Robert Talbert, Ph.D.

FEBRUARY 11, 2022

Here's the one from Winter 2021 for calculus and here's the one for modern algebra. The extent to which communication was a burden to students. What I mean is that communication itself was work for students in a way that's different from past cohorts. Three things that surprised me 1.

Mathematics 52

Mathematics Algebra Communications Computer Science 52

Cool Cat Teacher

MAY 10, 2022

And all of a sudden I'm taking Algebra 2, I'm taking Calculus. How about two way communication? So now here we are having a two way conversation with someone you wouldn't have been able to communicate with at all without these tools. He gave me a math test that I can just do it in my own language. What a gift it is.

Accessibility 257

Accessibility Communications Schooling Research 257

Futurum

OCTOBER 4, 2022

A participant wearing a smart soft contact lens during the continuous monitoring of ocular pressure © Springer, Nature Communications, DOI: 10.1038/s41467-022-33254-4. Pinterest. A tear-soluble contact lens with silicon nanoneedles for painless and long-term sustained drug delivery © AAAS, Science Advances, DOI: 10.1126/sciadv.abn1772.

Biomedical Engineering 107

Biomedical Engineering Engineering Research Research 107

PCS Edventures

MARCH 4, 2020

Algebra , which incorporates unknown variables into arithmetic equations. Calculus , which calculates rates of change and infinites. Cryptographers combine cryptography, the science of designing algorithms for secret communication , and cryptanalysis, the study of breaking those designs.

Mathematics 52

Mathematics Energy Architecture Government 52

Robert Talbert, Ph.D.

APRIL 15, 2022

It’s a legitimate concern; but this can be addressed through mindful course design (see the next section) and regular communication. But all of the pillars are grounded in the idea that grading should be about growth , and this takes time, effort, communication, and patience. Limit the frequency of reassessments. Wait, what?

Academic Standards 52

Academic Standards Communications Calculus Argumentation 52

Stephen Wolfram

MARCH 23, 2023

And in the end, as we’ll discuss later, that’s a more flexible and powerful way to communicate. And writing this prompt is a strange activity—perhaps our first serious experience of trying to “ communicate with an alien intelligence ”. But ChatGPT has by this point learned a certain amount about writing Wolfram Language itself.

Computer 145

Computer Mathematics Math Achievement 145

National Science Foundation

MARCH 2, 2022

chemistry, biology, and physics or both calculus and Algebra I) or to teach and work in other roles in the school such as coach and bus driver. It is not uncommon for rural educators to teach multiple grades and/or a variety of courses within and across content areas (e.g., Another example is a focus on place-based pedagogy.

Schooling 76

Schooling STEM Research Research 76

Stephen Wolfram

JUNE 28, 2023

Line, Surface and Contour Integration “Find the integral of the function ” is a typical core thing one wants to do in calculus. But particularly in applications of calculus, it’s common to want to ask slightly more elaborate questions, like “What’s the integral of over the region ?”, or “What’s the integral of along the line ?”

Computer 118

Computer Calculus Construction Mathematics 118

Stephen Wolfram

SEPTEMBER 9, 2021

Mathematics is normally done at the level of “specific mathematical concepts” (like, say, algebraic equations or hyperbolic geometry)—that are effectively the “populated places” (or “populated reference frames”) of metamathematical space. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930).

Physics 65

Physics Science Sciences Mathematics 65

Stephen Wolfram

SEPTEMBER 9, 2021

Mathematics is normally done at the level of “specific mathematical concepts” (like, say, algebraic equations or hyperbolic geometry)—that are effectively the “populated places” (or “populated reference frames”) of metamathematical space. And the same issue arose for Alonzo Church’s lambda calculus (introduced around 1930).

Science 64

Science Sciences Physics Mathematics 64

Stephen Wolfram

AUGUST 22, 2023

It didn’t help that his knowledge of physics was at best spotty (and, for example, I don’t think he ever really learned calculus). Then McCarthy started to explain ways a computer could do algebra. It was all algebra. And Minsky mentioned work a student of his was doing on the “AI problem” of symbolic integration.

Computer 68

Computer Physics Science Sciences 68

Stephen Wolfram

NOVEMBER 10, 2021

For example, we know (as I discovered in 2000) that (( b · c ) · a ) · ( b · (( b · a ) · b )) = a is the minimal axiom system for Boolean algebra , because FindEquationalProof finds a path that proves it. But what about other models of computation—like cellular automata or register machines or lambda calculus?

Physics 122

Physics Mathematics Computer Construction 122