"As a joint initiative, METS and DESE collaborated to develop a comprehensive K-HS mathematics curriculum document that specifies content priorities (core concepts), learning goals and performance indicators for each grade (K-8) and core high school courses (Algebra 1 and 2, Geometry, and Integrated Mathematics 1, 2, and 3). This draft document is the result of that collaboration. "
"This document presents a draft of curriculum priorities (core concepts), learning goals and performance indicators for K-12 mathematics in Missouri schools. "
"This document is a draft and as such, is intended to stimulate review and discussion. Feedback is encouraged. The writing group will consider all feedback in producing the final draft to be submitted to the State Board of Education in September 2008 (see http://dese.mo.gov/divimprove/curriculum/unitindex.html for options for providing feedback). "
"Recent state and national initiatives have prompted the call for the development of new K-12 mathematics goals, to replace the existing grade-level expectations (GLE) document. These initiatives include:
• The governor’s METS Alliance has recommended changes in the GLEs for math and science in order to support 'inquiry-based instruction based on internationally recognized best practices.' "
"This effort is co-chaired by Cindy Bryant, DESE mathematics consultant, and Barbara Reys, professor of mathematics at the University of Missouri. Writers of the new document include K- 12 teachers, curriculum coordinators and university faculty. We expect a draft copy of the goals to be ready for public review in March, and we hope to present a final version to the State Board of Education in September, 2008. "
(N.B. Barbara Reys is actually a Professor of "Learning, Teaching and Curriculum" at the MU College of Education, and is not a Professor of Mathematics at MU. )
"I strongly urge the state Board of Education to reject the proposed draft and ask the Department of Education to commission another writing group under new leadership.
Such a group should mirror the full range of expertise that was represented by the members of the National Mathematics Advisory Panel. The panel was charged by the secretary of education to integrate the best practices from the fields of education, mathematics and cognitive science.
The panel’s recently released final report has been broadly accepted as the definitive document on K-12 math education. It is imperative that Missouri align with its conclusion that all students learn authentic mathematics."
"Members of prominent university mathematics departments in Missouri are calling for an evaluation of state standards and expectations in K-12 math curriculum."
"Dated May 5, the letter was sent to the Missouri Department of Elementary and Secondary Education. It was signed by 39 faculty members from MU, six from Washington University in St. Louis and seven from Missouri University of Science and Technology, formerly the University of Missouri-Rolla."
The letter to Commissioners Stein and King - with endorsement signatures
"For all these reasons, we urgently request that you, as commissioners with major responsibilities for Missouri education and as members of the P-20 Council, institute an immediate review of both the K-12 draft and the college entry-level document to determine their adequacy in the light of the NMAP. The review must include persons with training and experience in mathematics per se. We write with urgency, not only because of the seriousness of the matter, but because we understand that adoption of the proposed K-12 document is expected by September. We believe, however, that if a delay is necessary, that is far preferable to locking Missouri into standards based on old ideas out of step with the direction of the NMAP and the nation as a whole. We stand ready to meet with you to discuss these important issues, to answer questions, and to assist in any way that would be useful in achieving the goal of better mathematics preparation for Missouri young people. We hope for a response in the near future."
" 'There are no research mathematicians on the writing group (for the standards),' said Barbara Reys, co-chairwoman of the writing group for the K-12 mathematics standards and a professor of mathematics education at MU. 'In hindsight, the organizers probably should have invited their participation. We are continuing to seek feedback from all interested parties, including mathematicians from Missouri and elsewhere.' "
"The writing group for the math curriculum draft is made up of 26 K-12 teachers, school administrators and higher education faculty from mathematics departments and colleges of education."
"Feedback on this first incarnation of the standards would be most timely between now and August, May said."
