Core-Plus Information HERE

From the Conclusion:

Given the expertise and prominence in the mathematics education community of the authors of the 1997 and 1998 reports and the February Phi Delta Kappan article,

**I find it difficult to believe that they would actively engage in an attempt at deception. But many of the points I have made in these posts show a pattern of attempting to place Core-Plus in as attractive a light as possible while obscuring or withholding data that might lead to alternative conclusions about the efficacy of the Core-Plus system of instruction.**

regards, Kim Mackey

Kim Mackey

Box 1996

Valdez, Alaska 99686

## 10 comments:

This was all available in 1999, without anything so much as a comment from Core Plus or NCTM. It is a deception of the worst order. The results in classrooms for children have been devestating. Especially, when you read McKay's last comment that Core Plus appeared the best of the four textbooks sic curriculum.

Can we now conveniently say now the truth that Hirsch, Ziebarth, Schoen, and Hart are first order a..holes?

I think the whole lot should be thrown in the trash heap. An educational blight is what they started.

I like this essay - it has style. Bachelis's own study was attacked and I hope he gets some vindication for having the courage to speak out when he did. Core plus was a dog and it still is a dog...

Building Bridges In Mathematics Between

High Schools And Colleges: Keeping

The Tail From Wagging The Dog

by Gregory F. Bachelis (WSU)

This article is a follow-up to Roger Verhey's article in the last Newsletter entitled "Building Bridges in Mathematics Between High Schools and Colleges". The impetus for that article was the "reform math" programs being instituted in many high schools. These programs are usually labelled "Integrated Math" and are mainly the result of the promulgation of new NCTM Standards in 1989. They have many "strands", including the usual high school topics plus probability, statistics or data analysis, and discrete math. Some, such as Chris Hirsch's Core-Plus from WMU, include modeling and simulation. According to the proponents, symbol manipulation and rote learning are replaced by higher order thinking and real world problems.

Now Verhey's article was quite low-key and unobjectionable, so one might wonder what all the fuss is about. Well, to put it succinctly, the math education people, in many of these reform programs, have turned high school mathematics on its head. They have changed the way mathematics is presented, from a deductive discipline to an experimental science, heavily dependent on graphing calculators. They claim that this is better than traditional methods, and that it is suitable for all students, which include those who are college-bound and intend to major in science or engineering. Rather than calling it "reform math", I think a more accurate description would be "deformed math". When Verhey & Co. talk about building bridges, what they want is to insure that students who do well with this deformed curriculum get a warm reception when they get to college.

Well, as far as I am concerned, a bit of rain needs to fall on this parade. Let them play all the games they want with the kids who formerly wouldn't have done well when it came time to get serious about math; that's fine with me. For many of these kids this new approach may in fact be better than the old methods, and in number they may indeed be a majority of the students; but we shouldn't let the reformers impose this masquerade on the kids who need to get serious about math in high school. And we certainly shouldn't let them force a change in the way college math is taught by sending us a bunch of calculator-dependent, algebra-starved students, and expecting us to change our methods accordingly. (If you are thinking of Harvard Calculus at this point, then you will also realize that even it makes regular use of symbol manipulation, as does its pre-calculus younger sibling.) Now I know that all sorts of colleges have endorsed Core-Plus as college-preparatory, so perhaps these endorsements should be revisited, as currently are the endorsements of the NCTM Standards themselves (see next paragraph).

If you think I am just ranting and raving, then I suggest you do the following, as I have done. Read some of the front page articles in leading newspapers about the "math wars" or the "new new math" (for example, Detroit Free Press 10/27/97, Wall Street Journal 11/5/97, Detroit News 11/23/97, New York Times 11/27/97 these also include changes in elementary math education, which I won't get into here), and read the article in the 10/15/97 issue of Education Week. Also read the articles in last summer's AMS Notices, and check out the MAA website, where they publish the minutes of their committee which is reviewing the NCTM Standards. (The AMS also has such a committee.)

