Submitted by: Catherine C. Aust, Chair
Academic Advisory Committee on Mathematical Subjects (ACMS)
Thank for asking for our input as you construct a response to the Georgia Department of Education concerning the modifications that they have made to the Georgia Performance Standards.
These comments include input from one other member of the ACMS in addition to my own thoughts. I was delayed in sending out the call for input because I was away from campus when your memorandum arrived, and I suspect that many faculty are not working full-time this summer and may not have yet seen my email soliciting input. However, based on the extensive input that the committee gave for our initial response, I feel that these comments, which address the extent to which our earlier concerns have been addressed, reflect the sentiment of the members of the ACMS.
Our initial response listed several issues or areas of concern. Some of these have been extensively addressed in the revisions of the Georgia Performance Standards for K-12 Mathematics. The revised standards have much greater specificity in the statement of the standards, classify topics under the correct strand, correct many of the misuses of mathematical terms, and reflect extensive editing of the content to improve the clarity of statements. However, some very significant concerns have yet to be addressed.
As a sequence of courses Mathematics I-IV and Foundations of Mathematics I-IV still seem inadequate to give students solid preparation for Math 1111, the beginning University System course for many majors. Since the Precalculus description is not available at the Web site, it is not possible to determine whether the inadequacies of the Accelerated track have been corrected and whether students will have the in-depth coverage of function concepts and attention to algebraic manipulation needed for success in the AP Calculus course that concludes the track.
The plans for teacher training are not currently posted at the GPS Web site, so we cannot know whether plans have changed from those originally posted. We do know that such a drastic revision of the curriculum needs to be supported by the availability of extensive teacher training. There are many fine teachers in our public schools who have the mathematical background to do an outstanding job of implementing these standards, but many others, who have concentrated their teaching at one grade level or one subject area for a number of years (geometry, for example), will find themselves faced with teaching many new topics and need time to explore these topics in depth before they have the responsibility of teaching them. In addition, the few tasks, samples of student work, and teacher commentary that were originally included have been removed. The Executive Summary says that these are an important part of the standards, and they are. Even teachers who have ample mathematical backgrounds to present the required material need additional clarity about what is and is not to be covered at each grade level or in each high school course.
The posted implementation schedule has not changed; thus, all of our previous comments about the problems with this schedule are still relevant. We read these standards as a significant revision of activities and expectations for students at every level. Thus, an implementation schedule that has many students expected to perform at the level of the new standards in the higher grades when they have not experienced the new standards throughout their school years will be very difficult for students and their teachers.
The issue that these standards borrow substantially from the Japanese mathematics standards without adequate consideration of cultural differences also remains. Members of the ACMS are strong in their belief that a key element in the success of the Japanese curriculum in Japan is the amount of time that Japanese students spend in homework. These standards depend on students spending extensive time exploring concepts through activities with manipulatives, technology, and model building. There is not enough time in the school day for sufficient exploration and reinforcement of concepts. This curriculum will require a dedication to regular homework throughout all grade levels. We believe that this will be a significant issue for many families.
I close these comments with some specific content issues that still need attention. The list is by no means exhaustive; I simply listed items that caught my attention as I reviewed the document.
The first mention of the idea of function appears to occur in standard M6A; yet this first reference refers to "further development" of the idea of function. Students need to experience specific functions in context, and the sixth grade is an appropriate place to start. However, at some point the concept of function, in the abstract, needs attention. We have not been able to find such a content section in the high school curriculum, and it definitely belongs there. Students who have studied linear, quadratic, exponential, and piecewise functions should have a sound foundation for studying and examining the concept of function and exploring the idea of which types of relationships between two variables are functional relationships and which are not.
The Executive Summary needs to be updated to coincide with the revisions in the GPS; for example, the summary states that there are three strands in the K-2 curriculum yet the GPS now include four strands at this level.
The list of Concepts to be maintained at each grade level needs to be consistent with the topic revisions of the previous grade level; for example, the list of concepts to be maintained in Grade 1 includes "Ordinal numbers" but this concept has been deleted from the Kindergarten curriculum.
There is still a need to correct grammar. By leaving the old text to show the revisions, it is easy to overlook errors that remain. These should be obvious once only the new version is included; for example, the second sentence in standard M3N includes "understand the the four arithmetic operations." See standard M4M2 for another obvious grammar error.
The explanation of the two interpretations of division in standard M3N4b is unclear. Perhaps the first interpretation is intended to refer to understanding division as repeated subtraction, but if this is what is meant, that's what the standard should say.