![]() Truly unfortunate representations of data (9).Questions from middle school teachers (6).Questions from middle school students (10).Place value and the Lattice Algorithm (or A Simple Task, Years in the Making).If a function is a vending machine, then.My Shape is Sam – Math Book Magic on The hierarchy of hexagons.My Shape is Sam – Math Book Magic on Classifying hexagons.My Shape is Sam – Math Book Magic on The hierarchy of hexagons, continued.Carnival 150: Keeping Playful Math Alive – Denise Gaskins' Let's Play Math on A circular conversation with a 4-year old.Carnival 150: Keeping Playful Math Alive – Denise Gaskins' Let's Play Math on It’s about understanding.Posters Posters Posters! (plus a prize drawing!).You can buy tiling turtles, pattern machines and my book Common Core Math For Parents For Dummies, (with more items coming soon) at the Talking Math with Your Kids Store Math On-A-Stick, Oreos, Talking Math with Your Kids….all are predicated on Experience first, structure later. This is theme that plays out in all of my work, by the way. Also, students end up lacking meaningful mental images for representing and triggering the formal structures. Typically they see no need for it, and struggle to incorporate these structures into their view of the world. I’m not a big fan of providing structure for things students haven’t experienced. This activity creates an experience for students, and then it’s my job to help students structure that in a formal way-through statement of and exploration of the Intermediate Value Theorem. This activity illustrates a curricular principle I sketched out recently, which is that lessons build on students’ experience, and help them to structure that experience mathematically. Only after that am I ready to state the Intermediate Value Theorem. AS LONG AS THAT FUNCTION IS CONTINUOUS!!!!! (Screen 16 for crying out loud).If the function starts negative and becomes positive, it has a root.There are sometimes not roots where it looks like there really ought to be.There are sometimes roots where you don’t expect them (Screen 8).In a classroom setting, I’ll discuss these examples once students have worked through them. In that discussion, I want to get students to verbalize the following things: In that spirit, you are told in this activity that the first three functions are continuous. a sign change between the interval’s endpoints.continuity on the interval in question, and.This is a little routine I developed as a Calculus teacher to spur conversation, and it contrasts with a standard textbook approach, which asserts the importance of three conditions for knowing there are roots: Behind which circles is it impossible for there to be roots?Īfter each round of questions, you have the opportunity to move the circles aside to see for yourself whether there are roots.Behind which circles might there be roots?.Behind which circle(s) must there be roots for this function?.There are four such graphs, and I ask the same three questions of each one. ![]() You see a function that is graphed on the coordinate plane, except that parts of the graph are obscured by large black circles. It’s a simple little calculus activity on the surface. ( Here is a link if you want to play along as a student-I recommend doing that!) ![]() I am on leave from my community college teaching this year, and am working at Desmos remotely from St Paul.Ī large chunk of my time involves working on the pedagogy side of Activity Builder, which we released this summer.Īctivity Builder lets you build a classroom activity using one of three basic screen types: graph, question, and text with image.įrom time to time, I’ll take the opportunity to turn something I’ve done in the classroom before Activity Builder and make an online version. ![]() Let me bring you up to date, in case you have not been following along.
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