Math and Python: level of difficulty
At 04:12 AM 1/24/2010, kirby urner wrote:
Back to the Litvin text, which has a lot going for it, I think it might be too difficult for some of the students we're hoping to reach.
Phillips Academy is one of the most prestigious, reminiscent of Catlin Gabel or Oregon Episcopal in our neck of the woods (I could rattle off a few more). The text comes across as "early college" i.e. college level for high schoolers, or at least as a kind of advanced Algebra 2 (thinking of the chapter on polynomials in particular).
It goes all the way through RSA (public key crypto) as I've typically advocated we do.
The good news is MFTDA (Math for the Digital Age) could be like TAOCP or SICP by Abelson, Sussman & Sussman, by forming the nucleus of a genre. In additional to full blown texts, we'll perhaps see a growing inventory of cyberspace assets contributed directly by teachers and students?
First, let me say I am honored to have our book mentioned in the same paragraph with Knuth and Abelson, Sussman & Sussman. :) Kirby is right: our book is suitable for students in a typical first-year discrete math college course. That doesn't mean, though, that a bright middle schooler or an open-minded 9th- or 10th-grader can't handle it. Unfortunately there is virtually nothing in the standard K-12 math that prepares students for this kind of math, Phillips Academy or not. If anything, younger students are more enthusiastic and open to actually solving problems. Maria (Litvin) recently asked her students Question 2 from Section 1.2: How many subsets does a set of 3 elements have, including the empty set and the set itself? Her students understood what a subset is, but only one from the whole class could answer the question. The others had no clue how to approach a problem -- any problem! Most of these kids are currently enrolled in AP Calculus or a more advanced math course, such as linear algebra... I suspect if you explain to an interested and reasonably bright 10-year-old what a subset is and ask the same question, chances are he/she will quickly list all the subsets and give you the right answer within a couple of minutes. It is true, of course, that the last two chapters, the one on map coloring and the one on number theory and cryptology, are quite technical. Only very bright students -- high school or college -- will be able to handle them. But we need to somehow keep these kids busy, too, don't we? Gary Litvin www.skylit.com
I would very much like to see this efforts expanded to earlier ages and stages in math development. I work with kids as young as three and on, using Scratch with them. They learn so much from programming, from coordinate thinking to increments and "gentle calculus" (e.g. that you program speed as the change in distance). Functions, grid reasoning, co-variation, equations and variables are just a few examples of Early Algebra topics that lend themselves extremely well to the programming approach, and become accessible to five-ten year olds who program. If any of you are interested in under-ten Math Club crowd (meaning middle and high school "everybody"), please let me know so we can join efforts. It would be nice to write it all up as a coherent resource. Cheers, Maria Droujkova http://www.naturalmath.com Make math your own, to make your own math. On Sun, Jan 24, 2010 at 9:59 PM, Litvin <litvin@skylit.com> wrote:
At 04:12 AM 1/24/2010, kirby urner wrote:
Back to the Litvin text, which has a lot going for it, I think it might be too difficult for some of the students we're hoping to reach.
Phillips Academy is one of the most prestigious, reminiscent of Catlin Gabel or Oregon Episcopal in our neck of the woods (I could rattle off a few more). The text comes across as "early college" i.e. college level for high schoolers, or at least as a kind of advanced Algebra 2 (thinking of the chapter on polynomials in particular).
It goes all the way through RSA (public key crypto) as I've typically advocated we do.
The good news is MFTDA (Math for the Digital Age) could be like TAOCP or SICP by Abelson, Sussman & Sussman, by forming the nucleus of a genre. In additional to full blown texts, we'll perhaps see a growing inventory of cyberspace assets contributed directly by teachers and students?
First, let me say I am honored to have our book mentioned in the same paragraph with Knuth and Abelson, Sussman & Sussman. :)
Kirby is right: our book is suitable for students in a typical first-year discrete math college course. That doesn't mean, though, that a bright middle schooler or an open-minded 9th- or 10th-grader can't handle it. Unfortunately there is virtually nothing in the standard K-12 math that prepares students for this kind of math, Phillips Academy or not. If anything, younger students are more enthusiastic and open to actually solving problems. Maria (Litvin) recently asked her students Question 2 from Section 1.2: How many subsets does a set of 3 elements have, including the empty set and the set itself? Her students understood what a subset is, but only one from the whole class could answer the question. The others had no clue how to approach a problem -- any problem! Most of these kids are currently enrolled in AP Calculus or a more advanced math course, such as linear algebra... I suspect if you explain to an interested and reasonably bright 10-year-old what a subset is and ask the same question, chances are he/she will quickly list all the subsets and give you the right answer within a couple of minutes. It is true, of course, that the last two chapters, the one on map coloring and the one on number theory and cryptology, are quite technical. Only very bright students -- high school or college -- will be able to handle them. But we need to somehow keep these kids busy, too, don't we?
Gary Litvin www.skylit.com
_______________________________________________ Edu-sig mailing list Edu-sig@python.org http://mail.python.org/mailman/listinfo/edu-sig
participants (2)
-
Litvin -
Maria Droujkova