Billy: “Banting, I have a question for you.”
It was 5-minute break between classes and I was trying to reset the random seating plan, open up the electronic attendance system, and load the image that would serve as a starter for the day’s lesson. During this small window of time, questions are usually about missing binders, requests for future work due to mid-semester holiday plans, or updates on my ever-present pile of grading. In short, I usually do not want to deal with them. Begrudgingly, I obliged.
Billy: “I need a piece of paper and a pen”
Continue reading Second-hand Student-ing
“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.
Continue reading Assessment in a High-Density Classroom
I transferred schools at the end of last year, so for the first time in seven years, every one of my students I meet on the first day of school will be a stranger. This means that the first hour I have with each of the four classes is not only their introduction to the course, but also their introduction to me. It won’t take long for them to make an impression of me, of mathematics, of their classmates, and how I expect us all to co-exist for the next five months or so.
I have written on first day tasks before, but not for several years. In that post I identify four “attributes” of an effective first-day task*. One of the tasks I settled on for this year was The Shoe Sale task from Peter Liljedahl. (Other bloggers have documented work with the problem as well: e.g. Fawn Nguyen and Chris Hunter).
Continue reading Shoe Sale Remake
Let it be known that I am not a huge fan of math board games. That being established, I have tried on multiple occasions to create one that I like because the undeniable engagement factor is there. One of two things always seems to happen to my attempts:
- The game does nothing to change how students interact with the mathematics. Rather, it divulges into an attempt to get students to complete drills in order to win points of some type. Here, the math and the game exist as ostensibly separate entities.
- The game mechanism does not support flexible mathematics without a plethora of complicated rules. In an attempt to ensure that the first problem does not occur, the game soon balloons out of control until the simplistic spirit of gamification is lost.
Continue reading Prime Climb Puzzles
There is no dedicated course for geometry in Saskatchewan’s secondary curriculum. Instead, the topic is splintered amongst several courses. There are advantages and disadvantages to this, neither of which will be the focus of this post. I just thought that, especially for the non-Canadian crowd, a glimpse of context would be helpful.
The notion of a geometric proof only appears in one course. It is presented as a single unit of study during a Grade 11 course and is preceded by a short unit on the difference between inductive and deductive reasoning. I have taught this course a lot over the past few years, and have always had mixed emotions toward this portion. I love the metacognitive analysis students participate in during the inductive v. deductive reasoning unit. It is a (metric) tonne of fun to teach because it largely entails the completion of games, puzzles, or challenges and a subsequent interrogation of our thinking patterns. This could be my favourite week and a half in the course. After we have experienced the difference between induction and deduction, we spend a couple weeks slogging through angle relationships and parallel lines, triangles, and polygons using the ultimate edifice of deductive reason: The two-column proof.
Continue reading Constraining the Two-Column Proof
A colleague and I have often bemoaned our attempts to teach the concept of scale factor in higher dimensions. A topic that has such beautiful and elegant patterns and symmetries between the scale factors consistently seems to sail directly past the experience of our students. I have tried enacting several tasks with the students including some favourites from the #MTBoS (Mathalicious 1600 Pennsylvania and Giant Gummy Bear). Each time, the thinking during the task seems to dissipate when new problems are offered. It just seems like students have a hard time trusting the immense rate that surface area and volume can grow (or shrink). In the past, I had used digital images of cubes growing after having their dimensions scaled by 2, 3, 4… etc.; students seemed to grasp the pattern yet under-appreciate the girth of 8, 27, 64… etc. times as many cubes.
Continue reading Experiencing Scale in Higher Dimensions
The progression followed by most teachers and resources during the study of surface area and volume is identical. Like a intravenous drip, concepts are released gradually to the patients so as to not overdose them with complexity. Begin with the calculation of 2-dimensional areas, and then proceed to the calculation of surface area of familiar prisms. (I say prisms, so a parallel can be drawn to the common structure for finding the volume of said prisms. That is, [area of base x height]). In this way, surface area is conceptualized as nothing more than a dissection of 3-dimensional solids into the now familiar 2-dimensional shapes.
Continue reading Solid Fusing Task
Last week, I caught myself saying something to a pre-service teacher as we planned a Grade 1 lesson for the making of 10s. I asked her,
“Why would the students need to know how to make up 10s?”
When she was auspiciously silent, I filled the space with a statement said entirely tongue-in-cheek. It was only upon reflection, that I kicked myself for not being able to shut up and allow her to think. I said,
“…because my job is to convince teenagers they need logarithms, and that is much more difficult.”
Continue reading Real-World: An Attack on “Relevance”
Most probability resources contain a familiar type of question: the two-dice probability distribution problem.
Often times, it is accompanied with questions concerning the sums of the faces that appear on each dice.
Roll two fair, 6-sided dice. What possible sums can be made by adding the faces together?
What is the probability that:
a) the sum is 6
b) the sum is a multiple of 4
c) the sum is greater than 15?
Continue reading 100 Rolls Task
On June 15th, my Grade 9 class and I hosted our second annual math fair. What started out as a small idea has grown into a capstone event of their semester. This year, we had 330 elementary school students visit our building to take part in the fair’s activities. Several people (following the hashtag #TDCMathFair2016) commented that they would like to do similar things with their student transitions. This post details the rationale behind the event, how we structured it, what stations we had, and feedback/advice from our exploits.
Continue reading TDC Math Fair 2016: A Summary