Northshore School District Jr High Math Textbook Review
By Arthur Hu April 21, 2009 arthurhu at hufamily.com
425-891-2619 3521 214th pl se Bothell, WA 98021
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I went to the Northshore district presentation on the next two math textbooks they have chosen to replace the current sequence for jr high school in grades 6 and 7. They have already adopted Connected Mathematics Project in grade 6. The persons there said that on the basis of the texts that best aligned with the state standards. However, what I found is that the while the 8th grade Gencoe book appear to be reverting to a normal textbook with very good explanations and deep coverage a topics that are traditionally important, the CMP2 is just a rehash of the problematic Connected Mathematics Project 1 books marked by numerous complaints that it is just a radical implementation of constructivism so extreme that it does not even permit the printing of most formulas or methods in the student textbooks. This renders the books useless as a reference for parents or even students who are asked to compute the volume of a sphere
only after stuffing a cylinder made of paper with modeling clay to derive their own formula, but the formula is not in the student book. By contrast, Glencoe in grade covers many of the same topics, also using investigations, but also includes all the formulas and methods, and explicitly explains important essential algebra concepts as oppose to CMP which emphasizes graphic calculators, and ask students to about their own ideas to solve algebra-like problems rather than presenting standard methods used in college and industry. Unfortunately, I was told that it is too late to adopt Glencoe in both grades.
Grade 7: Connected Mathematics 2 (CMP2)
Grade 8: Glencoe Mathematics: Applications and Concepts Course 3
If you're familiar with my previous reviews, I've been appalled by texts such as
used in Seattle, Bellevue and Lake Washington which in elementary school are built around the ideology that mathematics not only needs to be taught differently, but the very basics of standard methods of arithmetic should no longer be taught. Standard methods such as regrouping/ carry / borrow and long division are simply not taught. Teachers are instructed to discourage use of standard methods if students demonstrate they have this knowledge. In one white paper, it is claimed that a 2nd grader incorrectly uses the standard method, while a student who constructs his own algorithm by using properties of negative numbers demonstrates the superiority of the Investigations approach. Of course, one wonders why a 2nd grader is learning subtraction if they are familiar with the jr high topic of negative numbers. Even the "add up the numbers and divide by how many items" definition of an average is presented as an unacceptable learning outcome for average. Worst was the consistent awful homework which in my estimation, always takes forever to figure out, takes forever to cut or paste or laboriously write lots of numbers, and when you're done, you
Everyday Mathematics (elementary)
is currently used by Northshore. Unlike Investigations, it does not outlaw standard methods, however it spends a lot of time on very unusual and inefficient non-standard methods. Many parents complain they are confused by the homework, and cannot help their kids. It is replaced by Connected at Grade 6
Connected Mathematics 1 and 2
CMP 1 has been used in the jr high schools for some years, CMP2 has been used in Grade 6 since last year. CMP2 was selected for grade 7 because they said it aligned with the new state standards, even though the point of the "new" standards was to get away from fuzzy constructivist math, which is what drives CMP. The most striking feature of CMP is that it has been reviewed as one of the "worst math textbooks ever written" and does not explain ANYTHING. The cover of the book with formulas contains one formula, but it's the ONLY formula given in the entire book! The book that covers the area of a circle DOES NOT CONTAIN THE FORMULA PI R SQUARED ANYWHERE IN THE STUDENT BOOK. It only has a crazy exercise in cutting up a square in a circle into tiny bits which asks if a ratio might be somewhere in the vicinity of 3, and what magic numbers might they have heard about - oh, maybe it's pi. Traditionally, it is taught without the derivation because the formal method of derivation requires cutting up a circle into an infinite number of pie wedges into a trapezoid/rectangle that is pi on one side and 1/2 pi long. Similarly, the book about cones and spheres does not contain ANY description of the formula. You look at the section from the index, and all it does is ask you to stuff a cylinder with a sphere of play doh, or pour rice into a carefully constructed paper cone. The homework asks you to compute the volume of a sphere or cone from its dimensions, but any parent who tries to help will NOT FIND ANY FORMULAS OR EXAMPLES ANYWHERE IN THE BOOK. The teachers at at book showing explained that the students are supposed to write the formula in their notebooks. They did not at all agree with my assertion that a book that purports to teach how to find the area of a circle, or volume of a sphere SHOULD CONTAIN THE FORMULAS NEEDED to compute these numbers, and I find this even more disturbing. All they have to do to 90% fix the books is ASK THE KIDS TO WRITE THE FORMULA INTO THE TEXTBOOK. Only an extremist constructivist ideology can explain why for every key math concept, THE ACTUAL METHOD, ALGORITHM OR FORMULA is deliberately OMITTED FROM THE STUDENT TEXTBOOK. Even the teacher book lacks a formal explanation of the method except as "one possible student response is ...." I have a number of traditional math textbooks covering the area of a circle, and EVERY SINGLE ONE has a full explanation of every method and formula. The teachers there said "oh these books are much better, they're very different", but CMP 2 omits every method just as the first one did. I have seen one review that mentions that CMP1 omitted ENTIRE ESSENTIAL SKILLS such as how to divide fractions, where CMP at least covers, but again, DOES NOT ACTUALLY PRINT THE METHOD. CMP is completely useless as a reference book as you cannot look up the method to anything. Finding the method is treated as homework, even though my son reports the teacher just gave out the formula anyways in CMP 1 which just defeats the design of the textbook. The method is treated as the answer that can only be printed in the teacher edition, not just the answers to the homework problems.
