I mentioned the curriculum analysis project led by Bill Bush a while ago. Here is the final product. It provides analysis sheets to help school districts look at curriculum materials and decide how well they reflect the standards. There is also a powerpoint for professional development of evaluators. If you have any questions, send an email to Bill Bush.
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Geometry is the part of school mathematics which has fallen apart the most. The treatment
suggested here for geometry is inadequate. Geometry is not a major topic in grades k5,
where number and operations are the main focus, yet there is no indication of this in the
curriculum analysis project. Geometry in grades 68, especially 8, is a major focus, with
there being an informal treatment of congruence via rigid motions, and then of similarity
based on congruence. This last aspect is not suggested in the current draft by giving
similarity first as a topic to look at. However, it is high school which is very poorly done.
Where is any mention of the concurrence theorems and the fact that they should be
proven, not just stated as happens in many current books? What should people look
for about circles in high school. There is much more than just using a circle to extend
the definition of trigonometric functions. A tangent line is perpendicular to a radius is
one example, and the fact that an inscribed angle in a circle which cuts off a diameter
is a right angle is another.
One of the greatest challenges for teachers is knowing which lessons in a textbook should be emphasized and which could be skipped. The CCSS will help greatly with those decisions. But consider what happens when lessons in a textbook go beyond the core, such as for division of fractions in Grade 5. CCSS recommends that students learn to divide by *unit* fractions but does not mention dividing nonunit fractions until Grade 6. In my tutoring of middlegrade students, I find that many students have just memorized a trick for dividing and do not know the meaning of dividing by a unit fraction (or any fraction). So, I completely agree with the CCSS approach of emphasizing division with unit fractions a year before nonunit fractions. Now, for my main point related to analyzing curriculum… In addition to analyzing content coverage, I think the reviewers should indicate lessons that go beyond CCSS. Ideally, textbooks will be revised to add more emphasis to CCSS while moving advanced content to ancillaries. However, having worked for textbook companies, the more likely scenario is that the companies will just insert extra lessons to cover CCSS while leaving the rest of lessons untouched or minimally changed. This could still allow books to get high marks using the content coverage rubric. I do see that content analysis tool has a section called Overall Impressions that includes this question: “Within this domain, is the treatment of the content across grade levels consistent with the progression within the Standards?” Perhaps there should be an additional question for each domain saying, “For this domain, which pages in the chapters/units have significant content that is not required by the Standards?”
Unfortunately tool 1 only deals with one subtopic under each main topic for 912 Math. This could be dangerous since it is not cleat that that is what they are doing. This could result in textbooks that do not cover the standards, just a small subset. Please, at least make it clear that it does not cover all 912 Mathematics.
Thank you for providing a comprehensive tool to help districts evaluate their mathematics programs.
A good activity to help ensure that all participants are evaluating the curriculum similarly would be to provide samples for each of the “levels” found in the rubrics and ask reviewers to put them in order. Do you have any samples that could be used?
It would also be nice to provide examples of the Mathematical Practices using common curriculum activities to demonstrate an example of a weak usage and a strong usage using a lesson for the same standard. Do you have any of these examples that could be used?