I love creating curious tasks for my students. I love anticipating their thinking, observing their milestones of thought, and then posing new, interesting wrinkles to sustain their problem solving. It really is what fuels my practice. Honestly, interacting with students keeps me coming back for more–day in and day out. It’s what I enjoy most about the job.
I think that’s why I’ve always hated assessment events. They always seemed disconnected from the students.
A few years ago, I came across the following multiple choice question:
Argue about the solution all you’d like (oh, and people argue about the solution), the beautiful part of this, for me, is that the question is not really the question. The point of the exercise is not to complete the exercise, it’s to dwell a while in the complexities it offers. By constructing the argument, you interact with notions of odds, randomness, probability, and the like. This is similar to the idea of #SandwichChat, where the point is not to define what a sandwich actually is, but, rather, to play with emerging definitions and consider their consequences. I love these sorts of activities, because they, almost unexpectedly, turn our own thinking upon ourselves. They have a way of snapping us out from the familiar ebb and flow of the mathematics classroom, whereby prompts are passed to solvers who manufacture resolutions and, in turn, re-sell them back to teachers at increased costs. Teachers cover this inflation by remunerating the students with a most precious commodity–grades. And so the classroom economy ticks forward.1
Since the onset of my career, I have been keenly interested in how students work together in the contexts of school. We know that students (and humans in general… actually animals in general) form collectives to accomplish elaborate tasks. These traffic jams of human interaction transcend individuality to the point where the level of activity is so dense that groups begin to synchronize into a sort of group mind. However, we have a school system built on individuality and (unfortunately) competition, and triggering these collective structures is extremely difficult in part because students know that, when push comes to shove, they will be weighed and measured as an individual.
“How do you assess this?”
This is the question I eventually field during every opportunity I get to share pieces of my classroom with other stakeholders in education–be it teachers, administrators, or pre-service teachers. I don’t mind fielding it; it is a good question, one teeming with complexities and littered with implicit values.
My department has a set of 10 iPads for mathematics instruction. I use them primarily for the powers of Desmos. When I introduce teachers to the program, they get excited about the possibilities, but are immediately worried about one thing:
I’ve tried many forms of student written reflection in my classroom. No matter the format, I have always phased them out due to the administrative details and increased time burden. I liked the idea of having students reflecting on their learning, and believe in the benefits of writing across all curricular areas. What I needed was an easy way to orchestrate the process.
This week I had the privilege of chatting with other math educators about an article written by Richard R. Skemp in 1976. We have formed a sort of ad hoc reading group built around reading classic and contemporary pieces of mathematics education research and discussing their application to our daily crafts. The inaugural meeting (so to speak) consisted of Raymond Johnson (@MathEdnet), Chris Robinson (@absvalteaching), Nik Doran (@nik_d_maths), Joshua Fisher (suspiciously un-twitterable), and myself(@NatBanting).
The full conversation–facilitated through Google Hangouts–can be viewed on Raymond Johnson’s blog here.
This year my department decided to make using whiteboards as formative assessment tools our department focus. This was nice because I had already began to experiment with the process. It just meant that:
I have been playing around with several ways to get students to realize why they make mistakes. I am fed up with the traditional grading process where the student completes a task and then is handed dead feedback–stuff to do the next time. In my opinion, the student needs to be the one seeing the diagnosis.
I guess you could call it “active assessment” or “confidence assessment”. My goal is to get students looking into the patterns of their mistakes and isolating skills that they need to practice.
Yesterday I took part in a multi-division professional development day on assessment and critical thinking. My division has been enamoured with Assessment for Learning for the longest time, but I have not been able to effectively transfer that knowledge into effective summative assessment in my math courses. I have, for the most part, stuck with the traditional assessment methods.