The book on algebra covers the use of graphing calculator, but I could not contain any formal coverage of anything resembling what I was taught in algebra 1 that would allow solving ax + b = c. In the fuzzy math sequence that goes from CMP to Core, I don't see anywhere will students will get a formal instruction in symbolic algebra, because it is not covered in CMP2, and I couldn't find it covered in Core either. In high school science and college (i.e. REAL real life math) you need to know algebra backwards and forwards, and you don't need to know about 85% of the zillion topics that have been thrown in to integrated math books in the name of "raising standards".
Glencoe - adopted for grade 8
The Green Glencoe math book is a traditional book, I have a copy from the early 1990s. It has been chosen as appropriate for grade 8, even though it's to the same state standards, covers much of the same topics, and is completely normal and convention as CMP is radical. When it covers volume of a cone, you can also pour rice into a paper cone, but it ALWAYS CONTAINS A FORMULA that you can use to do the problems with, and can be used as a reference book.
Even the algebra looks like the sort of treatment we got in algebra 1, it explains how you can add, subtract, or mulitply or divide by both sides to solve an equation instead of asking students to find patterns and guess how you might do these things. This is the sort of book that could be used in place of a distinct 8th grade algebra class, and preparation for more advanced math.
There is an online version of the book at http://freebooksource.com/?p=23886
Some parents asked if there was a 7th grade version and I'm sure there is, but it was stated that the decision and piloting has already been done, and there is no way the district will waver from its selection. In my judgement, this would actually be a much better book for my son who is going into double honors than jumping into Core which is mostly worthless in terms of learning the actual math you'll need in college and industry, just a lot of fancy math concepts for showing off "high standards" that don't mean anything.
In my opinion, CMP2 is just as ridiculous and probematic as the CMP1 with only minor improvements such as how to divide fractions in 6th grade, and I'm not aware of any improvements to grade 7 other than de-emphasizing the Logo programming language which just was a way to show off a now-obsolete technology in CMP1. It is so constructivist that it cannot be used a reference for any method, which must be derived in class, and must be written in a student notebook or looked up on Wikipedia. The video that was shown even admitted that parents complain they cannot help their students homework, it did NOT explain this is because the textbook does not contain any examples or explanations that parents can use. I don't have the slightest idea what the formula of the volume for a sphere is, and neither do most parents, and they should not have to use google to do their children's homework.
Glencoe on the other hand is a tested book that has been used for years and years without generating an internet full of complaints and negative reviews that it is "the worst math textbook ever written", or have parents testify to school boards that the lesson on area of a circle doesn't even spell out pi r squared. It is even suitable as a stand-in for a standalone algebra and geometry course, which they told me the district will be developing for next year or so, to replace the integrated approach that has been so criticized as useless for any student that actually plans to continue in math or science in college or career, and is too much math for students who aren't college bound, and even too much math (espeicially calcuator based) and not enough depth than they'll need in college.
The school board needs to re-evaluate the selection of a CMP2 which is widely known in math circles as a radical and largely failed experiment in math instruction that has serious problems when it is designed to deliberately omit nearly all explanations of standard methods that must be mastered. The school board also needs to ask why so many of the math instructors accept such as radical and troubled math approach rather than taking a critical look at its problems and why so many people have complained about this approach. The district should adopt Glencoe in both grades, and continue to phase in real algebra and geometry to replace the scattershot integrated math such as Core which has frustrated so many students and parents.