The response letter from Commissioners Stein and King
"We understand that additional mathematicians have been invited to review the proposed curriculum. This is timely as K-12 and higher education review the gap analyses that have been completed and explore potential changes to either document. Please be assured that whatever indicators and standards are adopted are intended to be dynamic, depicting a snapshot in time, and are subject to modification as state and national recommendations evolve. "
Review of the Algebra I/Integrated I material in the March 08 draft (8 pages - pdf) - Profs. Christiansen and Mitrea
"Our overall impression of these standards is that, if adopted, they will not adequately prepare Missouri students either for studying mathematics at the college level or for using mathematics in other disciplines, particularly science and engineering. The proposed standards are griev- ously ﬂawed in many ways. The standards, including the “Learning Goals and Performance Indicators” condemn our students to a second-rate education via the “tyranny of low expectations.” They omit some essential topics or concepts altogether. Moreover, they are vague and ﬁlled with words and sentences devoid of mathematical content. As such, they provide little concrete direction to educators and make it impossible to assess whether a given student has attained them. Additionally, they are scatter-shot and have little depth. "
"In summary, the current version of the K-12 METS standards are ﬂawed at multiple levels: they promote low standards in our classrooms, they omit critical topics, they provide little depth and they involve colloquial, imprecise language lacking mathematical clarity and speciﬁcity. They will not adequately prepare Missouri students either for studying at the college level or for using mathematics in other disciplines, particularly science and engineering. We strongly feel that they should be rewritten from scratch taking into account the recently released Final Report of the 2008 National Mathematics Advisory Panel. The K-12 METS standards should not be used as the working draft for a new document. Simple rearrangements or additions will not suffice to make this an acceptable document, at least for the upper grades. In addition, it is imperative that research mathematicians be an integral part of the committee charged with writing the K-12 mathematics standards. Adopting the METS proposed standards without doing this would be a disservice to the state of Missouri and will hurt its students for years to come."
Review summary (2 pages - pdf) - Prof. Milgram
"The draft that I evaluated, dated March 31, 2008, is very rough. Much of the language in the learning goals is sloppy, and there are a number of outright errors. I have made extensive comments at all grade levels. While I believe that the material in grades K - 5 is acceptable after being edited, I do not believe this to be the case for the material in grades 6 - 8. These standards need to be rewritten."
"Whatever the reason, the effect is that the grades 6 - 8 expectations are so weak that they are basically not salvageable. To explain this and to help give guidance for what was actually hoped for by the authors of the Focal Points, I have prepared a discussion of the intent of the Focal Points in grades 6 and 7. The language I use is that of high level mathematics since it is the language in which I can be sure that I am saying exactly what I intend to. It goes without saying that I believe it should be direct for solid mathematics educators to translate from this language to a language more accessible to teachers, students, and parents."
Annotated review of the March 08 draft (102 pages - MS Word) - Prof. Milgram
"Understand and use a variety of strategies (involving related concepts of place value and properties of operations) to compute multiplication problems (with products to 10,000) fluently."
Prof. Milgram's comments include:
"What mathematicians mean by algorithms are the actual numerical operations with the expanded forms of numbers, not the ways in which these processes are realized with the shorthand notation that IS place value notation. So it is completely irrelevant whether numbers are carried above or below the line, etc.
Here is a consequence of this. Students will seldom do large multiplications without calculators during their lives, so the fact that mathematicians, engineers and other professionals in technical areas want students to learn the EFFICIENT algorithms is not what you might think. What it is is that this country desperately needs more scientists, engineers, and similar professionals. Much of what they do involves programming computers, and computer programs are just very large algorithms. So students need a solid understanding of how efficient algorithms are constructed and what they look like.
The standard algorithms are probably the best preparation for this in school mathematics provided students understand them at the level I've indicated above, not in a purely procedural manner. "
"Make connections among representations of fraction addition and subtraction situations with objects, diagrams, words, expressions and equations."
Prof. Milgram's comments include:
"I do not know what any of this means. At best, it means something like, in representations of fractions such as on the number line or an area model explain what addition represents. (In the area model, adding areas, in the line model on the non-negative part, it means adding lengths). But the actual words make no sense. "
"Compute fluently, using a variety of strategies, including the standard algorithm, in problem situations involving multiplication and division of nonnegative rational numbers in fraction and decimal form. "
Prof. Milgram's comments:
"What is the point of 'using a variety of strategies?' It becomes ever harder to compute fluently if one has to learn a variety of strategies. If you want students to have a choice of “different” strategies for computation, then do that (as you have in the lower grades), and let them choose the appropriate strategies to use in mastery situations."
Item 1): "Compute fluently to solve problems involving rational numbers written in both fraction and decimal form."
Item 2): "Distinguish between rational and irrational numbers, and use estimation to solve problems involving real numbers. "
Prof. Milgram's comments:
"This is mostly two years below grade level in this country. It is even further below grade level if we look at the expectations in the high achieving countries."
