Experimental Sketchpad Web Page based on ISED Listserv Gathering of Names (Spring 2001)

Steve Bergen "Summercore" Teaching Company ...

Why Use Software in Teaching High School Math
(from The Summecore Primer)


In 1983, I heard Seymour Papert, creator of Logo and author of Mindstorms, give a talk about the potential of computers in education; at one point he said “the computer is the only way to make subjects like math and grammar come alive.” I was shocked. I was upset. As a math teacher who took a lot of pride in trying to make math come alive for my students, I took his comment personally, since in the years 73-80, I had never used a computer as part of my math classroom and yet thought that I was doing something special mathematically for my students. I took offense at Papert's statement and lost some respect for the person whose book, Mindstorms, had been the catalyst for my starting The Teaching Company the previous year. I even changed the slogan of our company from “a consulting firm for computer education” to “a consulting firm for (and sometimes against) computer education.”

In 1984, I returned to teaching math part-time. I had heard Tom Snyder speak frequently about using one computer in a classroom and how the best way to use software for the first time was as a “rainy-day” activity: one computer, one big screen with students divided into teams. It did not seem like my style, but one day when subbing for a sick colleague, I decided to try The Factory, a problem-solving package produced by Sunburst. I was astounded by the results. These seemingly sophisticated high school students, split into teams, playing a game for arbitrary points were “completely into it.” They were building models of cubes out of paper, rotating them, exploring changes in orientation, verbalizing mathematics and collaborating in ways that were different from my traditional lecture/dialogue class presentation.

I was hooked. Over the years from 1984-1990, as a part-time math teacher, I incorporated various software projects into my geometry, algebra and calculus courses. The school was using primarily Apple II computers; I had the flexibility of using one big screen in my room, several computer stations or the entire computer lab.

Each year, I felt I was getting better at the pedagogical and management strategies, but only by encountering mistakes and feeling like a first year teacher again. The first year I incorporated Logo, I made Tuesday our Logo day and tried to do the standard curriculum the other days. What a mistake! Immersion is the key, I finally realized; and so in subsequent years, we concentrated on Logo in January and did not attempt the schizophrenic model of grabbing one day a week for computer time.

Another mistake I made involved my naivete that computers could be implemented without making any dent in the curriculum. As the years progressed, I realized that the Logo and Geometric Supposer projects were competing for time with the intellectual and mathematical values of proof-solving geometry which I have always cherished. Ultimately, I decided with some anguish that the emphasis on proofs needed to be diminished. By limiting “solving proofs” to one unit of the course in the first semester, I freed enough time in the second semester to accomplish the Logo and Geometric Supposer projects.

Top Ten Reasons to Use Software in the Math Curriculum

Reason #10 ... Using software is a way to incorporate the writing-as-part-of-math theme for across-the-curriculum writing assignments.

Reason #9... Using software can be very useful for both slow learners who need more drill and practice on certain areas and bright, capable learners who need enrichment and extra challenges.

Reason #8 ... Using software can broaden the appeal of mathematics, making a course more multidimensional and helping to bridge sometimes disturbing male/female attitudinal differences.
Reason #7... Using software allows students to leave their legacy behind, producing explanation sheets, posters and write-ups that younger students will then encounter and value some day.

Reason #6 ... Using software can help address the need to modify our pedagogy to address the learning needs of different individuals. As Papert says in Mindstorms, “the computer is the Proteus of machines. Its essence is its universality, its power to simulate. Because it can take on a thousand forms and can serve a thousand functions, it can appeal to a thousand tastes.”

Reason #5... Using software facilitates projects that are multi-dimensional, and allows for the Howard Gardner emphasis on teamwork, cooperation, problem-solving, and inter- and intra-personal learning experiences.

Reason #4... Using software can help focus on theory and concept by saving time and allowing for easy manipulations and investigations with graphs, equations, spatial relations, probability, statistics and many other topics.

Reason #3... Using software is essential to subjects like fractals and modeling that come out of the marriage of mathematics and computers as part of the intellectual world of the 21st century.

Reason #2... Using software can be a facilitator of professional colleagueship for math teachers in talking about experiences, pedagogy and curriculum as well as colleagueship with other departments who need to “lean on math teachers” for help with formulas.

Reason #1... Using software is exciting for teachers, since it presents a new pedagogical challenge and becomes a facilitator for re-examining curriculum areas and classroom styles.

