CORRECT LYRICS
Lyrics : I don’t understand my dissertation (and what this means for Mathematics Education)
I read my PhD thesis earlier this week. My research was in a Pure Mathematics field called Functional Analysis which, in short, meant it was self-motivated and empty of concrete real-world application. I submitted the thesis in 2011 and made a quick exit from research mathematics after good 'defence.'
I was interested to see how much I could still remember, five years after the fact. I couldn't hurt my ego if I refreshed my mind with past mathematical glories
How bad I was
This wasn't my casual reading in mind. The notation is foreign. I even had to scour the examiner's report for key results. And while I could have sworn this was a well-written thesis, my own prompts constantly bamboozled me. "The result now follows easily..." may have made sense back then, but now the author-turned-confused reader can profess it definitely doesn't easily follow, at least in his own mind
My dissertation snapshot. The inference is no longer trivial to me, the effect of (b) is no longer immediate, and I have no idea how (d) Proposition 4.2.6 follows
Such a humbling experience raises the question: what's the point? Since I retained precious little of what I devoted to over four long years, was this a misdirection of my talents (whatever they are)? A lengthy work delay proper?
Beyond barely extending the limits of dark mathematical understanding, what practical difference has a PhD brought to my life?
These aren't just a mathematician's musings. They are important to all of us in education as we test the reasoning behind current mathematics curriculum and evaluation models
So let's ask the question more generally: what's the point of studying math? I give you three explanations, each with a firm conviction that after all, my doctorate was worthwhile
Mathematics is an excellent solution proxy
My PhD made me a better problem-solver. I can't prove this except to say study provided me with unrivalled problem-solving tools: scouring journal articles to gain insight into current processes, brainstorming with colleagues, seeking new approaches... the list is endless
My field option was irrelevant; Functional Analysis was mere proxy to drive my problem-solving skills to new heights
Mathematics, through its succinct and logical nature, solves problems (it is not unique in this regard)
Choices about content are much less important than the opportunities they enable students to learn thinking and problem-solving skills
Policymakers lose this appreciation of how to nurture critical thought. Curriculum expectations are focused on what students should know (with some movement towards performing discrete acts of reasoning, itself very limited). Assessment is driven by short-term information gains obsession. But information without comprehension carries no currency to train students in the world
In the data-driven transparency age, educational assessment must concentrate on learning processes. Problem-solving is an imaginative and even holistic endeavour; it cannot be completely codified or recorded. Mathematics is beyond rigid calculation, and mathematical reasoning can never be limited to knowledge acquisition
Mathematics embodies students' character
Rich mathematical perceptions are steeped in so-called non-cognitive abilities (you know those—grit, endurance, mentality, etc.)
A thesis describes a very small subset of good ideas. It does not involve failed efforts, but they define most of the research experience. These failures also contain crucial observations that motivated the final breakthroughs. They mentally toughen the mathematician. My own results came after three years of disappointment and dissatisfaction (which included several renewed commitments to quit the damn thing altogether).Academic Master is a US based writing company that provides thousands of free essays to the students all over the World. If you want your essay written by a highly professional writers, then you are in a right place. We have hundreds of highly skilled writers working 24/7 to provide qualityessay writing services to the students all over the World
That's largely what made me a better problem-solver. They gave me a reluctance to give up, always trumping natural intuition
The mark of a successful mathematics problem is multiple solution paths that enable students to experiment with different approaches. And a good instructor will provide a healthy atmosphere for students to take chances and fail, stressing the value of positive values and mentality
Mathematics' fun
Nothing deep here. I had fun learning mathematics, and the privilege was modestly rewarded. There are worse arguments for a 4-year engagement and few positive ones
Students deserve opportunities that bring them joy and happiness. This would also suffice as a utilitarian statement, as these characteristics outlast narrow advances in understanding and have a more positive effect on the planet. Mathematics, in its purest form, is the ideal expression of human thought marrying logic with creative expression. There's much beauty to seek in mathematics learning and teaching. Isn't that justification enough?
I was interested to see how much I could still remember, five years after the fact. I couldn't hurt my ego if I refreshed my mind with past mathematical glories
How bad I was
This wasn't my casual reading in mind. The notation is foreign. I even had to scour the examiner's report for key results. And while I could have sworn this was a well-written thesis, my own prompts constantly bamboozled me. "The result now follows easily..." may have made sense back then, but now the author-turned-confused reader can profess it definitely doesn't easily follow, at least in his own mind
My dissertation snapshot. The inference is no longer trivial to me, the effect of (b) is no longer immediate, and I have no idea how (d) Proposition 4.2.6 follows
Such a humbling experience raises the question: what's the point? Since I retained precious little of what I devoted to over four long years, was this a misdirection of my talents (whatever they are)? A lengthy work delay proper?
Beyond barely extending the limits of dark mathematical understanding, what practical difference has a PhD brought to my life?
These aren't just a mathematician's musings. They are important to all of us in education as we test the reasoning behind current mathematics curriculum and evaluation models
So let's ask the question more generally: what's the point of studying math? I give you three explanations, each with a firm conviction that after all, my doctorate was worthwhile
Mathematics is an excellent solution proxy
My PhD made me a better problem-solver. I can't prove this except to say study provided me with unrivalled problem-solving tools: scouring journal articles to gain insight into current processes, brainstorming with colleagues, seeking new approaches... the list is endless
My field option was irrelevant; Functional Analysis was mere proxy to drive my problem-solving skills to new heights
Mathematics, through its succinct and logical nature, solves problems (it is not unique in this regard)
Choices about content are much less important than the opportunities they enable students to learn thinking and problem-solving skills
Policymakers lose this appreciation of how to nurture critical thought. Curriculum expectations are focused on what students should know (with some movement towards performing discrete acts of reasoning, itself very limited). Assessment is driven by short-term information gains obsession. But information without comprehension carries no currency to train students in the world
In the data-driven transparency age, educational assessment must concentrate on learning processes. Problem-solving is an imaginative and even holistic endeavour; it cannot be completely codified or recorded. Mathematics is beyond rigid calculation, and mathematical reasoning can never be limited to knowledge acquisition
Mathematics embodies students' character
Rich mathematical perceptions are steeped in so-called non-cognitive abilities (you know those—grit, endurance, mentality, etc.)
A thesis describes a very small subset of good ideas. It does not involve failed efforts, but they define most of the research experience. These failures also contain crucial observations that motivated the final breakthroughs. They mentally toughen the mathematician. My own results came after three years of disappointment and dissatisfaction (which included several renewed commitments to quit the damn thing altogether).Academic Master is a US based writing company that provides thousands of free essays to the students all over the World. If you want your essay written by a highly professional writers, then you are in a right place. We have hundreds of highly skilled writers working 24/7 to provide qualityessay writing services to the students all over the World
That's largely what made me a better problem-solver. They gave me a reluctance to give up, always trumping natural intuition
The mark of a successful mathematics problem is multiple solution paths that enable students to experiment with different approaches. And a good instructor will provide a healthy atmosphere for students to take chances and fail, stressing the value of positive values and mentality
Mathematics' fun
Nothing deep here. I had fun learning mathematics, and the privilege was modestly rewarded. There are worse arguments for a 4-year engagement and few positive ones
Students deserve opportunities that bring them joy and happiness. This would also suffice as a utilitarian statement, as these characteristics outlast narrow advances in understanding and have a more positive effect on the planet. Mathematics, in its purest form, is the ideal expression of human thought marrying logic with creative expression. There's much beauty to seek in mathematics learning and teaching. Isn't that justification enough?
