I was lucky enough to teach the rarely offered 'Math for College Technology' course this semester. I had a blast teaching it and I think the kids did too. Why? It's all about Spiralling. Not posed, I swearCovering the curriculum strand by strand, unit by unit is over. At least for me. Spiralling the curriculum gave me the flexibility I needed to have a successful semester with the students. Course Structure:The curriculum was covered in 4 cycles. Each cycle had a theme. Complexity increased as the course went on. **Cycle 1**- Introduction to the types of functions (polynomial, exponential, sinusoidal)**Cycle 2 -**Modelling with functions (polynomial, exponential, sinusoidal)**Cycle 3**- Solving equations (polynomial, exponential, sinusoidal)**Cycle 4**- Vectors- Sprinkled in each cycle were unit conversions and geometry
Here is a link to my cycle plans for the semester.Activity Structure:Each cycle contained multiple activities. An activity would last 3-6 days on average and would be structured as follows: **Activity**[1-2 days] - hands on to collect data, work through an investigation**Lesson**[1 day, half period] - explicit instruction formalizing the skills used in the activity**Practice**[1-3 days] - in-class problems in handouts (not too many, not too hard) followed by group problems they answered on white boards (as many as necessary for them to really get it) followed more in-class problems. Practice problems were often collected as assignments to reward hard work and a good use of class time.**Assess**- short exit/entrance quiz for each topic (or multiple per topic), quiz after 1 or 2 activities, test at the end of the cycle.
I made the structure of the course clear to the students from the beginning of the semester. They were totally on board with the idea of spiralling. Some quotes when I explained it to them on the first day: "This way makes so much sense!" "Why don't all math courses work this way?" This is the first semester I tried spiralling (in both MCT4C and MFM2P) and I'm sold. Though it's daunting at first, I now think it is much more flexible to plan and a much more natural way to learn.
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Move the x-intercepts of the polynomial around.
- What happens when 2 zeroes get close together? When they are on top of each other?
- What happens when 3 zeroes are on top of each other? 4?
- What happens to the graph when the zeroes are far apart?
Open in Desmos to change the degree of the polynomial (by activating a different functions) or change the 'a' value to scale if things get too crazy. |
## Lukas NottenTCDSB Educator ## Archives
March 2019
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