The best thing about online communities (IMO), is the emergence of artefacts from the collected actions of many people. The online math education community (known as the MTBoS) has seen many of these collections throughout the years, most of which are aimed at supporting imaginative mathematics instruction in grade school. Personally, I have felt the community around Fraction Talks explode right under my nose, and it has been a joy to see how the prompts have sponsored amazing student reasoning. A few months ago, I had another idea for a task structure–that I dubbed #MenuMath–and began to collect examples from engaged math teachers. Since then, the collection has grown and become bilingual thanks to the translation work of Joce Dagenais. I love hearing about student and teacher creations, and you are encouraged to submit menus via my contact page if you feel inspired to do so.
Category: logic
Everyone knows that you can’t wish for more wishes, but no one says you can’t wish for more genies.
According to the binding rules of genies (as published by Disney in the 1992 film, Aladdin), there are a few restrictions on what can and cannot be wished for. Probably the most famous restriction is that there is unequivocally no circumstance in which one is permitted to wish for more wishes. This is grouped with three other limitations stating that genies will not kill people, make people fall in love, or revive people from the dead. Other than that, the wishes are limited only by the imagination of the master.
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.
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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).
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Fair Dice Task
The recent curriculum renewal has placed a (well-deserved) heightened emphasis on counting, set theory, and probability. Just under a half of a Grade 12 “Foundations of Mathematics” course now covers the three topics. This is a huge improvement from the token, disjointed topics strewn around the last courses. It allows teachers to set a different tone–a tone of curiosity that seems inherent in probability.
I came across the idea of Grime Dice (named and pioneered by Dr. James Grime @jamesgrime) late last year after I knew I was to be teaching probability this winter. I knew right away this was a great task to get students tinkering with probability before defining its inter-workings theoretically. A great description of their function can be found on the PlusMath website written by Dr. Grime himself. They are available for purchase from MathGear.co.uk.
My involvement with a provincial math executive presented me with an interesting task recently. Like most tasks, I turned to get some input from the strong contingent of math teacher tweeps.
I needed to develop an activity for 100-115 students in grades Seven to Eight. All I was told is that it should be about an hour and a half, and be active in nature. The students are taking part in a math contest in the morning, and it would be great to get the blood pumping. I turned these demands to twitter, and came up with some excellent options:
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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.