New answers tagged secondary-education
5
votes
Questions to test highest level of competency
As asked, it is a bit too general to answer with anything but other generic words. So let's play with some simple particular topic like finding maxima of functions on intervals.
The lowest level: find ...
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1
vote
SMSG: Did any school districts actual teach the curriculum as planned and what were the results for the teachers and students?
I had it in my Lansing, Michigan 5th grade class in 1961. I recall that approximately 30% of us were 'selected' somehow. Loved it.
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4
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Questions to test highest level of competency
What you might be looking for is cognitively demanding questions. Students/Pupils have typically comparatively easy time with algorithmic exercises (including the kinds of exercises, calculations or ...
- 5,442
2
votes
Questions to test highest level of competency
I think you're better off concentrating on performance of actual problems versus memorizing definitions or theorems, when teaching math for general STEM. It is much more lasting to anchor something ...
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3
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Multiple proofs for the same problem
It just crossed my mind that I can offer you some option you haven't probably considered yourself.
Once I experimented in my calculus course (which also involved some elements of analytic geometry and ...
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1
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Multiple proofs for the same problem
At the college level, see here, here, here, here, and here. Only the first link is suitable for high school courses.
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0
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Student asked me if it is necessary to simplify fractions at the end of answering a question. I'm not sure how to respond
If the student knows how to simplify and is, on purpose, not simplifying in order to save time to give themselves more time for the rest of the test, then this is an OK reason not to simplify, so long ...
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0
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Student asked me if it is necessary to simplify fractions at the end of answering a question. I'm not sure how to respond
I would say you might expect a meaningful answer.
In your case, there might be multiple meaningful answers:
$\frac{4}{5}$ : this is the answer in the most simplified form.
$\frac{40}{50}$ : this ...
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2
votes
Geometrical approaches in algebra
Here's a well-known one:
$$\sum_{n=1}^{\infty} \frac{1}{2^n} = 1$$
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0
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When writing log, do you indicate the base, even when 10?
Partially tongue in cheek, but it would feed two birds with one apple :
"Henceforth this book | article | thesis uses the following notation
$ ln( \sqrt {-1} ) = \frac \pi 2 i $
(*) or
$ log_e( \...
4
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Mathematical induction without simplifying equations or inequalities
The textbook I use for Discrete Mathematics has some lovely inductive proof problems. (And it's OER.) Discrete Mathematics: An Open Introduction, by Oscar Levin.
I especially like the stamps problem ...
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3
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Mathematical induction without simplifying equations or inequalities
Here are a few examples (for students at very different levels, since it's rather subjective what constitutes an "advanced level"):
The task in the Towers of Hanoi puzzle is solvable. (The ...
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-1
votes
When writing log, do you indicate the base, even when 10?
My experience as university student, researcher and teacher in technical and scientific fields in Italy has taught me that the only widely known unambiguous notation is:
ln(x) for base e log (most ...
7
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Geometrical approaches in algebra
I offer this (community wiki) only to illustrate the OP's 2nd example.
From the Archimedes Lab Project:
Quite beautiful!
4
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Geometrical approaches in algebra
This may not be what you have in mind, but your question reminds me of “proofs without words” aka visual proofs. The three examples you gave have relatively famous visual proofs.
There’s some ...
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1
vote
Why is absolute value difficult?
IMHO the main issue is that the absolute value doesn't satisfy any simple algebraic rules, so you cannot simplify the expressions including it. The computation itself is no more difficult than the ...
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14
votes
When writing log, do you indicate the base, even when 10?
I'm in Germany (chemist, FWIW). I'm familiar with:
$\log$: base is unknown/not needed (as in $\log (a) + \log (b) = \log (ab)$
natural logarithm: $\ln = \log_e$
base 10 logarithm: $\lg = \log_{10}$
...
3
votes
Why is absolute value difficult?
This answer is concerned with real numbers only. Adding to Dave Renfro's comment about absolute-value manipulations being—or at least feeling—different from usual algebraic manipulations, and Mark B's ...
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2
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When writing log, do you indicate the base, even when 10?
I think stereotypically that log means base 10 and ln means base e. That is how all the 8 different high school and college texts (published 30s to 80s) that I have use it. But I have noticed a (...
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36
votes
Accepted
When writing log, do you indicate the base, even when 10?
And a computer scientist thinks that $\log=\log_2$. I am using $\log$ for the natural logarithm by default in all my courses though I clearly state that in the beginning of each course (I teach at the ...
- 2,384
1
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Difference between the Cambridge IGCSE 0580 and 0607 mathematics courses
This answer assumes that both 0607 and 0580
are being considered
at the extended level
0607 is definitely a more challenging curriculum, primarily this is because it expects students to be extremely ...
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