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44 votes
Accepted

Are there science-backed effective teaching strategies?

In terms of controlled experiments, then, yes. Note that most are opposite or orthogonal to virtually all pedagogical norms in math education. Active recall. "Put away all your notes and ...
BravoMath's user avatar
  • 564
14 votes
Accepted

Why do you need to distinguish between apparently identical objects in probability?

The answers provided here so far give lots of good tips but I think they're not addressing a key part of the question, which is "why do we need to count two events (50,52) and (52,50), instead of one ...
juod's user avatar
  • 256
9 votes

Elementary Teacher Math specialist/ Basic Math Minor

The top priority should be ensuring that elementary education majors have a deep and mathematically-sound understanding of elementary school mathematics. They need to (re)learn the core mathematics ...
Justin Hancock's user avatar
7 votes

Why do you need to distinguish between apparently identical objects in probability?

This is a very good question. The issue comes up frequently. I explain this using a toy model: throw two regular six-sided die. What is the probability that the sum is 3? With some physical modeling, ...
user52817's user avatar
  • 11k
5 votes

Bloom's taxonomy

Bloom's taxonomy is not very helpful for maths, as many of the verbs don't make much sense, and ones that do have meanings occur in the wrong order. There are a couple of people (at least) who have ...
Jessica B's user avatar
  • 5,840
5 votes

Becoming a better instructor: where to start?

I would like to mention this recent opinion article in the AMS Notices (vol.66, no.7; PDF download) by Colin Adams (author of The Knot Book). His main point is that we should try "to impart a love of ...
Joseph O'Rourke's user avatar
4 votes

Why do you need to distinguish between apparently identical objects in probability?

I don't think I can improve on juod's excellent answer, but there are a few points worth elaborating. First, physical objects are always distinguishable. (I am here ignoring the phenomenon of ...
Will Orrick's user avatar
  • 1,122
4 votes

Are there science-backed effective teaching strategies?

Maybe not so concrete on practical strategies, but here goes: One key concept that has always resonated strongly with me is in David Tall's work where he talks about compression being the prime mover ...
semi-extrinsic's user avatar
3 votes

highschool's mathematics journal which citable in Google Scholar

The College Mathematics Journal is the closest I know to what you are looking for, because it is geared toward "the first two years", which nowadays would correspond to high school level in ...
Mikhail Katz's user avatar
  • 2,238
3 votes

Elementary Teacher Math specialist/ Basic Math Minor

[Caveat, I'm just a citizen, not a teach.] I like it. Call it a "math ed minor" to clarify it is different from say a chemist getting a "math minor". I think the two remedial ...
guest troll's user avatar
3 votes

What are the best places online where math educators can discuss their experience?

Many teachers use Twitter to share and discuss teaching. One large community includes teachers from early childhood to university level, mostly from North America but also from other countries. It ...
DavidButlerUofA's user avatar
3 votes

What are the best places online where math educators can discuss their experience?

For an absolute free-for-all with no restrictions on extended discussions (unlike here) or anything else for that matter, you could try sci.math at Google Groups. WARNING: It is currently infested ...
Dan Christensen's user avatar
3 votes

Why do you need to distinguish between apparently identical objects in probability?

The succinct answer is that there are two ways to choose $50$ and $52$ - if two boxes are chosen one could have $50$ and other $52$ or vice-versa - but this will be more apparent to a student if you ...
Dan Fox's user avatar
  • 5,869
2 votes

Why do you need to distinguish between apparently identical objects in probability?

I don't know from what principles you're teaching probability, but the answer I would give is the following: When calculating probabilities, it is important to remember the basic principles. We ...
DreamConspiracy's user avatar
2 votes

What are the best places online where math educators can discuss their experience?

There are a couple of Facebook groups that might be useful: If you are interested in discussing research in mathematics education (including "action research" in your own classroom, which sounds like ...
mweiss's user avatar
  • 17.4k
2 votes

What are the best places online where math educators can discuss their experience?

The Mathematics Teaching Community would seem to be a good place, but unfortunately it seems to be unavailable. (It has been unavailable for a few years now, I think.) From the University of Georgia ...
JRN's user avatar
  • 10.9k
2 votes

Why do you need to distinguish between apparently identical objects in probability?

You didn't disclose the level you teach. When I first ran into this issue (i.e. the need to explain this), I went to the example... You have 2 coins. There are 3 possible outcomes, 2 heads, One Head ...
JTP - Apologise to Monica's user avatar
2 votes
Accepted

Ideas and resources helpful in evaluating students with diverse backgrounds

You might like some of the puzzles and review sheets that Beast Academy puts out. Start with level 5 I think, but there might be goodies in levels 4 and 3 also. Here's one on LCM and GCF your students ...
Sue VanHattum's user avatar
  • 21.1k
1 vote

Why do you need to distinguish between apparently identical objects in probability?

I think there are a lot of good answers here, but one point of view that might convince some students is to use a simulation - not of the toy problems e.g. with dice suggested, but with this one. ...
kcrisman's user avatar
  • 5,986
1 vote

Why do you need to distinguish between apparently identical objects in probability?

Challenge him with the following: let‘s think it through with a soccer match. In how many ways can the match end, such that the sum of the goals is 3? According to his logic only two possible ways (1, ...
dingalapadum's user avatar
1 vote

Why do you need to distinguish between apparently identical objects in probability?

You could explain that the first box always goes to Alice, while the second goes to Bob. Then it becomes obvious that Alice getting 50 and Bob getting 52 is different then Alice getting 52 and Bob ...
stackzebra's user avatar

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