Math Projects & Software Used in 84-91 (oldies but goodies)


A Personal Summary of Math Software that I used in them days of old when I was teaching math .... 1984-1991 at Concord Academy, grades 9-12 (Steve Bergen)

Apple II
- Green Globs (Sunburst)
- The Factory (Sunburst)
- The Super Factory (Sunburst)
- Logo (Terrapin)
- The TC Function Grapher (Teaching Company)
- Geometric Supposer (Sunburst)
- Algebra Drill & Practice (Conduit)

Mac
- Calculus (Broderbund)
- Geometric Supposer (Sunburst)
- Hypercard

Using one computer in the classroom with big TV screen or overhead
Factory and Super Factory as “rainy day” or “special day” activities
Initial teaching of Logo or the Geometric Supposer

Assigning Drill and Practice for required outside-of-class review
Sample Projects that would span 1 to 4 weeks and result in a lab report
(1) Drawing a “dream” picture on paper of something that is meaningful to you; then using Logo skills, recreate that picture on paper and write a paragraph about it.
(2) Designing a known or original tessellation using Logo and write a paragraph that will become part of an informative poster.
(3) Using the Geometric Supposer to investigate questions at the start of the semester such as “what can you say when you draw the 3 medians of a triangle?” or “find the point(s) within an equilateral triangle that achieve s the minimum sum of the distances to the 3 sides (surfer) or the 3 vertices (spotter) of the original triangle.
(4) Playing Green Globs in team format with one big screen and then requiring students to win a Green Globs game with the 5 different conic sections; using a graphing program, students had to produce a graph to illustrate their game.
(5) Using a graphing program to compare the family of polynomial functions y = xn with the exponential family y = 2x. Students had to then demonstrate the remarkable statement that any member of the 2x family will eventually beat any member of the xn family. The culmination of the project was a graphic with an explanatory paragraph, making a one page poster.
(6) Using a 3D graphics program, construct a 3-D models with x, y and z coordinates.
(7) Using the Geometric Supposer, try to come up with a new and interesting mathematical relationship and verify it/disprove using the trial and error repetition of the Supposer with different examples.
(8) Writing paragraph reactions or explanations throughout the year to various questions and topics that are then word-processed and incorporated into an individual or collective publication at the end of the year.
(9) Using HyperStudio to create stacks & timelines of famous mathematicians and steps in solving geometry proofs.

Software usage/technology that I have not yet explored but would love to
- developing a spreadsheet unit as part of a standard grade 7,8 or 9 math class so that the formula manipulation within a spreadsheet is related to the basic manipulation of algebraic variables
- developing a problem-solving course or unit in a mathematics class based on using spreadsheets
- producing a series of in-house “geometry videos” to facilitate different learning styles and to use throughout a geometry course

Who's Who on this Experimental Sketchpad Listserv (sketchpad@nobles.edu)

