Explorations In Math

What We Mean by Sustainable Math Culture

Published on November 1 2011

As we at EIM talk with our different constituencies, there are questions that come up regularly. These are thoughtful questions from people interested in our success. Here’s an interesting question that came up recently; I hope you will take the time to respond and to ask additional questions.

Q: According to your website, your mission is “to build a sustainable math culture in elementary school communities.” Why “communities” instead of “schools”? And just what is a “sustainable math culture”?

Math, like reading, has to be more than just school-focused. For many years, reading has involved both families and the wider community in many ways, which is what we want to do with math. As examples, families read to their children regularly, libraries sponsor summer reading programs, schools hold family reading nights, businesses offer reading incentives, and there’s a nationwide yearly reading contest called Global Reading Challenge. Our mission is to do the same for math, take it beyond the classroom and the school and create an appreciation for the importance and enjoyment of math community-wide.

As for “building a sustainable math culture,” I’m going to draw an analogy once again to the culture of literacy that exists in virtually every elementary school in the nation. This culture comprises many elements. A partial list would start with the school library and would include reading assemblies, book giveaways, book fairs, extensive professional development, family reading nights, reading aloud to students and summer reading programs. Reading is far more than just what goes on in the classroom between 10:00 AM and lunch.

We would like to start a math movement that, over time, will develop into a comparable math culture in schools across the country. We’d like to see math assemblies, math tournaments, more math professional development, family math nights, summer math camps (EIM offers four summer math camps), and a math resource center in every school. The key to this is the word “sustainable.” EIM can work with schools to help develop a math culture but in order for it to grow and stick, it has to be engrained into everyday activities and unique to their students and educators so it will continue long after EIM the formal partnership has concluded.

Starting the Math Period

Published on October 25 2011

Teachers, here’s something to consider doing at the start of your math period: open with some mental math and/or a quick math game. Doing this accomplishes three things. First, because kids enjoy doing mental math and math games, you’ll get their attention quickly and easily without having to clap, whistle, ring a bell or any of the other things we routinely do. Just start saying the problem in a normal tone of voice and students quickly settle down. Second, you’ll have them thinking and doing math from the beginning of the period, and doing it in a way they enjoy. Finally, when the lesson starts, they’ll be in a math-positive frame of mind.

I sometimes hear objections to doing this. “I can’t do mental math!” is one. Nonsense! All it takes is a little practice. After a while, you’ll be able to reel off strings of numbers and operations and keep track of the answer. And when you do make a mistake (I certainly have!), it’s good for the students to catch and correct it.

“I don’t know any good, quick games to play!” is another objection. The solution to that is easy: visit our fun math games website and you’ll find several math games for grades K-5. These games are easy to learn, quick to play and require no elaborate set-up or clean-up.

“There’s just not enough time!” is a third objection, and this one is harder to argue with—there is simply not enough time in the day or days in the week to accomplish everything you need to do. But, as I noted above, starting with four or five minutes of mental math or with a quick game brings the class together quickly and productively and starts them off with a positive math attitude. You haven’t lost any time and may even have gained a little.

And, of course, the big benefit: kids are learning that math is fun and challenging, not boring and hard.

Dave Gardner

Mathematician in Residence

MathFest is Coming!

Published on October 19 2011

In 2 weeks the community will be gathering for our 5th annual MathFest at the Rainier Community Center. If you’ve been to MathFest in the past then you know what to expect: math games and math excitement. Last year’s MathFest drew nearly 1,000 folks who spent three hours enjoying Airplane Race, Function Machine, Multiplication Bingo, Mathemagic Mind Reader, Sudoku, Shut the Box, Puzzles and much, much more, including a raffle and prizes. These games and others, as well as some new ones, are a great way for parents, families and kids to discover the fun in math together. In addition, the MathFest Spirit Award is given annually to the Explorations in Math Partner School with the greatest percentage of staff and students attending.

There’s more! Admission is free and refreshments and a special area for tots are included. Doors open at 5:00pm on Thursday, November 3rd. If you’ve not been to MathFest in the past, make it a point to be there this year - you’ll be glad you did! Given the number of people attending, it’s wise to avoid the registration line by pre-registering.  You can register and learn more here.  We hope to see you at the Fest!

Dave Gardner

Mathematician in Residence

P.S. Congratulations to the 4th grade class at St. George Elementary in south Seattle for correctly answering both puzzles from two weeks ago. You’ll be getting a math game for your classroom! Well done!


Math Story Time

Published on October 10 2011

One of the ways we instill a love of reading in our children is the nighttime ritual of reading to them. Doing this communicates the importance we attach to reading, shows our love of reading, models good reading skills, opens opportunities for questions and discussion, and it increases our children’s vocabularies. There’s a way to capitalize on all this and also include a love of math as one of the reasons for reading aloud: read math-related story books. When you start looking for them, I think you’ll be surprised at how many good books there are, and at all grade levels. Talk to your school librarian or the librarian at your public library branch; they’ll be happy to help you. Meanwhile, here’s a great list to get you started.

