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Day 4 Math Forum Advanced Summer Institute
Posted:
Jul 10, 1998 2:05 PM
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Day four of the 1998 Math Forum Advanced Summer Institute began with
the daily morning project development time.
Nicole and Tushar returned to help participants further develop skills
needed to display Mathematica, Maple, and Mathview notebooks on the
Web. Nicole handed out a tutorial for Maple Tutorial on making a Maple
Notebook (http://forum.swarthmore.edu/spimsow/TutorialforForum.html),
with an example of Integrals and Maple
(http://forum.swarthmore.edu/spimsow/ExampleNB.html) and a "Neat
Graph" (http://forum.swarthmore.edu/spimsow/graphs.html). Nicole and
Tushar then worked with individual participants needing assistance,
and suggested a page that lays out The Set-Up Required to view the
SPIMSOW Mathematical Notebooks
(http://forum.swarthmore.edu/spimsow/set_up.html), a guide for
preparing your computer for using MathView, Maple, and Mathematica.
Following lunch, Dave Kershaw announced that Evan Glazer's and Jon
Basden's forms are looking great, and participants should take some
time to look at them:
Evan Glazer's forms ask for input (answer to a question) and give an
immediate response (correct or incorrect and/or an answer):
Up to the Ceiling
http://forum.swarthmore.edu/workshops/sum98/participants/glazer/phone/ceiling.html
Down to the Floor
http://forum.swarthmore.edu/workshops/sum98/participants/glazer/phone/great.html
Step Up
http://forum.swarthmore.edu/workshops/sum98/participants/glazer/phone/graph.html
Jon Basden's functional forms:
Submit Your Answer - 7 Red Math Challenge (a functional form)
http://forum.swarthmore.edu/workshops/sum98/participants/basden/hour2/submit2.html
Soma Cube Construction
http://forum.swarthmore.edu/workshops/sum98/participants/basden/somacube/construct2.htm
As his participant project, Evan Glazer presented a student project on
modeling temperature data
(http://www.glenbrook.k12.il.us/gbsmat/temp/temp.html). He noted that
the temperature data work well with a cosine graph; however, it is
possible to adapt the exercise by modeling parts of the data with a
linear graph. As Evan described the project, the student must always
live in a city where the temperature ranges between 65 and 85 degrees.
If, at some point during the year, the temperature is outside of this
range, the student must move to a new city that fits the temperature
criteria. The students get the data from an Internet site
(http://nimbo.wrh.noaa.gov/Reno/max.html), and analyze the data to fit
a cosine function. They then find airline reservations, go sightseeing
on suggested Web pages, and present their findings in a written
report.
Isaac then demonstrated how to integrate MathCad into this project. In
particular, he illustrated how the student can use the defined
function to predict a temperature on any given day, and how to show
graphically the period in which the temperature falls in the 65 to 85
degree range.
Judy noted that when you give middle school students only linear
models to test, they get a false sense that all data can be modelled
linearly. She suggested that perhaps students could learn how to model
the data using a spreadsheet without having to fully
understand all of the mathematics. Isaac suggested that while the
overall model is not linear, students can use linear approximations to
predict daily temperatures, as opposed to the more general monthly
average temperature.
Bob Panoff mentioned that in differentiability and continuity, the
concept of piecewise linear is important, and so it may be valuable to
introduce these concepts early on. He also suggested that another
lesson could present the idea that by introducing more data, the model
becomes more exact, and at some point, too much data produces extra
noise. Suzanne and Mel, middle school teachers, suggested that one
valuable lesson might be graph interpretation. Evan added that this
project piques the interest of non-mathematically inclined students,
appealing to those who are good writers and have good organizational
skills. Judy said this might be a good activity for group work, giving
the teacher the chance to bring students with different resources
together. Bob encouraged the participants to use any of the resources
he has made available on the Internet.
Bob also said that the Internet can be useful for posting data from
students' weather recordings from around the country. For example, in
Maryland high school students are comparing weather data for eastern
versus western Maryland. This provides an opportunity for the sciences
and mathematics to work together.
After some individual project development time, Suzanne Alejandre gave
a presentation of the thousand locker problem
(http://forum.swarthmore.edu/alejandre/frisbie/unit7.html). She
suggested that students begin in groups of two and use physical
manipulatives to model the problem: when a partner counts, it helps
get the problem to "click." Mel noted that by using many different
techniques of presenting (physical modeling, computer, mathematics), a
teacher can hope to reach many more students. By repeating the problem
in different ways, there is more reinforcement and a better chance of
understanding. Sarah encouraged using manipulatives in many situations
from early on in a child's education - for example, grouping foods in
sets during dinner. As a variant, Suzanne and Sarah also mentioned
lining the students up in a row and having them step forward and
backward to model opening and closing a locker.
Bobbie noted that this problem is rich in teaching about
problem-solving. It teaches the students that they should begin with a
simpler problem and use simulations when possible. In addition, this
is a good lesson for learning about divisibility and factors. Judy
mentioned two twists to the problem: keeping track of how many times a
specific locker is open and closed, and finding how many lockers are
opened exactly twice.
- Betsy Teeple and Sarah Seastone
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