  • BEAU ... bleonhart@ma.org writes: I use Geometers Sketchpad and am interested in exchanging ideas. Thank you, Beau Leonhart
  • BETH A ... I would like to be a part of the list serve on Geometry sketchpad. We will be having laptops next year and I will use the extensively. Beth Anderson 400 N. Happy Hollow Blvd. Omaha, NE 68132 email: beanderso@brownell.edu
  • BETH L ... I was at NCTM in Orlando and heard a guy from Summermath at Mt. Holyoke. I think his name is Charles Morrow. I am sure about the last name. He is doing some wonderful things with Sketchpad. Try him. Beth Lazerick St. Andrews School, Boca Raton Beth.Lazerick@saintandrewsschool.net p.s. to beth when you see Sid Rowell, tell him to "sell his Larry Bird Doll"
  • DAVID B... mburkholz@lacademy.edu writes: Steve: One of our math teachers, David Breeden, is interested. His email address is dbreeden@lacademy.edu. Mark Burkholz Director of Technology Lawrence Academy Groton, MA 01450 e-mail: mburkholz@lacademy.edu
  • DAVID M... I'm interested in joining such a list. Thanks. David Myers, Winsor School, MA dmyers@winsor.edu
  • DIANNE ... Hi Steve, Our math dept. uses geometer's sketchpad and may be interested in an exchange of ideas. I will talk to them tomorrow. Dianne Pappafotopoulos, DPappa@aol.com, Fontbonne Academy, MA
  • DOUG (the inspiration for this web page): My return to teaching Geometry this year, after a few years of not teaching it, has reminded me that many students are reluctant to draw figures when doing their work. Some are self conscious about how their drawings look, some can not even get started because they do not think that they can draw, and others just have difficulty with their dexterity and draw figures that are not particularly useful. I believe that Geometer's Sketchpad is a tool that will significantly aid these students in their study of Geometry in a way that the word processor helped students with the mechanics of writing. Sketchpad does not require the teaching of a lot of technology so that in a short time students are able to construct, measure, and transform shapes quickly and precisely which gives them the ability to test their conjectures. "What if?" is such an important question in Geometry and I believe that Geometer's Sketchpad will enable students to explore many more "what ifs" than in a traditional paper and pencil setting. Doug Guy, doug_guy@nobles.edu, Noble and Greenough School, Dedham, MA
  • ERIK ... My name is Eric Olson. I work with Tom Lawson at the Pingree School in S. Hmilton, MA. I would be interested in the Geometer's Sketchpad group you are forming. I teach geometry and AlgII/trig, and use GSP quite a bit. My own area of expertise--if you can call it that--is M.C. Escher-style tessellations through sketches that I have developed. I am hoping to get some examples of student work on our website at the end of this month. Please put me on your list, and let me know what I can do to help. I am quite busy this year, coaching and finishing up a masters degree, but next year looks a little better. Hope to hear more, Eric Olson eric-olson@pingree.org
  • FRED ... My name is Fred Lange and I would be very interested in your idea. I have used the sketchpad extensively this year in my geometry class. Next year, I am offering a cocurricular class once a week called the SketchPadLab. email: flange@usm.k12.wi.us
  • GERI ... Gerirose2@aol.com writes: I'm interested. I love Sketchpad and have used it in my own high school geometry classes since early in the 1990s. In 1995 I changed schools and extended my use to middle school and then to elementary. It, along with a word processor, is a tool to use for learning at any level. geri anderson-nielsen, georgetown day school, washington, dc
  • JAN ... Steve: Two teachers here who might be interested in exchanging ideas about Geometer's sketchpad are Claudia Brand (cbrand@mail.coloacad.org) and Milly Nadler (mnadler@mail.coloacad.org). --Jan, Colorado Academy, Jan_Beattie@ceo.cudenver.edu
  • JIM (and MARK).. I just scanned your first email about sketchpad. I've been working on it for several years, but things have just begun to pay off. I have a bunch of stuff done, but the note from Norfolk Academy caught my eye. This year one of my students was making the Ferris Wheel, but he wanted to put wheels rotating on wheels. Sketchpad wouldn't let him, but I gambled that translations of rotating wheels onto stationary wheels, translated to the Ferris wheel would work. It does. If you do just one point rotating about a circle that rotates on the ferris wheel, and trace it, you begin to get some very nice drawings. I can attach such an animation, but you probably don't need it.... ... also, this morning I managed to construct a sine wave that rolls up into a plane section of a paper cylinder (ellipse) as an answer to a student's question from yesterday's geometry class. I can't attach it either right now, because my email is not on the computer that has sketchpad on it ... We have a math teacher who is an avid user of Sketch pad and who is always looking for new ways to use it. I have observed several of his classes and am very impressed with what he is doing. He would very much like to be in touch with another teacher who is using the program. His name is Jim Ebert and can be reached at jebert@da.org. Mark Borkowski ( mborkowski@da.org) Director of Studies Durham Academy Durham. NC 27705 ... jim ebert Durham Academy (jebert@da.org)
  • KATHERINE ... I am very interested in exchanging ideas concerning Geometer's Sketchpad. Any in particular? Thanks, Katherine Belk (KABelk@saint-marys.edu)
  • KERRIE ... I would like to be put on your mailing list for ideas exchange for geometer's sketchpad. Thank you. My email address is ksena@spx.k12.nm.us Thank you. Kerrie Sena
  • KEVIN ... mnelson@thayer.org writes: Steve, We have some math faculty using Geometer's Sketchpad. Contact our Upper School Math chair, Kevin Cedrone, for more onformation. Mark Nelson Director of Information Technology Thayer Academy Braintree, MA. 02184