“Sugar-Coating” Math?

Published on October 3 2011

As we at EIM talk with our different constituencies, there are questions that come up regularly. These are thoughtful questions from people interested in our success. Here’s an interesting question that came up recently; I hope you will take the time to respond and to ask additional questions.

Q: I know EIM believes that making math fun is key to helping students do better in math. But doesn’t “sugar-coating” math perpetuate the perception that math is hard and boring? After all, we don’t “sugar-coat” reading.

The phrase “sugar-coating” is mistaken, we sugar-coat things that are unpleasant, burdensome or unpalatable. Math is none of these things and part of our mission is to help teachers, families and students understand and appreciate that.

I think we all agree that if we enjoy doing something, we’ll do more of it and, over time, become better at it because of the regular practice. When we make math interesting and enjoyable (“fun” if you will), student perceptions of math begin to change from “hard and boring” to “challenging and fun.” Games are a very effective way of doing this. Students enjoy playing them and they develop math skills doing so.

As for reading, one of the reasons reading scores are so much higher than math scores is that we have made reading fun, not so much with games but in other ways: cut and paste activities, coloring, skits, and making dioramas to name just a few. If reading were taught the way we’ve taught math for so many years, reading scores, too, would be abysmal.

None of this is to deny the fact that math is a rigorous discipline that penalizes carelessness and sloppy thinking. We believe that games are a way of instilling math competence and confidence in our children which will, in turn, lead to the kind of rigor and understanding that math demands.

Dave Gardner

Mathematician in Residence

Can you solve these Puzzles?

Published on September 26 2011

There is so much to enjoy about math! I’ve written about some of these in “Math Matters” over the summer: math games (whether commercial or otherwise), going to any of the math/science museums in our area (KidsQuest, Pacific Science Center, Museum of Flight), looking for patterns in both numbers and nature, and finding great math websites. Here’s another: math puzzles (or brain teasers as they’re sometimes called). There are two kinds of math puzzles. One kind involves no math but it does require the kind of flexible thinking and logical reasoning that solving math problems requires. Here’s an example of such a puzzle:

What number goes in the box with the question mark? Why?

Here’s a puzzle that does require math in addition to flexible thinking and logical reasoning:

A man was condemned to death by the king but told the man he would give him a 50% chance of saving his life. The king had two large urns brought into the throne room. “Prisoner,” the king said, “in one urn are 99 red balls and 1 white one. In the other, 99 white ones and 1 red one. You will be blindfolded and be placed between the two urns. Choose one of them and remove one ball from it. If it is red, you die; if it is white, you live.”

The prisoner thought. “If I pick the urn with 99 white balls, I still have 1 chance in 100 of getting the red one and dying, and if I pick from the other urn, I still have 1 chance in 100 of  living. Overall, my odds are 50/50.”

He then asked the king, “Sire, may I rearrange the balls in the urns to improve my chances?”

“As long as neither urn is empty, you may do as you please,” the king replied.

Quickly, the prisoner rearranged the balls so that his odds of living increased from 50% to almost 75%. What did he do?

I have given both these puzzles to students I work with and both actively engaged them. They refused to give up and didn’t want to be told the answer, even when we were running out of time. I’ll give you a week to solve them before I give the answers. Send your solutions to davega@eimath.org. The first person to solve both correctly will receive a math game. Enjoy!

Dave Gardner

Mathematician in Residence


“Allergic to Algebra?” Give me a Break!

Published on September 19 2011

One of my colleagues at Explorations in Math brought to my attention an online petition that I’d like to share with you. You have probably read or heard about the tee-shirts JC Penney was selling for a while. Aimed at girls, the message on the front, surrounded by hearts and flowers, read, “I’m too pretty to do homework so my brother has to do it for me.” This offensive message, focusing on a girl’s looks while at the same time disparaging school work, prompted an outraged public to demand that JC Penney stop selling the tee. Now there’s another anti-math tee-shirt being sold, this time by Forever 21. The front of this tee reads “Allergic to Algebra.” Again, it’s being marketed to girls and young women. These messages only perpetuate the current alarming statistics around girls and math that a recent University of Washington Study reported.  CREDO pulls no punches in its condemnation of these shirts:

“Sexist slogans like these play into and perpetuate the incorrect stereotype that women are innately bad at math or being pretty is more important than being smart. By selling these shirts, the stores give their implicit support of these stereotypes to convince girls that, to be stylish and fit in, they must be bad at math or less interested than boys in academic achievement.”

If you agree, I urge you to read more and sign the online petition here.  I did.

Dave Gardner

Mathematician in Residence

Memorizing? Or Knowing?

Published on September 12 2011

We’ve all heard the phrase “drill and kill.” This refers to the unreasonable and constant emphasis on having students fill out worksheet after worksheet of math problems (and always using the standard algorithm), of insisting on rote recitation/memorization of basic math facts, and, because it’s a “drill,” insisting that it be done in absolute silence. If we want to make learning as difficult and unpleasant as possible, surely, this is the way. It contravenes all we know about how to work effectively with our students. Let’s look at these practices one by one.

