Plan for James W. Hofmann
by abc · 11/07/2005 (6:46 pm) · 2 comments
I'm taking an intro differential calculus course right now. It's really a repeat for me but various things with the course system force me to take it over. One of my favorite tools for practicing calc problems that I discovered last year is Calculus on the Web. All it is, is a simple drill-and-practice tool. What makes it valuable is that most(unfortunately not all) of the exercises don't simply prompt you for the solution and then say "right answer/wrong answer." They force you to work through each step in getting the solution and offer advice on what mistakes you made, if any. This hand-holding is exactly what games make you do in the tutorial mode - every instruction is made as boneheadedly simple as possible, so that even a complex process can be learned.
It always amazes me that most educational software seems to avoid doing any real tutoring in favor of an "e-quiz" format. For early childhood subjects this makes some sense because the learning problems aren't complex; they just need rote work to be overcome. But most later subjects deal with systems of rules that can be applied in many different ways. And what happens to me, as a student, when I run up against the rules, is that I find myself wishing not just for a guide to solving each problem, but a "sandbox mode" where everything I am *allowed* to do is shown to me and I can choose it and see its effects, so that I can get a better understanding of each technique.
I'm especially thinking of algebra here: we've probably all run up against some algebra problem that seemed impossible but for a non-obvious trick. And what seems to inevitably happen is that the students(mostly) are unable to figure it out, and then the teacher demonstrates the solution. It happens over and over...which makes me conclude that most of us have only learned a tiny fraction of algebra - and probably most fields of math covered to the undergraduate level - because there were so many cases where self-discovery of the solution seemed out of reach. But we walk away feeling satisfied that we know something because we can solve the subset of problems that were specifically covered and are most applicable to other realms.
What I think a computer could do, if someone bothered to program it properly, is accelerate the discovery process. All that writing and erasing and flipping through pages to look up something you forgot can be as time-consuming as the thinking. And that really is true beyond math, I think. But math is the most obvious target.
Someday I'll have to try putting a little test together, something that lets me mess around with equations, and see if I'm right.
It always amazes me that most educational software seems to avoid doing any real tutoring in favor of an "e-quiz" format. For early childhood subjects this makes some sense because the learning problems aren't complex; they just need rote work to be overcome. But most later subjects deal with systems of rules that can be applied in many different ways. And what happens to me, as a student, when I run up against the rules, is that I find myself wishing not just for a guide to solving each problem, but a "sandbox mode" where everything I am *allowed* to do is shown to me and I can choose it and see its effects, so that I can get a better understanding of each technique.
I'm especially thinking of algebra here: we've probably all run up against some algebra problem that seemed impossible but for a non-obvious trick. And what seems to inevitably happen is that the students(mostly) are unable to figure it out, and then the teacher demonstrates the solution. It happens over and over...which makes me conclude that most of us have only learned a tiny fraction of algebra - and probably most fields of math covered to the undergraduate level - because there were so many cases where self-discovery of the solution seemed out of reach. But we walk away feeling satisfied that we know something because we can solve the subset of problems that were specifically covered and are most applicable to other realms.
What I think a computer could do, if someone bothered to program it properly, is accelerate the discovery process. All that writing and erasing and flipping through pages to look up something you forgot can be as time-consuming as the thinking. And that really is true beyond math, I think. But math is the most obvious target.
Someday I'll have to try putting a little test together, something that lets me mess around with equations, and see if I'm right.
About the author
#2
I do agree that the discovery process is incredibly important, and is lost in most of the classroom settings today. I too am looking to change that (Majoring in Education) and become a teacher some day :]
A good short book worth reading, probably costs $5 or so is "A Whack on the side of the head". It goes over how culturally we are brought up to avoid being wrong, avoid giving answers that may be percieved as wrong or get a negative response. Those ideas really put a damper on the discovery process. *sigh*
11/08/2005 (6:24 am)
Perhaps it's because I was taught Algebra in the manner described above, but I would find it awfully difficult to facilitate the discovery process with many mathmatical concepts. How would one go about getting the game to recognize and explain "It looks like you were trying to do XXXX here, that's close, but here, try this, you learned it previously. I do agree that the discovery process is incredibly important, and is lost in most of the classroom settings today. I too am looking to change that (Majoring in Education) and become a teacher some day :]
A good short book worth reading, probably costs $5 or so is "A Whack on the side of the head". It goes over how culturally we are brought up to avoid being wrong, avoid giving answers that may be percieved as wrong or get a negative response. Those ideas really put a damper on the discovery process. *sigh*
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