Negative Review of Arise math program Home Page 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