  • KIM ... I was notified of your e-mail by a colleague who read it on ISED-L. I have used Geometer's Sketchpad in my classroom the past two years, though am not teaching Geometry at present. I am not sure how much I can contribute, as I basically taught myself a few tricks and organized a few projects, but I would love to receive ideas and samples from others. Look forward to hearing from you, Kim Bacchiocchi Mathematics Department/Center for Academic Support Worcester Academy. kbacchiocchi@worcesteracademy.org
  • LAURIE H ... Our Assistant Head of school forwarded your email to me. I am finishing my first year using sketchpad and would love to exchange information. Laurie Heinricher, LBHeinricher@wt.k12.pa.us
  • LAURIE S ... I am a 6th grade teacher in Bethesda, MD, and I use The Geometer's Sketchpad in my class. I would like to be part of a listserv group that discusses different sketchpad uses, especially for students in grades 6-7. Could you put me on the listserv? Thanks a bunch, and I look forward to hearing from you. Btw, do you have anyone on the list who teaches at Milton Lower School? I taught 2nd grade there a few years ago. Laurie Sparling Washington Episcopal School Bethesda, MD 20816 email: laurie.sparling.br.92@aya.yale.edu
  • LAURIE W ... Csalkeld@gps.edu writes: Steve, I have a math teacher here at Girls Preparatory School who would like to join in the geometer's sketchpad idea exchange you mentioned on the ISED listserv. Her e-mail address is: LaurieW@gps.edu Thanks ... Cindy Salkeld ... Technology Coordinator ... Girls Preparatory School ... Chattanooga, TN 37405 ... csalkeld@gps.edu
  • LINNEA ... LOBrien@universityprep.org writes: Goodmorning Steven: I teach 7th & 8th grade math ... and am an avid fan of Geometer's Sketchpad. Would love to exchange ideas with your colleague. Happy Spring! Linnea OBrien lobrien@universityprep.org "Teaching is a JOY, not a JOB"!
  • LYNN This message is from my C++ online instructor, Steve. One of his math colleague's at Nobles Greenough School, MA is interested in exchanging ideas about Geometer Sketchpad. Please respond to Steve, if you are interested. This seems like a great opportunity for all involved. Holly, Julien, Susanne, Rich, Lynn, MD byankl@brynmawrschool.org
  • MARK ... I use "Geometry for Enjoyment and Challenge" McDougal Littell ... I was thinking of going without a book entirely and have the kids invent whatever they could. There are many sketches and bookmarked sites on my web page The tough part is keeping track of what my three different classes discover and creating appropriate assessment. I did this for two weeks last year and posted all work to the web site and made kids responsible for theorems discovered in other classes, but the workload was big. just click on any one of the eight sketches called Freize. I'm sending this to show the feature of sequencing animation buttons, something I just learned to do ... Look forward to sharing thoughts with ya'll. Mark Yates, myates@mccallie.org myates@mccallie.org p.s. I could not get the attachment opened.
  • MELKANA ... I have received a message with regard to your interest in exchanging ideas and samples fro the Geometer's sketchpad. I'd be happy to join you! Melkana Brakalova-Trevithick mbrakalo@mail.hotchkiss.pvt.k12.ct.us
  • MIKE W ... I would be the contact for sharing GSP ideas and samples. I teach geometry and AP Calculus at our school and regularly use GSP. Please include me on you list. Mike Wade The Community School Sun Valley, Idaho 83353 mwade@communityschool.org
  • MIKE M ... got your message from our tech person. always interested to learn and talk more about it ... mike m, fontbonne academy ... Micheal Moschella ... e-mail: moschell@mec.edu
  • NOUREDDINE ... Hi there, I'm interested in exchanging ideas about the sketchpad. Please add me to your list. Thanks. Noureddine El Alam, ElAlamN@sagehillschool.org Sage Hill School Mathematics Department Chair 20402 Newport Coast Drive Newport Coast, CA 92657 (949) 219-0100 (2214) (949) 219-1399 (fax) www.sagehillschool.org
  • PAUL ... Please include me in your correspondence. Paul Behson Christ School Arden, NC 28704 pbehson@christschool.org (828) 654-8183
  • RICHARD ... Hi, Steve, I have some special Sketchpad files which I would be glad to share with your math teachers and others. Sincerely, Richard Sisley, keckcalc@earthlink.net
  • STEVE ... one of my colleagues here at Nobles (Doug Guy) is beginning to use sketchpad in his geometry class .. his interest got me thinking about trying to form an e-community out of people on the ISED listserv who are into or "wanna be into" sketchpad .. as a former math teacher who got started in 1973 in Charlottesville, I became fascinated with Geometric Supposer by Sunburst and the Judah Schwartz philosophy back in 1984 when at Concord Academy ... Steve Bergen, Computer Coordinator, Noble and Greenough School, Dedham MA, bergen@chapin.edu
  • STEPHANY ... I have a teacher interested sharing/exchanging ideas about Sketchpad. Her name is Stephany Faulkner and she is a fantastic teacher and just informed me that she has taught in your part of the country before. Her email is sfaulkne@norfacad.pvt.k12.va.us here at school Thanks Ed Patterson, EPATTERSON@norfacad.pvt.k12.va.us Dir. of Media Distribution and Software Support Specialist Norfolk Academy, VA
  • SUSANNE ... I am really interested in being part of your mailing list. I teach 6th and 8th Math at Bryn Mawr and just started using the sketchpad. Rich, the Technology Director in the Middle School, coordinated an activity to plot points, construct polygons and then demonstrate addition, subtraction, multiplycation and division of integers through translations and dilations. It worked reaaly well with the honors 6th graders, I am hoping to do it again with the regular 6th graders. I played with the program too late to use it for slope and intecepts, and parallel and perpendicular lines with the eighth graders, but next year I will use it for those topics. It could also be used for systems of linear functions, although I liked the TI-83 and I think I will stick to it for that topic. Susanne Artinano ArtinanoS@BrynMawrSchool.org
  • TERRY ... I'd be happy to join the Sketchpad discussion. Best, Terry Coes Rocky Hill School RI LCoes@aol.com