Tag Archives: math

Not a “Math Person”? Wrong!

When it comes to math and mindset, there are two #eduheroes I refer to on a regular basis:  Dr. Jo Boaler, who is a professor at Stanford and the genius behind the YouCubed website, and Alice Keeler, who many know to be a Google wizard but also has a published book called, Teaching Math with Google Apps: 50 G Suite Activities.  You can imagine my excitement, then, when I learned that they would be presenting a session together at ISTE. (Dr. Boaler joined us through Google Hangouts).

Dr. Boaler wrote the book, Mathematical Mindsets.  Not surprisingly, it includes a foreword by Carol Dweck, the leading expert on growth and fixed mindsets.  Dr. Boaler’s main points are that we need to value the different ways that people see math and have more class discussions about math – rather than repetitive questions on worksheets. According to her research, people become proficient in mathematics when their brains have the opportunity to make connections between visual and numerical representations – not because they are born “math people.”  The least effective way to teach math is through lecture, while the most effective is with Project and Problem Based Learning.

Both Boaler and Keeler agree that we need to dispel the myth that those who can do math quickly are better thinkers than those who reason through problems.  In fact, Boaler says, “I’m unimpressed that you worked through it quickly because that tells me that you are not thinking deeply.”

Another controversial topic we all agree on – homework.  Recent studies have shown that assigning elementary students homework is ineffective.  Boaler and Keeler (and I agree) both believe that this is true for all ages, particularly when the homework is a worksheet of repetitive practice.  A better way to think about math is to do an activity like the one below, where students think about one problem in multiple ways.

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When an audience member asked about the problem of spending time on conversing about math when there is a scope and sequence to follow, both Keeler and Boaler expressed the feeling that it is actually a waste of time to “plow through” topics despite lack of understanding.  In Boaler’s words, “Pacing guides are the worst evil in education.” Amen!

Keeler shared several “Googlized” adaptations of activities from Boaler’s Week of Inspirational Math, including a nice Slides template for the Four 4’s challenge which includes links to individual slides for students to explain their work.  You can find links to more of Keeler’s templates in her presentation here.

Overall, I was so energized by this session that I was tripping over my words when I debriefed with my colleagues that evening.  I had stayed later just to attend this session, and it was definitely worth my time.  Thank you, Alice Keeler and Jo Boaler!

I want to close this post by helping Alice Keeler to honor her book’s co-author, Diana Herrington, a passionate math teacher who recently passed.  You can read more about Diana and her influence on Alice Keeler here.   One of many great quotes from Diana Herrington on Twitter collected by Alice Keeler is, ““I teach students not math.”

Clothesline Math

Chris Shore is quick to note that he did not invent Clothesline Math.  However, he is the author of the Clothesline Math website, and producer of many of the materials on the site, so I think he definitely deserves some credit!

When I first ran across this site, I was a bit dubious of the value of a Clothesline Math activity.  Basically, the teacher gives out a set of number tents to students, who then must hang them on a clothesline (which represents a number line).  However, once I watched Shore’s video explaining how he introduces Clothesline Math, I realized how this seemingly simple activity could really start some incredible math class discussions.  There are many decisions students need to make when they determine what benchmarks to use on the numberline, the order to place their numbers, and the amount of space in between.  Even with a set of 3 fractions (1/2, 1/3, and 1/4), you could take up an entire class period.

Shore provides different sets of printable numbers (from various math disciplines) and an answer document on his site.  Of course you can DIY with your own supplies and number sets based on whatever you are studying in math class at the moment.

I like the idea of students reasoning through this, and having to justify their responses.  It can also be a great visual and kinesthetic activity that will be much more meaningful that choosing from multiple choice answers on a worksheet.

For more intriguing math sites, take a look at 15 Math Sites That Won’t Make You Fall Asleep.  Let’s get our students excited about math!

clothesline
image from: MaxPixel

Robert Kaplinsky’s Real World Problems

Robert Kaplinsky uses images from everyday life to pose interesting math challenges for students in Kinder through high school.  You can choose problems by grade level on his site, or you can look at this spreadsheet that identifies the Common Core Standards covered in each problem.

Questions like, “How Many Combos are there on a Coke Freestyle?” are sure to elicit curiosity from your students.  Kaplinsky shares the image, a challenge, questions to be asked by the teacher to encourage discussion, and background information regarding the facts and the math related to each image.

Robert’s site inspired me to look for some other free images that might spawn some intriguing math questions, and I found this one on Pixabay:

sea-shells

Can you think of math questions for your own students that would correlate to this picture?

