Analysis of Connected Math and Core Plus Textbooks

A reader deep into math issues emailed these two reviews of curriculum currently used within the Madison School District:

  • Connected Math (Middle School); R. James Milgram:

    The philosophy used throughout the program is that the students should entirely construct their own knowledge and that calculators are to always be available for calculation. This means that

    • standard algorithms are never introduced, not even for adding, subtracting, multiplying and dividing fractions
    • precise definitions are never given
    • repetitive practice for developing skills, such as basic manipulative skills is never given. Consequently, in the seventh and eighth grade booklets on algebra, there is no development of the standard skills needed to solve linear equations, no practice with simplifying polynomials or quotients of polynomials, no discussion of things as basic as the standard exponent rules
    • throughout the booklets, topics are introduced, usually in a single problem and almost always indirectly — topics which, in traditional texts are basic and will have an entire chapter devoted to them — and then are dropped, never to be mentioned again. (Examples will be given throughout the detailed analysis which follows.)
    • in the booklets on probability and data analysis a huge amount of time is spent learning rather esoteric methods for representing data, such as stem and leaf plots, and very little attention is paid to topics like the use and misuse of statistics. Statistics, in and of itself, is not that important in terms of mathematical development. The main reason it is in the curriculum is to provide students with the means to understand common uses of statistics and to be able to understand when statistical arguments are being used correctly.

  • Core Plus (some high schools); R. James Milgram and Kim Mackey:

    In a recent issue of the NCTM Dialogues, Prof. R. Askey comments on a particular and remarkably inept misunderstanding in CorePlus, of some basic methods in probability Prof. R. Askey’s comments on a problem with Core Plus.
    Recently, Core Plus has begun to appear in the Minnesota High Schools, with the usual results, including servere questions from parents and the withdrawal of a significant number of students from the school system. This has also prompted a number of independent analyses of the program by other professional mathematicians. Here are the comments of Larry Gray, a Professor of Mathematics at the University of Minnesota. A Sample List of Mathematical Errors in the Core Plus program.