After doing all this, I suggest you examine some of the Core-Plus materials, where you can see for yourself how this unhealthy calculator dependence is engendered, and where you will also find misuse of math modeling terminology. See where whole areas of mathematics are galloped through, as if in some giant amusement park. Serious study is replaced by "cooperative learning". (I know, I know; reformers of college math like to stress cooperative learning, real world problems, and the use of graphing calculators; but believe me, the latter are making wavelets compared to the tsunami that Hirsch & Co. have created.)

Then attend some school board meetings in West Bloomfield or Bloomfield Hills, or other places where Core-Plus has been adopted (totally in the former, partially in the latter), where the controversies these adoptions have created unfold. Talk to parents whose children used to like math but are turned off by Core-Plus. I know, many students are thriving, but often they are the ones who wouldn't have liked getting serious about math, so as I said before, let them have their fun. Those who want to pursue mathematics in college will have to be "deprogrammed" after they arrive.

Now, as fast as I can say "standardized tests", some of you are ready to tell me to wait for results from SAT, PSAT, ACT, ITED, etc. to judge how successful Core-Plus is. Well, I have news for you. That won't work. For one thing, the tests are being "fixed" to be more Core-Plus- friendly. For another, many parents in Bloomfield Hills and West Bloomfield, and I'm sure in other "deformed" districts as well, are having their children tutored in algebra, to make up for what they are missing, thus contaminating the treatment group.

Even a cursory glance at the reform math curriculum by anyone who has taught its various strands at the college level, as I have, reveals that this is just too much material to cover in four years of high school in a serious way. So what do I suggest doing to remedy this situation? Well, you can forget about waiting for the evaluations of the NSF grants these reformers have. The evaluators are on the same team, after all. Now Senator Robert Byrd of West Virginia has denounced "rain forest algebra" on the floor of the U.S. Senate, so maybe we could politicize this battle even more than it has been. What I suggest is that traditional math be kept as an option in every district where Core-Plus or other programs of its ilk are adopted, and that all of us serious mathematicians support such efforts wherever we can. And also, as I mentioned above, we should look carefully again at Integrated Math programs individually, because there is such a wide variation to see which ones are really college-preparatory.

And for those of you who are ready to dismiss what I say as merely anecdotal, let me end this harangue by paraphrasing the late Senator Everett Dirksen of Illinois. "A few anecdotes here, a few anecdotes there pretty soon you're talking about real statistics."

Core plus = deformed math!!!

It makes absolutely no sense when you read Core '+', discard it, and everyone will be thankful. Otherwise, just put us out of our misery - its torture to read Core plus. You have to be kidding that kids are going to actually learn any math from this train wreck.

You know, I have to admit they tried to align the WASL to 'fit' Core Plus -- the alignment team consisted of 'curriculum' experts, most notable was one expert from Wisconsin (Norm the Webb who now sits on the advisory board with Spitfire Briars) who did the only independent Core plus evaluation study I can recall, but as we know from first-hand experience, this committee's efforts were not very successful. These are the fighter aces, the red barons, of standardized curriculum. May they go down in flames. Webb (formerly Project 2061/AAAS) is doing the MSP evaluation for SMATE(Nelson/AAAS/Project 2061) along with Merlino. Nelson thinks all textbooks should be smaller, since backpacks are too heavy. Happy landings jerks!!

Here's a project that should be finishing - imagine the consequences for testing, a centralized database that connects to all the state standards.

This is a very speculative enterprise - it presupposes that by the end of five years, one will be able to compare student achievement between states.

That is not the proposal of the investigators, but the database does lend itself to such abuses. It also ignores some of the laws of statistics, but as we know from past history, logic is hardly a factor used by the AAAS.

The purpose of this five-year project is to develop a bank of high-quality assessment items and related tools in middle- and early high-school science and mathematics that are aligned with state and national content standards; that are easily accessible by users; and that can be utilized throughout the educational system by curriculum researchers, curriculum developers, teachers, test developers, and the general public. The items will also be valuable as demonstration models of what aligned assessment looks like, models that can be used in college and university teacher education programs.

