Stanford University: How to Learn Math

Image from Geometry Daily.

I can’t say enough about how fantastic Jo Boaler’s online math class was. I finished it yesterday.

Jo is a Stanford University professor, and she created a free, online class for teachers and parents called How to Learn Math. Students (there were approximately 35,000 people registered) watched videos, wrote responses to prompts, and completed other tasks at their own pace. Some are still finishing; the course ends September 28.

Jo is working on a course for young people now. She has published a book called What’s Math Got To Do With It. I’m convinced that whatever Jo does in the future, it will be great. Keep an eye on her.

In a nutshell, Jo is all about dispelling myths about who is good at math and who isn’t, evangelizing about the growth mindset work of Carol Dweck, and giving teachers ideas about effective math education. She advocates for math as an inquiry activity, and really seeing it in a totally different way than most of us were taught in school and continue to teach today.

In Jo’s words:

Mathematics classrooms should be places where students believe:

• Everyone can do well in math.
• Mathematics problems can be solved with many different insights and methods.
• Mistakes are valuable, they encourage brain growth and learning.
• Mathematics will help them in their lives, not because they will see the same types of problems in the real world but because they are learning to think quantitatively and abstractly and developing an inquiry relationship with math.

Machines to Materials

I just watched two PBS NOVA shows that I must share. One is called Making Stuff: Smaller. The other is Making Stuff: Stronger. There are other Making Stuff shows I haven’t watched yet.

Check these out! You can watch them for free online (at least right now you can).

As an educator and a parent, these videos get me all fired up. Young people should be learning about cutting edge science and math, not just the stuff of textbooks and standards. I want to show these to students and then I’d expect to hear them talking about wanting to be a chemist, material scientist, or nanotechnologist when they grow up.

My favorite part of Making Stuff: Smaller was the concept of starting by using a machine to complete a task, and then evolving to using a material to accomplish the same task. This is a key feature of miniaturization, which is what allows us to have laptops and cellphones, among other things, today. Computer processing went from giant rooms of vacuum tubes to silicon chips, but the story I liked the most was the journey from behemoth pendulum clocks to quartz watches. If this makes no sense to you, watch the video.

Another awesome story in Making Stuff: Smaller is about driving a tiny robot around inside someone’s eyeball to deliver medicine. Holy cow!

Shrub

Edible Wasatch 2013, photo by David Vogel

My brother, David Vogel, and his partner, Rachel Hodson, are the owners and editors of a magazine called Edible Wasatch. It’s about local food in Utah, but I can’t wait for it to arrive in my mailbox in Vermont each season. It’s always full of gorgeous photos, great articles, and interesting recipes.

Shrub is the name of a syrup made from fruit, sugar and vinegar. I found it in the summer 2013 issue of Edible Wasatch I just received. You can add a small amount of shrub to seltzer water to make tasty, homemade soda kids will love.

Teachers and parents: Try making shrub with your kids. With this activity, you can combine wellness, local food appreciation, culinary skills, and math. What could be better? Then reward yourself by using some of the kids’ leftover shrub to mix up a delicious summer cocktail.

Strawberries have been so perfect around here lately, I think I would make shrub with those. However, you can use any fresh, ripe berries or other fruits. I have raspberries growing at my house now, so I might combine those with some local strawberries.

Here’s the recipe, straight from Edible Wasatch:

Basic Shrub

One part fruit or berries

One part sugar

One part vinegar

Wash and cut up the fruit and put into a bowl or a jar large enough to contain all of your ingredients. Add the sugar and stir or mash it with the fruit until it’s evenly distributed. Cover with cheese cloth or a kitchen towel to protect it from fruit flies and leave it to macerate - at room temperature for a few hours or overnight - until the fruit has broken down and become juicy.

Add the vinegar to the fruit and sugar mixture - apple cider vinegar or any kind of wine vinegar, not distilled vinegar. Stir or shake until the sugar is completely dissolved. Strain off the liquid and discard the solids. Store your shrub in a bottle in the refrigerator and enjoy for up to a year.

See their original article and recipe here.

Ideas for teachers and parents

Let kids do all the work, including deciding which fruits or berries are in season and would work well, picking or buying those, making the shrub, and making the soda. They could even sell it in the neighborhood instead of lemonade and hand out the recipe to customers.

Here’s some math. Ask kids things like...

• What does “part” mean in this recipe?
• How do we know how much of an ingredient to use when “one part” is called for?
• How is this measurement different than other kinds of measurements we’ve seen in recipes (teaspoons, cups, etc.)?
• How should we decide how much shrub to make?
• How much fruit, sugar, and vinegar would we need if we wanted to double the amount next time we make it?
• What would we do if we wanted to try making shrub that was less sweet?
• Have you ever seen another recipe that called for “parts”? How could you figure out how much you need for “parts” when you know the total amount of the recipe you desire?

