Wednesday, November 5, 2014

How much does the sequence of topics matter in Math?

I've always thought that place value concepts separated students who really "got" math and those that didn't.  Unlike learning algorithms for multiplication or long division which can just be memorized, place value really tests a child's basic understandings about the meanings of numbers.  And while I haven't used one in about 8 years, in every Math textbook our school district has ever purchased, place value was Chapter one in the book.  This always made sense to me since place value is such a foundational concept for understanding Math.

However, the new Pearson Envision Common Core edition has flipped the script on sequence of instruction a little bit.  

It lists the first 4 topics in 4th Grade Envision Math as:
  • Topic 1: Multiplication and Division: Meanings and Facts
  • Topic 2:  Generate and Analyze Patterns
  • Topic 3:  Place Value
  • Topic 4:  Addition and Subtraction of Whole Numbers 
  • Topic 5: Number Sense: Multiplying by 1-Digit Numbers

The sequence of topics made me scratch my head a little bit.  An explanation of the choice for this sequence is probably buried in the documentation somewhere, but couldn't find it easily.  So, I'm left to wonder why they decided to place multiplication concepts ahead of addition and why place value has suddenly be moved to third.
Where my books are stored for
occasional use

As I confessed earlier, I never use the Math textbook. This is no slam on Envision, as I think its easily the best math series we have purchased as a district.  I do use some of the worksheets and center activities from time to time and will use the online tools on occasion. But other than that, the student books remains on my shelf.  Knowing the cost of the book, I feel really guilty about that. But I believe that the textbook is not a tremendously effective instructional tool.  When I started teaching, the Math manual was very useful to me to help plan my Math lessons from day to day.  It was common to assign questions to be completed on loose-leaf paper from the book.  But after having four Math series and buying and creating so much of my own math "stuff" over 20 years of teaching, I really don't need it anymore.

And though I use the textbook as a general guide, I rarely follow the sequence of the topics/chapters in a Math series anyways.  Other than a few exceptions, the sequence of the topics is not as important as the sequence of your daily lessons in my opinion.  For example, I used to teach a unit on graphing (topic 17  in the book) right after addition and subtraction (second).  Why? I taught it there for a couple reasons.  First, it tied in well to a lot of the graphing that we did to show results of Science experiments.  And second, it gave my students more time to gain mastery of their basic multiplication facts that they needed to learn before we started to multiply greater numbers.

All this being said, you could probably ask ten Math teachers and get ten different opinions on the best sequence of instruction.  So, if you'd ask me: does the sequence of instruction matter?  I'd answer, if it does matter, it's not much.  What matters most is building upon the student's current understanding each day and making connections between new and old concepts a little bit at a time.

So what do you think?  Feel free to leave your opinion in the comments below.

This is a personal blog, so it should be assumed that I could preface everything I say with the phrase "in my opinion."  Feel free to agree or disagree (respectfully) if you like in the comments section.

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