The requirements of the new federal No Child Left Behind Act of 2001 have given high-quality assessment new importance. By mandating tests that are based on state standards, the legislation provides the impetus to design assessment tasks that measure understanding of the content specified in those standards.

As one of the first organizations to focus on content standards and their role in curriculum, instruction, and assessment, Project 2061 of the American Association for the Advancement of Science (AAAS) has been studying the alignment and effectiveness of hundreds of test items drawn from a variety of sources, including items from the Third International Mathematics and Science Study (TIMSS) and National Assessment of Educational Progress (NAEP) tests, items from state tests, released state test items, and items from various curriculum materials. Using specially designed criteria, Project 2061 and teams of experienced educators and assessment specialists have developed a procedure for analyzing and profiling items for their alignment with content standards and for other characteristics that affect the usefulness of the items to measure student understanding of those content standards (American Association for the Advancement of Science [AAAS], 2003). Application of the procedure leads to a detailed analysis of each item on such features as content alignment; comprehensibility; test wiseness; bias related to gender, class, race, and ethnicity; and item context. The results of the analysis can then be used as the basis for revising those items. In the project proposed here, we will extend our ongoing work with assessment items to further develop this analysis procedure by examining assessment items for additional linguistic features and for their suitability for testing students with limited English proficiency. This new work will draw on research being done by Rebecca Kopriva at the University of Maryland (Kopriva, 2000).

Our current work also involves developing assessment maps that can be used as conceptual frameworks for creating multi-item tests that measure student understanding of targeted content standards and related ideas. The assessment maps identify common misconceptions, prerequisite ideas, and ideas that come later in the developmental progression. These maps draw from the strand maps that we have developed for the Atlas of Science Literacy (AAAS, 2001) and from the work on progress variables in learning (Wilson & Draney, 1997). Tests built around assessment maps can be used to provide a diagnostic analysis of student understanding of ideas identified in the content standards.

Because the new federal legislation requires states to hold students accountable for the specific content standards of each state, being able to cross-link standards documents is essential in order to provide national resources to the states and to share resources from state to state. To accomplish this cross-linking, our proposed project will draw on existing efforts to create connections between the content standards of each state and to national content standards. The work done by Mid-continent Research for Education and Learning (McREL) and Align-to-Achieve, for example, allows one to match the content standards of approximately 40 states, the National Science Education Standards (NRC, 1996), and their own Compendix (http://www.mcrel.org/standards-benchmarks), a set of benchmarks and standards drawn from primary national documents such as AAAS's Benchmarks for Science Literacy (1993) and the National Research Council's National Science Education Standards, as well as various state documents. (AAAS's Benchmarks was used extensively in the creation of the Compendix and will soon become part of a complete set of content standards in the Align-to-Achieve database.) The proposed project will work with the linked standards already included in the Align-to-Achieve database to create a utility that will allow users to access test items matched to national content standards or to the content standards of any state

Did the study in this blog refer to core or to core plus? Is not core plus a newer version and published just recently? (during the last two years)

T^2

No, its not. I have the revised edition (1 book) and the original version (2 books).

The problems are pretty close to identical. The main difference is the 2nd edition has three extra lessons (unit 7) on quadratics that go in this order - this is not even a correct title, should be parabolas. -

1. trajectories

2. equivalent quadratic expressions

3. quadratic formula.

The entire unit and for that matter most of the book avoids solving problems with algebra, except with a calculator via graphs or by simple substitution.

This book emphasizes the discrete strand. It presumes that students have had exposure to algebra. Look at who consults for them

Doris Schattschneider - Tesselations

Richard Scheaffer - statistics and probability

Stephen Maurer

discrete algorithms

Deborah Hughes-Hallett - most experienced author (applied calculas - college level)

William McCallum (Also from Univ. Arizona) Probably helped write the unit on parabolas.

http://math.arizona.edu/~wmc/Talks/Western_Michigan_2008.pdf

Much to advanced for coursework in the eighth grade.

