A couple of weeks ago I was reading through some of my edu feed and I came across a post about assessing curricular competencies in the new BC science curriculum. The post discussed feedback cycles on the competencies. After reading the post I felt kind of anxious, which isn’t that uncommon for me when I read something that I know I can improve on, or should be doing better with. Later in the day I was still feeling bothered and then it finally dawned to me that when I read about assessing curricular competencies, I end up feeling crappy.

One thing that I’ve always struggled with is adding challenging questions to my assessments within a SBG scheme. Like a lot of people using SBG, I use a 4 point scale. The upper limit on this scale is similar to an A, and for the sake of the post I’ll refer to the top proficiency as “mastery”. If a student were to get an A in a course I teach, roughly speaking they would have to be at the mastery level in at least half of the learning objectives, and then only if they don’t have any level 2 grades.

I’ve written about my usual SBG scheme here. It works fine and many students take advantage of learning at a slightly different pace but still getting credit for what they know, once they know it. However, I’m interested in keeping small quizzes primarily in the formative domain, yet using an assessment tool that is based on clear learning objectives, re-testable and flexible. This post talks about a possible transition from using a few dozen learning objectives in quizzes to a new, larger goal assessment tool.

I’ve seen lots of pictures of math Thinking Classrooms on twitter and I’ve also come across a few videos. I haven’t seen anything that followed the dialogue in a classroom, so I thought I’d try to capture a bit of that aspect in this blog post. What I have below isn’t all that different from a lot of lessons except that you have to visualize how the students are situated. They are not copying something down from me.

Following up from my previous post, here is another brief set of notes on the action and dialogue in my grade 8 math class. We start the day out with some voting questions where we use Plickers and Peer Instruction. My general instructions for all classes when doing voting questions are as follows:
No talking allowed while voting. No sharing of answers or ideas. I want to see what your thinking and if you take your idea from someone else, I won’t know if you get it or not.

Research has long shown that fraction arithmetic is difficult for students. We also now know that success when working with fractions is one of the best predictors for success in post-secondary education. With this in mind, one of my prime focuses in math 8 is to do the very best I can with teaching fractions to my students.
The research on fraction arithmetic tells us that by grade 8, students have a success rate of around 50% when adding fractions.

I’ve been asking many of my grade 11 students what their ideal math lesson would look like. Not in terms of content, but in terms of process. I wanted to focus this question on math instead of science because I didn’t want to confound typical learning activities with demonstrations and experiments.
Most of the students cited very similar ideas, as follows:
take up questions about homework or last day’s work connect the new material to what they were working on last day possibly give some notes give (lots of) examples have them try some practice questions #1 above was universal, all students started with this.

Lately I’ve been thinking a lot about Modeling Instruction (MI) and Cognitive Load Theory (CLT). I started this post a couple of weeks ago and then was further inspired by a post by Brian Frank (if you read both posts you’ll see some similarities). In my head I know that I want to compare them, but that is something that I shouldn’t really do because MI is a teaching and learning methodology while CLT is a theory about how people learn.

I came across a paper on Piaget cognitive levels and learning in physics. There were lots of interesting things to think about from this paper but one thing in particular caught my attention.
The concept behind this paper is that people go through stages of cognitive development. In high school we typically get students that arrive with concrete operational thinking, and they hopefully leave as formal operational thinkers. The following two math problems are good ok examples for comparing concrete to formal.

So we’re just over 1/3 of the way through Physics 11. Despite my intentions to ward off predictable problems, they nevertheless continue to appear. One of them is Hooke’s Law.
My students did a lab to see the relationship between force and how a spring reacts to the applied force. They could graph the relationship and figured out that the slope was the stiffness of the spring. Most students also go an equation of the line from their graphs and I helped this process along by generalizing the equation to Fs = kx, aka “Hooke’s Law.