"TL;DR: an unassembled jigsaw puzzle takes up an area that is the square root of 3 times the area of the assembled puzzle, or about 1.7 times the assembled area. This is independent of the number of pieces."
This is the first question on a set of Review problems for Algebra II Honors. The students worked on these together in class, and there were a lot of excellent questions and discussions.
I was sure to let them know that these were, in general, harder than what they would see on their upcoming test, but that the very act of wrestling with them and discussing them would help them prepare by deepening their understanding. (Hard to tell how much they bought into that.)
Seems on the podcast that Pam Harris isn't over in mathstodon parts ;( I'm listening to https://www.buzzsprout.com/1062400/13776761 which is about division strategies and they're talking about how much you can do with knowing about halves, and all the different ways we represent division and ratios.
Thinkin' "and I want to hear that one about problem strings & strategies" (b/c I think my half lesson that went so well was basically "problem string" that inspired good strategies) and HEY! I rode the bus today, I know what I'll be doing on the way home...
A question for teachers, but I'd welcome thoughts from others.
In teaching, should one talk about a quadratic equation such as x^2+10x+25=0 as having one solution or a repeated solution, and do you think it matters?
Any A-Level teachers in interested in watching a video and giving me some feedback? It's a career talk, really ... how is A-Level maths used in my "career".
Looking for a fun little game to keep in your back pocket for those days when you have seven random minutes left at the end of class? Let me introduce you to the Game of Sim (invented by Gustavus J. Simmons) that involves drawing lines and avoiding triangles!
"Stock and flow diagrams" are a nice graphical tool for modeling systems. People have had success teaching them to students starting at a young age. It's a way to teach them math, economics, ecology, and other subjects in a unified way.
When you include functions describing the flows - shown as faucets here - you can turn these diagrams into differential equations. But you don't need to do that for young kids: there's a lot you can learn from these models in a purely qualitative way. Basic concepts like feedback, etc.
And once you introduce the flow functions, you can let software solve the resulting differential equations and graph their solutions even before the kids know anything like the definition of derivative! This is a good way to gently get them interested in calculus.
For example, below you can see a model of reindeer population on an island created by middle school students. The population soared and then crashed:
"Students built System Dynamics models to study human population dynamics, non-renewable and renewable resource utilization, economic influences, etc. In these lessons students were asked to build the model, anticipate model behavior, explain discrepancies between anticipated model behavior and actual model output, analyze feedback, then test policies on the model to determine leverage points."
"What are people's favourite ways of exploring Mathematical proof at A-level? Looking for some purposeful ways to start Year 12 off from September. Would love to hear your ideas "
Hi Mathstodon: Having seen all of the great teaching ideas people have floated here, I thought this would be a good place to share a really naive but I think also difficult question. I apologize for phrasing this question in a deficit-based manner; it would actually be really helpful if anyone knows a better way of reforming it! But let me just phrase the question the way that instructors in our department have been putting it:
Q: How do I teach precalculus or calculus to students who are having trouble with basic algebra?
Again, I apologize for asking an ignorant question! But I think that's where we are. So where do y'all think we should go from here?
To start getting connected you need to search for hashtags. If you're into #MathEd or #MathsEd the you also want to search for #ITeachMath and #MTBoS ...
"faculty teaching introductory college algebra rarely addressed students’ misconceptions, made references to their students’ prior knowledge, or employed metacognitive teaching strategies. Moreover, while being observed, faculty never applied a mathematical concept to real life. Moreover, mathematics instructors rarely praised their students" https://www.tandfonline.com/doi/abs/10.1080/87567555.2023.2221017 #ClosedAccess#EdDev#MathEd#Teaching