given 3 slices which together weight ⅓ of a pound, but his diet says that he is only allowed to eat ¼ of a pound. How much of the 3 slices he bought can he eat while staying true to his diet?**

There is a lovely book in the John J. Flynn Parent Resource Center these days. It’s called What’s Math Got to Do with It? How parents and teachers can help children learn to love their least favorite subject, by Jo Boaler. The book was published in 2009, but I have only recently discovered it.

Boaler includes many more problem-solvers like the one above. Don’t worry if you don’t know a formula to figure out how many turkey slices the man can eat. Start drawing pictures and think about what a whole pound would look like. Go slow and use your intuition. Says Boaler, “Children begin school as natural problem solvers and many studies have shown that students are better at solving problems before they attend math classes.”

…People don’t like mathematics because of the way it is misrepresented in school. The math that millions of Americans experience in school is an impoverished version of the subject and it bears little resemblance to the mathematics of life or work or even the mathematics in which mathematicians engage.

In addition to the prompt I shared in my last post “What do you think you should try next?”, Boaler shares more good prompts to use with children:
**How did you think about the problem?**
**What was the first step?**
**What did you do next?**
**Why did you do it that way?**
**Can you think of a different way to do the problem?**
**How do the two ways relate?**
**What could you change about the problem to make it easier or simpler?**

Enjoy.