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2 votes
Accepted

Truth tables. What does a truth valuation of a formula even mean?

I will take a pedagogical approach that aims to help the student build a conception of how truth tables are connected to their ordinary reasoning. In the second part, I hope to show how the truth ...
user1815's user avatar
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1 vote

Truth tables. What does a truth valuation of a formula even mean?

As other comments and answers have said, either implicitly or explicitly: these "propositional calculus" variables "$p$" and "$q$" are indeed variables, just as the ...
paul garrett's user avatar
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4 votes

Preparing students to face challenges caused by artificial intelligence

Your question is of the form "Here is a list of opinions, all of which are true. Therefore, what should we do?" I count approximately five opinions, and I don't agree with a single one of ...
ksdjlfhjkldfsh's user avatar
4 votes

Truth tables. What does a truth valuation of a formula even mean?

From the formal standpoint, truth tables are just the tabular representations of the Boolean functions (usually of 1 or 2 variables). You will, probably, find nothing mysterious about writing the ...
fedja's user avatar
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1 vote

Truth tables. What does a truth valuation of a formula even mean?

Maybe starting with a modified truth table would help: Then transition to the more standard presentation with T's and F's. BTW, you might avoid some confusion about implications by emphasizing, for ...
Dan Christensen's user avatar
2 votes

Truth tables. What does a truth valuation of a formula even mean?

Tom: You are actually asking a math question more than a math ed question. "What is the rigorous definition of a truth table". It's a Booleian Algebra question, I guess. (I donno...only ...
guest troll's user avatar
3 votes

What does math education research know about difficulty vs. effectiveness?

The keyword you're looking for is "desirable difficulty," which refers to a practice condition that makes the task harder, slowing down the learning process yet improving recall and transfer....
Justin Skycak's user avatar
2 votes

Correct notation of a Sample space

There is no correct here. While it is common to use capital letters for random variables and the corresponding lowercase letters for the values they assume, this convention is not a strong one and ...
Dan Fox's user avatar
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0 votes

Which cognitive psychology findings are solid, that I can use to help my students?

I don't know how well-replicated the findings are, but I understand that having students work in groups, writing on vertical (why?!), non-permanent surfaces helps substantially. I saw that effect in a ...
Sue VanHattum's user avatar
  • 20.8k
26 votes

Which cognitive psychology findings are solid, that I can use to help my students?

Having pursued the same question as the OP with same motivation for over a decade (as an undergraduate classroom instructor, and a facilitator of a faculty interest group in STEM education strategies ...
Daniel R. Collins's user avatar
3 votes

Which cognitive psychology findings are solid, that I can use to help my students?

"The What Works Clearinghouse (WWC) is an investment of the Institute of Education Sciences (IES) within the U.S. Department of Education that was established in 2002." They have looked at ...
JRN's user avatar
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58 votes

Which cognitive psychology findings are solid, that I can use to help my students?

There's a highly upvoted answer here claiming that practically no cognitive psychology findings hold up in replication. I don't think that's true at all. Sure, many findings don't hold up, but also, ...
Justin Skycak's user avatar
5 votes

Which cognitive psychology findings are solid, that I can use to help my students?

I highly recommend Daniel T. Willingham's "Why Don't Students Like School?" (from 2009, but there seems to be a new edition from 2020). It covers a wide variety of known results from ...
TomKern's user avatar
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6 votes
Accepted

Correct notation of a Sample space

It's true that you typically refer to a random variable by a capital letter (e.g., $X$) and a particular value by a lowercase letter (e.g., $x$). So, $P(X = x)$ would represent the probability that ...
Justin Skycak's user avatar
0 votes

Math Progress for Year 2 Student?

If your classroom discipline and the social situation allow, I would have him work on a self-guided instruction book while the others in class do the normal routine. Put him on a wall to isolate him ...
guest troll -1's user avatar
2 votes

Math Progress for Year 2 Student?

All of the comments seem helpful. I'd recommend that you ask the parents what they'd like for him while you are conducting math class with the others. They might have some great ideas. Does the school ...
Sue VanHattum's user avatar
  • 20.8k
2 votes

What is this symbol called?

For such a query, you might find it quicker to use one of the following tools: Google Image Reverse Search: Navigate to google.com and upload an image of the symbol. Google will display similar ...
LeafGlowPath's user avatar
8 votes

What is this symbol called?

Please check the entire Greek alphabet, as you can find it in this Wikipedia page: https://en.wikipedia.org/wiki/Greek_alphabet. I must add that there are two ways to write the letter $phi$ in MathJax ...
Dominique's user avatar
  • 2,119
7 votes

What is this symbol called?

That's lowercase Greek phi, pronounced with an initial f sound and rhyming with English pie, lie or sky. That said, some speakers may pronounce it rhyming with English see, key or me. See https://en.m....
J W's user avatar
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3 votes
Accepted

Theory of semiotic mediation in teaching math at high school

Here's what I understand to be the definition of semiotic mediation: The process that sees the use of the artifacts and signs as the center of human activity. In mathematics, the tool becomes a ...
Justin Skycak's user avatar
0 votes

How to teach math to someone who is neither [really] willing nor able to understand it?

Whenever I tell her she is wrong here and there, she tries to argue with me as if that would change anything. This alone implies that she does not want to learn. It has been a decade since your ...
user21820's user avatar
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