Other possible questions

• If we use a few teaspoons of shrub to make homemade soda, about how much sugar will one glass of soda contain?
• How does our homemade soda compare to a commercial soda? Amount of sugar? Type of sugar? Other ingredients? Taste? Color? Cost? Environmental and economic impact?
• What does “macerate” mean?
• What other ways could we use shrub besides making soda?
• Why can shrub stay in the fridge for so long without spoiling?
• What questions do you have?

PBS Kids Lab

New, high-quality resources for math education keep popping up.

Paula Kerger, of PBS, recently published a press release on the Huffington Post about some new things on the PBS Kids website. "...as we looked at our work with a critical eye, we realized that we needed to step up our efforts in helping kids learn math literacy. That's why this week we're launching "It All Adds Up," which aims to boost math learning at home -- and everywhere -- by providing resources for parents. With these free resources, which were developed in partnership with the Corporation for Public Broadcasting (CPB) through the Department of Education's Ready To Learn Initiative, parents can use their mobile phones or computers, or do hands-on activities, to help their children learn basic math skills."

PBS Kids has found what other education researchers already knew: "...nearly 30 percent of parents have anxiety about teaching their child math. In part, this issue stems from the fact that 25 percent of parents find it hard to incorporate math into conversations and activities at home. Math may seem harder to weave into natural discussions and activities in the home, leaving time- and resource-strapped parents unsure where to begin."

I visited the new PBIS Kids Lab and was impressed. There are resources there for parents and teachers. I liked Math Activity of the Day and the context-specific Ideas to Go. There are tons of online activities and mobile apps. I tried a bunch, and one I would recommend is Freddy’s Carnival Games (Ages 6-8, counting). I think it is best to test these first and give specific ones to kids, rather than turning them loose with the entire menu of options.

Radiolab Numbers

Radiolab is so cool. It’s a public radio show you can listen to on your public radio station or online. My dad recently told me about a Radiolab show called Numbers. It originally aired in November 2009. Each show is an hour long and has several segments on a single topic. If you listen to the Numbers show, you’ll first hear a Johnny Cash song, then learn about the innate number sense of infants, and move on to other fascinating topics like Benford’s Law, a surprising observation about the first digits of numbers, and a forensic accountant who uses it to investigate fraud, and on and on. The show is a very human take on numbers. I’m sure you’ll enjoy it.

What's Math Got to Do with It?

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.

Teach your children well

 

Here’s a nice article from the Wall Street Journal for parents, with an accompanying video. 

This short piece hits the important points when it comes to math and parenting. 

The one thing I would add is my favorite question for my daughter when she asks for help with her algebra homework: “What do you think you should try next?”

A Pickle

There are some interesting new websites out there. One is called Math Pickle. Shannon Walters, C.P. Smith Library Guru, alerted me to this one. So far, I like most of what I’ve seen on this site, although the layout is a bit clunky. Dr. Gordon Hamilton presents activities for students based on math problems dating back several decades to mathematicians like Issai Schur and Lothar Collatz. His decision to put young Vi Hart on the same page as some of the older mathematics greats is a good sign. Math activities are presented via video, and include footage of real students. I’m less impressed with Dr. Hamilton’s philosophizing about the way math should be taught in a video entitled “Let’s Abolish Elementary Mathematics”, even though I agree with most of what he is saying.

I like the Graceful Tree Conjecture as a means of practicing subtraction with third graders and the Collatz Conjecture for fourth graders. These are captivating problem-solving activities which are an excellent way to encourage students to work together, discuss different strategies, practice skills, check their work, and have fun. I would also try the magic cauldrons addition game for second graders. Teachers will find Math Pickle a useful site for finding new activities for math class and getting a thorough explanation of how to use them.

Caine's Arcade

My dear friend, Rachel Wynne, sent me the link to this wonderful video. Nine-year-old Caine designed and constructed an entire arcade out of cardboard. He taped calculators onto the front of the games so he could validate pin numbers using the square root function. So cool. Rachel, thank you for thinking of me and Jim when you saw this. Caine is an inspiration to us all.

Goodnight Math

 
Alex Reutter, C.P. Smith Math Night guru and super-parent, shared a great resource with me. It’s a blog called Bedtime Math. On it, parents will find a new, differentiated math problem every day intended to share with their children at bedtime.

The honorable mission of Bedtime Math is “to make the nightly math problem as common as the bedtime story.” Wouldn't that be something? Parents can sign up to receive a daily email with the current problem (for free!).