Stereotypes about Math

In our new technological world, employers do not need people who can calculate correctly or fast, they need people who can reason about approaches, estimate and verify results, produce and interpret different powerful representations, and connect with other people’s mathematical ideas.

The Stereotypes About Math That Hold Americans Back, By Jo Boaler. The Atlantic, November 12, 2013. 

Breathe collaboration

From Dan Meyer's You Pour I Choose Math Task

Steve Leinwand came to Killington, Vermont, on Wednesday night and I made sure I was there to see him. Dinner and the presentation by Steve was hosted by the fledgling local chapter of National Council of Supervisors of Mathematics (NCSM) called Vermont Math Leadership Council (VMLC). I made them a website at www.vermontmathleadership.org, where you can find resources shared by Steve, including his powerpoint from the dinner.

Here are a few things from the notes I typed on my iPad instead of eating dinner:

Take risks, make mistakes. The stuff we have now is bad. Enter the Common Core. Hope and change have arrived, like the calvary. This is a once in a lifetime opportunity to rescue ourselves and our teachers from all the problems we have had.

Effective teachers create language rich classrooms.

Effective teachers take every opportunity to build number sense.

Effective teachers embed math content and connect to the real world.

Effective teachers devote the last 5 minutes to formative assessment.

See Steve’s document called High Leverage Mathematics Instruction Practices for more.

I am not an effective leader if I don't breathe collaboration.

NYT: How to Fall in Love With Math

From WolframMathWorld

From yesterday’s New York Times Opinion Pages piece by mathematics professor Manil Suri.

Despite what most people suppose, many profound mathematical ideas don’t require advanced skills to appreciate. One can develop a fairly good understanding of the power and elegance of calculus, say, without actually being able to use it to solve scientific or engineering problems.

Think of it this way: you can appreciate art without acquiring the ability to paint, or enjoy a symphony without being able to read music. Math also deserves to be enjoyed for its own sake, without being constantly subjected to the question, “When will I use this?”

Letting Go

By Mica Angela Hendricks and daughter

My dear friend, Rachel Wynne, kindly emailed me the link I am about to share. It’s a blog post called “Collaborating with a Four-Year Old”. I just love it. It’s about a mom and her young daughter creating artwork together. The pictures are priceless, and the ideas about sharing and collaboration are profound.

“Those things you hold so dear cannot change and grow and expand unless you loosen your grip on them a little.” - Mica Angela Hendricks, The Busy Mockingbird

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!

Making Mistakes

Here's a TED Radio Hour show featured on NPR entitled "Making Mistakes". Excellent, and very relevant to mathematics education and life in general.

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?