Wait, another NEW SIM!
Our classic Calculus Grapher is now in #HTML5, with multiple new features, like the ability to explore tangents, area under the curve, and a predict mode.
Check it out!!
#math#iteachmath#calculusphet.colorado.edu/en/simulat…
Challenge: prove that the blue path and the red path have equal lengths.
No spoilers, please!
Instead, share thoughts on useful hints to help students with this problem.
#hintchat
Huge thanks and hat tip to @DavidKButlerUoA for this problem!
#iteachmath#mtbos
For more than 50 years, mathematicians have sought an “einstein”--a simple shape that can only tile the plane nonperiodically. Now a retired print technician has found one! My latest for @QuantaMagazinequantamagazine.org/hobbyist-…
Some bright spark decided it was a good idea to sell lemonade and ice cream spiders at lunchtime to raise money for something. My Year 7s literally bounced off the walls this afternoon - for real. One student proudly told me he had 3 of them. It showed 🤪.
Terrific lesson today using @DrFrostMaths Live! game to do a full 50 mins of revision practice with Year 7 students fully engaged for the whole period.
Conversation with a new maths teacher about their university training to become a high school maths teacher : they did lots of Vygotsky, Piaget and Bloom's Taxonomy , but never shown Geogebra or Desmos!
Latest from me in Schools Week on why ChatGPT is great but doesn't mean we have to re-imagine the curriculum.
It's "You can't just look it up", 2023 version!
Chatbots are not going to be revolutionary for teachers or schools or learning. But they might prompt changes in how we do things.
pershmail.substack.com/p/cha…
Today's reading (thank you to authors for sending me a copy!) : "Not a One-Way Street: Bidirectional Relations Between Procedural and Conceptual Knowledge of Mathematics" link.springer.com/article/10… poses some very strong challenges.
"much more research is needed on the most effective dosage and timing of instruction on concepts and procedures. We suspect that there are multiple routes to [...] competence, such as instruction that iterates between a focus on concepts and procedures throughout instruction"
"In many Asian countries [...] practice is viewed as a route toward understanding, where there is a public perception that only through a great deal of practice can true understanding be developed."
"We consider possible reasons for why mathematics education researchers often believe that a conceptual-to-procedural ordering of instruction is optimal and why so little research has evaluated this claim. "
Just stumbled across Derek Hurrell's great 2021 paper on conceptual and procedural knowledge. Really helps provide a framework for thinking about teaching mathematics and the learning sequences files.eric.ed.gov/fulltext/E… . And lots of lovely references to recent studies.
Sadly I can't read most of the references because they are locked behind journal paywalls. My university alumni library membership doesn't include online access.
We see first hand the issues of making English (not to be confused with Literacy) compulsory in NSW Year 11 & 12. Ask any English teacher. The same will happen if/when Maths is made compulsory. Unhappy students, shortage of teachers, reduced participation in other subjects.