56
The evidence says no
What research I'm aware of is all about how giving any overall data about their own performance is actively harmful in promoting further learning. They learn considerably more from instruction about what to do differently in the absence of a grade or numerical score. To repeat; individual scores discourage learning! (Explanations for ...
45
You need to slam him on the grade. That is what he earned. Don't be so easily manipulated by his comments on your teaching.
Also I would not have sent an email apology. Just offered to meet with him to discuss his concerns. But still slammed him on the assignment.
If you let these kids walk over you, you'll never survive. You're in charge. Doesn't ...
30
First of all, I believe this question is quite similar to the question "How to give homework for integration technique?". I avoid the temptation of repeating my answer for that question. Instead, I try to give an answer from a different angle based on a recent experience I had in a numeracy class with adult students. One of the questions I asked was inspired ...
16
Imagine you had to look up every word you wanted to use, because you had a poor vocabulary. This would get old, fast.
The trouble is, many people don't have a genuine need to internalize computational technique as a way to see.
As a researcher, I find one of the main values of manual calculation is as error correction for reasoning, and a source of ...
15
One technique which is fairly obvious, but (at least for some of us) surprisingly difficult to implement consistently, is to just model for them in class what you expect them to write on their own. When I solve a problem in class, I try to show the same work and write the same explanations that I expect them to show. I also try to talk about it as I do it, ...
15
"Cheating Lessons" by James M. Lang argues (and has many references to back up) the claim that smaller, more frequent, lower stakes assessment both improves student learning outcomes and decreases the frequency of cheating.
13
Since you remark that your question is "deliberately non-specific," here is a (necessarily) incomplete response: First are two links to documents about assessment that might be of interest, and then two grading schemes that I have encountered in mathematics courses.
Documents:
As far as the philosophy of creating examinations, early work on this was done ...
13
I am not a mathematics educator but I feel the need to chime in from the student side of this. I have taken numerous hard math classes during my BSc, and I have had my fair share of feeling hopeless, lost, and frustrated. You didn't indicate which math class you teach, and to be honest it is irrelevant.
Unlike the other answers I don't feel like this is ...
12
A question that occurs with a project like this (broader than one department, as you put it) would be: Who is qualified to make those assessments? Probably not any other department at a particular college, certainly -- the one department is, by definition, where all the experts in that subject work.
To some degree this actually is done in places, in the ...
11
My immediate response is 'wait a few years'. I've spent a fair amount of time with 3 year olds, and most of them are busy learning how to be a person in their own right, how to have a conversation, what the difference is between real and make-believe, and (often) how to tell when they need the toilet. I've read that they can't understand metaphors by that ...
11
Here's another too-long comment posted as an answer:
We tell undergraduate students that they should study two to three
hours for every hour they spend in class. We know that many students
don't follow through with this nearly to the degree that they should.
I've become pretty unconvinced that raw amount of study time is a significant factor to ...
10
It doesn't exactly solve the problem, but one way to make positive use of Wolfram would be to use some Wolfram Demonstration Projects.
There are some that attempt to gamify calculus calculation practice.
Some help with intuition. If the students can see how the ideas could be of use to society as a whole (say through higher-dimensional calculus), even if ...
9
The math classroom standard "show your work" is really just a version of "communicate your reasoning" or "explain yourself", required in any profession. We sometimes do a disservice by implying that math classes have a special show-your-work requirement that is somehow not used in other disciplines.
I do model this communication in my own writing in ...
9
Set up a grading schema, awarding points for grammar, spelling, correct use of the technical terms. Central should be points for correct, logical overall structure, and enough explanations to lead the reader from one step to the next.
You can publish the grading schema for their guidance, and perhaps write up an example of how their work should look like. ...
9
There's a compromise between "correctness" and "completion" called "Standards-based grading". Here's a few links about it with various people who have tried using it for Calculus: http://blogs.cofc.edu/owensks/2014/01/08/sbg-calculus2/, http://alwaysformative.blogspot.com/p/standards-based-grading-implementation.html, http://speced.fivetowns.net/lcs/content/...
