Book Study – Mathematical Mindsets Chapter 4

Oh, this book!  It is challenging every thing I’ve ever (thought I’d) known about teaching (and learning) math.  And I love it SO very much!  I stop after every chapter so that I can really process the information and write each post, but IT’S SO HARD!  I just want to read straight through to the end.

So…  Go get this book.  Now.  Read it.  You’ll be a better teacher for it.

Traditional math teaching focuses on procedures in isolation and perfect examples to illustrate math concepts in textbooks.  Not only is this not how real math works, but it isn’t the best way to teach or help students learn mathematical concepts.  This chapter explains best practices for helping students to learn number sense and math facts.  There’s also a game-changing section on math practice.  (Pure gold, people.)

My Big Takeaway
I’ve done everything wrong.  Memorizing math facts?  Wrong.  Dozens of practice problems?  Wrong.  Math fact fluency?  Wrong.  Teaching math conceptually and giving students opportunities to work flexibly with numbers achieves all of what we’re looking for without stressing out our students and making them hate math.  And?  It helps them to learn math BETTER.

My Three Favorite Quotes (and how they’ll affect my classroom)

How often do you see this?  I’ve always thought that the kids that struggled with math needed those basic skills to be able to do the “harder” stuff.  WRONG.  Everything I’ve been doing for those kids has been wrong.  I’m sorry, kids.  I really did mean well.  I thought I was doing the right things.

This also makes me think of how you hear of struggling schools cutting out the arts or recess or non-tested subjects.  And then those school don’t make any gains.  Taking away the beauty of learning and the world won’t inspire students to learn more or be more interested.  It makes so much sense when you put it that way, but it seems that when a child struggles, we (or at least I) have always tried to break it down into the simplest possible “solution”.

So…now what?  I need to help students see the why before the how.  I need to help them to see the bigger picture when they struggle.  I have to remember that isolating skills will NOT help them.  I need to view them as a child who is trying to understand the world and not as a set of skills that need to be taught.

This goes back to how we tend to break things down into their simplest forms so that students can understand them “better”.  But it doesn’t work.  Because kids only recognize an equilateral triangle as a triangle and not one that looks wonky.  The wonky one has three sides and three angles and has all the characteristics of the triangle, but kids don’t recognize it because it doesn’t look like all the perfect examples we’ve given them.  While providing our students MULTIPLE and VARIED examples, it’s also best practice to give them non-examples so that they can solidify the characteristics we are trying to teach.

So…now what?  I want to make sure that I am showing a true picture of what I’m teaching and not just making it simple and easy for them to grasp.  I’m not doing anyone any favors by “dumbing it down”.  So…wonky triangles (and pentagons and hexagons and all shapes for that matter) are welcome.

I’ve always thought that teaching students specific strategies and types of problems would help students to really understand problem solving and lock those strategies into their brains to pull out whenever needed.

But in the real world?  True problems don’t have a canned answer.  We often have to combine ideas from previous problems we’ve solved and use them in new ways.

So…now what?  I’m not honestly sure!  I absolutely adore what I’m learning from this book, but I’m still not sure how to practically apply it when planning my lessons.  I’ve been exploring the website for ideas and have found some good ones, but I’m on the hunt for anything I can find.

Final Thoughts
It is so easy to read these ideas and love them and so very hard to truly change your practice.

For example…
First, some background:  For the past few years, my team and I have done a “Keeping Skills Sharp” routine.  Our students do a few practice problems every day that are generally review, and then once per week we give them a test on those skills to see if they know them.  This year we did some revamping because we had been using a purchased product and it didn’t always match our pacing guide.  We plan to tailor or students’ practice to our current skills and review skills as needed or for maintenance.  A super improvement, right?  Totally!

So…today was the first test.  We’d only done some review from last year to get kids into the routine.  As I was grading them, it was SO hard not to write WOOHOOs and WOWs and LIKE A BOSSES on the 100% papers.  Yay!  They understand the skills.  But didn’t we say that mistakes grow your brain?  And that we should celebrate mistakes and NOT getting everything right?  We had practiced five IDENTICAL types of problems each day of the week and then given them an IDENTICAL problem on the test.  Didn’t I just read that that is NOT best practice?  Didn’t the kids just do EXACTLY what I’d asked them to do?  And I’m not supposed to celebrate it?  I’m having a crisis over something that I had, up until a few minutes ago, been looking at as an improvement in my teaching practice.  HELP!

I don’t exactly know how to meld my new learning into my current practice, but I’m open to trying.  I’m excited and nervous and slightly terrified of this new adventure.  Who’s with me?


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