I’ve been thinking about the way we structure the flow of high school courses. A typical sequence for the “average” student is Algebra I, Geometry, Algebra II, Pre-Calculus or some type of Trig/Stats class.
As far as I can tell the only difference between Alg II and Pre-Calc is that trig is taught during Pre-Calc and Pre-Calc introduces the concept of the limit. Functions are developed a bit more rigorously too.
The first semester of Algebra II is mostly a repeat of Algebra I as they’ve forgotten it with the year “off” during Geometry.
Why not then teach Geometry first? I’m talking about plane and solid geometry with an emphasis on reasoning, and right angle trig. Obviously there would need to be some supplementing needed (work with radicals, solving equations). Most students have “seen” the solving of equations in 8th grade (Have they mastered it? No, of course not).
I’m thinking that a high school sequence could be structured as: Geometry, Algebra I, Algebra II with Trig, Calculus or Stats.
Analytic geometry could be moved into Algebra II – and there would be time as the “review” of solving systems wouldn’t be needed as there wouldn’t be the year off.
So, I’m looking for some valid reasons why this wouldn’t work. What am I missing? Help me think through this.
Categories: General · Math
Tagged: course sequence, Math
I have been working through the lessons for one of my new preps next year. I am working day by day through each activity/assignment – as both a student and a teacher.
First I “just do” the assignment as a student would. However as I’m doing this, I’m not only doing the math, but making notes to myself regarding the wording of questions, how long each problem takes, what is needed to do the homework (graph paper, calculator, … ), and misconceptions students may have.
Next I’m switching into teacher mode. I’m asking myself questions about goals:
- What is the mathematical goal of the lesson? What idea/concept/skill is this addressing? At what level… exposure, mastery, or extension?
- Is it a worthwhile goal?
- Is this the best way to meet the goal?
- How does each activity contribute to the overall goals of the unit?
- Will supplemental activities be needed? (I have a hard time with this one – how am I supposed to know now, what my future students will need?)
- What is the process goal? How will the students develop the mathematical goal?
- How will I know if the goal is met?
- What will I do if it isn’t?
I’m open to suggestions, thoughts, ideas, … is there anything I’m missing? A better way to do this?
So far I’ve worked through one of the five units. I’ll be posting my reflections on the first unit soon.
Categories: Math
Tagged: Goals, Lesson Planning, Math
