Author: natbanting

What Makes a Task “Rich”?

In my short career, I have seen the death of the lesson. I remember creating ‘lesson plans’ to the exact standards of my college of education, and then never looking at them when I began to teach. I was never really in tune with the rigidity of the plan, but knew that there were certain learning goals I needed to get to by the end of an hour.

The scene has shifted away from the harshness of a ‘lesson’ toward more student-action-centred words like project, problem, prompt, or task. I like these words because they accurately describe what I am trying to do as a teacher–make the students think.

Animating Patterns

There is a very strong emphasis on linear relations and functions in the junior maths in my province. In Grade 9, students begin by analyzing patterns and making sense of bivariate situations. The unit–which I love–concludes with writing rules to describe patterns and working with these equations to interpolate and extrapolate.

Grade 10 students continue along this path in the light of functions. There is a large degree of abstraction that occurs in a short amount of time, and droves of students abandon the conceptual background (pattern making) in favour of memorizing numerous formulas. (Slope formula, slope-point, 2-point-slope, slope-intercept, etc.)

**Some (much prettier) quadratic patterns, which are introduced in 11th Grade, are posted here**

factors fractions games investigation logic tasks

Fraction War Task

A while ago I wrote a post on embedding atomic skills into tasks so that the basic skills are developed and used as tools of mathematics rather than the ultimate goal of mathematics. I try to develop tasks that follow this framework. I want the student to choose a pathway of thought that enables them to use basic skills, but doesn’t focus entirely on them.

Recently, I was reading Young Children Reinvent Arithmetic: Implications of Piaget’s Theory by Constance Kamii and came across one of her games that she plays with first graders in her game-driven curriculum.

data analysis probability ratios tasks vine

Spinner Data Task

The difference between what should happen and what does happen is a difficult distinction for students. They are so used to finding exact answers in the back of textbooks, that differing experimental results create an sense of uneasiness. At an early age (Grade 9 in my province) we begin to introduce students to the ideas of sampling and experimental probability.

The topic is usually approached with a project or survey of schoolmates. The results are then tallied and then used to create “probabilities” of various things such as favourite sports team, food, or colour. I love the philosophy behind the project approach; student initiative and autonomy is a powerful thing. I, however, don’t like that the experiment involves humans. Here’s why…

flipped classroom Khan Academy technology trigonometry vine

Ambiguous Case Vines

We all live in a consumer’s world, and we do an amazing job at acting entitled. These two factors have culminated in the invention of Vine–an app used to create six second, looping video clips.

Yet another way in which students can create, share, and network around media. Unfortunately, I feel like my students don’t often have an attention span longer than a Vine video.

logic numerical flexibility pattern tasks

Dice Sums Task

Dice are familiar tools in most mathematics classrooms. Their use in primary school games allows students to build preliminary notions of number and autonomy. (see Kamii) As the grades progress, dice sums become too simple and the tool is pushed into the realm of probability and chance. There, alongside decks of cards and coloured spinners, it enjoys almost godly status; it seems that there is no better way to calculate odds than to role dice and spin spinners (in outrageous cases—simultaneously).

measurement ratios tasks unit analysis

Leaky Faucet Task

This idea is not my own. The only problem is, I don’t exactly know who it belongs to. I remember tweeps talking about about a task where a leaky faucet’s effect was analysed on a water bill. When I encountered the situation at my Uncle’s house, I had to capture the modelling in action.

The best part was the conversation from intrigued (and weirded out) relatives as I ducked and dived around the tap to get a good angle. We got into a conversation about teaching, and they were happy to present any questions that came to their minds.

talking with children

Talking with Children: Shape Centers

Post author By natbanting
Post date May 18, 2013
5 Comments on Talking with Children: Shape Centers

I have been spending considerable effort looking for situations to “mathematize” in my daily interactions with students. Sadly, upper-level students are so mark and answer focused that they spend little time wondering about emerging problems with me.

This is not the case with my 8-year old friend.

While he was inventing his word problem, he stumbled upon the idea of a middle. Specifically, he told me that four train tracks met in the middle. I quickly asked him if three tracks could also meet in a middle. He responded with an annoyed, “of course”.

A problem was born.

talking with children

Talking with Children: Word Problems

Post author By natbanting
Post date May 7, 2013
1 Comment on Talking with Children: Word Problems

My wife and I spend a lot of time with friends who have three young children. I spend most of that time engaged in a combination of trampoline dodge ball and mathematical discourse. The middle child is most willing to think mathematically. During one of our conversations, he decided to turn the tables. What resulted is a wonderful look into a child’s perception of what “mathematics” does.

Him: Maybe you can answer my question?
Me: Sure. What is it?
Him: Ummm… (literally scratches head)

numeracy numerical flexibility reflection

Vedic Maths: Lipstick on a Pig

Post author By natbanting
Post date April 17, 2013
1 Comment on Vedic Maths: Lipstick on a Pig

I was alerted to this video by a pre-service teacher that helps in my room every week. Before this post makes any sense, you should watch the video below. Try to watch the whole thing–I found that task very difficult.