Musing Mathematically Blog

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What High School is (Often) Missing: A Conversation with a Kindergartener

Post author By natbanting
Post date February 8, 2015
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Sometime after pyjama time and before bedtime, a math conversation broke out. My wife and I were visiting some good friends, when the topic of a recently purchased board game came up. It was bought at a teaching specialty store and designed to teach addition and subtraction of twos. After examination, I didn’t like the overly symbolic structure, and asked their 5-year old if she wanted to play a math game. She ran and got a piece of paper. When she finally got called up to bed (much later than expected) I took the page and folded it into my back pocket.

Here it is:

reflection

Bloggable Distributions: Reading #MTBoS Blogs in 2015

Post author By natbanting
Post date January 4, 2015
1 Comment on Bloggable Distributions: Reading #MTBoS Blogs in 2015

Twenty-fifteen will be the fifth year that my little corner of the blogosphere has been dedicated to digitally curating my own thoughts and experiences regarding the teaching and learning of mathematics. It represents a wide array of posts regarding a wide array of topics. Much has changed from new teacher status to graduate student, and the posts reflect that. Still, the heart of its posts and pages is pragmatic: I write about classroom events that seem to matter (for some reason or another, they catch my attention) in hopes that other teachers might find the same phenomenon.

I am going to call these episodes: bloggable moments.

equations systems of equations visual

Visualizing Linear Systems

Post author By natbanting
Post date December 7, 2014
2 Comments on Visualizing Linear Systems

My Grade 9 students don’t see an equation for the first two weeks of their unit of solving linear equations. That is because I think students get all bogged down in the notation, and lose their problem solving intuition.

Instead, I play around with a key metaphor for solving linear equations–the balance scale.

functions polynomial

Polynomial Personal Ads

Every year, my students study the general characteristics of polynomial functions. We investigate the various shapes of various functions and slowly shift parameters to watch changes in the graphs. Eventually, we deduce the roles of the constant term, leading coefficient, and degree.

It should be noted that Desmos makes this process much easier than years previous. Just set up the generic polynomial, add sliders, set specific ones to play (depending on what you want to investigate), and have students discuss in groups.

math wars reflection surface area

CCSS: Support from the North

Post author By natbanting
Post date November 11, 2014
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I can’t–for the life of me–understand why someone would argue to eliminate high level mathematical reasoning in favour of memorized tricks, but that seems to be the case with those arguing against the Common Core State Standards. I cannot fathom how this can be the case except to chalk it up to a case of “he-said-she-said”. Change (especially in something as resistant to it as mathematics education) breeds ignorance. And Ignorance breeds fear.

Let’s face it: The public is scared of reform efforts and most teachers aren’t far behind.

probability

Egg Roulette

I find probability to be one of the most difficult topics for students to grasp. Beyond the simple experiments of spinners, coins, and dice, students have issues operating on uncertainty. This issue is compounded when multiple events each involve such a calculation as well as the relationship between them. Soon they find themselves neck-deep in notation and lose all rationality–they forget what they are solving to begin with.

This past week we found ourselves mired in another battle with conditional probability. The initial questions were completed at a high level:

classroom structure discourse

Math Class Starters

I am very distractible. Students know this; I know this. For this and multiple other reasons (including insipid tardiness on the part of my students) the first few minutes of class is often filled with retrieving forgotten textbooks, quieting down the pockets of flirtation, and acknowledging the students who show up two minutes late with a coffee.

Numerous factors have led me to the institution of class starters for grade 9s. I will do my best to summarize them here and introduce my framework, theory, and pedagogy behind them.

Why Starters? (The multiple influences)

classroom structure reflection

“__BL” : Education’s Obsession With Labels

Post author By natbanting
Post date July 23, 2014
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Last week there was an interesting twitter discussion on the nature of projects versus the nature of problems.

@dandersod @samjshah @k8nowak @leslie_su76 How is Mega M&M a project rather than a problem?

— Dan Meyer (@ddmeyer) July 17, 2014

It occurred with specific reference between the differences of PBL (project-based learning) and PrBL (problem-based learning). If you follow this blog or scan the provided tags you will find PBL does occupy some space here. There is also a large amount of posts detailing “tasks”. This is a rather artificial term I use to refer to a piece of mathematical work to be done or undertaken.

classroom structure investigation pattern problem posing

Problem Posing with Pills

Post author By natbanting
Post date June 25, 2014
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My class always welcomes conjectures. This is made explicit on the very first day of the semester. This goes for everything from grade nine to grade twelve. As the grades advance, the topics have us venturing into increasingly abstract concepts, but conjectures are always honoured.

Certain class structures promote conjecturing more than others. Students offer questions during lectures, but they are often of a surface variety. They notice a pattern that has occurred in three straight examples, or think they have discovered a short-cut. I don’t like using tricks, but if they are “discovered” or “re-invented” (to borrow a term from Piaget and genetic epistemology), then we use them.

Pythagorean theorem right triangles tasks

Garbage Can Task

The following task happened by accident:

I was about to introduce a problem to my Math 9 Enriched class that we were going to complete with group whiteboards. Before I could introduce, life got in the way. Students wanted to know about their most recent examination. As I launched into a speech on their performance, a student got up to sharpen their pencil. She walked right in front of me. I made a comment, and she replied that the garbage can should be in the back corner where it would be more convenient.