Welcome...
To Calculus 1 (Math 221)
I’m Doug Baldwin.
Supplemental instruction leader Madison Rodgers.
Some Motivation
Gallileo and how objects fall — where a falling object is when, etc.
Gallileo was able to relate distance to time, with data something like this (though these specific numbers are completely made up):
| Time (arbitrary units) | Distance (arbitrary units) | Avg Speed |
|---|---|---|
| 1 | 1 | 1 |
| 2 | 4 | 2 |
| 3 | 9 | 3 |
| 4 | 16 | 4 |
What’s the relationship between distance and time? Distance = time squared
What can you say about speed? It changes, i.e., there are different speeds at different times. You can calculate it by dividing distance by time. But that gives you an average speed over a time interval, it doesn’t tell you the exact speed at some instant. Can you do that? (Gallileo couldn’t, but calculus — which hadn’t been invented in Gallileo’s day — allows you to deduce such relationships between functions.)
Learning
Rank these from easiest to learn to do to hardest:
- Memorize terminology, facts, etc. (Remembering)
- State/explain facts in your own words (Understanding)
- Use knowledge to solve problems (Application) ***
- Explain the relationships between pieces of knowledge (Analysis) *
- Evaluate the validity of claims about some area of knowledge (Evaluation) *
- Discover new knowledge (Synthesis, Creation)
(These are the levels of “Bloom’s taxonomy of levels of learning”)
Which levels do you think we’ll work with in this course? Asterisks above indicate the levels I expect to emphasize.
Which levels would you say you’ve worked with in the past? Most up to evaluation in some sense, for at least some people.
What things do you do in order to learn something at these levels?
- Practice problems (ideally via multiple methods)
- Study examples
- Explain a process to self or others
- Take notes & review
Note that these are things you do, not that a teacher can give you (though teachers can provide things to take notes on, or examples to study). This is true of learning in general: it’s something a learner has to do and work at. I will encourage that in this course, e.g., through problem sets, in-class problem-solving and discussion, etc.
Next
Details of how this course will work — the syllabus.
Hand out syllabus
Please read it for Wednesday, identify any questions you’d like us to talk about.