Explorations In Math

I was in a second grade classroom the other day at the start of a math lesson. The teacher, focusing her students, said, “If I have to give you a second warning, you will not participate in math.” Wow! Never before have I heard a teacher use math as a reward, a payoff. I have seen it used as a threat and even as punishment, but this was a unique experience. That was so cool! I thought to myself, and so natural. This is how math should be treated, as something you look forward to, something you enjoy, something that will challenge and engage you. And taught properly, as this teacher does, all this happens automatically.

Now contrast that episode with this story told to me by a colleague. Her seventh grade daughter came home one day and started talking about her social studies lesson that day. At one point, she dropped this bomb: “My teacher says he hates math.” Again, I have to exclaim, “Wow!” but this Wow! is entirely different from my first Wow! What was this teacher thinking? Did he even consider that telling students that he, a successful educator, hated math gave them permission to hate math also? After all, if he’s successful in spite of hating math, why wouldn’t they be?

This teacher is helping to create and perpetuate an anti-math culture. A culture consists of beliefs, behaviors and attitudes. He believes math is something to dread, he expresses that belief in his behavior to the class, and his attitude is very clear.

All the above helps explain why Explorations in Math strongly believes that making math fun, interesting, challenging and rewarding is essential to successful teaching and learning. And the payoff for the teacher is more than just having a class of students who are successful in math. There’s that sense of satisfaction, even joy, that comes from watching kids as they work through a problem, discussing it with other students, becoming excited and culminating in that wonderful phrase we all love to hear, “Oh! I get it!”

Dave Gardner

Mathematician in Residence

One of the Seattle Times’ popular comics, Baby Blues, ran this strip recently: Hammie, the young son, is showing his list of Halloween costume ideas to his mom. “They’re the scariest costumes I could think of,” he explains. His mom reads the list: “Vampire…Zombie…MATH TEACHER?” The boy’s response is, “Long division gives me the willies.”

OK, we all need a little humor in our lives, a chuckle now and then. But the continuing harm done by comics like these far outweighs the benefits of any chuckle. If this were the only example, or even a rare example, it might be tolerable, but it’s not. Baby Blues ran another let’s-make-fun-of-math comic strip some time ago. Mom, dad, Zoe (the daughter) and Hammie are sitting at the dinner table. They’re talking about the forty-foot colon that was brought to their school for a science exhibit. “Well, not a real colon.” Zoe explains. “It’s more like a tunnel that you crawl through.” “Did you do it?” asks mom. “Are you kidding?” Zoe asks. “If you had the choice between sitting through math class or crawling through a forty-foot colon, which would you choose?” Dad chimes in, “Every math class I ever took made me feel like I was crawling through a forty-foot colon.” Another undeserved low blow to math.

I don’t mean to pick on Baby Blues but they’re two I had at hand; other strips are also guilty of eliciting a laugh at the expense of math. What are my objections? That math is so frequently portrayed as something hard and boring, something to be avoided at any cost. We never hear that about reading; on the contrary, reading is almost always presented as something fun and desirable. No one ever says they were bad at reading or that they hated reading or that they hate to read now, as adults. But for some reason, that’s perfectly acceptable, almost a badge of honor, when it’s said about math.

We need to do all we can to promote math positively and to discourage portraying math negatively for the sake of a laugh. Here’s a website with some fun math cartoons with humor that doesn’t mock math. And for more, simply enter “math cartoons” in your search engine – you’ll be rewarded with dozens of sites and scores of cartoons.  BTW, one strip that always portrays math positively is Foxtrot. Enjoy!

Today’s post is from Erin Tierney, Development and Outreach Specialist at Explorations in Math, who is blogging live from the 2012 NCTM Conference in Philadelphia.

Greetings from NCTM!  A long day of travel closed on Wednesday for the Puget Sound contingent hosted by Explorations in Math as math teachers from all over the world flew in for one of the most formative conferences in their field. The mood is light – math jokes are traded frequently – don’t let them fool you, math teachers are sassy.

