My goal this semester was to continue to improve my use of formative assessment (largely through the use of whiteboarding) and expand the role of Project-Based Learning in my classroom. Up to this point, I have developed a wide-scale PBL framework for an applied stream of math we have in the province called Workplace and Apprenticeship Math. Those specific topics lend themselves very well to the methodology; they are a natural fit for PBL. I am still looking for ways to branch the intangibles from PBL into a more abstract strand of mathematics–one that includes relations, exponents, functions, trig, etc.
Categories
Sorting Set(s)
Set Theory, Counting Methods, and Probability are probably my three favourite topics to teach. For the first time under our new curricular framework, I got to teach these topics to a group of seniors. I decided to build up large themes and understandings through introductory tasks; my goal was to create an “unflippable” entry point where students could work together to complete tasks and filter out necessary details such as rules, notation, etc. I began our study of Set Theory with this task.
The students were introduced to the idea of what a set is. They also were given some elementary verbiage. I wanted them to become comfortable using words like set, subset, and disjoint throughout the task. I did not introduce them to the idea of intersection and union–those were to be formalized through the task.
One of the coolest experiences in my university training was the opportunity to invite a kindergarten class into our mathematics methods class for a mathematical field trip. Our class was divided into groups of three or four and were given the task of designing a mathematical activity that the students would try. The afternoon was a hit. Each group set up shop around the room and the kids freely moved from station to station as they mastered each activity.
Somewhere along the way, mathematics becomes formalized and stationary. I imagine it is around the time of fractions. I assume this for no better reason than teachers and students alike seem to blame most of their problems on fractions. That is until Grade 10, when polynomial factoring squeezes out fractions as the most hated mathematical procedure.
This post contains no real lesson or task ideas. That is a rarity for me, but every so often a philosophical battle ignites in my brain. More often than not, the question does not come from an established professional development vessel. Our division provides numerous officially sanctioned “PD” events throughout the year. They serve their purpose, but rarely motivate like those questions that come from within–or, in this case, from a student.
Every teacher is familiar with the following conversation:
Teacher: Can you please pay attention?
Student: I was paying attention.
Teacher: No you weren’t. Please put your _____ away.
Student: I was so–I have all the notes.
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 wasn’t obligated to try yet another “thing” in my room.
- I would be given better materials and funding to work with.
- Other math teachers in my building would see the enormous benefits of the technique.
Categories
A Discussion on Slope
I have taught Grade 10 math more than any other class. I still have lessons that I created during internship that I use. Other sections of the curriculum I have perfected over the years. Today, I added another lesson to the list of those that I will do for a long time. This is my desperate attempt to describe and catalogue it. If I don’t do it now, it will filed as a good, but vague, memory.
My goal was to introduce the idea of slope and be able to get numerical values for slopes from graphs. I also wanted to introduce the four types of slope: positive, negative, zero, and undefined.
The class began with a quick discussion on how rate of change relates to slope. I handed out student whiteboards at the beginning and drew four lines GeoGebra.
Categories
Webbed Assessment
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.
There are two schools of thought when it comes to PBL:
- Start with a large-scale project and fit the specific outcomes within it, or
- Build toward a larger project with smaller tasks.
I love the idea of large projects, but also aim to make my work as accessible as possible for those who want to take it and improve on it. I just don’t see option one working within my traditional classroom of 35 students for one hour a day. The existence of an overarching curriculum only further decreases its accessibility.
Categories
On a Smaller Scale
I was watching Saturday morning cartoons when this commercial was aired.
High energy music and neon flashes of light are often used to sell car related toys on these stations, but this commercial caught my eye. Upon first viewing, I thought I saw them advertise speeds of
The giant gummy bear problem has been floating around the blogosphere for a while. When I first saw it, I knew I wanted to use it. I finally have the perfect opportunity in Foundations of Mathematics 20 this year. (Saskatchewan Curriculum).
History of the Problem (As far as I know)
- Originally presented by Dan Anderson here. Included original Vat19 video and driving question about scale.
- Adapted by John Scammell here. Edited video and new driving question.
- Dan Meyer provided a 3Act framework for the problem here.
- Blair Miller adapted his own 3Act structure here.
My apologies go out to anyone else who played with or re-posted an original interpretation on the problem.