9
The book goes into detail giving the two-dimensional cross-sections of a sphere. You could ask the class to find the cross-sections of a cube or of another 3D object more complex than a sphere. It seems hard to find all possible cross-sections of a cube, but you could assign points for each possibility they do find. (It would be interesting to see how many ...
9
Personally in my own math courses, I have found that the gold-standard is to have an advance cycle of short-answer responses, document the most common student responses, and then turn those into the multiple-choice options in the future.
Disclaimer: In general I frown upon multiple-choice testing, since the math discipline is inherently about explaining/...
9
To avoid misinterpretations, I'd give it to them in a mathematical sentence and ask them to explain what they believe 'unique' means in this context.
For lack of knowing where you are in the course, I might give them an exit ticket such as
Consider the sentence, "The equation $x^3 - 2x + 3 = 0$ has a unique
solution." What do you think the word "...
8
The notion of "gateway" (exam or other thresh-hold) is not universal, and generates some conflicts, but addresses the issue head-on. That is, throughout a course (perhaps at the beginning, but this is in some ways the most harsh and least hopeful/optimistic) separate "exams" are given that test exactly and only the absolutely indispensible skills. Not only ...
8
You can also use Wolfram Alpha to look up definitions of words. So by reductive reasoning, there is no need for infants to learn vocabulary because when they are old enough to use a smartphone, people can always look up the meaning of words in Wolfram Alpha.
Being less reductive and less cynical, there is no need to learn a foreign language because you can ...
8
I have always found this to be an extremely hard proposition in the US system of grading (hw + 2-3midterms + final=Grade).
All of the systems I've seen were imperfect, but some were better than others.
I find it is essential to correctly structure the final exam in the first instance. You want to make sure that the students performance on it actually in ...
8
I have students present (in classes ranging from grades 7 to 12) and use the following rubric. It is not original, and googling various snippets suggests to me that it has been pieced together from several different sources. Perhaps modifying this could yield something useful (note, e.g., that I have the students present in groups — so if you are having them ...
8
Use them for what they're best at testing, like conceptual understanding questions.
One way to do this is by having students evaluate statements they would never be expected to come up with on their own, but should be able to understand the truth or falsehood of. This can also be useful for questions that have many different way of getting to an answer ...
7
Two questions from Lynn Arthur Steen are perhaps not addressed frequently,
but seem important to me:
(1) Are students learning how to use mathematics in other
subjects? Do students recognize similar mathematical concepts
and methods in different contexts?
(2) Do faculty take responsibility for the quality of students’
learning?
These are from "...
7
I think that your point here is spot on: "Qualitatively, colleagues have noticed that when faculty over-organize student work, students continue to expect this and don't take on adequate responsibility for their mastery in later coursework, whereas too little guidance in early courses simply leads to disastrous outcomes since students seem to leave high ...
7
Having one's mental abilities fall off after about 90 minutes is consistent with having eaten 20 - 30 grams of sugar before the exam started, but not having eaten any starch at that time.
Can you last an extra hour if you also eat about 40 - 60 grams of starch before the exam? Can you last the full exam length if you bring a snack (with another 20 - 30 ...
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 have tried using "pre-class quizzes." In my opinion, it was not a success.
The idea of the preclass quiz is to assign reading for every class period, then set up one easy question from the section that must be completed online. The question must be answered less than 24 hours before the start of the class.
The goal was to make sure students had to ...
6
This is an "in my experience" answer. However, I should say that my experience is slightly odd in that I teach students from a "wide variety" or backgrounds (I have fewer than 10 students from any individual country in my foundation first year courses).
So, in my experience, grading is pointless but marking is useful (I would argue even "necessary"). This ...
6
For a "writing in the disciplines" course, which it sounds like this is, think about what it means to be a writer in this discipline. For a writing in mathematics course, I'd expect writing of a quality that could be published in a mathematical journal. This means that, yes, I would expect proper spelling/grammar/punctuation/formatting. But primarily I'd ...
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