The conference was kicked off by an amazing keynote, educational historian and researcher Diane Ravitch. She spoke from experience – having served as the Assistant Secretary of Education and formerly leading the U.S. Department of Education’s Office of Educational Research and Improvement. And the topics were hot – No Child Left Behind, Race to the Top and Value Added Assessments. Her resounding conclusion was that the best person to determine the success of teachers was a fellow professional – not test scores. Or legislators. Or politicians.

So, with all of the conflicting views of how to best teach our kids the question remains – where’s the hope? Where are people saying “it gets better?” As our Explorations in Math scholarship recipients reflected on this these past few days, it became clear that it’s up to us as individual communities to be the champions for our kids. To MAKE it better. To find what hope looks like in our communities. It’s working with teachers, students, parents and administrators alike to tailor a culture of change directly to our individual school environments. It’s listening to our students instead of teaching AT them, to encourage and guide them to come to conclusions and discoveries on their own. To recognize that children learn differently and foster that. To not simply GIVE them the answers, but to say “now YOU tell ME more”. Because education is not a spectator sport, and real change can inspire our kids to be champions.

This week’s post is by Michelle Gnuschke, Program Manager and Teacher at Explorations in Math.  If you are interested in the summer math camps we have in a community near you – check out our 2012 Camp Schedule and secure your kid’s spot today!

There are just a few kids that would jump for joy when you tell them you have just signed them up for a week of summer math camp.  Those kids love math.  They get it.  They thrive on challenge and are highly motivated to seek solutions to problems.  But the majority of kids usually equate a week of math camp with a week in a dark dungeon.

So how do you get a child that is less than enthusiastic about math to show up without resorting to bribery?  That’s what drove the staff at Explorations in Math when putting together our camp curriculum.  The one word answer is G-A-M-E-S.  We began by choosing a fun theme and then built in math games, activities and experiments to surround students with fun ways to explore math concepts.  Imagine learning about grid coordinates by reading and creating pirate treasure maps in Adventures in Arrghrithmetic.  How about studying geometry in architecture by designing and building the tallest and strongest possible building made entirely of playing cards and straws?  Your kids might come home and teach  YOU the historical origins of multi-cultural strategy games like Tapatan or Mancala!  These are the kinds of creative activities students explore  in an Explorations in Math Summer Math Camp.

You might ask why kids would need an academic camp in the summer.  Why can’t they just have some carefree fun for those few short weeks?  Don’t they get enough instruction in the school year?  Because these camps focus on the fun quotient and not instruction, students don’t even realize that they are learning new skills.  They are practicing basic facts while building self-confidence in math. Sure, having an educational component is a bonus. But it’s the joy and appreciation of math that really gets some polish in summer math camp.

One week this summer can inspire creativity and enthusiasm for a lifetime. That is the ultimate goal here…. to improve a student’s lifelong relationship with math. 

Michelle Gnuschke

Program Manager and Teacher,  Explorations in Math

In honor of National Volunteer week, our guest blog comes to us today from Carol Ryan, Director of Volunteer Engagement here at Explorations in Math.  If you’re interested in volunteering to create math culture in Puget Sound, please visit our Volunteer Opportunities page.

It’s National Volunteer Week and we at Explorations in Math are celebrating our volunteers.  People like Jessica Dust, Anna Menses, and Bola Agbonile.

Jessica, Anna, and Bola are members of Explorations in Math’s current Hands On Leadership (HOL) team, a Seattle Works program that matches trained volunteers to specific projects with non-profits. Our HOL team members are helping us document how to replicate our successful MathFest event beyond the Seattle area. They hit the ground running, joining us six weeks before Eastside MathFest at Lakeview Elementary in Kirkland March 24. Among the many tasks they took on, Anna turned a hand-drawn map of MathFest into a legible graphic everyone could read, Bola almost single-handedly packed snack bags for volunteers, and Jessica helped with scores of details relating to MathFest volunteer recruiting and check-in. With the successful event behind them, team members now are poring over all the various documents we use and organizing them for use by groups elsewhere interested in putting on their own MathFest.

Jessica, Anna, and Bola are just three of the more than 350 of you who continually amaze me with your contributions of time and talent to some part of Explorations in Math’s efforts to strengthen relationships with math. We are grateful for each and every one of you.