"This is low level material and has already been asked for in grades 7 and 8. It was already pointed out in grade 8 that the Focal Points expect students to be able to solve TWO linear equations in 2 unknowns in grade 8. Consequently, Algebra I needs to be at a higher level. Let me make this more explicit. Here are the expectations for Algebra (Algebra I and II together) in the report of the National Math Panel:
(click here for the complete list of Algebra topics)
This lays out the Core Concepts of algebra about as well as one can do this. Note how very little it looks like what is currently here in these draft standards. Yes, it is true that these topics should be measured out and shared between Algebra I and Algebra II. But it is THESE TOPICS, not the vague “philosophical” discussions of the “meanings” of a few of these topics that we see in too many of the the draft standards here. Algebra, by its nature, is the set of calculational tools in mathematics. So calculation with these concepts is crucial, not the “discovery” of them. It is certainly helpful if students can understand the proofs of results like the quadratic formula or the expression of the coefficients in the binomial formula as quotients of factorials. It is also helpful if students are able to discover for themselves a few of the easier initial steps leading to these results. But it is not essential. It is essential that they understand and apply these techniques fluently."
"Review Process: A Draft of the document was posted on the Missouri DESE website in late March 2008 and all interested individuals and groups were invited to provide feedback. In addition, state and national experts were invited to provide a review of the Draft. Over 300 pages of suggestions and comments were received. The Writing Group met in the summer of 2008 to review the feedback and to modify the Draft in response to feedback and to the recommendations included in the final report of the National Mathematics Advisory Panel report released in March 2008. "
"The organizing agencies (DESE and METS) and members of the Writing Group offer their sincere appreciation to everyone who offered feedback on the DRAFT. In particular, we note the following individuals who provided feedback at the request of DESE and METS:"
Comments - Profs. Mitrea and Christiansen
"The Algebra I component of the revised document 'Missouri K-12 mathematics: Core Content, Learning Goals
and Performance Indicators' is a minor improvement over the Algebra I component in the previous version of this document. While the most egregious aspects we singled out in our previous review (which were just samples of how badly written the document was) were addressed, the document continues to be flawed at multiple levels: it promotes low standards in our
classrooms, omits critical topics, and provides little depth. Placing the new and old versions side-by-side shows only small changes - a few simple rearrangements and word additions. As such, they do not make this an acceptable document. Adoption of the proposed standards would be a disservice to the state of Missouri and will hurt its students for years to come."
"I was able to go through grades 6 - 8 and my comments are attached. I found grade 6 to
be MUCH improved, grade 7 basically ok with a few errors that are easily ﬁxed. However,
Grade 8, while better than it was, still represents a dramatic dumbing down of the the
expectations of the NCTM Focal Points. The emphasis on transformations is, frankly, silly
in eighth grade. There is no way, at this point that students can achieve anything more
than a hand-waving familiarity with them, and by doing so, they take crucial time away
from the much more basic material such as the structure of the solutions of two linear
equations in two unknowns, that is necessary for a reasonably rigorous understanding of
transformations, to say nothing of many other vital topics it supports".
"Since I had already pointed out these issues in my original invited review of these
standards, I can only assume that the authors are consciously determined to deprive
Missouri students of the opportunity to learn this more and more vital part of elementary
mathematics well enough to be able to realistically major in technical areas at the
(N.B. Except for the paragraph cited above, the Fall 2008 DRAFT appears to be substantively unchanged from the August 2008 DRAFT)
Cover Letter (email) - J. Segert (November 11,2008)
"Enclosed please find my comprehensive review of the revised DESE/METS Mathematics Learning Goals, submitted in response to the invitation on October 7 copied below. I will also post this on my website http://missourimath.org/
The verdict is very mixed:
1) Grades K-7 are significantly improved and close to the 2006 NCTM Focal Points. These grades could be fine with some relatively minor fixes.
2) Grade 8 still has serious problems. This is significant because Grade 8 is an important transition to high school and authentic Algebra as per the recommendations of the 2008 report of the National Mathematics Advisory Panel (NMP).
