What were they thinking? In a word - terrible. Another reviewer notes the fact that there are no clear definitions of the fundemental tools or formulas. Honestly, I was a bit shocked to hear that these things were intentionally omitted!
I am 46 years old. Just an average ordinary guy. Graduated H.S. with a 3.52 GPA and was in honors math. Took a few quarters of college level math and got a CUM GPA of 3.9. Made a pretty decent living in the software industry, making a > 6 figure income. I raised two sons who are 21 and 24 who managed just fine in school prior to all of the "new" (HA!) learning.
Now we are hosting an exchange student from Japan. Granted, she is not a 4.00 student, but has a pretty good grasp on English, and did OK in math back home. She is very frustrated with the "wordiness" and "social" aspects of the books exercises.
Trying to be a responsible parent and stay involved with our kid's studies in school, I try to help her with her homework every night. I have to say that I fail to see how or why leaving all the explanation out and confounding the student (AND their PARENTS, for crying out loud) is suposed to be GOOD for anybody involved. I find it extremely difficult to help my exchange student with not only the subject matter at hand, but trying to decipher exactly what the correct answer is supposed to look like. Just exactly what is wrong with providing the answers to the odd numbered questions in the back of the book, and assigning the even numbered problems for homework anyway? Am I missing something here? How is intentionally leaving THAT out supposed to HELP? HELLO!?!?!
I agree with the other reviewer that states math is a precise language. The questions and outputs should be unambiguous by definition, not muddled in some kind of pretentious quasi-subjective scholarly blabber.
These are KIDS for crying out loud. Math is hard enough for most of them. Now we are making it like some kind of punishment by taking away the "how-to's" and the odd-numbered answers in the back of the book. Some of us call those "LEARNING TOOLS". The other reviewer hit the nail on the head - no sense of wonder or discovery, no "a-ha moments", just a lot of head scratching and deflated egos.
I don't blame the creators of the material, or the decision to improve the standard of education in the U.S. but did anybody actually USE this book before deciding to implement it in any school districts? Smells like somebody got their palms greased, and is laughing all the way to the bank. Personally I fail to see the humor.
C'mon people, what the heck happend to the good old 3 R's?
A Disappointment Both of my sons and both of my nieces have been through this curriculum. If we were given any alternative math options, we would take them.
While this program was rated highly by an educational group, it has been a major disappointment to us. Many of the parents have supplemented the math taught at the High School with extra courses for high school students, given by State Universities.
As an engineer, math is extremely important to me. My oldest son hopes to become an engineer, and I'm struggling with how to 'patch' his poor math background. He frequently comes to me with questions that he should understand, but that are poorly communicated in the book.
The teachers often would say "there's an error in the book on page..." My kids said this happened daily.
This shouldn't be necessary. Math is foundational, and texts written for math should be very critically edited, to make sure mistakes are removed, that concepts are well explained, and that the fundamentals are all covered. These steps did not happen with this coursework. And the creators of this material have not responded with improvements to the curricula.
Integrated math as a concept may be very positive. But this series is probably one of the poorest ways to do it. If you're sold on integrated math, try another program.
excellent resource for teachers- poor curriculum I have studied this curriculum intensively as a potential math teacher. I have seen it in action in urban schools. I have taught it briefly. My daughter suffered through it two years ago.
There is a lot of mathematics in this curriculum. The curriculum is a rich source of ideas for teachers. Every potential math teacher should work through it. It is a poor choice for a high school curriculum for several reasons.
First, Core-Plus is a very, very wordy math curriculum. At risk students will not understand it. Nor will they work with texts that are this dense. As a very well educated and mathematically sophisticated parent, I had to struggle with the text to help my 14 year old daughter because it is so poorly written. The essence of mathematics is the precise use of language and I often became infuriated at how hard I had to work to figure out what they were trying to say.
Some students with very strong verbal skills and a good work ethic will do well, with Core-Plus without learning enough mathematics to succeed at the university level in the sciences. The assessments put a premium on busy work, written and oral communication skills and social skills. Mastering symbol manipulation to the point where a student is equiped to learn physics gets short shrift. On the other hand, Core-Plus will strengthen non-math skills for many students.