Something special happens when you give of yourself to a cause you believe in: relationships grow, a community forms, and in some small way, the struggles of the world become a bit less daunting. It’s truly inspiring to be part of a group doing just that. Thanks Jessica, Anna, Bola. And thank you.

Carol Ryan

Director of Volunteer Engagement, Explorations in Math

This week’s guest post is by Michael Smith from iTutorMaths, an online math tutoring organization in the UK. If you would like to write a guest post, please contact Dave Gardner.

‘What’s the point of math?’ is a question every teacher has faced and every parent has squirmed under when trying to convince their child to be engaged in math. It can sometimes be tricky to answer, especially when they have a sheet of equations in front of them that are in no obvious way grounded in the world we know.

The perception of math among students has always been part of a math teacher’s battle. The concepts introduced in math are often so far removed from a student’s reality that it doesn’t take  long for them to start asking ‘what’s the point?’ But a good teacher’s way of explaining math is engaging: he’s found a way of making math accessible to the students.

Explaining the point of math is a problem discussed in the book Made to Stick. The book answers the ‘what’s the point’ question by asking them to imagine a trip to the gym to lift weights or run on the treadmill. What is the point of going to the gym and weightlifting? The answer, of course, is that the muscle conditioning gained from the weightlifting transfers to other aspects of their lives. That makes it easy to see the point of weight lifting: you feel the benefit whenever that muscle’s put to use in your daily life, whether you’re playing sport or lifting a chair.

Math is mental weight lifting. The logic and analysis skills students cultivate solving math problems transfer to every other aspect of their lives, whether figuring out a problem on a computer game or splitting the bill at dinner.

Why is it that some ideas capture the imagination and ‘stick’ and some fade away, no matter how often they’re drilled into the receiver?  The authors argue that it is not simply the content of a message that defines its impact on the receiver. There are six characteristics of ideas that communicate:

• Simple – finding the core of the idea
• Unexpected – comes as a surprise
• Concrete – can be grasped and remembered later
• Credible – the idea must be believable
• Emotional – it must resonate with the receiver
• Stories – told through a narrative

If we look at the weight lifting example, it ticks each of these criteria boxes. Indeed, you think of any idea that’s ‘stuck’ in your mind, it’ll tick the majority of these

Organizations like Exploration in Math in the US and Maths Inspiration in the UK work hard to ensure the ‘math is boring’ gripe doesn’t become a self-fulfilling stereotype.

The formative years of a child’s introduction to math are crucial if we are to spark an interest that will drive them into advanced mathematics. In these early years, it is imperative we find a way of making math ‘sticky’ and capturing their imaginations.

This week’s guest post is from Ginger Warfield.  Ginger has been a passionate mathematics leader for over 30 years.  She has served on Explorations in Math’s Advisory council for the past 3 years, is a Principal Lecturer Emerita in the Department of Mathematics at the University of Washington and was the former Chair of the Education Committee of the American Women of Mathematics (AWM) and a longtime Education Editor of its Newsletters.  The blog post below is her education column for AWM’s upcoming Newsletter.  If you would like to write a guest post, please contact Dave Gardner.

In the current state of the world, it can be far too easy to focus on the troubles and dangers that beset K-12 education and be drained of energy by that bleak viewing. It was therefore a particular pleasure to me when at a recent conference of WaToToM (Washington Teachers of Teachers of Mathematics) a presentation on the Common Core State Standards (CCSS) permitted me not one but two patches of optimism. In a general effort to spread the sunshine, I decided to present them here.

