Wednesday, November 16, 2011

Math on My Mind: Does this compute?

Math is on my mind this week.  In particular, computation methods, or algorithms - the fancy term mathematicians use.  No matter what grade I have taught students always seem to struggle with some computation methods.  When I taught fourth grade it was long division.   For my second graders, it's subtraction with regrouping, especially across zeros.  Addition with regrouping isn't so bad, but when we get to subtraction they hit that proverbial wall.

The purpose of algorithms should be to provide students with quick and efficient methods for computing.    Simple.  Painless.  Success for all.  When I am spending months teaching the standard method and I still have many students that can't perform the method consistently then I begin to think maybe I need to change my teaching.  

Over the years I have explored some non-standard methods, or I should say, methods that don't appear in most U.S. math textbooks.  It seems to me that the math textbook publishers are determining how we teach math in this country.  Just because the textbook teaches it one way doesn't mean that is the best way, or only way to teach a skill or concept.  My goal is always to find ways that work for my students.

When I taught 4th grade I taught my students 2 different methods for multiplication.  The traditional method and a method called Partial Products.  When I polled my students asking their preference the results were split down the middle.  I like to give my students a choice.  I want them to be active learners and find what works for them.

Now as I teach second grade my 3rd grade colleagues tell me that second graders don't remember how to subtract when they get to third grade.  This does not surprise me, because there was always a good amount of fourth graders who struggled with subtraction computation.  So, last year I decided to experiment with other subtraction methods I had learned about over the years.  I taught my second graders the Trade First method.  I like this method for several reasons.  First, it allows students to work from left to right, which is usually more natural for them.  Second, it is not that different from the the traditional subtraction algorithm.  Finally, I like this method because it works for ANY subtraction problem, even subtacting across zeros!

Trade First Subtraction Method

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This year I plan on teaching both the Trade First and standard methods.  My goal is to get my third and fourth grade colleagues on board because it doesn't help if my students aren't allowed to use the method of their choice after they leave my classroom.

Do your students struggle to learn computation methods?  Have you tried teaching alternative computation methods?  I would love to hear your experiences.


  1. We learn MANY different methods for subtraction and addition. I do show the standard algorithm at the end if a student does not show it as we discuss strategies. I love other methods because I feel like the kids have more understanding of the whole number. It is too easy for the students to turn addition and subtraction into single number problems. Example: 62 - 49
    One strategy we use is to use an open number line. 49 to 50 is 1, 50 to 62 is 12 so the difference is 13. Traditional would say trade a ten for ten ones. Now you have 12, take away 9 equals 3, then most kids say now I have "5" take away "4" which equals "1". See the difference in using the true number? :)

  2. Miss McLaughlin,
    Yes, I agree. Giving students a chance to develop strong number sense is so important. I spend a lot of time with mental math strategies before I go into standard algorithms. I love when a student explains their own methods for computation! Each year I have a student who describes your open number line method! When students "invent" these methods I usually name the method after them. "So lets all use Serena's method to solve this problem." Thanks so much for sharing your math thoughts!

  3. I am so glad I stumbled upon your post... I teach students with LD and memory challenges, so I LOVE having different strategies for the kids to choose from. I haven't heard of this before, but I can't wait to show my kids. I also love the number line strategy from Miss McLaughlan!
    I am your newest follower :) Stop by and check out my site if you have a chance!
    Learning Outside the Box

  4. Hi CK,
    I am so excited to have some followers and that my post about alternative algorithms will help your students. The Trade First method is successful because you don't have as many steps to remember. Anything with a visual aid, like the number line method always helps kids understand the concept or skill! Sometimes grown-ups forget how difficult these skills can be when we are first learning them. I also have some alternative multiplication and long division methods. Of course, we don't use them in second grade! Maybe I will do a post about them in the future.