Saturday, December 7, 2013

Vermont Math Leadership Council

the view from my porch
Vermont has a new education organization - Vermont Math Leadership Council - thanks to Julie Conrad, Tracy Watterson and others for getting it off the ground. Thanks to me we have a blog with the easy URL Thanks to Tim Whiteford, there is a bunch of great posts on the blog! Check it out. We’d like to get more material from more voices on this blog and increase our readership. Anyone can join the organization. Our next meeting is January 29, 2014.

I was about to post something here on my blog about the new Institute of Education Sciences Educator’s Practice Guide called Teaching Math to Young Children. But then I saw that Tim beat me to it by posting about the very same thing on the VMLC blog. So, read his post here.

What I like about this publication is that it helps both rookies and veterans understand how best to work with young children and math. There are clear, specific recommendations that are easy to follow and a selection of easily usable games and ideas that illustrate the concept.

Whereas we often encounter activities or lessons and need to figure out what math we’re really going for, this resource communicates the math goals clearly and first, then hands us the activity to use.

Saturday, November 16, 2013

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. 

Saturday, October 26, 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, 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.

Monday, September 16, 2013

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?”

Saturday, August 31, 2013

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

Monday, August 26, 2013

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!

Sunday, July 21, 2013

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.

Sunday, July 7, 2013


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?

Friday, June 21, 2013

What Google has learned about hiring

A few days ago, the New York Times published an interview by Adam Bryant entitled “In Head-Hunting, Big Data May Not Be Such a Big Deal”. Bryant interviewed Lazslo Bock, a Google executive, about what Google has learned about what works and what doesn’t when it comes to hiring new employees.

Google has the resources to crunch numbers on employee performance or success and match that to hiring criteria. Most of the rest of us don’t, so this is worth reading. Here are a few things that stood out for me, as someone who participates on hiring committees and tends to wonder how good I am at judging applicants.

“Years ago, we did a study to determine whether anyone at Google is particularly good at hiring. We looked at tens of thousands of interviews, and everyone who had done the interviews and what they scored the candidate, and how that person ultimately performed in their job. We found zero relationship.”

“On the hiring side, we found that brainteasers are a complete waste of time...What works well are structured behavioral interviews, where you have a consistent rubric for how you assess people, rather than having each interviewer just make stuff up...[also] where you’re not giving someone a hypothetical, but you’re starting with a question like, “Give me an example of a time when you solved an analytically difficult problem.”

“Twice a year, anybody who has a manager is surveyed on the manager’s qualities...We then share that with the manager, and we track improvement across the whole company. Over the last three years, we’ve significantly improved the quality of people management at Google, measured by how happy people are with their managers...for most [managers], just knowing that information causes them to change their conduct.”

Lastly, this is my favorite bit from the article:

“...G.P.A.’s are worthless as a criteria for hiring, and test scores are worthless...We found that they don’t predict anything...the proportion of people without any college education at Google has increased over time...academic environments are artificial environments. People who succeed there are...conditioned to succeed in that environment. One of my own frustrations when I was in college and grad school is that you knew the professor was looking for a specific answer...You want people who like figuring out stuff where there is no obvious answer.”

These insights have far-reaching implications for teachers, not just members of hiring committees.

Saturday, June 8, 2013

Assessment Items

There is a new Smarter Balanced Practice Test released. You can choose a grade level (3, 4, 5, etc.) and choose math and see an early version of the Common Core math assessments that will replace the NECAP.

I can get the practice test to work on some computers, but not on my personal laptop because it won’t let me drag and drop. I have no idea why. And if you can’t drag and drop, you can’t answer test questions or advance to the next question. Try it yourself and hopefully it will work. I submitted a report to SBAC but they said they can’t reproduce that problem so they really didn’t have any advice for me.

These practice tests are worth a look. Pass them along to students to try this summer, and/or do the problems with your classes in the fall. Answers and scoring guide is due to become available in July.

This fall, students will take their last NECAP tests. Here are all the NECAP released items, which serve as great practice over the summer or in the fall before the assessment window.

Tuesday, May 21, 2013

St. Louis STEM Reader

I attended the NSTA STEM Conference in St. Louis last week with several colleagues. It was a very worthwhile trip.

Top Quotes
“Engineering naturally integrates mathematics, science, social studies and language literacy.” - Tamara Moore

“Tell kids they are doing engineering. Use that word. Students, especially girls, tend to go to medical school or major in science in college if they enjoy STEM. Very few choose engineering because they don't know what that means.” - Liz Parry

“If you are not iterating, it is not engineering.” - Ann McMahon

“Is it really STEM or is it just John Dewey?” - Tara Bell

Top Takeaways
1. High-quality STEM education is more about the how than the what. We can’t teach students everything they will need to know. We can help them learn how to learn.

