Negative Review of Arise math program
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Date sent: Thu, 6 Nov 1997 13:04:16 -0500
From: Marti Gaydish <73633.2665@compuserve.com>
Subject: ARISE Math
This is my report on the Arise math program, after I sat in sporadically
over about six weeks. This is an integrated high school math, substitute
for traditional algebra, geometry, and is one of two choices, along with
CPM, offered at the high school my daughter attends in Vallejo. It has
its own web site at www.napanet.net/~jlege.
I sat through two units. The first was three weeks and covered three person
elections--the 1980 NY Senate race, with Buckley and two others;
Wallace-Humphrey-Nixon and Clinton-Bush-Perot. The purpose of this unit was
to learn about matrices. What we discovered, after three weeks of effort,
was that if you have three people running for office, it is possible for
the successful candidate to win with less than 50 percent of the vote.
After we did that, we compared the popularity of various lunch items, with
the same result: the winner had less than 50 percent of the vote.
The students described various ways of arriving at this answer, and
prepared and presented a group speech. What they learned about matrices
was, apparently, how to make a chart with rows and columns. There was no
manipulation of the matrices. My math is 30 years old, but can't you do
algebraic and numeric functions with matrices? Isn't that what they are
supposed to be learning?
The second unit is encryption. I did observe a nice video that enhanced the
presentation of information about encryption. That is, it is a better
learning experience if the material is presented in several ways. In this
case, there was written material, teacher's discussion and the video. It's
just that there was no math in this. The students spent several days
decoding and encoding material in the text, and then creating their own
codes. Each group then gave a presentation to the class on how their codes
worked.
This is supposed to present linear equations. As part of the activity, they
used graphing calculators to see how the curve changes as the number in the
equation changes. The teacher kept telling them how much more they were
learning than students in her Algebra 2 class. Whoopee.
I was totally unable to keep up with this, so that I could provide no
feedback to Jennifer as she was doing the work. This has effectively cut me
completely out of the homework loop. The teacher does not look at the
homework. She says the students get feedback from her as she walks around
the room listening to the various teams. And, they get feedback from each
other.
Clearly, this is how "collaborative learning" is supposed to work. The
students take the problem, in this case decoding a message, work together
to solve the problem, and come up with a solution. They never know if that
is the correct solution, or, apparently, receive any instruction on how to
actually solve for variables in a linear equation.
In my opinion, if you do not get feedback and confirmation that your
solution is correct, you never stop floundering. You must have firm, secure
knowledge to move to the next level of learning. I base this not just on my
high school and college education, but on my experience in teaching
expatriate tax to adults. The earlier and more concrete the feedback, the
better the tax preparers learned and retained what they learned. If you
withheld feedback, they floundered and guessed at the correct method and
did not retain enough knowledge to get better at doing their job.
For the record, as many of you suggested, I have ordered John Saxon's high
school math program which should be here shortly. If we find time to
complete that, and her understanding of the concepts presented in Arise
improves, I imagine the teacher will give herself the credit.
I came in last in the school board election; sixth out of six for three
seats. I got a lot of positive responses from strangers, so I expected
better.
Marti
Why are they teaching college level stuff to kids who don't
even understand algebra???? I thought they were complaining
that US education taught too many topics too shallow.
Here's the stuff on the web page:
ARISE Program Features
It is common to find applications in mathematics curricula, but the
applications are usually after- thoughts that seem artificial to
students. In ARISE, the mathematics truly arises out of applications.
The units are not centered around mathematical topics but rather
application areas and themes with the mathematical topics occurring as
strands throughout the units. Students analyze real-world situations,
develop mathematical models to fit them, check the models against
reality, and improve them. The modeling approach results in a natural
integration of mathematical topics that avoids the artificial
compartmentalization of the past.
ARISE units include materials for teachers and students. There are
explorations appropriate for collaborative learning, as well as
student reading, homework and assessments. Student materials are
distributed gradually as the units develop rather than at the
beginning of the year or term. All units are content and application
based, and incorporate a variety of technologies. Each unit, for
example, includes a video, which introduces the context setting or
shows professionals engaged in a career area. Some include computer
software and/or graphing calculator programs, and most utilize the
TI-82 graphing calculator's capabilities.
There is usually an overriding problem to the unit -- one which
introduces the main contextual problem, is revisited again during the
unit, and which can provide the basis for assessing student learning
at the end of the unit. A lot of the units begin with a physical
activity or a manipulative to build concrete awareness for the
problem. A lot of time, a homework problem will introduce students to
the next lesson's material as a way of building preliminary
understanding. Several of the units are designed to be investigative
explorations, so students can explore the material in different orders
or delve into sub-problems independent of the "class" as a whole. Many
of the units end with a project, so that students can concretely
demonstrate what they have learned or relate it to their own community
situations.
How ARISE Differs From Traditional Programs
In order to truly "paint" a picture of what the ARISE program IS, it
is necessary to draw the inevitable comparison to what it isn't. It
ISN'T the traditional 3-year sequence of Algebra 1, Geometry and
Algebra 2. It ISN'T an "integrated" approach that is fashionable with
textbook companies, in which all the traditional math is simply
reshuffled and doled out over a 3-year period. It ISN'T a watered-down
approach that takes Algebra 1 and spreads it out over two years.
