Category: tasks

Building the Proper Ecology

Post author By natbanting
Post date February 4, 2012
1 Comment on Building the Proper Ecology

The beginning of semester poses many challenges–new classes to teach, names to learn, and class sizes to manage. No challenge is greater than building the correct atmosphere in the classroom while balancing the students’ preconceived notions about you, your class, and mathematics. (Hopefully not all three impressions are poor).

Students talk. They let their friends know how your class runs. This is all the more reason to set the proper atmosphere, because a poor semester can follow you like a plague for semesters to come. I would like to propose that there is more to an effective class than the atmosphere. (This is a duh moment). In fact, as teachers we need to embrace a terminology shift.

Lesson Planning; Lesson Participating

Post author By natbanting
Post date January 28, 2012
6 Comments on Lesson Planning; Lesson Participating

Occasionally, I give a task to my students before I have done it myself. Sometimes it is because the solution is fairly straightforward and I can see multiple ways to arriving at it without actually doing it. Other times it is because I want to have no impact on my students’ thought pathways. The practice also makes class time more exciting as students reason through methods that I would not have though of–I am trying to move from a monotonous state of lesson planning to a more exciting one of lesson participation.

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Embedding Atomic Skills

This post marks a couple of milestones for Musing Mathematically. First, this is the 50th post overall. For some reason that seems significant. Second, this post marks the blog’s first coined phrase–Atomic Skills.

I love the term atomic skills, but I can’t remember when I started using it. I believe it was the result of my limited vocabulary attempting to explain the current disconnectedness of math education. An atomic skill is a foundational skill. An atomic skill is a skill that holds no real ‘stand-alone’ significance, but can build toward a very significant solution. Atomic skills are usually practiced in isolation of each other in a very repetitive fashion. In school mathematics, atomic skills often make the difference between a good and bad student. Students classify errors with atomic skills as “stupid mistakes”.

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Trigonometric Mini Golf

Christmas time brings immense stress for math teachers, at least in my division and province. As the days dwindle away, teachers begin to get a more accurate picture of how much they must cover before semester’s end. Once again, I found myself in this position with my Grade 10 Foundations and Pre-calculus class. (Saskatchewan Curriculum) My original plans called for 20 teaching days to adequately cover, in my opinion, the topics of trigonometry and systems of linear equations. Of course, by the time I sat down to calculate this I only had 11 remaining.

In previous years I would have panicked and switched into jam-packed lectures to “cover” all the content. This year I decided to re-think that approach. I wanted to find a project or anchor activity that could facilitate a wide swath of outcomes and motivate a high level of learning so close to holidays. I tried several creations, but settled on this one for its native curiosity and deep flexibility.

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Linear Functions With a Bang

Post author By natbanting
Post date November 12, 2011
No Comments on Linear Functions With a Bang

Many teachers tell me that it is their creativity that limits their ability to be adaptive in the classroom. Somehow the “reform” movement (or should I say re-movement) has pigeon-holed itself into a connotation where high-energy teachers give vague tasks to groups of interested students. Out of all this, curricular outcomes explode in no particular order. This can’t be further from the truth. In my view, the biggest steps toward changing student learning is changing teacher perception.

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In the Footsteps of Gauss

Post author By natbanting
Post date September 5, 2011
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I like to introduce each topic with a task or activity. These do not necessarily have to be long, but should activate mathematical thinking. The idea has slowly evolved for me throughout my short career. They are the amalgamation of the ideas of a “motivational set” and discovery learning. I felt that both components are positive things to include in a math class, but both had severe implementation problems.

The motivational set is far too passive. In my college, a picture, story, or conversation could serve as a motivational set. It was essentially a transition tool that was completely void of any mathematics. Every lesson begins with the same routine whether it be a national anthem, attendance, or a short time of homework recap, but each learning experience needs to begin with an active brain. I found that the purpose of the motivational set was important, but needed a stronger method to get brains engaged in the day’s learning.

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First Day Tasks

You don’t get a second chance to make a first impression.

This is naturally true, and although I don’t believe that you can build or destroy a successful semester in one class, it is definitely important to put your money where your mouth is on the first day. I have spent the past few days digging around my materials for the best possible starter activities.

I had some very helpful responses from the twitter-verse, and it prompted me to somehow sort out the information being provided to me. In the past, I have had very productive lessons on the first day. Not productive in the “coverage”sense, but rather in the “intriguing” sense. My goal was to define a set of characteristics that, in my opinion, create a suitable opening day problem.

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Un-Locking Prior Knowledge

Post author By natbanting
Post date August 8, 2011
2 Comments on Un-Locking Prior Knowledge

I enjoy mathematics in the morning. It wakes my brain up, and makes my coffee that much more comforting. Much of the deliberate mathematics learning that I do takes place in the morning. I say deliberate, because mathematics always finds ways to sneak itself into all parts of my day. Morning is just when I open the door and embrace the learning with open arms.

Today’s dose came courtesy of @republicofmath via @jamesgrime. The problem took longer than I expected, but the result was quite eloquent. I ended up using a method that I had no intention of ever using again. It was the use of this prior knowledge that made the experience valuable.

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Large Number Numeracy

Gigantic numbers are all around us. This has never been more apparent since the US Debt ceiling became a major issue. The facts and figures are thrown around by the news, and joked about on Late Night television to the point where their potency is diluted. Not many Americans seriously understand what a trillion dollars is. That statement can be broadened to include all earthlings. The comprehension of large numbers is a very interesting task, especially given the role that the media plays in our students’ lives.

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Measuring Roots

I stumbled upon the “root” of this activity late in the school year after I had already taught the unit on radicals and their approximate values to my Grade 9s. I modified its purpose, but the original framework is credited to John Scammell. (@scamdog) I found the concept to be a fairly easy one for the students to grasp once the identity of a root was explored. Students know what a square root is. In fact, I was challenged by a 7 year old boy who I was babysitting just the other day. His older sister–an 8 year old genius–was obviously giving him a crash course in radical mathematics. She had explained to him that square roots can be presented as a problem. He challenged me with this:

“What is the Square Root of 3? I mean, what is the square root of 9?”