Gail Burrill - moved over from connected math

Notices: Starting in 1968, the government funded a huge study called Project Follow-Through. It cost a billion dollars and ran almost thirty years. The purpose was to examine how different teaching methods or philosophies affected student performance. What they found was that the traditional, "direct instruction" method was the most effective. Are you familiar with this study?

Burrill: I have never heard of it.

(reincarnated space cadet)

Eric Hart - Vedic Math at the Maharishi University (discrete)

Non Algebra

unit 1 Patterns of change

unit 2 Patterns in data

unit 4 Vertex edge graphs

unit 5 exponential functions

(students will recognize and represent exonential growth and decat in symbolic form)

the part about solve problems involving exponential change I looked it up and couldn't find anything except in a lab called the bouncing ball which I know is often covered in physical science or used as an easy introductory assignment for doing lab work. Otherwise, zip.

Unit 6 Patterns in Shape

Geometry - students describe two and three dimential shapes with drawings. Topics include triangle inequality (big deal!!!)

Unit 8 Patterns in change

construct sample spaces of equally likely outcomes (flipping coins omfg)

This textbook is like a dead cockroach on a firetruck.

hosed up.

unit 3 Students use spreadsheets to construct lines on their calculators

Unit 7 Lets chuck pumpkins

And this is the best of the five curriculum. Naw, lets forget about textbooks that can't possibly be the problem why we have kids performing like idiots on the WASL. Lets all talk about curriculum, what we want students to be able to do (ad nauseum)

Without any introduction vocabulary or anything. p. 388

On your own....

12. You can prepresent the diagonals of a quadrilateral with two linkage strips attached at a point.

a. What must be true about the diagonal strips, and how should you attach them so that the quadrilateral is a parallelogram?

b. what must be true about the diagonal strips, and how should you attach them so that the quadrialteral is a rectangle?

c. what constraint(s) must be placed on the diagonal strips and their placement if the quadrilateral is to be a kite?

Give reasons to justify that the shape with your arrangement of diagonals is a kite.

d. What constraints must be placed on the diagonal strips and how they are attached in Part a if the quadrilateral is to be a square? give reasons to justify that the shape with your arrangement of diagonals is a square.

You want to make kids crazy - just let them work out of Core plus for a year. How about three years?

This is slam dunk FUBAR - I think they were smoking something when they wrote this book.

Observing a classroom that uses Core plus is like watching an AA counselor addicted to tricylcics trying to teach students how to use a TI84. Its pathetic, a bit like watching a tv series starring the golden asse.

I taught Core-Plus at the middle-school level for three years. When Core-Plus was introduced, all of the math teachers in the school district were required to take 1-week-long classes to learn how to teach the material. I have a B.A. in Math, Chemistry, and Physics, plus an M.Ed. in Secondary Science Education, and a D.C. (Doctor of Chiropractic), along with 35 years' industrial experience.

The presentations made by the publisher's representatives were interesting and entertaining, but provided almost nothing about the underlying mathematics. When successful mathematics teachers have to be re-trained to unlearn the mathematics that has served them so well in their careers, there is something basically wrong with the program.

The teachers in our district were told that the Core-Plus material could be supplemented with whatever we felt necessary to "fill out" the curriculum. I did NOT stick to the strict Core-Plus program, but included the Algebra manipulation skills necessary to handle linear, parabolic, exponential, and logarithmic equations. We always learned to manipulate the equations and expressions manually. Only AFTER the students demonstrated mastery with paper and pencil, were the graphing calculators brought into play.

I did not want to send my students out without the Algebraic skills that were so lacking in the curriculum.

As a follow-up, many of my former students keep in touch with me on Facebook and routinely thank me for the excellent mathematics background they received in my classes.

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