What is Mathematics? Why do we learn Math? What is the best way to learn Math? This will be one of those articles which I hope will serve as an exploration/dynamic document so that I and perhaps others can get better informed. As a young kid and till very recently I saw Mathematics as being that subject that is at once utilitarian and at the same time an aesthetic experience-most of these realizations came to be through rote learning or through pure accident. However the discipline itself has never been that enjoyable or engaging to me.
Now as adult and as an educator I would argue for its value as a perfect training ground for 'logic' and I am determined to master it. I recently ran across an argument that talks about preparatory learning starting with the Trivium (Explained by Sister Miriam Joseph: Grammar- is concerned with the thing as it is symbolized, Logic is concerned with the thing as it is known and Rhetoric is concerned with the thing as it is communicated) and leading to the Quadrivium. Math seems to be essential in terms of its role in preparatory learning and as a stage for critical inquiry. It's apparent usefulness as a tool to create rigorous models that can be tested and argued across different disciplines seems to be essential in terms for checking for errors in our judgment and I think we need more of that in our time and place in our world.
The discipline required in order to master 'mathematical thinking' requires you first of all care about the subject. However it is often presented as a dead subject with knowledge that is contained, defined and without much exploration- not a good introduction to all the adventures you could have with the many tools and conceptual models in Math. Knowing full well my tendencies to get all caught up in the superficial nature of a subject- I thought I would gather a few friends (Friends= people whose judgment and thinking demonstrate they are further along the path then I am:) ) along the way and explore what the teaching and learning of Mathematics could look like. Dan Meyer is one of those friends- I got to know him when another friend sent me a link to a TEDx talk that he did. Dan articulates a lot of his thinking on his blog which I have found incredibly useful as I try and understand what it would take to be a good teacher in Mathematics. Another good 'friend' whose work I am slowly trying to understand is Maria Anderson yet another person whose work I am closely following is Sal Khan- founder of Khan Academy whom I have written about in another blog post.
I am really curious to know what it means to be a mathematician, most of my experiences in formal learning environments as I have noted above both as a kid and as an educator- resulted in a lot of confused faces, furrowed brows and very little insight and understanding into the heart of this discipline. Seeing what Dan Meyer did on one of his intellectual adventures- this time around 'melting cheese' really got me thinking about the value of linking genuine real world problems whilst studying math. I can only imagine if one of the tools called Euraqa I ran across whilst reading the comments on his blog post was actually used to try and synthesize the vast amounts of data that you could potentially get from real world investigations. To elaborate, Eureka from Cornell is apparently a "software tool for detecting equations and hidden mathematical relationships in your data. Its goal is to identify the simplest mathematical formulas which could describe the underlying mechanisms that produced the data."
The thoughtful discussions that arose from people who commented on his little experiment and challenge were absolutely fascinating to read through and I was blown away that this is happening in real time. The whole thing impressed me so much that I thought I would try and exercise to push my own boundaries of ignorance on the discipline of math out a bit further. I don't really have any conclusions at this point but do see this as an open ended post that I will probably come back and revisit a few times over. I do look forward to your comments.
Rahim
Now as adult and as an educator I would argue for its value as a perfect training ground for 'logic' and I am determined to master it. I recently ran across an argument that talks about preparatory learning starting with the Trivium (Explained by Sister Miriam Joseph: Grammar- is concerned with the thing as it is symbolized, Logic is concerned with the thing as it is known and Rhetoric is concerned with the thing as it is communicated) and leading to the Quadrivium. Math seems to be essential in terms of its role in preparatory learning and as a stage for critical inquiry. It's apparent usefulness as a tool to create rigorous models that can be tested and argued across different disciplines seems to be essential in terms for checking for errors in our judgment and I think we need more of that in our time and place in our world.
The discipline required in order to master 'mathematical thinking' requires you first of all care about the subject. However it is often presented as a dead subject with knowledge that is contained, defined and without much exploration- not a good introduction to all the adventures you could have with the many tools and conceptual models in Math. Knowing full well my tendencies to get all caught up in the superficial nature of a subject- I thought I would gather a few friends (Friends= people whose judgment and thinking demonstrate they are further along the path then I am:) ) along the way and explore what the teaching and learning of Mathematics could look like. Dan Meyer is one of those friends- I got to know him when another friend sent me a link to a TEDx talk that he did. Dan articulates a lot of his thinking on his blog which I have found incredibly useful as I try and understand what it would take to be a good teacher in Mathematics. Another good 'friend' whose work I am slowly trying to understand is Maria Anderson yet another person whose work I am closely following is Sal Khan- founder of Khan Academy whom I have written about in another blog post.
I am really curious to know what it means to be a mathematician, most of my experiences in formal learning environments as I have noted above both as a kid and as an educator- resulted in a lot of confused faces, furrowed brows and very little insight and understanding into the heart of this discipline. Seeing what Dan Meyer did on one of his intellectual adventures- this time around 'melting cheese' really got me thinking about the value of linking genuine real world problems whilst studying math. I can only imagine if one of the tools called Euraqa I ran across whilst reading the comments on his blog post was actually used to try and synthesize the vast amounts of data that you could potentially get from real world investigations. To elaborate, Eureka from Cornell is apparently a "software tool for detecting equations and hidden mathematical relationships in your data. Its goal is to identify the simplest mathematical formulas which could describe the underlying mechanisms that produced the data."
The thoughtful discussions that arose from people who commented on his little experiment and challenge were absolutely fascinating to read through and I was blown away that this is happening in real time. The whole thing impressed me so much that I thought I would try and exercise to push my own boundaries of ignorance on the discipline of math out a bit further. I don't really have any conclusions at this point but do see this as an open ended post that I will probably come back and revisit a few times over. I do look forward to your comments.
Rahim
If you have 10 minutes to spare- do spend it on this strategic video, I take my hat off to Sal Khan- he is a master educator in my eyes http://www.youtube.com/watch?v=hw5k98GV7po&feature=player_embedded#at=429
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