2. The habits of mind related to engineering can be a thread running through all content areas. Empathy, collaboration, failure, iteration, perseverance, social justice, activism, leadership.

3. STEM has the potential to make a real difference for equity and diversity. It has been shown to be an effective way to engage struggling or at risk students. Currently, success in STEM subjects in school and in careers is very skewed toward certain demographic groups, and something needs to be done to change that.

Favorite Presenters

Bob Goodman (New Jersey Center for Teaching and Learning: Ridgewood, NJ) Demystifying Science with the Progressive Science Initiative (PSI) Equity requires that all high school students learn physics, chemistry, and biology. PSI is a free open-source program that is helping schools achieve that goal.

Liz Parry, Coordinator, STEM Partnership Development, The Engineering Place, College of Engineering, NC State University

Ann P. McMahon Ex-Aerospace engineer. Strategies for integrating STEM with social and emotional learning. Ann recently gave a TEDx talked titled Engineering Empathy (use password tedxgladstone).

Beth Bender, Principal of Gateway STEM High School, St. Louis. A public magnet school, 85% FRL, 55% African american, increasing ELL. There is a lack of awareness about engineering, and it is mostly male. Engineering students give demonstrations for other students during lunch; recruiting for the high school is done with hands-on tasks, live puppies.

Tamara Moore, University of Minnesota. STEM Education Center. Said she would soon be running a pilot program of K-6 STEM integrated units that include a heavy children’s literature component.


Family Engineering (book and website recommended by Liz Parry)
National Center for Universal Design on Learning

Monday, April 29, 2013

Geometry Daily

I love the images on this website. A new one is created daily and generously shared with the world. I would like to use these with students. The only prompt would be, simply, “What do you see?”

Sunday, April 28, 2013

Estimation Jars

Today I’m creating Estimation Jars for Math Night at John J. Flynn Elementary School. This is always a highlight at Math Night and it’s fun to watch kids at work on their estimate. I have one jar full of Rolos (there is something appealing about the gold wrapping), a smaller jar containing Skittles, and a very small jar with unpopped popcorn.

This year, I plan to accept all estimates within a reasonable range for each jar and then randomly draw a winner. That’s different than past Math Nights when the person who estimated the number closest to the actual number won the jar. I am hoping this helps promote a more correct understanding of estimation, with the goal being to produce a reasonable estimate, not to land on or closest to the exact number.

It is a good idea to have a few jars containing different sized objects so students can think about how the relative size of the objects affects the number that fit in a space. Ongoing math explorations can be done using estimation jars outside of an event like Math Night. Here is an excellent write-up and video about how classroom teachers can use estimation jars with their students, with a focus on the all-important concepts of doubling and halving.

Thursday, April 18, 2013

NCSM Denver - Brilliant Minds

Penny Stearns and I flew to Denver for the NCSM 2013 conference. NCSM is an organization focused on mathematics education leadership. They have resources on their website. The powerpoint presentations from the conference presenters aren’t posted yet but I hope they will be soon.

We’ve seen some incredible speakers over the last 3 days. These include the following:

Cathy Seeley
Marilyn Burns
Kati Haycock
Jo Boaler
Steve Leinwand
Cheryl Adeyami
Greg Tang
Deborah Ball
Heather Hill

These are folks you will want to look up. I will definitely get their entire presentations when they become available.

Steve Leinwand is my new hero. He yells, which I appreciate. Speak truth to power, Steve says. He talked about how he helped turn around a middle school in Missouri. His stories and learning from that process are fascinating. Steve keeps teachers and students at the center of his school reform work. At the end of his compelling talk, he showed a slide listing the names of the teachers at the Missouri school. He thanked them and dedicated the talk to them.

Steve shared 9 research affirmed practices for improving a school.
Number one is that effective teachers respond to most student answers with Why? How do you know that? or Can you explain your thinking?

Instruction is everything, says Steve.

Regarding the Standards of Mathematical Practice: Practice #3 is where it’s at. Those 9 words are the most important words in the entire Common Core standards. Construct viable arguments and critique the reasoning of others.

Finally, Steve said we probably shouldn’t be talking about an achievement gap. This makes it sound like it is the students’ fault. We should instead be talking about an instruction gap. Wow.

I was going to write something about these other speakers as well, but I wrote so much about Steve that I think I will postpone. More to come.

Here is Steve today. I took this with my phone. Go Steve!