It seems that every educational blogger has voiced an opinion on the growing popularity of the Khan Academy. I am actually quite surprised that Musing Mathematically has largely avoided the topic during its meager 5 month existence. The movement of online lecture snippets has polarized those in the educational community; some teachers detest that Khan claims that sitting in front of his computer can even be close to “education” while others realize the efficiency of his method and subscribe wholeheartedly. I have been sitting passively over the last few months reading developments and arguments, and yesterday evening found an article that solidified my opinion of Khan. As an educator, I applaud his vision and initiative, but I feel like he is overestimating his project’s niche of influence.
Author: natbanting
I have spent the better part of 2 weeks going over various mathematical relationships in my Grade 10 class. They have been represented as tables of values, arrow diagrams, and sets of ordered pairs. Relationships, both qualitative and quantitative, have been defined, analyzed, and graphed. My focus on graphical literacy has been previously detailed on the blog. See this link for details.
Numerous relationships were handled. Students we required to create a family tree and then represent its branches as a table of values and set of ordered pairs. Throughout the various exercises, the words “input”, “output”, “domain”, and “range” were consistently used. My family tree mapped the connection between a Domain of “Names” to a Range of “Familial Relationship”. Some of my ordered pairs then became:
My school division has been pushing literacy for a few years now. The division priority has filtered its way down into many programs at the school level. As a basic premise, if students are exposed to literate people and perform literate activities, their skills will grow.
As the term is dissected, it seems that every stakeholder can find a way to skew the term to mean that their discipline is a crucial part of being literate. Reading and writing skills are an obvious avenue, but the ideas of technological and social literacy have emerged as important parts of every student’s school experience. Riding shotgun to these ideas is the idea of Mathematical literacy–Numeracy.
My province is in the midst of a major overhaul on its curriculum. This puts me in a very interesting situation. I am a new teacher in a large division filled with veteran teachers that all feel as overwhelmed as myself. I can’t decide if this is a curse or a blessing; I simply continue to roll with all the punches that curriculum renewal brings. On top of the nuts-and-bolts of each new course (5 of which I teach for the first time this year), the division heaps on division, school, department, and personal learning priorities. To make matters even more confusing, each initiative comes with about 35 acronyms. I can’t tell the difference between AFL, PLO, PLP, PPP, SLI, PBL… you get my drift. Amidst the chaos of red tape, I believe I have found something to hang my hat on.
I recently finished up a unit on sequences and series with my grade 11 pre-calculus students. The unit is somewhat of an enigma because it contains relatively simple ideas bogged down in complex notation. This coupled with the overlapping definitions makes for a fortnight of rather rigorous cognitive exercise.
The unit was supported through group tasks as the topics moved along. Arithmetic sequences and series were linked to linear functions through the toothpick problem. Students were asked to arrange toothpicks into boxes and record how many toothpicks it took to make ‘x’ number of boxes. Their results were extrapolated and tied to variables from the linear functions notation. From there, I introduced the new terms of “common difference” and “term one” instead of slope and y-intercept. The arithmetic portion usually goes smoother than its geometric cousin for two reasons:
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All Factors Considered
I have only been teaching for 2 years, but am already beginning to encounter the recursive nature of the profession. I have had several repeat classes in my 4 semesters of teaching, and they require the achievement of the same outcomes. This does not bother me, in general, because I am excited to see the improvement in my teaching. There is one unit, however, that has already frustrated me. Its ability to sabotage creative exploits is unrivalled throughout the mathematics curriculum; I am speaking of the unit on polynomial factoring.
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.
My fascination with infinity began early on in life. I went to a small private school in Prince Edward Island for my entire elementary school career, and it was outside on the playground where I first tasted the enigma of infinity and the power it held.
Across the cul-de-sac parking lot stood the swings, slide, and monkey bars; I still remember the first time I encountered infinity under those bars. You see, we had been learning the base-10 number system that day, and my friend Jason and I somehow got into a counting contest of sorts. We began at very small numbers, and gradually cycled through the digits at varying positions until we countered each other with unusually large–and most likely inaccurate–numbers. Trillion, Quadrillion, Bazillion all made appearances until Jason ended the contest with one word–infinity.
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Exploring Negative Bases
I love it when math works as it should. Such was the case last night when I was looking for a problem to explore. I began by checking my favourite blogs for a quick puzzle before bed. Nothing really stuck, so I tried some searches on twitter. (#math #mathchat #puzzle usually get the job done). I found a puzzle that intrigued me and began to work.
Before I mention the puzzle, I want to say a quick word about school maths. I have a great personal interest in mathematics, and am able to move on past problems that don’t pique my curiosity; we do not afford students the same opportunity. I wonder, if students were given more freedom, if they too would find puzzles and topics that interest them. This is a not the topic for this post, but is an interesting debate in mathematics education. I digress…
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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.