11
votes
Accepted
Critiquing Proof Style During Class
I found this an effective teaching technique.
I take a topic they know, and find a Wikipedia article discussing that topic.
If you are specifically focused on proofs, as opposed to
more generic ...
- 28.9k
11
votes
Accepted
Acceptability of creative questions in assessments
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 ...
- 23.2k
10
votes
Accepted
what could be some replacement language for the term "spoon feeding"
No one can make any universal guarantees as to whether or not any particular student may find your usage of spoon-feeding or any other term offensive or insensitive. However, spoon-feeding as a ...
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10
votes
Acceptability of creative questions in assessments
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 ...
- 11.5k
8
votes
Acceptability of creative questions in assessments
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 ...
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7
votes
What exactly does 'abstract' signify in a course like Harvard's Math 55 (Honors 1st yr)?
One definition of "abstract" is " disassociated from any specific instance".
In mathematics, we "abstract" by finding properties which underlie a class of examples. For instance, the concept of a "...
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7
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What explains why a student can learn philosophy well, but fail in abstract math?
I was also a double major in mathematics and philosophy as an undergraduate (at a state university in the U.S.). I think that both are incredibly important, and I'm happy to have both under my belt. ...
- 22.8k
6
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Teaching students to find and correct their own errors
One possibility to encourage sanity checks is to practise sanity-check-type questions and include them in tests. An integration-related example could be:
A student has calculated the area bounded ...
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5
votes
Critiquing Proof Style During Class
There are quite a few textbooks that have critiquing sample proofs as exercises. Here are three I know of:
A Transition to Advanced Mathematics by Smith, Eggen, and St. Andre
The Foundations of ...
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5
votes
Critiquing Proof Style During Class
Go to Mathematics Stack Exchange or MathOverflow. There are many questions there looking for proofs and there are many different answers, some good, some bad (some are even wrong). Ask your students ...
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4
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what could be some replacement language for the term "spoon feeding"
A term for the same or similar that has positive connotations is 'scaffolding'.
I want my students to understand the connection between a function's graph and the graph of its derivative, so I ...
- 19.2k
4
votes
How should mathematics tests be designed?
"The problems from which the test is composed , should they be
routine, typical ones which mimic the ones in the students’ textbooks?
Or new ones which need a lot of thinking and imagination, yet ...
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3
votes
Teaching students to find and correct their own errors
Give your students a multi-step problem and 5 different "solutions" written by fictitious students (you, really).
Say:
Here are five different solutions to this problem. First, rank them from best ...
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3
votes
Teaching students to find and correct their own errors
This is something that I've been specifically grappling with in my college remedial algebra classes for the last few years. JoeTaxpayer's observations in his answer very much match my own (that many ...
- 22.8k
3
votes
Tips and References for a 15 days Course on Math
You might engage them in billiards on an elliptical table
(1st ref below), or on a circular table but aiming to hit
a second ball (2nd ref below).
Nice analytic geometry coupled with intuitive ...
- 28.9k
3
votes
what could be some replacement language for the term "spoon feeding"
You might consider the phrase "algorithmic learning" vs. "deep understanding". Those who learn algorithmically, often memorize steps with no understanding of them and then can't ...
- 7,839
2
votes
what could be some replacement language for the term "spoon feeding"
Education tends to use loaded terms rather than thoughtful arguments. "Drill and kill" must be bad, right? "Mastery" must be good, right?
For spoon feeding, in particular, I've ...
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2
votes
Accepted
The spatial thinking course for primary school - what to use?
Well, this is not a systematic course proposal, but a list of useful references I've collected about the subject:
A must read for your staff team (it brings arguments from neuroscience): Mind in ...
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votes
What would you recommend for the math thinking course for school?
Have them work through a few chunks of Euclid's Elements. Then they are doing proof, rather than reading about logic in a theoretical way, which is probably too abstract for kids in the age group you'...
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Is there research to back up the claim that math classes help develop analytical skills?
The idea that math-study imparts certain fundamental intellectual skills was taken for granted for most of the history of Western education, and reaches back at least to Plato, who (reportedly) ...
- 111
2
votes
Tips and References for a 15 days Course on Math
My advice: Look at the test itself. If possible get some statistics on common errors. If not, ask other teachers or at least use your intuition. I.e., make an intelligent guess, "Bayesian estimate"...
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Acceptability of creative questions in assessments
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 $g(3)$ ...
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2
votes
What explains why a student can learn philosophy well, but fail in abstract math?
Obviously it's hard to tell from a distance. Here are some explanations:
She may be more motivated to think about the material in the philosophy course. This may be because she can relate to the ...
- 341
2
votes
Teaching students to find and correct their own errors
One of the crucial points here is that verifying a result must be different than repeating the calculation, let me explain:
Verify that 221/12 = 18, rest 5:
Instead of doing the calculation all over, ...
- 1,340
1
vote
Teaching students to find and correct their own errors
A pair of fresh eyes may see goodies and errors alike, that you cannot see yourself after writing the assignment.
Thus, I experiment with letting students peer-review (an anonmized fraction of) ...
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