Brenden

PhD | Mathematical Modeling | Cognition | Education

[Brenden @sumofangles]

@olicav I think it provides a working framework with the least number of axioms needed.

I think about it like Euclid’s postulates when he was building geometry.

It’s not perfect, but it’s good!

[Brenden @sumofangles]

instruction) gets applied, extended, and stressed-tested against reality. Build mathematics first, then sequence into modeling and modeling tasks.

[Brenden @sumofangles]

Mathematical modeling is not a place to introduce content. I see many teachers using modeling or modeling adjacent tasks to attempt to explain the reasoning as to why the students are about to learn some topic.

Modeling is where existing knowledge (gained through explicit

[Brenden @sumofangles]

https://t.co/rOVLZbyRMW

New article discussing the difference between mathematical modeling and discovery learning and why the mix up is suboptimal!

#math #matheducation #mathematics #mathematicalmodeling #mtbos #desmos #teacher #education

[Brenden @sumofangles]

6) I am writing the full argument over at Math Modeling Lab this Tuesday.
https://t.co/BXgAU2VsVd

#mtbos #mathteacher #teaching #math #matheducation

[Brenden @sumofangles]

1) Every time I explain mathematical modeling to a teacher, the same thing happens. Around the part where I say "students make their own assumptions," they smile and say "oh, like discovery learning." No. Not like discovery learning. And mixing them up is quietly ruining modeling

[Brenden @sumofangles]

5) But it only works if the math foundation is already there. Content first, modeling second.

Because the task requires the content to already be operational. Sequence isn't optional.

[Brenden @sumofangles]

Modeling can only effectively occur after requisite knowledge is mastered.

Every attempt at engaging in authentic modeling before that is cognitive overload.

[Brenden @sumofangles]

https://t.co/GfatEGq3CN

[Brenden @sumofangles]

Modeling requires students to:
Take mathematical tools they already have
Apply them to an ambiguous situation
Make assumptions about what matters
Build a representation
Execute the math
Interpret the result in context

Every step presupposes the math is already accessible.

[Brenden @sumofangles]

https://t.co/KRybIPUJjb

[Brenden @sumofangles]

@Britannica 1/1000

[Brenden @sumofangles]

I believe AI will be detrimental for aspects of mathematics education. Students will get worse at adding/subtracting, multiplying/dividing, solving equations because the cognitive work is offloaded.

However, I think mathematical modeling education will grow with AI which is 👍

[Brenden @sumofangles]

My x algorithm is messed up.

Half of it is about AI destroying all jobs/education/humanity

The other half is posts made with the help of AI

[Brenden @sumofangles]

@PhD_Genie -2

3

[Brenden @sumofangles]

🤦

[Anna Stokke @rastokke]

😲Wow. This ed prof even says that declining math scores could be a good thing. “The fact that our scores might be declining at some levels could even be a positive thing because we are diversifying our mathematics awareness and understanding.” https://t.co/PbodxEJF1d

[Vince Boley @VinceBoley]

A list of evidence based peragogy that I'd wager 90% of educators in America don't know but should:

🍎 John Sweller’s Cognitive Load Theory
🍎 Barak Rosenshine’s Principles of Instruction
🍎 Retrieval practice and interleaving
🍎 Explicit instruction
🍎 Frequent opportunities to respond
🍎 Cold calling

Why don't American teacher prep colleges teach these things?