Thoughts and Policy for Building a Better Pennsylvania

Math Students: Sense Makers Not Mistake Makers

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lImage by wecometolearn CC BY 2.0

For many, if not all, students, achieving mastery in mathematics involves intense struggle. Often, that struggle is seen as a negative thing, by teachers and students alike, and becomes the source of frustration. But what if we were to shift our perspective on students as “mistake-makers” to “sense makers”? What if we celebrated the process, trials and errors and all, as much as the ability to solve a problem and get a right answer?

This perspective, students as sense-makers, is championed by math teacher David Wees. In an article in MindShift, Wee is quoted:

“I want to know the ways that they [the students] are thinking rather than the ways they are making mistakes . . . My interpretation that they’re making a mistake is a judgment and usually ends my thinking about what they are doing.”

This way of thinking is also celebrated by mathematician Paul Lockhart who writes:

Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself.

Wees says that “Kids ask questions: 1) to find out if they did the problem right; 2) because the teacher is standing near them and they can, and; 3) occasionally they ask “I wonder what if” questions, which show they are thinking about the math.” In order to help his students develop their mathematical thinking abilities “Wees took to not answering the first two kinds of questions and encouraging the third. He found himself often asking the same question, whether a student had gotten the problem right or wrong. He’d ask them to explain their answer or how they could check to see if they were right or wrong.”

To explore more about this philosophy of mathematics, check out my series on parental engagement in math. And to read about how we can turn everyone into a math person, click here.

Let’s Turn Every Child Into A “Math Person”

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Are you a “math person”? Most likely, the way in which you answer this question determines how well you understand mathematical concepts, and just as important, how much you appreciate/enjoy mathematics. But what if that is the wrong question?

What if we are all math people, at least until we’re convinced that we’re not?

A writer for an article on Quartz explains that the research just does not support the notion that we are genetically predisposed to either understand mathematics or not. Instead, he proposes the “love it and learn it” hypothesis, which is more supported by the research and which has three elements:

  • For anyone, the more time spent thinking about and working on math, the higher the level of mathematical skill achieved.
  • Those who love math spend more time thinking about and working on math.
  • There is a genetic component to how much someone loves math.

So what are the implications if this hypothesis is true? The article goes on:

If the “love it and learn it” hypothesis is true, it gives a simple recommendation for someone who wants to get better at math: spend more time thinking about and working on math. Best of all: spend time doing math in the kinds of ways people who love math spend time doing math.

if a kid has a bad experience trying to learn math in school, or is bored with some bits of math, the answer isn’t to say “Well maybe you just aren’t a math person.” Instead, it is to find some other way to help that kid with math and to find other bits of math that would be exciting for their particular kid to help build her or his interest and confidence.

Why do so many people get convinced that they are just “not a math person”? If someone has an awful math teacher as a student, it’s common for the student to associate his/her frustrations with math, rather than the teacher. Another big problem is that classroom instruction is not set up to be student-paced. The article quotes blogger Cathy O’Neil who writes:

There’s always someone faster than you. And it feels bad, especially when you feel slow, and especially when that person cares about being fast, because all of a sudden, in your confusion about all sort of things, speed seems important. But it’s not a race. Mathematics is patient and doesn’t mind.

Being good at math is really about how much you want to spend your time doing math. And I guess it’s true that if you’re slower you have to want to spend more time doing math, but if you love doing math then that’s totally fine.

Click here to read the rest of the article. It’s fairly lengthy but well worth reading.

Summer Learning Event @DemmeLearning

Last Friday, Demme Learning hosted students from La Plaza, an after-school program based in Lancaster city that uses our Math-U-See and Spelling You See programs. We gave them a tour of the office and warehouse and had stations setup where employees would share how they used math and spelling in their day to day jobs. Here are a few pictures from the visit:

Arriving!
Arriving
Justin, our design manager (in orange) and I handing out pencils
Justin handing out pencils and explaining how he uses math in designing websites
Carolyn, our marketing manager, entertains with Simon Says
Carolyn entertains with Simon Says and talks about the math used in marketing
Sindy, from customer service, hands a pencil to one of the students
Sindy talking about the importance of addition and calculating percentages in customer service
Steve, the guy from the videos who tells those punny [funny] jokes
Steve giving a tour and telling punny jokes
One of the learning highlights from the event was when I took the group to my office. Immediately, they headed over to the globe. Soon they were asking me, “Where’s Pennsylvania?” “Where’s Peru?” “Where’s the library?” and “Hey, what about Mexico?”

Looking at the globe
Looking at the globe

We finished off the tour with some cake and snacks to help everyone remember to be lifelong learners.

The cake
The cake

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Group photo!
Group photo

We had a great time hosting the students and are happy to support such a great after-school program.

Summer Learning and Local Parks

Caledonia State Park

One of my favorite places to visit during my staycation is Caledonia State Park located between Chambersburg and Gettysburg in Pennsylvania. The furnace was owned by Thaddeus Stevens. Right before the battle at Gettysburg, a Confederate raid burned down the furnace. Stevens suffered devastating financial loss but continued to pay his employees and eventually rebuilt the ironworks. You can read more about that story here.

It can be fun and educational for you as a family is to discover when, why, and how your state was formed. You can also explore how your city or town was created and who were the first people to live where you do. Teaching your children the history surrounding the location where you live is helpful not only in providing them with geographic roots but also in inspiring them to care for and cultivate their community by being active and involved locally.

Sometimes a two-hour trip to a national state park can be just as meaningful and fun as an exotic trip abroad. As you prepare for your summer, consider planning a staycation! You never know what exciting adventures lie just around the corner.

And if you’re looking for some summer fun that’s also educational, check out our new KinderTown summer camp:

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