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Teaching Mathematics

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How ‘Deprogramming’ Kids From How to ‘Do School’ Could Improve Learning. iStock One day, Adam Holman decided he was fed up with trying to cram knowledge into the brains of the high school students he taught. They weren’t grasping the physics he was teaching at the level he knew they were capable of, so he decided to change up his teaching style. It wasn’t that his students didn’t care about achieving — he taught at high performing, affluent schools where students knew they needed high grades to get into good colleges. They argued for every point to make sure their grades were as high as possible, but were they learning? “I felt I had to remove all the barriers I could on my end before I could ask my kids to meet me halfway,” Holman said. The first thing he did was move to standards-based grading.

He told his students to show him they’d learned the material, it didn’t matter how long it took them. “The kids realized this made sense,” Holman said. Holman didn’t just change his grading policies. “Students clearly learned in Mr. The Hexagon of Proof. Following up on the work of Serra and De Villiers, and in the spirit of recent discussions about the success Bloom's Taxonomy has had in penetrating classrooms, I present the Hexagon of Proof. There are six components to the Hexagon of Proof. Learning is a messy affair that doesn't follow any sort of strict hierarchy, so a math classroom should involve all six of these aspects of proof. Still, if teachers find that their students are having trouble proving things in some area in math, students may benefit from time spent disagreeing over or debating some related mathematical propositions. The idea is that the reasons that are needed for proof can be developed through a variety of contexts that kids are more familiar with, such as arguing with each other over something controversial.

Here's how this might look in class: Disagreeing - Hook the kids into a disagreement. Debating - In the face of disagreement, ask kids to defend their views. "Knowing Alongside" - DOING MATHEMATICS.

Mathematical Tasks

The Puzzle Solutions You’ve Been Waiting For…. | mathcoachblog. This post will present solutions to two puzzles I have presented here on the blog, and some ideas for extending the learning with your students. This is a game I proposed a while back on the blog, and it took my friend Anthony from Twitter’s gentle nudging to ask for a solution.

Here’s a re-cap of the game: 23 marks are placed on a boardOn each turn, a player must remove 1, 2 or 3 marksThe player who clears the board wins I often challenge classes with this game, letting kids play me and try to figure out the secrets. The beauty here is that my students are often polite souls, and will let me go first…which leads them to doom. It will often take a few days before a student can conquer me. Here’s a video example: And here is the message I sent back to Anthony, who requested the secrets to the game. Here’s the secret to the take-away game – if I can make it so that the number of dots remaining is a multiple of 4, then I will win the game – guaranteed.

Have fun Like this: Like Loading... My “Fake World” Task | mathcoachblog. Dan Meyer’s recent post on “fake world” math tasks has me thinking about many of the openers and games I have used in my classroom. I have written about The Take-Away Game before, and I still use it often…until the kids learn how to beat me and the strategy is revealed. This next one is not so much a game, but more of a task, similar in some ways to the Locker Problem. In this task, chairs are placed in a circle. Chairs will be removed from the circle using the following rules: Chair #1 is removed first.The next remaining chair is skipped, and the next chair removed.This continues, with chairs skipped and removed until only one chair remains.Once a chair is removed, it is “out” of the circleWhoever is sitting in the last remaining chair “wins” Here’s a brief Doceri video which shows some game playings: Like the “Take-Away Game”, I can’t recall where I first encountered this problem.

Why I enjoy this problem: It’s not intimidating. There are a number of ways to express the solution. The Take-Away Game | mathcoachblog. A recent visit to a 6th-grade classroom gave me a chance to introduce a simple game I have used in the past as an-going challenge. Even after a few pop-ins to this 6th grade class, I am still undefeated, and don’t plan on giving up my championship belt anytime soon! THE TAKE-AWAY GAME – Rules On a board, or piece of paper, draw 23 X’s.

Players will alternate turns, and on each turn a player must erase 1, 2 or 3 X’s. The winner is the player who erases the last X. It’s an easy game to understand. With a class, I will give students a chance to use dry-erase boards and play against each other. Eventually, students will gather around to suggest moves. As students master the game, we can ask some extension questions: Does the number of X’s we draw change the game?

For now, play the game with your students, and I look forward to retaining my Inter-Galactic Take-Away Game Championship Belt! Like this: Like Loading... My Love Letter To Orpda. This is my love letter to Orpda, an invented number language in Base 5 that I learned about through Christopher Danielson. Half of what I want to say about Orpda is "Go read Danielson's post! " (A quarter of what I want to say is "Go read Weltman's ba-na-na post! " That leaves me a quarter to talk about what actually happened in my 4th Grade class.) (The last quarter is sort of long.) We start with this: Then we draw another red circle and ask kids: "What do we call this many things?

" What's the point of this? A nice solution is to shift to a similar, but unfamiliar context. (This is basically Danielson's fade-away jump shot. (That and the hair. So, here's why Orpda is a solution to a teaching problem of mine. So? What to expect from the kids Here's what my kids came up with for representing the next number in Orpda: $ + #@@@@@##@Invent a new symbol for that many dots. All of these options were considered. Super-flock! Then we count, out-loud. Then, we get stuck. ... Random Thoughts.

Geometry

What It Feels Like to Be Bad at Math. As a math teacher, it’s easy to get frustrated with struggling students. They miss class. They procrastinate. When you take away their calculators, they moan like children who’ve lost their teddy bears. (Admittedly, a trauma.) Even worse is what they don’t do. Ask questions. There are plenty of ways to diagnose such behavior. Math makes people feel stupid. It’s hard to realize this unless you’ve experienced it firsthand. Thanks to a childhood of absurd privilege, I entered college well-prepared.

But senior spring, I ran into Topology. Topology had a seminar format, which meant that the students taught the class to each other. My failure began as most do: gradually, quietly. But I didn’t seek out that jolt. So I did what most students do. I blamed others for my ordeal. Sing it with me: “I hate math!” My first turn as lecturer went fine, even though my understanding was paper-thin. As the day approached, I began to panic. I was sweating in the elevator up to his office. Like this: Www.maths.ed.ac.uk/~aar/atiyahpg.pdf.

High-Leverage Practices

Interesting Mathematics. MKT. My Problem Based Curriculum Maps | emergent math. The following Problem Based Learning (PrBL) curriculum maps are based on the Math Common Core State Standards and the associated scope and sequences. The problems and tasks have been scoured from thoughtful math bloggers who have advanced our practice by posting their materials online. The Scope and Sequences for Algebra 1, Geometry, Algebra 2, Math 9 (Integrated), Math 10 (Integrated), and Math 11 (Integrated) are from Pearson. Other Scope and Sequences were developed by me, modeling a similar visual style. Grade 3 CCSS PrBL Curriculum Map Grade 4 CCSS PrBL Curriculum Map Grade 5 CCSS PrBL Curriculum Map Grade 6 CCSS PrBL Curriculum Map Grade 7 CCSS PrBL Curriculum Map Grade 8 CCSS PrBL Curriculum Map Math 9 (Integrated) CCSS PrBL Curriculum Map Math 10 (Integrated) CCSS PrBL Curriculum Map Math 11 (Integrated) CCSS PrBL Curriculum Map Algebra 1 CCSS PrBL Curriculum Map Geometry CCSS PrBL Curriculum Map Algebra 2 CCSS PrBL Curriculum Map Geoff Update 4/12: I added a Grade 8 curriculum map.

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