Greetings, Math-Phobic and Mathaholics,
I wanted to share a bit about my relationship with math, and to ask some of the questions that are on my mind. You see, it's clear that something about math is not readily accessible. What is it, I wonder?
Although fascinated at an early age, my middle school teachers did little to help me fall in love with equations, and my college professors preached an utterly frightening breed of numbers. Thinking back, I can't remember why I didn't enjoy the subjects; I just know that I didn't. Little has changed; the twittering youthful masses tweet their thoughts in real-time.
Yet, whether it relates to the area or size of a garden enclosure, the fibonacci sequence, logarithms or the physics of a raindrop falling in a puddle, there are an unlimited number of possibilities - and needs - to access and apply numeric doing.
Two individuals who (I think) deserve applause for their work in bringing math to kids are Norton Juster, author of Phantom Tollbooth and The Dot and the Line. Theoni Pappas also deserves to be more widely known for her work - take a minute to explore; i think you'll find it worthwhile!
Beyond that, I ask you:
What is your relationship with math doing? What is it that makes math scary? And, could you roll back time, what qualities would you give your teachers to make it more understandable?
Cheers,
--Dave
p.s. If you can't tell, my relationship with things math-related has changed from "it's complicated" to "we're inseparable".
Comments
Not scary to me.
Math was never, ever scary to me. As I've gotten to know lots and lots of other people and how their minds and emotions work with math, I'm extremely grateful to my father and my seventh grade and tenth grade math teachers, respectively.
I'm a verbal, linear thinker and have to really sweat to ponder the big picture. In hindsight, average math instruction would have had me memorizing the way to the right answer for a given section, and never considerign how it fit together. HOwever, my father was on the other end of the big picture spectrum and pointed out connections with utter fascination. Mr. Cherry and Doc McNelis also made sure we saw those connections. Last but absolutely, definitely not least was that pervasive cultural role identity: I was smart. Therefore I should have fun with math. Therefore, I should messa round with these ideas until I could sound smart about them.
I realized in teaching that when I was confronted with a weird problem, I would look at it and think "there's no way I have enough information to get to the answer." But then, I'd figure out what I *could* do with the information -- and almost inevitably, find a way to get to the answer (with a misread something 15-20% of teh time; I didn't get *A's* in math, mind you). And I *was* fast with what I did, so since I had a very solid foundation of the simple stuff, I could do a ton of simple stuff until I found the right thing. What this also meant was that if it were a multiple guess problem -- standardized tests -- I ended up doing even better on the math than the verbal stuff, even though I was using verbal skills, not mathematical ones.
Another subtle psychological difference that I've seen in some of my students is that it's the nature of math to go from "impossible" to "obvious," sometimes like a light bulb. (That's a "style thing," I suspect -- I think for my father the light slowly brightened; for me, it was "Aha!")
My stomach sank the first time I heard a student voice taht gosh! This stuff is so obvious now! ... I must be a complete moron not to have seen it before!
That's right... the student *gets* it... it's *easy* ... but it adds to their feeling that they are bad at math. Aaargh!!!
I try to pay attention to whether a person is getting just the details or just the big picture, and fill in the gap (and teach the metacognition of being aware of that), to teach the connections and patterns, and to try to establish that emotional culture of expecting to be able to get to the answer even if it really looks limpossible at first.
Hmm.
Jenny,
Hmm. Great question -- I'll think about it and respond later this week. I'm wondering if something specific kicked in, or what it might have been that turned it all around...
--Dave
So Dave, you were a former
So Dave, you were a former math-o-phobe? Amazing. I want to hear more about how you came to like it.... Article forthcoming??
Re: Coming to enjoy all things mathematical
Hi Jenny,
It might be a little disappointing, but I can't remember any specific time that "math became less scary". It seems to have been a gradual process of realizing that my fear was predicated upon the teachers who taught it, and upon my lack of deep understanding of its structures, its intricacies, and its importance.
But more generally, I think "science is really cool", no matter the discipline. My view evolved over the past 10 or 12 years, after the pressures of college; so it might be that real-world interaction with science made the value of numbers clear.
My comments aren't of much value to teachers and students, I'm afraid, who face these pressures in the classroom each day; but there is a book I've run across - "Why Is Math So Hard for Some Children?: The Nature and Origins of Mathematical Learning Difficulties and Disabilities" that I'm curious to explore in answering this question more generally.
Finally, if anyone out there would like to share their own story about math, we'd love to hear!
Cheers,
--Dave
Math Turnaround
Hi Dave--
I wasn't going to comment, as I'm not really the commenting type, but there were too many overlapping pieces to ignore. First, I'm here on this site b/c of my friend whom you contacted recently about getting some people together from HGSE in late May; I'm also in MBE :). I appreciate what this org is trying to do and think it's really necessary. It's funny--we were reflecting during our last MBE class of the year about what had changed in our thinking...we all said that we came to Harvard thinking that we were going to find all the answers, we were going to find amazing research and study all the people who who making great strides in our field--but then we got here, and we realized those people are us! It's been disappointing, to realize there's not as much going on in the math research world as we hoped, but it's almost made us more determined to change that. :)
Also, I highly recommend the book you referenced above (Berch & Mazzocco, 2007). They are two people I see really leading the field and calling for practical reform, such as deciding on a consensus definition, vocabulary, and diagnostic tools around mathematical disability. I referenced this book extensively for reports and find it inspiring to hear what some people are studying. Another book that also draws from that research and provides really good practical information is Number Sense and Number Nonsense. It's more accessible and I recommend that one to teachers and schools who are beginning their research into cognitive bases of mathematical differences and how to adapt their instruction.
I'll share a quick math-turnaround story, since you asked and I always like reflecting on something that truly was a life-changer for me. I came to Harvard specifically to study math difficulties and discrepancies in the students I taught. I've now done so and intend that this will be what I continue to study during my career. However, all this happened only because I was "forced" to teach math six years ago, after the woman who was supposed to have that responsibility quit! I was an English/creative writing major and taught only that and social studies for years up to that point. Oh, and I failed Algebra I at least once in middle school and was always behind in that area. My life changed when I got up in front of my class of 5th graders and decided that I was going to explore concepts with them. I think because of my background with struggling to understand concepts and also, actually, because of the experiences I had teaching language and history in exploratory ways, math became a whole new adventure for these students--and definitely for me. Their understanding and engagement when through the roof! It became the highlight of our day and is something that is so infinitely intriguing to me now. It's our goal at HGSE to provide experiences which allow for deep conceptual understanding to occur. I look forward to perhaps meeting with you in May or another time in the future. We've got some cool projects to share, as well!
Thanks--
Christine
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