Sometime in the last six months I started referring to mathematical equations as ‘math sentences’, since they convey meaning just like English sentences. This convenient little explanation lead us down an interesting road this last week, as we compared the structure of sentences in both English and mathematics…
In both their ETC and Singapore books in the last few days, the girls serendipitously were asked to ‘fix’ sentences, in both English and math, that had been scrambled. This lead to exploring a problem solving strategy: identify what goes first and last, then fill in the middle.
In sentences in English, we put a capital letter first, and a period last. Addition and subtraction sentences use different punctuation, like the ‘=’ sign goes before the last number, and operational symbols (like ‘+’ and ‘-’) go in between the other numbers. We discovered that when unscrambling English sentences (where the final period gets attached to a word, for sake of clarity), proper names got confusing, since then one would have more than one word starting with a capital letter that could be a contender for First Word. (Non-proper noun words with capital letters were eventually declared to be ‘obvious’.) We haven’t gotten much beyond “action words are verbs, things are nouns yet, so subject/object and sentence diagramming aren’t on the agenda at this time.
In math sentences, one had to decide first if one was doing addition or subtraction. In addition sentences, the biggest number came last, and it didn’t matter what order the other numbers were in, whereas in subtraction sentences, the biggest number had to go first, but then, again, the other numbers didn’t matter, as it would be a correct statement either way. (Yes, I briefly explained negative numbers. We aren’t going there yet, but this way they at least know that they are learning a ‘for now’ rule, which I’ve found helps cut down on black and white thinking in the long run.)
I would like to be able to say that this was one of those brilliant spontaneously constructivist moments, but although I didn’t plan for these connections, I did seize them when I saw them, and guided their thinking. Sure, this all sounds really obvious to those of us who are literate in both English and math, but for my girls, who are also (wonderfully!) becoming increasingly aware of both their cognitions and their problem solving approaches, it was deemed pretty darned cool.