First, worksheets. Why do we give our students so many worksheets with the same kinds of problems, for example, 25 multiplication problems? Once they’ve completed a couple of these successfully, they’ve shown us that they know how to do them. What’s the point of the next three, four, or half dozen worksheets with the same kinds of problems? Shouldn’t that time be put to a better, more productive use?

And those basic math facts? Unquestionably, if our students do not know them, they will get nowhere in math; knowing them is critical. But, did you notice the subtle change of wording? There’s a big difference between ‘memorizing’ and ‘knowing.’ A parrot can memorize basic facts but obviously doesn’t ‘know’ them. We want our students to know them, and that means not just memorizing 4 x 6 = 24 but also understanding why that is so. When they know the why, then the how makes more sense and is easier to learn.

Finally, do we really want our students working in absolute silence? Well, yes, but only sometimes. Testing, for example, or those occasions when we want to know if students can do the work unassisted. Other than that, our students gain much from working together on a common problem and having a mathematical discussion around that problem. Of course it’s going to be noisy, but it’s what I call “productive noise” - students are on task, talking about their work, learning from each other. This is a much more relaxed atmosphere and far more conducive to learning, rather than memorizing.

Dave Gardner

Mathematician in Residence

The Influence of Test Scores

Published on September 1 2011

As we at EIM talk with our different constituencies, there are questions that come up regularly. These are thoughtful questions from people interested in our success. Starting with this post, I’ll be addressing these questions regularly here in Math Matters. I hope you will take the time to respond and to ask additional questions. This kind of dialog helps keep us focused and open to possible changes. Here’s the first question, and it’s an important one:

Why are we seeing no changes in math test scores in the schools where EIM has a presence? How do you know your work is making any difference?

There are two reasons for this. First, there is no way to tease out any impact Explorations in Math has on test scores; they are dependent on too many variables ranging from overall attendance, parent/family support, socio-economic status, self-esteem, and quality of instruction to more child-specific factors: Did the child sleep well the night before? Is she not feeling well the day of the test? Is she coming to school stressed for whatever reason? Did she skip breakfast?  Was she absent when, for example, fractions were introduced? To isolate EIM’s impact would require a longitudinal study involving several schools, something we’re not equipped to do at this point.

The second reason is that, while we believe our work does have a positive influence on test scores that is not our mission. Our mission is to work with schools to help establish a sustainable math culture – to transform beliefs, behaviors and attitudes around math. Let me illustrate.

Six decades ago Rudolf Fleisch published his ground-breaking book, Why Johnny Can’t Read. That book ignited a literacy movement across the country that resulted in creating a strong culture of literacy in schools. Some of the signs of this culture are extensive professional development, literacy specialists and literacy teams, family reading nights, leveled reading books, reading assemblies, book fairs, distribution of free books, and, of course, a well-stocked library with a professional librarian.

This culture of literacy is so pervasive, none of us even think about it. But if we were to try to cut back on any of these activities, there would be strong opposition.

Now look at math. What have we done to create a culture of math? Nothing. On the contrary, as I’ve noted in previous blogs, we’ve turned math into drudgery, into “an impenetrable swamp of disconnected procedures, rules, algorithms, facts, formulas and definitions.” This is where EIM comes in. If we can help schools and families build a sustainable math culture, one where math is seen as important as reading, where teachers are confident and competent in their teaching of math, then we believe it’s inevitable that our children and our students will develop an understanding and appreciation of math, will discover the joy and the beauty of math, just as they have for reading. This will go a long way to improving test scores.

Dave Gardner

Mathematician in Residence

Explorations in Math

Hands On!

Published on August 25 2011

Children, young children in particular, need concrete, hands-on experiences to help them understand mathematical concepts by moving from the concrete to the representational to the abstract. This means using manipulatives both at school and at home. A child who plays with blocks or Legos®, for example, is developing spatial-mathematical intelligence. Pattern blocks introduce the child to geometric shapes and patterns. Interlocking cubes help a young child learn to count and an older child to better understand fractions. For very young children, filling different size containers with water helps them understand ‘less’ and ‘more,’ ‘bigger’ and ‘smaller.’

There are so many things that can be used as manipulatives. Beans, toothpicks, small candies, and buttons, for example, can help younger children to understand the concept of “number” and provide experience with counting, comparing, sorting and classifying. Coins can be used to teach about money, counting, adding and subtracting. Measuring cups are useful for a child learning fractions. And, of course, an added benefit of manipulatives is that they engage children by making it fun and we want our children and our students to be engaged in the mathematics they do, at home and at school.

I suggest reading Scholastic Magazine’s post on manipulatives, explore this interactive site for virtual manipulatives for all grade levels and visit Math Playground for more math fun.

Dave Gardner

Mathematician in Residence, Explorations in Math