Having fun with the damped spring in #p5js for teaching ODEs:

https://dynamicmath.xyz/math1052/lecture-13.html#/damped-spring-simulation

#iteachmaths #ilovemaths #ODEs 😃

This could be an interesting discussion:

https://mathstodon.xyz/@Kingevo/110811941339524982

#MTBoS #MathEd #MathsEd #ITeachMath #ITeachMaths

(Side note: I always "CamelCase" because it helps screens readers identify word boundaries)

Question for #MathsEducation people (particularly, but not exclusively, UK A level teachers):

Why do we teach binomial expansion (non-integral powers) with initial step factoring out: \((a+b)^n = a^n(1+\frac{b}{a})^n\)?

Wouldn't it be less prone to errors simply to teach:

\[
(a + b)^n = a^n + \frac{n}{1} a^{n-1}b + \frac{n(n-1)}{1\times2} a^{n-2}b^2 + \frac{n(n-1)(n-2)}{1\times2\times3} a^{n-3}b^3 + \cdots\]

with radius of convergence given by ensuring that the "common ratio", \(\frac{b}{a}\) has magnitude less than \(1\).

#mtbos #ITeachMaths #ITeachMath #mathed

Wrote this task for our factorising unit last year, since we now cover surds before factorising at GCSE.
Don't think it quite achieves what I want yet, so going to have a tinker.
#MTBoS #MathsEd #ITeachMaths #MathsTeaching #MathsEducation

Adding hashtags:

#MTBoS #MathEd #MathsEd #ITeachMath #ITeachMaths

Also:

Calling @Chartodon ...

@ablinstein @phonner @dougholton

Exploring Riemann surfaces with @paulmasson's MathCell

https://complex-analysis.com/content/riemann_surfaces.html

#iteachmaths

Created a new resource this morning.
Introducing solving linear and non linear simultaneous equations.
Includes worked example with prompts and backward faded quesions.
https://kshancock.co.uk/lessonresources.html#quadraticSimul
#MTBoS @mtbos
#EduTooter @edutooters
#ITeachMath #ITeachMaths

Complete the Quadrilateral: What is the largest kite you can complete using the sides given.

Sending my hopes into the universe. Can anyone programs this (https://nrich.maths.org/11234?part=clue) into an interactive @desmos
activity?

@mtbos @edutooters #iteachmaths

@peterrowlett I use this in my introduction to logarthims because it so beautifully illustrates log scale and why log scale is necessary to handle the universe or I can just post the XKCD cartoon https://xkcd.com/1162/
@mtbos @edutooters #iteachmath #iteachmaths #edutooter

Is Ben Orlin on an instance somewhere?

I'm reading "Math Games with Bad Drawings" and (in the book) he's just posted a puzzle so I now can't read any further until I have a go at solving it.

#GoodMathBooks #ITeachMaths #MathGames

One of those "obvious when you think about it" thoughts: compound angle formula follows from the existence and uniqueness of solutions of ODEs.

Fix \(\phi\) and define \(f(\theta) = \cos(\theta + \phi)\). Then \(f''=-f\) so there are some \(a\), \(b\) such that \(f(\theta) = a \cos(\theta) + b\sin(\theta)\). Comparing \(f(0)\) and \(f'(0)\) then gives the formula.

So, when should I introduce uniqueness of solutions of ODEs to my students so that I can use this?

#ITeachMath #ITeachMaths

Thought I'd put together some Christmas Teaching activities.

https://github.com/loopspace/Teaching-Resources/releases/tag/Christmas-2022-12-04

#ITeachMath (well, actually, #ITeachMaths)

Satisfying and self-checking with a technical bite: asynchronous lesson about isosceles and equilateral triangles by @MrsArnoldPlus1@twitter.com and @AndreaBecker@twitter.com with a

#desmos #iteachmath #Mtbos
#iteachmaths #education

https://teacher.desmos.com/activitybuilder/custom/6388b42fd9427da5a0692cd1

Amanda Ghassaei has amazing simulations. 😃

I used them for my classes to talk about ODEs and PODEs.

https://dynamicmath.xyz/math2001/chapter-06.html#/6/4

#iteachmaths #simulation #ODEs #PODEs

Uplifting the amazing work of Andrea Becker (https://twitter.com/MsBeckerMaths?s=20&t=HGC-L1oPhe3VRfsZ-1mVow): Proving Triangles Congruent through Constructions and experimentation. Classic flavor with constructivist twist and a ribbon of ongoing feedback, sprinkled with strategic bitmojis. Would use again. https://teacher.desmos.com/activitybuilder/custom/63864032cc844a45c64c7d92
#iteachmath #Mtbos #desmos #iteachmaths

It's written - Spreadsheets for A Level Scientists and Geographers.
That's a lot of worksheets.
@edutooters #ITeachMaths #MTBoS @mtbos

Worked through a fascinating lesson by Open Up Resources about visualizing Quadratic Products using Area Models and negative numbers. I always found algebra tiles a baffling model for negatives since intuitively negatives are reduction in space but this is nice explanation.

How have you found the Area Model effective for your students?

#iteachmath #iteachmaths #highschoolmath #Mtbos
Full lesson here: https://access.openupresources.org/curricula/our-hs-math/integrated/math-2/unit-2/lesson-7/teacher.html

Finally!! A Curriculum that integrates visualization of quadratics in an intuitive way.

https://access.openupresources.org/curricula/our-hs-math #iteachmath #mtbos #iteachmaths

Still not quite complete - hopefully all done by next week!
#Spreadsheets #ITeachMaths #EduTooter

@ColinTheMathmo @icecolbeveridge this is a wonderful thread/tootstorm/fanfare...
But don't forget #TMWYK (talking math w/your kids)
#MTBoS #iTeachMath #iTeachMaths