Math Smarts

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“Teaching is mostly listening, learning is mostly telling.”
-Deborah Meier

As we dive in to the new school year, those of us in the Olympia School district will be meeting our new math curriculum, Bridges, for the first time.  Many parents will be trying to decode the words “Common Core” in the context of this new way of teaching.  The most difficult part for many will be allowing their children to struggle with (and through) the math.  This will require us to redefine the job of teachers.  This will also force us to redefine what “math smarts” are.  Even though this may be challenging, the upside is that more kids will have a stronger understanding of math concepts and more will identify themselves as mathematicians.

The job of teachers is shifting.  No longer are we the “Holders of Knowledge” whose purpose is bestowing computation fluency upon our pupils through direct instruction.  Actually, good teaching requires just the opposite: teachers are no longer the center of the classroom.  Good teachers coach their classes to work collaboratively, provide group worthy tasks that help them access key mathematical concepts, and then retreat to observe and assess, intervening only when necessary.

The idea of being “math smart” is now outdated.  First of all, as Carol Dweck points out, it leads to a fixed mindset.  If people say that Johnny has math smarts, it leads him to believe that it is an innate power that he has always had.  You either have it, or you don’t.  Most people think they don’t.  Also, many people mistakenly place far too much emphasis on getting correct answers in math, especially in computation.  This definition must now change to show that math is a verb.  It is something that we do.  The list  of math skills must now include listening, communicating clearly, helping others, asking good questions, improving reading skills, flexible thinking, struggling, persisting, and persevering.

In our new era of “Common Core” and Bridges, the most important thing that parents can do is to avoid telling kids how to do their math.  Rather, model the curiosity and inquiry that we are asking of our kids.  Please, resist the urge to show your kids the shortcuts.  No more “this is the way I learned to do it when I was a kid.”  Instead, take the time to just listen to your kid explain their thinking.  Ask them “why?”  Who knows, maybe you’ll learn something, too.

Sources:
Carol Dweck, Mindset: The New Psychology of Success.
Jo Boaler, How to Teach Maths.
Featherstone et al., Smarter Together.

Blue Brain

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Brain research now confirms that deep conceptual learning requires making mistakes, and that the more positive we feel about mistakes, the more we can learn.  That’s because brain freeze, or what my sixth graders have started calling “blue brain” is real.  Many of my students have such an aversion to making mistakes that instead of digging into new ideas, they become paralyzed, hoping not to make a miss-step instead of trying out new ways of thinking.  I can see why. For sixth graders new to middle school the stakes are high: new friends, lockers (and combination locks), crowded, confusing hallways, five or six teachers, lunchroom rules, free time at lunch but no recess, PE and band lockers, binders, dividers and pencil pouches.  It’s a lot to keep track of and they don’t want to miss out on anything or be the focus of negative attention.  Some of them try so hard to get it all right that they have a hard time doing what they are at school for to begin with:  learning.

This year, about one third of my students tell themselves they are bad a math if they make a mistake, and more than half feel negatively about math mistakes.  If my students are going to grow to the greatest potential they need to break out of this mindset. They need to change their minds about mistakes and learn to see them as learning opportunities, even though the pressure they feel to succeed works to convince them of the opposite.

Luckily, in spite of all their efforts not to make a mistake, they are making mistakes anyway. And they don’t feel happy about it yet.  Rather than forcing them to feel happy, in our class they have started to call the uh-oh feeling you get when you make a mistake ‘blue brain.’  They got the idea of blue brain from a short BBC clip that shows the stop in brain electrical activity following a mistake as blue, and then shows the powerful mistake-fixing activity that follows as red.  The end of the video contains just fifteen seconds on the difference between positive and negative reactions to mistakes, but that was enough to support students to come up with the following list of things they could say to themselves to recover from blue brain more quickly.

  • Try harder next time.
  • Gosh I made a mistake, I’d better fix it.
  • It’s okay everybody makes mistakes.
  • I am learning.
  • Try again.
  • Keep going!
  • I’m just getting smarter.
  • Don’t feel bad, just fix it and move on.
  • That is okay!
  • Keep trying.  You know you can do it.
  • Mistakes make me smarter.
  • I will get it next time.
  • No one is perfect.
  • I’m just learning a whole new way!
  • That’s ok. It’s part of learning.
  • Now you can learn from your mistake.
  • So what?  Just fix it.
  • It’s not the end of the world.
  • You can’t learn without making mistakes.
  • Oh well, I will get another chance.
  • You can bounce back.
  • Let’s find a solution.
  • Don’t worry.
  • We can always try again.

As we enter the second full week of school, most of them aren’t yet happy to have the opportunity to fix mistakes, but at least they are beginning to have some tools and language to help themselves get back into the learning action as quickly as possible.

Algebraic Thinking

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One of the most exciting things for 5th grade students is learning about algebra. They have been anticipating this subject for some time. What’s interesting is that they have been working with abstract mathematics forever, but it just isn’t often called algebra.

When we ask: 5 x 5 = ?, this could be written 5 * 5 = X sometime early on in elementary school. This introduction to variables can be a huge stumbling block for many students. It’s really important to get comfortable with variables in mathematics early on. We can make this problem slightly more difficult by asking it another way.

5 * X = 25 or finally 5X = 25 – now we’re doing simple algebra.

This week we have been looking at systems of equations and solving for all of the variables. These are wonderful problems that help students get familiar with variables in equations.

Here is a sampling of some of the problems we have worked on. Feel free to create some on your own. As long as you have a unique equation for each variable, there will be one and only one answer.

A + B + C = 36

A + A + B = 26

B + B + B = 18

The next problem we tried was

2A + B + C = 48

A + B + C = 40

2B + A = 18

At least one class tried this one

2/5A + B = 17

A + B = 20

And most challengingly some attempted the following

2A + B + C = 30

A + 2B + C = 35

A + B + 2C = 37

 

Wow! Stanford Online Class for Kids

Check out this amazing opportunity! This would be a wonderful thing to do with your child. Professor Jo Boaler is an exceptional mathematics educator and is offering this class for free. Class starts in late May or early June and can be completed at your own pace at any time through December 2014. This could be your summer math plan…

https://class.stanford.edu/courses/Education/EDUC115-S/Spring2014/about

About This Course

How to Learn Math is a class for learners of all levels of mathematics. It combines really important information on the brain and learning with new evidence on the best ways to approach and learn math effectively. Many people have had negative experiences with math, and end up disliking math or failing. This class will give learners of math the information they need to become powerful math learners, it will correct any misconceptions they have about what math is, and it will teach them about their own potential to succeed and the strategies needed to approach math effectively. If you have had past negative experiences with math this will help change your relationship to one that is positive and powerful.