RE: Mathematica for High School Students

*To*: mathgroup at smc.vnet.net*Subject*: [mg24127] RE: Mathematica for High School Students*From*: "Ersek, Ted R" <ErsekTR at navair.navy.mil>*Date*: Wed, 28 Jun 2000 02:11:46 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

I want to clarify some things I said earlier: The way I see it a high school teacher/college professor/text book author should set the curriculum of a course such that all students except those who are simply in the wrong class can keep up. Of course nearly all seniors in a typical high school will have far less ability than students in the freshmen class at MIT, and that should be reflected in the curriculum. Also I think one shouldn't be REQUIRED to learn about features in Mathematica that are not fully intuitive until their 3rd year of college (except in a Computer Science class about Mathematica). Even in the 3rd and 4th years of college I would only encourage gradual introduction (as required learning) of less than intuitive features in Mathematica. Obviously I am not saying one shouldn't be permitted to learn more difficult subjects. I think mostly the same stuff should be taught that was taught before 1998, but use of Mathematica should make it easier to learn. Since a lot of stuff should be easier thanks to Mathematica, more material can be crammed into the curriculum. _____________________ Dave Park wrote: And what features of Mathematica are not "fully intuitive" so that the student "shouldn't learn" them? Would you hazard to put forward a list of Mathematica statements to which young students would be restricted? Or a list that would be banned from their use? ______________________ Ted Ersek Replies: Banned features: None Stuff that should not be required learning: Any use of level specifications Making buttons from scratch Box expressions for 2D expressions Cell expressions Manipulating notebooks Elaborate pattern matching Features for a Computer Science course on Mathematica should include functional programming, non-trivial pattern matching, UpValues/DownValues, The Mathematica evaluation process, .... I am not qualified to say at what level use of Map, Apply, Thread, .... should be integrated into the curriculum for average students. I think it might be appropriate to gradually introduce these features in the 3rd and 4th year of college. On the other hand it might be good if science/engineering students were required to take a computer science course in Mathematica during the first or second year of college. If that were the case these features should not be considered "difficult" after they have this course. One of the notebooks Dave Park provides uses Map and pure functions to manipulate equations step-by-step. This sort of thing equation manipulation is much easier to follow once a package by Roman Maeder is loaded. Hence we don't need Map and pure functions for this application. Download the package from: http://www.mathsource.com/Content/Enhancements/Algebraic/0209-124 After down-loading the package I can do the following: In[1]:= <<EqualThread.m In[2]:= 3x+4y/b==6(x-y); In[3]:= %-3x Out[3]= (4*y)/b == -3*x + 6*(x - y) In[4]:= %*b/4 Out[4]= y == (b*(-3*x + 6*(x - y)))/4 In[5]:= Factor[Map[Expand,%]] Out[5]= y == (3*b*(x - 2*y))/4 If Expand has the Listable attribute (and it normally doesn't) Map isn't needed in the last line above. Once the EqualThread package is loaded the lines above are sufficiently intuitive that I might use something like this if I were a 9th grade algebra teacher! Except I might add a line to (init.m) that gives Expand the Listable attribute, and instruct the students to copy it to their computers. ----------------------------------- Dave Park asked: Would you allow the young student to use Solve? Ted Ersek Replies: Yes, and encourage them to do so. In other areas I agree with Dave Park on how students should be permitted to learn topics more advanced than the standard curriculum. --- Regards Ted :)