Most high school math teachers are not equipped to teach this curriculum well. Because the approach is almost exclusively problem solving, the interconnections between the different strands of mathematics are below the surface and often are just not there. The teacher must be skilled enough to bring them out, reinforce them through review and extra practice and supply the missing links when necessary.
This curriculum is deficient vis-a-vis the 2000 Standards in that there is an over-emphasis on data-analysis (statistics) and a serious underemphasis on symbol manipulation (algebra) algorithms and proof. The latest version of the NCTM standards corrects the many extremes and deficiencies in the 1989 standards and is far closer to a consensus of what mathematicians, teachers, educationists and psychologists believe are best practices in math education.
My daughter and all her friends hated Core-Plus passionately. She's no mathematician, but I find it so so tedious. There is no joy of discovery, no pleasure in mathematics itself in these books. The texts are ugly. There is no humor. I love Michael Serra's reform Geometry textbook because he thinks like a 13 year old, has a phenomenal sense of humor and is infectiously in love with math.
Core-Plus should not be used with heterogeneous classes in inner city schools because 75% or more of the students lack the requisite math skills and study skills. There are not enough students who are sufficiently competent to sustain the pace of the group work. These students, who have some hope of a college education, simply will not be prepared for serious study in any field that requires math skills.
I wish I would have written these texts. Contemtorary Mathematucs in Context is a program that build on the theme of mathematics as sense-making. Through investigations of real-life contexts, students develop a rich understanding of important mathematics that makes sense to them and, in turn, enables them to make sense out of nes situations and problems. Yes, it enables them to think.
The materials are designed to implement the vision of high school mathematics portrayed in the National Council of Teachers of Mathematics "Standards" documents. The curriculum materials include thew following features:
Multiple Connected Strands (Algebra and Functions; Geometry and Trigonometry; Statistics and Probability; and Discrete Mathematics.)
Mathematical Modeling (including data collection, representation, interpretation, prediction, and simulation.)
Access to core mathematical topics for all students. Differences in students in performance and interest and be accomodated by the depth and level of abstraction, by the nature and degree of difficulty of applications, and by providing opportunities for student choice on homework tasks and projects.
Technology (Numerical, graphical, and programming link capabilities found on many graphing calculators are assumed and capitalized upon. These provide opportunities to emphasize multiple representations and to focus on mathematical thinking, rather than mere computation.)
Active Learning (Instruction and assessment practices are designed to promote mathematical thinking. Collaborative groups and individual work are used as students explore, conjecture, verify, evaluate, and communicate mathematical ideas.)
The curriculum promises to make mathematics accessible to a diverse student population. Developing mathematics each year along multiple strands nurtures the differing strengths and talents of students and simultaneously helps them to develop diverse mathematical insights. Developing mathematics from a modeling perspective permits students to experience mathematics as a means of making sense of data and problems that arise in diverse contexts. Engaging students in small groups to work together on tasks develops their ability to both deal with, and find commonality in, diversity of ideas. Using calculators as a means for learning and doing mathematics enables students to develop versatile ways of dealing with realistic situations and reduces the manipulative skill filter which has prevented large numbers of students from continuing their study of significant mathematics.
Furthermore, in cases where the mathematics departments or admissions offices have reviewed Contemporary Mathematics in Context, the courses have been approved as meeting the mathematics admission requirements of those intitutions. Many students have applied, been accepted and are succeeding in many colleges and universioties across the country.
Lastly, I have been teaching high school mathematics for 27 years and have seen many programs come and go. I have also heard others use the phrase "This too shall pass." The reform movement is the right movement for students in this country. We do not need to focus on a curriculum that is a mile wide and an inch thick. Contemporary Mathematics in Context provides the depth to allow students the opportunity to be able to think, not just process. I hope that this mathematics movement does not just "pass." I really wish that I would have written these texts. I believe in them and the curriculum embedded within. And so do my students!
Very weak on mathematics, very strong on social goals. Connected Mathematics In Context (referred to as CPMP for its development team, Core Plus Mathematics Project) is a four-year course that would like to replace a traditional Algebra->geometry->advanced algebra->pre-calculus sequence. This course will have a strong appeal for adults whose math skills are weak and whose interest is in process over content. Unfortunately, CPMP is intended for students.
