- Require complex and non-algorithmic thinking.
- Require students to explore and understand the nature of mathematical concepts, processes or relationships.
- Demand self-monitoring or self-regulation of one’s own cognitive processes.
- Require students to access relevant knowledge and experiences and make appropriate use of them in working through the task.
- Require students to analyze the task and actively examine task constraints that may limit possible solution strategies and solutions.
- Require considerable cognitive effort and may involve some level of anxiety for the student due to the unpredictable nature of the solution process required.
Category: Philosophy (Page 1 of 2)
So you’re at a PD, a really awesome one at that. Everybody is quietly thinking about the prompt “What is assessment?” Your neighbors are writing things like “Assessment is knowing where kids are, where they need to go, and what you should do next.” These poetic statements allude to many parts of a real-time data gathering and analyzing process . Diagnostic assessment, summative assessment, formative assessment are all critical pieces of information that end up letting the teacher know what they need to maximize student growth and learning. The information gained from assessment become the ingredients that “Chef Teacher” can use to create any number of delicious stews, or salads, or souffles.
The facilitator tells everyone to stop writing and to stand up and share with someone new. After 15 awkward seconds of trying to lock eyes with someone, you find a partner across the room. After shaking hands you read your poetic statement with a serious flourish. Your partner responds with the following:
Assessment is how you give kids grades.
You wonder for a second if their table was given the same task. This statement describes a calculation chore that happens at the middle and the end of each term. Grades are what you show to parents and administrators if they want to know how the kids are doing. Assessment is a process that ensures that you have the information at any given point to be able to make the grade, but also to do so much more. Assessment can help you make decisions in the moment, tweak tomorrow’s lesson, or even alter your unit structure. Your assessments can tease out which students understand what you taught today and which ones are relying on the trick they learned last year. Viewing assessment as only a tool for finding grades is like “Chef Teacher” going to the kitchen, by passing all the groceries, and microwaving a Hot Pocket.
You rack your brain for how to begin a conversation about Grading, Assessments,…and Hot Pockets, when your partner cracks a smile. Turns out he was messing with you. He didn’t really believe that Assessment is solely for producing grades, but lots of teachers out there do. How would you describe all the things that assessment could be to someone who thinks it is only for getting the numbers to put on the report card?
This year our school is talking about student work in mixed groups. We have been placed into 7 groups of teachers and social workers, each of whom are related to one student. After each session, the teacher bringing the work gets ideas for their teaching, and the group gains insights into the student and how our work affects them. These conversations have only involved essays so far, but this past Friday I was the presenter.
Due to realities of our schedule I provided a student’s partially finished math project for our descriptive inquiry group to look through. It was a project where the student had to create a set of equations that then help her solve a larger problem. The student make a mistake early on in the assignment and continued finishing the work, not being able to see that answers stopped making any sense. The discussion about this did not just allow for us to talk about the student. It allowed the members of the group a chance to step into a math teachers shoes and decide to how to respond to student misconception.
Talking about this student’s work flared up and we ended up having to scrap the rest of the inquiry protocol. The issue that broke our group apart happened after I explained the project and everyone gave their initial impressions. Someone noticed that the student made the a mistake. “The student should have multiplied these answers by x,” the teacher stated, referring to the column with numbers far to small to make sense in the situation, “so the teacher should show them what correct answer should be.” I began to feel a little uncomfortable. My instincts say the first thing to do would be to understand why the student made the mistake. I would need to ask a series of questions before I gave any kind of instruction. Thesequestions would intend to help the student to understand why the need to correct it, not to correct the multiplication, thus preventing the student from making sense of the problem.
For a few weeks last June I was one of the lucky volunteers who were able to review proposals for San Antonio’s 2017 NCTM conference. It was a lot of reading and it is a great opportunity to hear what math educators from around the world think should be talked about at the conference. Reading the words from hundreds of speakers provided a glimpse of math education thinking from the minds of teachers and educators across countless numbers of different contexts. It was a rare kind of opportunity that was both a great honor and also genuinely fun.
The Access and Equity Question
After reading over two hundred proposals, I noticed that some of the prompts from the application were better addressed than others. Particularly, the responses to the Access and Equity question were at times brief, or sometimes didn’t seem to address the question that was being asked. This question is the last written section of the proposal application form and asks:
“How does your presentation align with NCTM’s dedication to equity and access?”
So I was playing with these unifix cubes and it made me think about my work as a teacher and an administrator.
I imagined that each cubes represented one unit of productivity. So maybe this block represented one worksheet that I created, or a game that kids can play. For now let’s just say that this is instructional productivity, and not other things like discipline our data analysis.