This is just another post about grades, feedback and “good” math questions. I’m at a loss, so feel free to dive in. The context of this post is about providing students with one or two rich open ended math problems instead of quantities of more of the same. You know, textbook work. Please consider the following (sings Bill Nye theme):
So I wonder: until we have a major assessment and evaluation reform, prompting math questions will not be the norm as prompting questions are difficult to evaluate? When I say “prompting” I mean rich, open ended math tasks instead of the quantities of repetitive questions where a small number has changed but the procedure has not.
The math lesson formula – Question, Example, Solution, Practice, Practice, Practice – where we tell students what strategies to use – is quite structured and easily falls into a rubric category. It’s a safe go to, parents understand it and we can quantify it with a numerical value. Besides, the textbook follows this procedure. I am curious about the use of levelled rubrics when so many teachers have to assign actual percentages come report card time.
I also wonder why we look to changing math questions first, rather than how to evaluate them. If we never give a primary student a level 2, will they always approach rich tasks with an open mind rather than the “I’m no good at that” mindset? After all, can’t we “assess” without giving a grade?
Why is it OK to give one open ended prompt in English class?
“Why do you think_____. Use details from the text and your own ideas to support your answer for a final mark out of 30.”
Could you imagine: “What is the surface area of this bizarre meteor. Explain your mathematical reasoning and thinking to justify your answer for a final mark out of 30.”
How can we move away from teaching strands in isolation to giving rich problems? I’m all for the “Rich Problem” instead of “Math Topic” approach but this requires the teacher to have an incredibly firm understanding of their curriculum so they can assess and evaluate it when they see it which isn’t always easy.
Markbooks are in structured rows and columns and gaps provide levels of discomfort. Isn’t it much easier to teach isolated strands and “tedious” math questions? I’m not sure we have evolved passed the “fill the mark book” mindset. If that’s the goal, how many rich probing math questions will teachers give?
If we continue to provide rubrics, even great ones, won’t there always be minimum and maximum limits to learning?
If we have to provide grades, won’t we always need concrete evidence on a levelled numerical scale rather than an open ended unbiased solution?
If we focus strictly on feedback and provide open ended problems with various methods of solving them, will we improve the mathematical “literacy” of our students? Don’t they need some fundamental understanding of “tedious” math in order to solve rich tasks?
Without a general consensus, are we failing our students when they progress from grade to grade and from teacher to teacher?
Whose job is it to “prepare” students for what comes next?
Are we doing our best to prepare for the kinds of students coming to us?