As a general math course for non-technical students or students not college bound, CPMP may be a valuable resource. For schools with high drop-out rates and low college attendance rates, CPMP might be a very good choice. CPMP is a very poor choice for college-bound students.
The design of CPMP calls for leaving out all mathematical definitions from the student text. CPMP even leaves out the definitions of sine, cosine and tangent in the trigonometry unit (Course 3, Unit 1, Lesson 2, "Algebra, Geometry and Trigonometry"). In addition, other critical information is intentionally omitted from the student text -- such as every important mathematical formula and most of the important properties of number systems and other mathematical objects. Mathematical presentation, as characterized by an orderly sequence of ideas with a clear logical connection between statements (that is, proofs of at least the main assertions), is completely lacking until Course 3, the third year. Even in Course 3, nearly every proof displayed in the student text is longer than my first thought for an alternate proof. Selecting "the hard way" to do math does not show a student anything valuable. Good math should make your life better, not worse.
The range of subject matter listed is extensive and impressive. There are four strands: algebra and functions, geometry and trigonometry, statistics and probability and finite mathematics.
Statistics dominates the presentation and is of consistently poor quality. The first year begins with about 3 months on statistics. The "sigma" sum notation is introduced early on but is never used for anything other than statistics. [The sigma operator shares many properties of integration in calculus yet is much more easily understood. Limiting its use to describing statistical measures ignores most of its utility.] Eventually probability is introduced in Course 3 and the course attempts to derive probability from statistics. The text appears to confuse empirical relationships among probability distributions (based on classroom activities) with mathematical proof.
The finite mathematics, mostly a collection of graph theory and combinatorial topology topics in this treatment, seems to be the second most important strand and, in my opinion, is done better than any other strand. There are no proofs but there is interesting discussion and problems. The emphasis appears to be on topics which have been well implemented in commercial software packages.
Algebra, that is the study of solving problems with equations, is never really exposed to view. There is a weak attempt in Course 3 mixed in with the introduction to deductive proof. There is also a brief discussion of logic that manages to make transitivity hard to understand. (Transitivity is this triad: if "p implies q" and "q implies r" are both true then "p implies r" is true.) The text avoids mathematical terms, such as "number field," "real numbers," "integers" or "complex numbers." The quadratic formula finally emerges in the middle of Course 3 soon after the difference of squares formula. The difference of squares formula is: x^2 - y^2 = (x-y)(x+y). This little gem is probably the single most valuable formula for scoring well on the SAT, GRE and American Math Competitions. It is also great for multiplying: for example, 103*97 = 100^2 - 3^2 = 9991 something that almost anyone can do without a calculator. At least it gets a mention in CPMP.
Trigonometry (followed by geometry) is bungled. The usual trig functions are mentioned briefly in the second course. When Course 3, Unit 1 (presumably in September) introduces the trig functions on page 28, the sine, cosine or tangent of an angle are not defined in the student text. I never found a definition of the trig functions other than in the teacher's guide for Course 3. This introduction jumps to discussing the Law of Sines and the Law of Cosines without examing the most basic properties of trig functions, some of which are scattered through the textbook. Similar triangles (the basis of trigonometry) come in nearly 5 months later.
Perhaps the strongest year is Course 4, still in development as of May 1999. The first half of Course 4 includes a number of useful topics that are presented in a reasonably decent fashion, as long as you can tolerate a complete lack of defined mathematical terminology and several material errors in the physics discussions. The errors may be corrected in the final version, so these may not be important. However, the mathematical definitions are again hidden or omitted by intent.
There is a great deal of statistical data at the Core Plus Mathematics Project which they claim supports the effectiveness of the program. This material is not compelling above the level associated with the placebo effect in pharmaceuticals. Certainly CPMP can be taught by a motivated teacher who will supplement the material appropriately. CPMP may have a valid use in locations where teachers need a great deal of support. The teacher's guides are quite detailed. If I liked the approach and presentation of the math, I would love these teacher's guides. However, a student cannot learn math from these books without a teacher. Just one day's absence can result in a gap that even a talented student has no way to patch without an outside meeting with the teacher.
Anything Goes Trivia
Megaton Man
Trevor
