Teaching in the Inner City

Addition – Two students use Manipulatives and Spiderman Math

This video was taken in my class two weeks ago by a friend.  The video shows two students playing a math “game” while independently practicing two digit addition.  Using two dice (or die, I could never tell), one student rolls the “tens” while another student rolls the “ones”.  They do this twice, writing down the two digit addition problem they have created.  Then, they add using manipulatives.  Listen carefully to the boy’s think-aloud.  He actually says he “expands” the number using manipulatives.  Then, the two students add using “Spiderman” math.  Spiderman math is just a fun way of calling addition using expanded form.

Spiderman math is the scaffolding step between using manipulatives and the standard algorithm.  These two students are not quite ready for the standard algorithm yet, but they are more than proficient with manipulatives…they are in the in-between stage, thus they use both manipulatives and Spiderman math.

These students are not ready to regroup, which is the old fashion carry and borrow concept.  The next problem they do which involves regrouping, they become totally confused.  They are able to do the problem using manipulatives, but don’t know what to do even in Spiderman math.  Imagine forcing these students to use the standard algorithm immediately.  They will spend the next two to three years of their lives randomly putting a “1” on top of their addition problems.  Ask third and fourth grade teachers if this is not true.  Allowing them to first explore addition using manipulatives, then Spiderman before the standard algorithm will help them understand when and why regrouping is necessary.

Other students in the class are at various stages.  Six students can only use manipulatives, and even then, two or three are having difficulty counting.  Two students are able to add two and three digit numbers using mental math quickly and accurately because they can visualize expanding the numbers, mentally grouping the tens and ones together.  And yes, I teach them this because if they can do this, they are truly understanding addition.  They are definitely NOT adding one column of number, then moving to the next to add that column of number, which is what many teachers demonstrate to students, thinking that the shortcut will help the students get the right sum.  Yes, the shortcut will get the students to the correct sum, but it will not help them understand addition and learning how to regroup will become even more difficult.  How do I know that these two students are not simply adding one column, then the next?  I listen to their think alouds.

Our class have not started learning to regroup yet, though most of my students are already able to do it using manipulatives.

I like teaching math like this.  I use games rather than an impersonally generated sheet of problems because the students are more motivated and they have fun.  Given a choice between a sheet of problems and generating your own problems using dice, which would you have more fun with?  Here, I am also tapping into many different modalities.  My tactile students have the dice and manipulatives.  My social students have partners.  Obviously, my verbal student is talking himself through his problems.  My visual students can see the numbers using manipulatives.  What other modalities can I tap into?