ARISE is a core curriculum; it is a program that allows students "in",
not keep them "out". It demonstrates that mathematics doesn't have to
be ability-grouped in order to be effective. It answers the age-old
question, "When am I ever going to have to use this?", so that
students can concentrate on the learning. It simultaneously prepares
students for college and for vocations. It is equally effective in
block schedules and in traditional schedules. It can be an alternative
program, an academy program or the program for a math department. It
is a model of what the NCTM Standards were addressing, an actual
mathematics curriculum, and a source of new teaching materials on
applications of mathematics.
The material that is covered in the ARISE units will be better
understood by students for a variety of reasons. They spend more time
on the topic, study it from concrete representation to abstraction,
and have a "natural" connection to a real-world application setting.
They are continually challenged to process their learning, to make
connections to previous understanding, to explain their thinking, and
to extend their knowledge to new situations or different contexts. The
students are liberated to understand what they do, rather than to do a
lot in the hopes of eventually understanding what they are doing. Key
concepts like linearity and variability of data come up continually in
a variety of contextual settings, rather than being covered in a
single chapter and then relegated to the shelf until the next year.
The order in which content is presented is determined by what is
appropriate to understand the situation, rather than artificially
established by a linear set of algorithms to be mastered. ALL students
get an understanding on some level from each unit, and because the
units are somewhat self-contained in their content, students can come
into the program after the year begins without being set up for
failure. The continual problem-solving nature of the program, and the
critical thinking required to work through the questions imbedded in
the material will address student shortages in both areas.
Because it is so different from a traditional program, there are the
usual concerns over preparation for university level work, SAT and ACT
tests, college admissions, etc. So, here's an honest admission:
students won't be exposed to the same level of algebraic symbol
manipulation that they would by taking 2 full years of algebra in high
school. There's no way they could! However, most students who DO take
2 years of algebra in high school don't really know their algebra. A
lot of them have to retake courses again when they get to college.
Today's technology does all of those algebra skills faster, more
accurately, and easier than by rote algorithmic processes, assuming
the correct algorithm is applied in the correct fashion. And for the
student who decides he/she isn't going to go to college (at least,
right away), what have they gotten out of the exercise? Testing
processes are being adjusted to reflect what the NCTM Standards have
charted as the course for math education, and will align themselves
with the Assessment Standards relatively soon (at least in our
lifetime). Even college admissions have loosened up, and allow for
programs like ARISE to be viable options for college preparedness. As
far as being "college-prep", can you do linear regression? Parametric
equations? Scalar multiplication and addition of matrices? Modeling of
exponential growth? (These are topics coming out of the first year
course!!!) What about game theory? Graph theory? This is definitely
college-prep material! Will students be prepared for college by
studying ARISE? While it's too early to quote statistics, my feeling
is that "Some will; some won't!" I wouldn't expect it any other way;
even in a traditional program, that's reality. To create a core
curriculum, and allow all students to participate in it, it would be
ridiculous to claim otherwise!!!
How ARISE Differs From Other Reform Programs
If you try to follow what's happening in the math education area, then
you probably already know about the various NSF core curriculum
projects. ARISE is closest to the Interactive Math Program (IMP), out
of the Lawrence Hall of Science, U.C. Berkeley, in that it consists of
thematic units and features a lot of the instructional and assessment
practices recommended by the California Framework and NCTM Standards.
ARISE provides an intuitive environment for the studying of
mathematics: real-world applications. There is a greater emphasis on
data modeling and discrete math topics, and has the advantage of
having been developed after the publishing of the NCTM Standards.
Since it is the newest of the NSF core curriculum projects, it also
has the luxury of being able to improve key elements that make these
kinds of programs successful and to modify ones that may not have gone
well.
Unit 2
Secret Codes & the Power of Algebra
Context Overview
This unit is concerned with coding. Its central question is: How can a
message be coded so that it won't be easily deciphered by unwanted
parties, yet will be easily decoded by the party to which it is sent?
This type of code is different from a code that is used to speed the
flow of information (an application that is not central to the unit,
but is given some attention). The secret coding context has three
primary foci: coding, decoding, and code cracking. At nearly all times
in the unit, students are examining questions related to at least one
of these three. Because we would like students to see the techniques
they are learning used in other contexts, the unit also gives some
attention to simple number tricks as a context similar to coding.
Primary Mathematical Topics
Functions
Domain, Range
Multiple Representations
Variables & Constants
Order of Operations
Function Inverses
Algebraic Expressions
Simplifying Expressions
Distributive Property
Problem Solving
Graphing Calculators
Matrix Operations
Frequency Distributions
Solving Linear Equations
modular arithmetic
Unit 4
Animation/Special Effects
Context Overview
Animation serves as the context for the investigations within this
unit, and the accompanying video segment shows a variety of animation
and illusions of motion. While many features of such illusions are
mathematical in nature, the focus of this unit is on analyzing their
"micro" structure -- the motions of single points within a stationary
coordinate system. Thus we specifically avoid investigating the
relative motions of points within a moving object: that is, changes in
the shape or orientation of an object as it moves. However, examples
of this kind of motion are presented in the video so that various
levels of complexity within mathematical descriptions will be more
apparent to the students.
Primary Mathematical Topics
Coordinate Systems
Variables
Rates of Change
Linear Functions
Linear Equations
Recursive Representation
Closed Form Representation
Parametric Equations
Time Series Graphs
State Space Graphs
Time-Lapse Graphs
Elementary Programming
Matrix Addition
Scalar Multiplication