Stop Using Base 10 Blocks to ‘Teach’ the Algorithms!

Add-Subtract-Place Value | 16 comments

The book study over at Math Coach’s Corner on the book Teaching Numeracy: 9 Critical Habits to Ignite Mathematical Thinking by Margie Pearse and K.M. Walton is in full swing.  Below are my thoughts for the week (Critical Habits 3 & 4).  If you want to join in, all you need to do is start reading and post comments on her blog posts for the book study:

Habit 4, Represent Mathematics Nonlinguistically, really piqued my interest with the discussion of using the Concrete-Representation-Abstract model because too often we use the concrete manipulatives incorrectly.  Heibert (1997) encourages us to let the students make sense of tools (and manipulatives) for themselves.  There is no meaning within a manipulative, they can represent anything, but we force a meaning upon them for our students.  Then we use that meaning to teach students a way to solve a problem.  Take for instance Base 10 Blocks, in early elementary we use them to represent the numbers 1, 10, 100, and 1,000.  Then as kids start working with decimals, we tell them the block that used to be 100 is now worth 1…the blocks can be whatever we want them to be, but we force the meaning onto the manipulative.

In my week-long PD trainings, I show a video from the CGI (Cognitively Guided Instruction) group that shows a young boy solving a problem using cubes, however he uses some of the cubes as a ‘marker’ to notate each bag within the problem.  Every time I show the video there is an audible gasp when he places them because everyone assumes that when he goes back to count to determine his answer he will mistakenly count the cubes he used to mark the bags.  What is so intriguing to the teachers is that the boy does NOT count them.  I believe it is because he made sense of the tools for himself; he knew which cubes represented cookies and which cubes represented the bags.  We need to let students decide how to use the tools and manipulatives they have, instead of us telling them how they should be used.

Let’s revisit Base 10 Blocks, most textbooks use them to show kids how to do the algorithm.  But the algorithm is only one way that you can use them.  Let’s say we are subtracting 51-29.  If I start modeling that problem with Base 10 blocks, the U.S. traditional algorithm is the last way I would use them to solve the problem.  Here are some ways kids could potentially use Base 10 Blocks to solve the problem if we would let them decide how they wanted to solve the problem (Just an FYI, these images were all created using the Number Pieces app by The Math Learning Center and cropped using the Skitch app):

Base10_Block_Subtraction4

51-29 is commonly solved by subtracting 30, but then many kids, and adults, don’t know what to do next. Do you add or subtract that “extra one”? Using Base 10 Blocks or a number line can help kids understand that they took away one more than they should have so they need to put one back in.

Base10_Block_Subtraction5

When the numbers being subtracted are close together, some kids find it easier to just add up to find the difference between the two numbers.

Base10_Block_Subtraction3

Kids often like to decompose the number they are subtracting to take it away in friendlier chunks. This strategy can easily be done with Base 10 Blocks and on the number line.

Base10_Block_Subtraction1

Some kids like to take the 29 away in easier pieces and they see how easy it is to take the 9 away from a full 10. Then they put the extra blocks together to get their answer. This is a precursor step that some kids do before moving to the ‘algorithm.’ Kids don’t see the sense in combining the 10 and 1 to make 11 and then take 9 away, when they can just take the 9 straight from the 10.

Base10_Block_Subtraction2

This is what we teach kids to do with Base 10 Blocks when subtracting; break one of the 10s apart to get enough 1s to be able to subtract 9. However, this is the least intuitive way for kids to use the blocks.

 

Are there other ways that you have seen kids use Base 10 Blocks to solve a subtraction problem?  Or are you seeing kids only using them to model the traditional algorithm?

 

 

Hiebert, J., Carpenter, T. P., Fennema, E., Fuson, K. C., Wearne, D., Murray, H., et al. (1997). Making sense: Teaching and learning mathematics with understanding. Portsmouth, NH: Heinemann.