I caught myself doing something terrible! Ok, not terrible, just really wrong. Well, maybe not wrong, but it is very common: I worked a problem out on the board and left the answer, 20, out there. All. By. Itself.
No context, no units, no connection to anything. It was just there. My co-teacher jumps in, “Is this the right answer?” The class chimes in with a chorus of yesses, but I knew it was wrong. I looked into each smiling face, one after the other, waiting for someone to notice what was missing. One of them came through for me! “It’s hours, it’s gotta say hours!”
My mistake is one we math teachers make all the time – we get the answer, the right number, and we stop there. And move on to the next problem. But, you say, there is no context, it’s just a practice problem.
Skill drill and kill…
I believe that is the all too common, and really wrong way, to approach the teaching of math. Yes, children need practice, as noted here. Numbers without context are just numbers. They tell us, and our children, nothing!
I asked my class, how many of you know how to solve the problem, do all the steps in the right order, and still get the wrong answer!” Hands hands went up, heads nodded. “Me, too,” I said.
We do the steps. We make the right moves. The answer, that mysterious, magical, right answer eludes us. Why? I read an interesting paper this morning. The premise is that students don’t lack the basic math skills, they lack the ability to apply those skills. You are sitting there nodding your heads in agreement! This is a challenge we all share. This is the challenge we must address with better questions.
The best questions are those that require students place answers in the context of the question.
Because of that moment, above, where I realized what was doing, I now purposefully ask students to give the answer to a problem in a complete sentence. I build up to it with a short series of questions – using the above noted question that produced the answer “20” as my example:
“What about the twenty hours?” The job took twenty hours.
“Why twenty hours?” That’s when the jobs would cost the same amount of money.
Light bulbs began popping all over the room. (Admit it, you are beginning to frame a possible math problem in your head right now, aren’t you?
Students began making a connection to the answer from what they did to get it. I have not witnessed such zeal for tearing into the next problem as that which was shown by those students in that moment – a moment in which they knew they could succeed.
The phrase “content is king” is attributed to Bill Gates, over twenty years ago, speaking of the Internet. That expression has begun to change, precisely because of the way people – including our students! – think about themselves and their world. It has to do with what they find relevant and worth consuming, remembering and using. Now the phrase is, “context is king.”
(Does anyone but me get the fact that the letter “x” is somehow involved here?)
“…the key to ensuring great experiences moving forward is serving targeted messaging and content at the exact right time and based on the user’s exact current circumstances, to maximize contextual relevance.” (Posted by Willie Pena on March 16th, 2015)
Isn’t that what we are trying to do as we formatively assess where each child is – to try to walk up to them as we see them struggling and ask the exact right question that will unlock the relevant information, or give them the nudge that helps the lightbulb glow, or helps the sleepy student come alive, wanting to participate because, hey, this suddenly became interesting! I realize this may not be possible in a class of 30+ students, but it is becoming MORE possible (read Pena’s post again) through technology. Games like Kahoot-it, google docs and the like for assignments, GeoGebra work posted in real-time by students, ALL of these things are opportunities for us to step in to each student with real time questions and prompts, to give immediate feedback, to create immediate and needed relevance for our students.
My next step is to take that sheet of practice problems and give it context! OR, maybe I’ll give it to my students and ask THEM to create the context: “what could the numbers in this problem be talking about?” (Ooh, I like that question! Tally-ho people, I’ve got a worksheet to re-design!!)