Early in the mathematical journey, students develop counting strategies, such as synchrony, one-to-one tagging, counting all and counting on.  Many times students never move on to additive thinking.  They produce work that suggests they can add, but they are really counting.  We want students to develop the ability to think in larger chunks than one, and to be fluent in multiple relationships between numbers.

Take 57 + 5.  You can use the standard addition algorithm and line them up vertically, although that doesn’t give additional help in this situation.  You can count 57 objects, then count five objects, and then count all the objects.  It works, but it takes so much time.  We celebrate when students start to add on: 58, 59, 60, 61, 62.  Those are both counting strategies, but we need students to move to additive thinking as early as first grade.  When you can think about the 5 as 3 + 2, then you can think 57 + 3 is 60, and then 2 more is 62.

Or you could start with 55 from 57 – 2; then, 55 + 5 is 60, a nice friendly number, and then add the 2 back to get to 62.

Students need to be have additive thinking before they can develop multiplicative thinking, and then proportional reasoning.  You may already reason additively, come learn how to foster it in your students.  Or, you may be like Pam for whom it didn’t come naturally; come develop your own additive thinking and lean how to foster this in your students.

This workshop is appropriate for teachers grades 2-12.