17

This is not really a math problem, it's a social problem. Some schools, such as West Point and Cal Tech, have their own honor code systems for this sort of thing. From what I understand, they work very well. However, most schools do not have any such system. Social scientists and psychologists have studied what factors promote or prevent cheating. Cheating ...


15

Agreeing with comments and other posts: If you want more conceptual answers, give them less details in the set-up. Using your velocity problem, here are a couple of examples of making it more conceptual: Suppose that a truck's distance from you in meters at a time $t$ seconds after the big bang is given by the function $p(t)$. What does $p'(19)$ tell you (...


10

I think the given example is highly appropriate. You cannot cover every possible combination of ideas in class. Students display understanding of a concept (rather than "recipe following") by showing the ability to adapt at least a little bit to novel conditions. I think the problem you gave is a great homework problem. I personally like homework to be a ...


9

I would frame this issue a little differently than you have. I think it's unreasonable, at least in the context of courses which aren't well into a math major, to ask students to do something they have not been taught to do. That is, the problems on an assessment should be the same as problems they've seen already. The catch is that "the same" is actually ...


8

Asking students to explain why something happens can be useful for assessing understanding, although it is often harder to grade and works best with many demonstrations before the exam. (Students need to know what your expectations for a thorough explanation are.) I have found that asking students to critique a process will sometimes help me assess their ...


7

Comment-answer, but too long for a comment: I think you are thinking about this wrong. Tests are some of the MOST valuable hours in a course. They are high stakes performances (like in music or sports). Preparation for them drives a lot of learning. Then the actual execution and subsequent feedback is often much more valuable training than routine ...


7

My advice is to minimize the amount of such synthesis required. Don't make it a large fraction of your tests, if at all. Teach the students the methods you expect them to display on the exam. Not something requiring some spark of creativity. Program for success. Creativity is tough in general and even tougher under test conditions. If you push too ...


6

In recent literature, this issue would be referenced as multiple measures placements. There's been quite a bit of work in this area in recent years, and a number of places cite positive results (in terms of shortened time to gain more credits, etc.). The displayed effect is usually stronger for English, and weaker for math. It certainly makes intuitive sense ...


6

I agree with @BrendanW.Sullivan's comment. That is, when teaching an undergraduate course, like calculus, students need more than procedural knowledge. For a deeper understanding, and efforts to evaluate such, students should be asked on exams to answer a few "free form" questions, like the one Brendan suggested. A good question to ask following any ...


5

As stated in other comments, try not to "invite" your students to merely apply rules they do know. In the specific example you mention, I would prefer a multiple choice question of the form: A truck's distance in metres from you as a function of time $t$ (in seconds) is given by a smooth function $p:[0,+\infty)\to\mathbb{R}$. Knowing that $p(19)=12$, $p'(...


4

Your point about less weighting of the final exam is made as both a con and a pro (not logically consistent). The issue of less flexibility to alter the curriculum is not purely a con, can be a pro. I know this will raise hackles of community of instructors here who enjoy flexibility and see themselves as Robin Williams in Dead Poets. But there can be a ...


3

I am a high school teacher with three preps this year. Two of them have a "final" that are written by an external party (a Geometry final from the New York State Board of Regents and an AP Calculus test written by College Board). I don't mind either of them. I fully admit that I "teach to the test", in the sense that I trust the test to be well-designed ...


3

I taught algebra at a community college for several years (recently switched to CS), and this was largely my goal for weekly quizzes (given in online multiple-choice format via Blackboard). Roughly half the questions were directly computational or symbolic manipulations, with the other half an attempt at being conceptual. I've taken my quiz source document ...


3

In Spain such placement is impossible, because university curricula are fixed in the first few years (there are no choices to be made). On the other hand, entrance into a given degree program is based on a mix of high school grades and performance on (state level) exams administered at the end of the final year of high school (these cover high school ...


2

What one has to do to test for conceptual understanding is hard to state in terms of general principles (although Polya's books on Plausible Reasoning do a pretty good job of addressing the issue) and maybe is best addressed via examples. Here is one example. Consider a cubic polynomial in one variable that is increasing as a function of its argument. ...


2

I suggest to research the placement tests and psychrometry of USMA, USNA, USAFA, etc. They have a very long experience in doing these tests and assessing how well the resultant students do in their courses. You could even reach out to someone in one of the departments and see what insights they give you. In general, whenever you are looking for large data ...


2

Leave more conceptual questions for take home. They have more time, can think things over. Encourage using technology, ask for a sketch of how they think the solution to something hairy looks like (Asymptotes? Increasing? Maxima?). Explore e.g. the effect of initial values on the plot of the solution.


2

This is an interesting question! One option could be testing the quality of how you do math, for example: Count how many careless mistakes you are making when doing maths that you usually do; Measure how long you can stay focused doing maths while you are still productive and you are not easily distracted. I think the interventions you mention enhance ...


1

A compromise approach could be to give a problem (with parts), as you might on a guided worksheet. Such as: A function $f$ has domain $(2,4)$. We define $g$ by $g(x) = f(x-2)$. a) Is $g(3)$ defined? b) Is $g(5)$ defined? c) What is the domain of $g$? You might even give a follow up problem (perhaps as extra credit) along the lines of: A function $f$ ...


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