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Sunday, May 14, 2017

Math in Practice: Proficiency and Beliefs

There are a few things that I always love.  Getting packages in the mail, peanut M-n-M's, and great math tasks are up there pretty high on my list of great things.  Take a look at what came in the mail.

This picture shows the fifth grade set, plus samples from all grades and publication information.
This is one of Heinemann's newest publications.  Math in Practice comes with two books: A Guide for Teachers and Teaching Fifth-Grade Math. But don't worry there's a set for every grade K-5.  I thought I would take a peek in the fifth grade set and see if it was worth a blog post.  But I have to's better than I hoped.  So instead of a blog post, I've decided to make this into a small series of posts.  Today will be Part 1, Math in Practice: Proficiency and Beliefs.  Our mathematical beliefs are so important to us as teachers, as well as to our students.  What we believe as math teachers affects the way we teach, the way we look at students, and the way students think of themselves as mathematicians.  So let's dip into the introduction of A Guide for Teachers.

What is mathematical proficiency?  This is such a loaded question and I know my answer has drastically changed over the years.  Proficiency is so much more than getting the right answers or knowing all of your math facts.  So what do we want out students to do?  Page 4 gives us a list of ten things we want our students to do.

  • Understand the big ideas  I can't even count the number of times I have taught a lesson and focused on getting my students to the right answer rather than the big idea.  
  • Create models of math ideas  Modeling mathematical ideas is not just for young mathematicians.  Our older students can use models to think deeper, show their understanding, and justify their thinking.
  • Have computational fluency  This is so much more than memorizing facts, it includes performing operations with decimals, fractions, and whole numbers in efficient ways.
  • Have a strong sense of numbers  Number sense is something we talk about a lot in the lower grades, but older students need it too.  We want them to compose and decompose quickly.  We want them to perform computations in a variety of ways, make predictions, and interpret solutions.  This all requires a strong sense of numbers.
  • Understand the math procedures they do before memorizing them  Getting to an efficient algorithm is important, but not until they have a deep understanding.  We need to allow time for students to export concepts and develop their understanding first.
  • Understand how math ideas are connected  Our students can't build on prior knowledge, if they don't see or understand the connections.  Everything in math is connected, our students need to see this.  
  • Solve a variety of math problems  Students not only need to know how to perform computations, but they need to know when to perform them.  Applying their math skills to real life situations is important.  They need to learn to use their skills and strategies in complex situation.
  • Reason mathematically  This includes analyzing, proving conjectures, and drawing conclusions.  Reasoning mathematically is so much more than getting the right answer.
  • Communicate their math ideas  The conversation is so important in today's math class.  Rich mathematical discussions can allow students to share their ideas, defend and refine their thinking, and learn from one another.  Students also need to learn to communicate their ideas through writing.
  • Have a positive disposition  I love math and I want my students to love math.  I don't remember ever having a first grader tell me they hate math.  But by the time they get to fifth grade, I'm shocked at how many kids have a negative attitude toward math. We have to change their attitudes if we want them to persevere through hard tasks, take risks, and feel confident in their own abilities.
I honestly can't tell you how excited I am about this book series.  A math book for each grade that is full of fabulous tasks and questions and holds the same beliefs I do about teaching math?  I didn't even know that was possible.  But this is it.  You can use this with whatever program your district currently uses. It's not a full math program, it's a book filled with great tasks, questions, hands-on activities and teaching resources.  I have already been using some of the fifth grade content and that's what my next post will be about, but there's a book for each grade. You can check this resource out at Heinemann.  You can also read my second post about this series here.

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