Questions tagged [critical-thinking]

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5
votes
0answers
67 views

Long-form, multi-step, skills-integrating applied mathematics problems in calculus I, II, III

When recently teaching Calculus II to college students, I instructed my students to read and be ready to work through the first 8 or so questions of James Walsh's climate modeling differential ...
8
votes
2answers
274 views

What explains why a student can learn philosophy well, but fail in abstract math?

An undergraduate double major in math and philosophy, my cousin learns philosophy well, but she's failing her abstract proof-based courses (Group Theory, Real Analysis and Linear Algebra). Presume ...
1
vote
1answer
128 views

What exactly does 'abstract' signify in a course like Harvard's Math 55 (Honors 1st yr)?

Source: Logan R. Ury. Burden of Proof. Dec 6, 2006. Wikipedia on Math 55. While Harrison ultimately chooses to remain in the class, such conferences motivate several more students to drop, ...
24
votes
9answers
1k views

Teaching students to find and correct their own errors

Many students have a fairly good grasp of the topics they are learning but fall down because they miss fatal errors in their work. Some don't check for errors at all, while many simply can't find them....
18
votes
3answers
329 views

Critiquing Proof Style During Class

I would like to spend a day with my students analyzing mathematical writing. One way I might accomplish this is to offer multiple proofs (some good, some poor) of the same simple statement and ask ...
8
votes
3answers
340 views

Teaching Critical Thinking Skills

I am currently tutoring a few students in an entry level physics course and had some trouble recently when it comes to helping them with problem solving. The students I am helping don't have many ...