By the way, I’ll be adding this to my, “15 Math Sites that Won’t Make You Fall Asleep” post – which will actually make the current number of recommended sites 17 at this point 😉

PBS Cyberchase Games

When my Kinder GT class learns about “Scientist Thinking” and classification, I like to use a PBS Cyberchase Game called, “Logic Zoo,” which helps them to understand Venn Diagrams.  You can find that game, and other fun math problem solving interactives for elementary and middle school students on this page.  (You need Flash to play these games, so they probably don’t work on mobile devices.) In addition to “Logic Zoo,” I love, “Pour to Score,” and, “Cyberchase Squares.”

The games are many different levels, so make sure you test them out before assigning them to your students!

Logic Zoo
Screen Shot from PBS Cyberchase game, “Logic Zoo”

Frog Jumping

Gordon Hamilton is the amazing mind behind one of my favorite math sites, Math Pickle. (For a list of interesting math sites, check out this post.) Numberphile is an awesome YouTube channel for anyone passionate about math.  So, when the two collaborate, you know that it is going to be good.  “Frog Jumping” is one of Hamilton’s recent math challenges featured on Numberphile. I would definitely invite your students (probably 3rd grade and up) to try each problem he poses throughout the video – pausing for them to make their attempts. As for his final frog-jumping challenge, I may have to take him up on it, although it’s hard to imagine that I could solve something that eludes Gordon Hamilton!

Frog Jumping
screen shot from “Frog Jumping” video by Gordon Hamilton and Numberphile

15 Math Sites That Won’t Make You Fall Asleep

My students, especially my 4th and 5th graders, love math challenges.  If I can, I find ones that don’t show the answer so we can all try to figure them out.  I think it’s good for the students to see me struggling (and I really do!), and how I handle frustration over particularly devilish problems.  Last week, my 5th graders and I spent a good 30 minutes on this “easy” problem on Steve Miller’s Math Riddles page. (Technically, they had an excuse since they hadn’t exactly learned the math skill needed to solve the problem – yet.)

If you are looking for some unique math problems that will feel more like brainteasers than standardized test practice, here are some sites that I haven’t mentioned before:

And here are some that bear repeating (*sites include activities for primary grades, K-2):

With more and more articles coming out every day about the importance of modeling a good attitude toward math (like this one and this one), it seems kind of as simple as 1+1=2 to come to the conclusion that the people who have fun doing math will be more inclined to do it more often.

UPDATE 4/26/17 – I can’t believe I forgot to include this one: Estimation 180. So, there’s a bonus for you!

UPDATE 5/8/17 – I may have to change the title of this post soon because I keep finding more great sites!  Here is another one: Robert Kaplinsky’s Real World Problems.

polyhedrons
image from: fdecomite on Flickr

The Hidden Secret to Understanding the World

In my 4th grade gifted and talented class, the students study masterpieces.  In addition to masterpieces of visual art, we talk about literary, musical, and even mathematical masterpieces.  When I saw the title for Roger Antonsen’s TED Talk, “Math is the Hidden Secret to Understanding the World,” I thought it might fit in well to the mathematical masterpiece section.  Little did I expect that it would tie everything together that we had discussed all year.

I should mention that this year’s 4th grade class has some very passionate mathematicians in it.  They worship Pi, see Fibonacci in everything, and sit on the edge of their seats whenever I mention that a math activity is imminent.  But I wasn’t sure they would find Antonsen’s talk as revolutionary as I do.  I was willing to overlook the mathematical examples that were over my head in exchange for appreciating the bigger picture, but would they?

Fortunately, Antonsen’s visualizations managed to maintain their focus, and even their awe at some point, as he gradually brought his audience around to the idea that mathematical equations and representations are actually different perspectives (a few heads raised a bit whenever he said this word, as we regularly talk about multiple perspectives).  The “a-ha” moment, however, was when Antonsen said this, “So let’s now take a step back — and that’s actually a metaphor, stepping back — and have a look at what we’re doing. I’m playing around with metaphors. I’m playing around with perspectives and analogies. I’m telling one story in different ways. I’m telling stories. I’m making a narrative; I’m making several narratives. And I think all of these things make understanding possible. I think this actually is the essence of understanding something. I truly believe this.”

There were audible exclamations in my class when the word, “metaphor,” was used.  We started the year by learning about figurative language.  And the concentration in 4th grade in Texas is on Writing as it is tested at this level for the first time.  So, looking at math as a way to tell stories and show different perspectives really captured the attention of my students.

I often tell my students about my childhood struggles with math, how I was often congratulated on my writing skills but made holes in my math assignments due to all of the erasures.  It wasn’t until high school that I had a few great teachers who taught me to love math and helped me to see that my only obstacle had been my own fear of the subject.

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from Roger Antonsen’s TED Talk

If I had seen Antonsen’s TED Talk when I was in 4th grade, things could have been different for me far sooner.  Instead of feeling like math divides people into those who can and those who can’t, I might have realized that math is actually the language that brings us all together.