(a ROUGH DRAFT of something I'm considering for my linear algebra class next semester...)
Every week you'll have an assignment intended to help you acquire and practice skills and concepts that are, well, foundational to the study of linear algebra. The ideas, procedures, and calculations in these assignments are essential to success in this course.
You'll get the weekly FS&C assignment in discussion; they'll also bea vailable on the course Moodle page. We strongly recommend working from a paper copy, for several reasons, as you'll see below.
Here's what we recommend:
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Sometime over the weekend or early next week (FIXME: think about timing here; should fit in with homework due dates. Or should FS&C for week N be distributed in week N-1? That sounds right. also consider issues of spacing!)
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After reviewing your notes from the week and reading the relevent sections in the text, work through the assignment the first time with no book(s), no notes, no internet, no help from friends. These are basic, foundational skills; you need to know and do this stuff without help. You could think of this as a quiz that will tell you how you're doing.
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If you don't know how to do a problem, that's perfectly okay! This is where the confidence rating comes in. Next to each problem is a box for recording your own assessment of how well you know how to do that problem. Use a 1 to 5 scale:
5: I'm very confident I know this; there are at most one or two minor details I'm not very certain about.
4: I'm pretty confident I know this; there's an important step or two that I'm confused about.
3: I know some things for this problem, but I'm not sure I know how to do it.
2: I have an idea for this problem, but I really don't know how to do it.
1: I have no idea how to do this.
After doing each problem, look at the question, your answer, think about what you've just done and write down your rating. Be honest -- this is only for you and your own studying. Inflating your confidence score will only make your studying less efficient and effective.
Solutions will be posted on Moodle. [FIXME: when?] Check your answers and mark them correct or not. Keep your original work -- staple or paper clip it to the assignment sheet. (This is why we recommend you work with a paper copy, so you have a record you can come back to over the semester.)
Keep these. you can use them throughout the semester, all the way up to the final exam.
Use these to make your studying for the exam more efficient: take out all the FS&C assignments for that exam and see what category below each problem falls into.
| you got the problem... | |||
| right | wrong | ||
| your confidence | high | quick review (4) | uh oh! (1) |
| rating | low | check understanding (3) | figure these out (2) |
[table will look better on final version]
The numbers above tell you the priority for things to study.
Also, since this course (like most math courses) is cumulative, as the semster goes on, it's a good idea to continue to return to old FS&C assignments. In the 7th week of class, say, look at the assignment from the 2nd week. Can you do all the problems? Are you more confident now about your ability to do them? Your goal should be to eventually have confidence level 5 for every single problem on all the FS&C assignments.
To do well on homework and exams, it is necessary to have built a foundation. These assignments are a key part of building that foundation and in that sense are graded. You won't hand these in, and they won't be directly graded, but they are an important stepping stone to the 90% [FIXME coordinate with other grading stuff] of your grade related to assessments.
It's perhaps unlikely you've had this kind of assignment before; here's a bit on why we're doing it.
First, on a practical level, this will make your studying more effective. Get together with other students in the class -- go through your assignments. If someone got a problem right and others got it wrong, that person should explain it. If everyone got a problem wrong, work on it together until everyone feels they're confidence level is 5. You'll know exactly where to start studying. And if you come to your TA's or professor's office hours, bring your assignments, as those will give us a place to start helping you with the class.
Second, by asking you to rate your confidence (and later check your answer), we help you avoid the illusion of knowing -- the feeling that you have mastered a topic when you actually haven't. Cognitive science researchers have found that people are very prone to this. The confidence rating and correct/incorrect checkbox are an easy, objective way to check your ability.
Third, the problems on these assignments are in no particular order. In textbooks, it's traditional to group similar problems together, but research has shown that students learn and retain information much better when the problems are mixed up. To use a sports metaphor: anyone can hit a fastball in practice if you know it's coming, and if the last 5 pitches were fastballs -- but in a real game, you don't know what pitch is coming. In your academic work, you will not know what concept or skill from linear algebra you will need to bring to bear on a problem. We will therefore make your practice as much like the real game as we can.
Fourth, some problems on these assignments will be from previous topics, and not the current week. This allows us to bring in a problem and ask you to do it just when you might be forgetting. Again, research has shown that this process -- of being forced to recall something just when you've started to forget it -- is a very powerful method for lasting learning.
In solutions; include similar problems students can do for practice?
include spaces on the assignments for the clicker questions from class!