The first had to do with the Standards themselves. I have been so pleased and excited about the Standards of Mathematical Practice and the way that the CCSS keep them in the foreground, that I missed another key feature. For decades now the phrase “Mile wide, inch deep curriculum” has been so firm a mantra of everyone involved in mathematics education that I have wondered how many household parrots might by now be able to repeat it. It has seemed to me, though, that any efforts to deal with it have simply produced a shuffling of the elements rather than any narrowing or deepening. The writers of the CCSS addressed this problem by standing it on its head: instead of starting by looking at everything a kindergartner should be able to take in and working their way upward, they started at the top and chose a small number of advanced concepts that any educated citizen should have the opportunity to learn. They then worked their way backwards down the levels and produced what they called mathematical progressions that led to these concepts. With those progressions established, they put in some benchmarks for when students need to arrive at specific levels along the route. In doing so, they made strenuous efforts to avoid requiring any topics, even attractive ones, that are not needed for one of the progressions. The goal — plan — hope is that keeping the requirements focused and non-bulky will leave some room for optional topics that teachers choose to teach. In any case, it will provide a structure such that teachers should be able to find out readily which concepts their students should already have available to use and which they are going to need in the next year or two. All of which has at least the potential to keep the curriculum flowing down a narrower, deeper channel. Encouraging.

For the second patch of optimism I need to drop back and throw in a little local history. Back in the 90′s almost all states, my home state of Washington included, produced State Standards. Washington then went farther and was among the relatively few that produced assessments to go with its Standards. The writers of the resulting WASL (Washington Assessment of Student Learning) took note of the absolutely central role of understanding and communicating the ideas behind the (also necessary) mathematical procedures, worked incredibly hard, and produced a test such that if a teacher successfully taught to the test he or she would indeed be teaching what the Standards intended. Unfortunately, the onslaught of No Child Left Behind loaded the WASL with stakes it was not designed to bear, and after a decade or so it wound up essentially eliminated. I was thoroughly disheartened until a conversation with a high school teacher of whom I think a world, in which she said “Yes, but all the teachers I know are teaching very differently and way better as a result of trying to prepare our students for the WASL. We’ve learned a lot!”

Now two large consortia are hard at work producing assessments to correspond to the common Core State Standards. The WaToToM presentation that I mentioned above included some emerging details about the one that Washington is heavily involved in, Smarter Balanced Assessment. Again I was already familiar with a number of key points, such as their determination to de-emphasize summative testing whose results provide information that fails to benefit either students or teachers, and offer formative and interim assessments designed to give teachers information that they can use to improve the learning of the students they have. They also plan to provide a variety of formats of assessments, including some open-ended one or two day projects that will give students an opportunity to demonstrate a very different set of abilities from those required for timed multiple choice or short answer tests (which will also be used, but in moderation.) Smarter Balanced has a long way to go, but what struck me as I listened was that if they succeed in following the path they have laid out for themselves, then they, too, will have created an assessment such that teachers who “teach to the test” will be giving their students exactly what they need, and learning a lot as they do so.

These are harrowing times, and not even my Pollyanna side can maintain that The Solution has been achieved. But despair has very few virtues, and correspondingly I feel enormous gratitude for the incredible efforts the writers of the CCSS and the folks at the Smarter Balanced consortium have put in and are still putting in. I plan to hang fiercely onto the hope they are proffering!

“Mathematics, in the common lay view, is a static discipline based on formulas…But outside the public view, mathematics continues to grow at a rapid rate…the guide to this growth is not calculation and formulas, but an open-ended search for pattern.” -  Lynn Arthur Steen, from On the Shoulders of Giants

The more I think about this quote, the more I like it. Note that Steen isn’t saying that calculation and formulas are not part of math or that they’re not necessary. I’m sure he’d agree that they are a very necessary part of math. But what drives math, he is saying, is the open-ended search for patterns.

The open-ended search for patterns. Two things strike me about this phrase. First, growth in math, whether we’re talking about the growth of the discipline itself or the growth of students learning math (which is what I’m focusing on), occurs when students are encouraged to explore math ideas, play with them, discover the underlying concepts and then apply them in practical situations. Of course they need the calculation and formulas that Steen mentions, but if we confine students only to calculations and formulas, if we don’t encourage divergent thinking and exploration, then our students will be mechanical solvers rather than creative problem solvers.

The other thing I like is his emphasis on patterns. Math has been called the science of patterns and patterns are everywhere in math, often in unexpected places. For example, take this problem I present to third graders:

Kim has 3 hats and 3 jackets. How many different combinations of a

hat and a jacket can she wear?

