My wife (Josie) was showing me the work she is doing with her first grade students in math. They are talking about grouping tens and ones, ultimately looking to explore place value. Her activity was to have students imagine situations involving collecting groups of items, and then looking at the mathematical structure behind those groups. One wrote about how a thief had a container that could only carry 10 ice cream cones at a time, which meant that he had to leave some of the ice cream cones he was stealing from a house behind. Another talked about the Grinch stealing twenty Christmas trees at a time from a forest that had 255.
There are two things that I really like about the approach. One is that it doesn’t do the common backwards approach I have seen in elementary math programs where the math problem comes first. It seems off to asking students to add 3 + 4 = 7, and then ‘make up a story problem’ that matches this abstract idea. Here, the students are coming up with problems that matter to them, and creating organization (groups) that make sense to them. Going from abstract to concrete works marginally well at best at the high school level for developing understanding, let alone for six and seven year olds that are wrapping their heads around abstract ideas like place value.
I also really like that Josie didn’t push the students to consider only even groupings. (255 trees into groups of 20? There’s a remainder. THERE’S A REMAINDER!) Word problems are often contrived to have even numbers only to make them ‘easier to understand’ and consequently even less real world. I just thought it was neat to see that she is making her students manage that messiness from the beginning.
This is clearly different from the higher level courses that I usually concern myself with in high school, but the idea still transfers well, regardless of the level. It’s always great to see things being done right by the younger students as well.