Wednesday, February 3, 2016

Subtraction Strategies in grades 1 and 2, and how they impact learning in the upper elementary grades.

Subtraction is the first nearly universal struggle math learners stumble upon in the early elementary years, before division, fractions, and eventually algebra.  It doesn't work like addition, it is not commutative (i.e. the turn-around rule does not work in subtraction), the answer is called the "difference" (confusing word in math), and we use about ten different words to represent it (minus, take away, subtract, minuend/subtrahend, how many less, decreased by, how many left over, how many fewer,  how many more, what is the difference, etc!).

By the time students reach third grade, they have been introduced to a variety of different subtraction strategies (see grade 2, unit 3 for a list), but as the authors of the Everyday Math units tell us, we should not expect every student to be able to master every subtraction strategy.  Students are introduced to subtraction in kindergarten, and practice only basic subtraction in first grade.  By the end of second grade, they should have tried all the strategies introduced, and they likely will have latched onto a couple.  In third grade, we really want them to be considering strategies to use beyond counting on their fingers.

Third grade involves a lot of subtraction practice in units 2 and 3, where your students should be "building their understanding of place value to develop methods for subtracting 2- and 3-digit numbers." (<-- from the Mathematical Background: Content section in the grade 3 TLG)  Here, expand-and-trade takes front and center as a major algorithm for students to practice and use.  This is an important piece of their understanding for future computation and problem solving, and really tests their understanding of place value.

It is not intended to be an algorithm they latch onto for life; expand-and-trade is like training wheels for the more traditional vertical subtraction most adults are familiar with.  Parents may see their child struggle with expand-and-trade, and not have the faintest idea how to help them.  "That's not how I learned it," they may say to themselves, or express to you in a frustrated note attached to a homework assignment.  Unfortunately, the temptation is to just go ahead and teach the traditional vertical subtraction method instead, because it makes more sense to the adult.  But do what you can to prevent this.  Expand-and-trade is designed to slow down the steps and deconstruct the numbers so students can see precisely when they are subtracting ones, tens and hundreds.  When they eventually transition to more efficient methods, they are well-versed in what each step of subtraction represents, and are better equipped to catch their own errors when they happen and know when their answers are in the ballpark or not.  In short, they become more confident with their subtraction.

It is the confidence that we are aiming at, because that confidence carries over to the rest of their math learning.  If they can add and subtract with confidence, then learning how to multiply and divide will not produce as much anxiety.  When they can multiply and divide with confidence, fractions are less confusing and intimidating.

Subtracting numbers is one of the most important things your students will learn how to do while in first, second and third grade.  The more opportunities your students have to work on subtraction in the early years, the better they will do in the later years.  And your fourth, fifth and sixth grade teaching colleagues will really notice a difference.

Here is a link to the VLC with some resources related to subtraction:

Subtraction Resources on the VLC

Lastly, don't forget to access the Grade Level Resources option toward the bottom of the grey menu when you log onto ConnectED.  There are lots of tutorial videos and visual aides and other resources in this section that can help you provide subtraction practice opportunities for your students.  Contact me if you need help accessing these tools.

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