3) Algebra 1, Geometry, and Algebra 2 are a DISASTER. The Writing Group has shown itself utterly unable and/or unwilling to meaningfully revise this material. This material must absolutely NOT be approved for use in Missouri schools (!) It takes a lsome time to even begin to appreciate just how bad this material is, I urge you to actually read my review (and the reviews of other mathematicians, particularly Milgram) on this material. "
Comprehensive Review of the revised August 08/Fall 08 draft - J. Segert (November 10, 2008. 18 pages, pdf)
"I strongly disagree with the Writing Group’s implied claim  that the document satisfactorily covers the ”Major Topics of School Algebra” as per the unambiguous recommendation of the National Mathematics Advisory Panel (NMP) "
"It is essential that Missouri students have access to a solid mathematics education through high school, an education that would allow them to study technical areas at the college and university level and beyond. In order to achieve this goal, I propose that a separate and independent writing group be formed to completely rewrite the standards for the Algebra 1 - Geometry - Algebra 2 sequence, and to work on grade 8 jointly with the current writing group. The current writing group would remain in charge of the lower grades, and of the Integrated track in high school. This represents a win-win situation for all parties, in particular Missouri schools could offer state of the art instruction in both Algebra - Geometry, and separately in ”investigation based” reform math. Students, teachers, and parents could
make appropriate individual decisions based on a student’s career goals, educational goals, and learning style." (originial emphasis)
"Some students may need additional help in Grade 7 as well as Grade 8 to prepare for success in an authentic Algebra 1 - Geometry - Algebra 2 sequence. It should be a high priority to make this option available to al l students who are interested, and to advise students and families about the NMP ﬁndings about the importance of this option for students who are considering continuing to a college or university education. Identifying and helping individual students who are capable of high achievement at this stage of their studiest should help to address achievement gap issues as well, and in a way which is better attuned to the needs individual students than the common strategy of condemning groups of students to permanently lowered expectations."
"Note that the response of the Writing Group to the NMP is limited to strategically 'moving' and 'placing' topics within the document. Compare this with the prior admonition of Professors Mitrea and Christiansen : 'The K-12 METS standards should not be used as the working draft for the new document. Simple rearrangements or additions wil l not suffice to make this an acceptable document, at least for the upper grades. ' "
"It takes a moment to process the astounding fact that the quadratic formula is not introduced until Grade 11 in the Missouri standards ! Even at that incredibly late stage, the quadratic formula is covered extremely shoddily, as almost a grudging concession rather than one of the central tools of elementary algebra." (original emphasis)
"Missouri recently revised their K-12 mathematics standards and successfully aligned their K-7 standards with the best current approaches available: the National Council of Teachers of Mathematics (NCTM) Curriculum Focal Points, and the report of the National Math Panel. However, the new standards largely fall apart in the critical grades 8 - 12 where the rubber actually hits the road. "
"Perhaps a ma jor part of the problem is that the people who are responsible for these new standards are the same people who have guided Missouri’s K-12 mathematics for at least the last 10 years. Their past results have been remarkably average when compared against national norms, for example “America’s Report Card,” the National Assessment of Educational Progress (NAEP) exam. And we should remember that the U.S. outcomes in mathematics rank at the bottom among developed countries internationally, so average is not something to be desired here. "
"Here are the comparisons of Missouri’s results with the national averages, and the performance of a key state, Massachusetts, that extensively revised their standards about 10 years ago enlisting the aid of top research mathematicians and top high school math teachers in creating standards that anticipated both the NCTM Curriculum Focal Points, and the conclusions of the National Math Panel....."
"Although the core content, learning goals, and performance indicators specified in this document are intended for ALL students, many Missouri students will be able to move through this content more quickly and will need more mathematics than is outlined here. For that reason, we urge local educational agencies to develop and implement policies and programs serving all students beginning in elementary school, including those who are ready for early advancement and need more mathematics than the material described in this document. As essential support for raising Missouri’s performance in mathematics, specification of core content, learning goals, and performance indicators for fourth-year high school mathematics courses is under development." (page 1)
"The National Council of Teachers of Mathematics (2000) describes five mathematical processes that are essential elements of K-12 mathematics. .... In this document mathematical processes are interwoven throughout the core content and learning goals so that they are not thought of in isolation but rather as part of learning the content of mathematics." (page 2)
Missourimath.org is maintained by Jan Segert, Associate Professor & Director of Graduate Studies, Mathematics Department, University of Missouri - Columbia