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20 votes

How to answer a three-year-old the question "Why is $2+6$ the same as $4+4$"?

I'm nearly sure I did this with my child when she was young. First, establish that she understands that a number, like three, is equal to $1+1+1$. Hold three fingers up and ask her "how many is this"?...
Nick C's user avatar
  • 9,639
15 votes

Why don’t all professors let students use notes, books, etc. on exams?

Making a course easier to pass is not the same as making a good course. There is a certain corpus of knowledge with which practitioners are expected to have instant recall (a.k.a: "automaticity"). If ...
Daniel R. Collins's user avatar
13 votes

Why don’t all professors let students use notes, books, etc. on exams?

I think that allowing students to use resources on exams can work well in certain situations, such as when the knowledge they can pull from those resources is peripheral (not of core importance to the ...
Jordan's user avatar
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12 votes

In math exams, how rigorous should the questions be?

On the one hand, the assumptions are an indispensable part of any theorem and many mistakes (well beyond the student homework) have been made exactly because somebody didn't understand that the ...
fedja's user avatar
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12 votes

Why don’t all professors let students use notes, books, etc. on exams?

I think it is usually counterproductive. Instead of building skills, it rewards students who are good at information retrieval. And I say that as one of those advantaged. Still remember a P-chem ...
guest's user avatar
  • 644
11 votes

Why don’t all professors let students use notes, books, etc. on exams?

I allow students to have one index card of notes during their exams. I believe this allows me to test for understanding and skills that are more important than the ability to memorize. I also ...
JRN's user avatar
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10 votes

Ten options for multiple choices questions

Presumably, you are trying to reduce the chance that someone will get a correct answer by guessing. In that case, I think that 10 options are more than you need. Suppose that we have an $N$ question ...
Adam's user avatar
  • 5,873
9 votes

Flashcards and Study Methods for Undergraduate and Masters Degrees

I think it all comes down to four things. 1. Solving Problems The most important thing is to solve challenging problems successfully while relying on as little assistance as possible (from people, ...
Justin Skycak's user avatar
8 votes
Accepted

Falling into the calculus trap

Echoing @AndreasBlass' remark, and having experienced somewhat similar episodes, it is already precarious enough to make such choices _for_oneself_. So, to directly answer your question: I think "no, ...
paul garrett's user avatar
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7 votes

Why teaching undergraduate-level mathematics is so complicated?

There are many reasons, but the classic explanation is that professors (especially at research universities) are picked (and compensated) for research ability versus teaching efficiency. (In general.....
guest's user avatar
  • 79
6 votes

How to answer a three-year-old the question "Why is $2+6$ the same as $4+4$"?

Blocks work well for thinking about addition. Have her count out 8 blocks, and then ask her about all the addition problems that have 8 blocks as the answer. A lovely children's book which looks at ...
Sue VanHattum's user avatar
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6 votes

Ten options for multiple choices questions

There's a fair amount of research about this, mainly from psychology and medical education as well es test development research for high stakes tests. In practical development, I usually resort to ...
SCS's user avatar
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5 votes

How cheating on homework affects student questions

Imagine a scenario where you don't have a hypothesis about your students' unwillingness to ask questions in class or during office hours. Your question may just boil down to: "How do you get students ...
Nick C's user avatar
  • 9,639
5 votes

Ten options for multiple choices questions

I do think that 10 options for a multiple-choice question is excessive. A few things to consider: This will be outside the range that standard automation tools can handle (TestGen application, ...
Daniel R. Collins's user avatar
5 votes

How to answer a three-year-old the question "Why is $2+6$ the same as $4+4$"?

A good answer to this question is one that (is correct, and) she finds convincing. As kids are growing up and making sense of the world around them, experimentation is often one of their key sources ...
yomplex's user avatar
  • 51
4 votes

Falling into the calculus trap

[VERY LONG ANSWER, needs patience to read through] I feel this is a problem many students who are good at maths face. They understand the simple tricks and patterns which are present in the school ...
Aviral Sood's user avatar
4 votes
Accepted

Why don’t all professors let students use notes, books, etc. on exams?

An exam is a totally artificial scenario. In real life you will never be in a scenario with all these fact at same time: a) you can not consult external resources or colleagues; b) you have limited ...
pasaba por aqui's user avatar
4 votes
Accepted

Ten options for multiple choices questions

I would say it completely depends on what is being asked. For example, something simple like "What is the derivative of $\cos(x)$ with respect to $x$?" could have as many as 10 options, because no ...
Nick C's user avatar
  • 9,639
3 votes

Ten options for multiple choices questions

Like others, I feel this is too much. It turns the question into almost a mini research project (assuming there is some reasonable amount of checking needed). It's one thing to just scan through ten ...
guest's user avatar
  • 61
3 votes

Flashcards and Study Methods for Undergraduate and Masters Degrees

Let me tell you my story on "memorising formulae": When I was in secondary school, I was awfully bad at memorising (I still am), and there was no way for me to remember the Simpson formulae. ...
Dominique's user avatar
  • 2,165
2 votes

Why don’t all professors let students use notes, books, etc. on exams?

I believe the choice is based on the expectations: what does the teacher expect the student to be able to do with the course content? If the student needs to show that (s)he is able to use the course ...
Dominique's user avatar
  • 2,165
2 votes

How to answer a three-year-old the question "Why is $2+6$ the same as $4+4$"?

None of the answers so far seem to give a name for the kind of concept in the inquiry. What you're asking is "how to make 8" or more generally "making numbers". See here and here. "Making numbers" is ...
Selene Auckland's user avatar
2 votes

Falling into the calculus trap

I will also chime in and say that the argument on the linked Art of Problem Solving site is unpersuasive, and somewhat misses a broader point. Ultimately, the real point of the mathematical ...
Daniel R. Collins's user avatar
2 votes
Accepted

Is Stewart Calculus a good book for AP calculus exam prep?

Your question is somewhat broad, and answerable, but this answer should not be considered as providing advice. Your question may have gone unanswered for two reasons. First, people may not know of ...
Thomas Perry's user avatar
1 vote

Is Stewart Calculus a good book for AP calculus exam prep?

There is a specific AP edition of the Stewart text that I have a sample of and it's fine. It's not that different from the one you have, it just has some pointers about AP-specific questions and their ...
Jon-Erik Storm's user avatar
1 vote

How to summarize textbook material?

I recommend to do some analysis of the situation. Telling us how the long the chapter is means nothing if we don't know how fast you have to cover things. Try to look at the situation as pages per ...
guest's user avatar
  • 19
1 vote

How to answer a three-year-old the question "Why is $2+6$ the same as $4+4$"?

Start with two equations that are the same in every way, like this: 2 + 2 = 4 and 2 + 2 = 4 Now, add "4" more to each of the two equations, one at a time, so you'll get 8 in each equation. But do it ...
Jamie Watts's user avatar

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