As an example of a poorly taught subject, I would cite the "Looking for Pythagoras" book.  I was extremely frustrated throughout the entire 4 week + ordeal of "discovering" the Pythagorean Theorem.  An inordinate amount of time was spent "counting" blocks on dot paper with the goal of measuring areas.  Eventually, the student used squares and rectangles to calculate the area of triangles and other odd shapes by halving the area (these areas found by adding blocks) of squares and rectangles.  They ultimately get beyond the dot paper and are able to calculate areas of rectangles using the "length times width" rule (the traditional approach).  The next big coup is discovering that the length of the side of a square is the square root of its area.  It became clear at this point that square roots should have been
discussed at length but they were beyond the scope of the text.  The square root concept, or shall I say the lack of, caused my child a lot of confusion.  I suppose that after all, who needs to know the "nitty gritty" details of square roots when a calculator is readily available?  It seemed to me that the children would have benefited greatly if they had been taught specifically about square roots and perfect squares, asked to memorize the squares of numbers up to at least 20.  This should have been followed with some time spent breaking up the sum of perfect squares prior to learning the Pythagorean Theorem.

Once the student learns that the length of the side of a square is the square root of the area, they proceed to right triangles.  For each leg of the triangle, the student draws a square with one side coinciding with one side of the triangle.  This leads to a right triangle with three squares attached to it. Through a discovery process (tables etc.), the student learns that the sum of the areas of the smaller squares is equal to the area of the biggest square and hence the Pythagorean Theorem has been "discovered".

My point is this.  Had the concept of square roots been introduced prior to the presentation of the Pythagorean Theorem (yes, I said presentation and not discovery) I believe the concepts would have made more sense to my child.  There would be no harm in spending a day, following the Pythagorean Theorem classes, presenting an interpretive class on the theorem.  I was shocked at the amount of time wasted during the "discovery" process throughout this unit.  I am disappointed to see that "Looking for Pythagoras" has been recommended for both the 8th grade math programs.

I have a similar opinion of every unit that I have dealt with during the seventh and eighth grade years.  The unit called "Frogs and Fleas" was another major sappointment.  I could not believe how long was spent working up to multiplying simple binomials.  The concept of starting with squares or rectangles and adding to the length of  their sides to model the "expanded form" was cute but certainly not worthy of the time spent.  What is wrong with presenting the basic properties of exponents, the commutative law, the distributive law, and the associative law, up front?  My son was asked to recognize that a parabola given was representative of an equation involving the product, (x+2)(x+3).  He had not a clue.  Had he been taught to multiply them out, he obviously would recognize the resulting squared
variable, x**2.  Since the class had not learned about the basic rules of multiplying these kind of factors, he was told to look at the equation and if there was an x in each factor then the resulting curve would be parabolic.  Do the authors feel that mathematical rules and terms are too frightening for the children?  I oversee my son's math homework regularly and have rarely found any value in the CMP program.  I often find myself trying to explain the basis for a unit to him early on for fear that he will miss the very important math concepts necessary for Algebra.