The simplest way for young children to solve this is with a diagram: connect the hats and coats and then count the connections:

The answer, of course, is 9. But what’s important here, and what hooks students every time, is the discovery of a very cool visual pattern. They begin to understand that math is not a morass of discrete algorithms, procedures, rules, and formulas but, rather, a unified and integrated whole that is logically consistent and makes sense to them.

Another good example of math patterns is Pascal’s Triangle:

In this triangle, if you add the numbers in each row you get consecutive powers of 2. Each row (other than the first) is a multiple of 11. If you look at the diagonals, each one presents us with a pattern: the counting numbers or triangular numbers for example. The diagonal next to the triangular numbers is a pattern where the pattern grows by triangular numbers. And then there’s the hockey stick pattern. (See if you can find it before going online for the answer.)

Finally, type in ‘Math Doodles’ in your search engine and you’ll be rewarded with short videos that explore math patterns in a delightful way. Here’s one of my favorite sites to explore.

Dave Gardner

Mathematician in Residence

This week’s guest post is from Dan Finkel from Math for Love. If you would like to write a guest post, please contact Dave Gardner.

Seattle’s first Julia Robinson Mathematics Festival is from 9:00 am to noon on Sunday, March 18, 2012 at the Evergreen School, 15201 Meridian Avenue North, Shoreline, WA. The festival is open to 4th-12th graders and their parents and teachers.

The festival features an abundance of inspiring mathematical activities for students to explore, led by mathematicians, teachers, and volunteers. These activities will range from levels that older elementary students will enjoy, to levels that will challenge the brightest high school students.

At the festival, there will be tables set up, and each table will be staffed by one or two volunteers to introduce the students to a mathematical problem or puzzle that requires creativity and exploration to solve. The activities are designed to engage students for about 20-30 minutes. The students will have an entire morning to explore a number of fascinating, interesting problems in mathematics with the help and encouragement of our volunteers.

The Julia Robinson Festival is challenging but noncompetitive, highlighting rich mathematical problems curated by adults who love math. It’s a perfect place for students who love math, games, or puzzles; for contest-goers looking to see what else math is about; or students who prefer the collaborative, noncompetitive aspects of math to contests.

You can register here.

This week’s guest post is from Steve Brugger, Board Chair for Explorations in Math. If you would like to write a guest post, please contact Dave Gardner.

A few months into 2012 and it’s already shaping up to be a big year for Explorations in Math.  My name is Steve Brugger and, after 4+ years on the board of EIM, I’ve been asked to take on the position of Board Chair. During those four years I experienced first-hand the amazing dedication and commitment of Katie Klein and then Laura Larson in the same role, so I did not make the decision to become board chair lightly. But what an amazing time to have this opportunity!

Our most recent newsletter goes to the heart of why I am so excited.  Over  the past 4 years I have watched as the EIM staff have worked tirelessly to improve each of our in-school programs, develop better measurement and effectiveness tools, increase the size and quality of our community events and build our base of corporate and community supporters.  Our goal was to build a solid foundation – a launch platform to take our message of fun, relevant and engaging math programs for elementary students to an ever widening audience.  And now, we are doing just that – growing!

In our own backyard, our success with our Seattle school partners, and on the Eastside with our successful launch into the Lake Washington School District, has gotten enough “buzz” that we are now being approached by other schools and districts that want to implement our programs to build a positive math culture in their schools.  The word is certainly getting out!

And our two pilot programs are just as exciting. In partnership with the Pacific Science Center, we are integrating our programs into their successful science outreach efforts that service communities and schools, and will be able to touch thousands of students and families throughout the state.

Our second pilot program came about in a somewhat serendipitous way.  Last year we invited Greg White, the CEO of LEARN Charter School Network in Chicago, to speak at our annual fundraiser about building a culture of success in inner city schools.  He knew very little of our work in our community but when he arrived here and saw our programs in action, he knew he had to present us to his staff.  Our team immediately won them over and just last month we launched EIM programming in the South Chicago LEARN Campus – and are planning launches in five more!

I am honored to be able to work with the staff, board and all our loyal supporters who believe so strongly in the mission of EIM – to build a sustainable math culture in elementary school communities. Thanks to you, we ARE making a difference and helping our kids to be successful in tomorrow’s world.