I’d like to first thank the Board and Commissioner Schulte for giving me the chance to speak as a representative of the mathematicians at the University of Missouri.
I’d also like to offer my thanks to the writing group and reviewers who have worked very hard on this difficult and important task.
Let's start with a favorite topic from math class -- the exponential growth of money put in a bank, at various interest rates, from 1992 to 2007:
You may notice that you are earning an interest rate slightly below national average, but perhaps not so far below as to raise alarm :
But how do you know when your bank isn't performing well, and you should consider switching banks?
Compare your interest rate with other interest rates you could realistically get. Realize that every detail counts.
You need to have ALL of your money earning interest, not just part of your money, and you need to shop around for the bank that produces the best results. One of the facts that makes life simple is that every dollar is like every other dollar -- you don't invest half your money at low interest and half your money at high interest.
Everyone agrees that we want ALL Missouri students to learn math, and many people have worked hard with that goal in mind. Naturally, this is a more complex problem than dollars in a bank account -- individual students have a wide range of backgrounds, abilities, and school environments. Moreover, the measures of success are less obvious. But what is clear is that we must pay attention to every detail, for every student, of every ability.
Little differences compound to big cumulative changes.
Grade 8 NAEP, National Assessment of Education Progress, known informally as the “Nation’s Report Card”: (From data compiled by Prof. Milgram of Stanford University, who was one of the mathematicians invited by the writing group to review the Missouri document. )
Missouri starts above the national average, fluctuates a bit, and ends up barely above the national average:
How do you know when your state's mathematics education program isn't performing well, and you should consider some new ideas?
Increasing the performance of all students generally increases the percentage of students who meet specific perfromance benchmarks. The graph below shows percentages of students scoring at or above "proficient" level on the 8th grade NAEP:
I should tell you that the largest enrollment in a mathematics course at MU, the state’s premier research institution, where many of Missouri’s best and brightest students go, is in a course generously called “College Algebra”. This course is not even at the level of Precalculus and contains nothing that should not already have been learned in high school. By adopting low level standards, and taking into account that compounding effect we’ve seen, many MU students will continue to need College Algebra . Most of these students are then cut off from the possibility of being scientists or engineers.
So how does Massachusetts differ from Missouri?
Massachusetts moved towards high-quality math education standards during the late 1990's, culminating in the adoption of the high-quality 2000 Massachussetts Mathematics Curriculum Framework. Massachusetts has been reaping the compounded benefits of high-level standards and expectations.
Missouri has languished at the opposite end of the spectrum:
Evaluations of MA and MO standards, from The State of State Math Standards 2005, Fordham Institute:
2005 State Report Card | ||
Massachusetts | ||
Clarity: 3.67 | A | |
Content: 3.67 | A | |
Reason: 2.00 | C | |
Negative Qualities: 3.50 | A | |
Weighted Score: 3.30 | Final Grade: | A |
2000 Grade: D | ||
1998 Grade: F |
2005 State Report Card | ||
Missouri | ||
Clarity: 0.67 | F | |
Content: 0.33 | F | |
Reason: 1.00 | D | |
Negative Qualities: 0.50 | F | |
Weighted Score: 0.57 | Final Grade: | F |
2000 Grade: F | ||
1998 Grade: F |
Some comparisons of individual items from MA and MO standards:
A word about curricular choices -- Is there valid research data on curricular efficacy ? Yes, but it is very infrequently cited, and often suppressed and resisted by promoters of specific curricula or education ideas. It is not just a question of debating different ideas, although it unfortunately often comes to that.
The U.S. Department of Education published a controlled study comparing sthe achievement of students in schools using four popular elementary school curricula. The two "inquiry-learning" (or "reform") curricula (Investigations/TERC and SFAW) did not do well. Small differences perhaps, but we know there is compounding....
Study Design. An experimental design was used to evaluate the relative effects of the study’s four curricula. The design randomly assigned schools in each participating district to the four curricula, thereby setting up an experiment in each district. The relative effects of the curricula were calculated by comparing math achievement of students in the four curriculum groups.
The figure shows that: Student math achievement was significantly higher in schools assigned to Math Expressions and Saxon, than in schools assigned to Investigations and SFAW (Scott Foresman-Addison Wesley). Average HLM (Hierarchial Linear Modeling)-adjusted spring math achievement of Math Expressions and Saxon students was 0.30 standard deviations higher than Investigations students, and 0.24 standard deviations higher than SFAW students.
For a student at the 50th percentile in math achievement, these effects mean that the student’s percentile rank would be 9 to 12 points higher if the school used Math Expressions or Saxon, instead of Investigations or SFAW.
So what is wrong with the Missouri plan?
After a contentious year, we have a set of standards that are improved from the original. Let us suppose that these standards, aimed at ALL students, work best for students at approximately the 20th percentile. Let us suppose that standards for good college-bound students should be aimed at students at approximately the 80th percentile. The writing group argues that the current Missouri standards are for ALL students, i.e. for the 20th percentile student. The writing group recommends that these standards should be adopted without delay, so schools can start basing their curricular decisions on these standards. A year later schools can expect a minor addition with standards for high-achieving students taking a 4^{th} year of high-school mathematics (pre-calculus):
"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 performanceindicators for fourth-year high school mathematics courses is under development."
(From the Introduction of the Spring 2009 Missouri standards document, p. 1. Emphasis added.)
"There has been a good deal of concern among mathematicians that many students and families may misunderstand what this document is. It is intended to describe mathematics content for ALL students; the content specified in this document does not prepare for admission to many colleges and universities, and it is not adequate preparation for many mathematics-rich careers such as science and engineering. "
(From the report by Dr. Melvin D. George, May 29, 2009. Emphasis added.)
We firmly believe that this approach is wrong.
We think that Missouri will be much better served if we do the job fully (including that 4^{th} year pre-calculus course) and produce a high-quality set of standards for all grades. These should include specific guidance for the 80th percentile college-bound students, as well as specific instructions for OMITTING the most advanced content to suit students achieving at lower levels. Schools can then select high-quality curricula and teacher training which allows them to prepare the 80th percentile student, and simply omit and/or slow down content for students at lower levels. In fact, under the proposal being considered, with its low standards, we will have many fewer students ever attain the level necessary for a serious 4^{th} year of high-school mathematics (there’s that compounding effect again --- small losses at each grade level k-11 yields many fewer students at a high level in grade 12).
We believe that the current proposal puts the cart before the horse.
If the current standards aimed no higher than to 20th percentile students (“ALL”) are published, schools will base their curricular decision on these low standards and will already be committed to these curricular decisions. It is not easy to buy new books or start new professional development programs.
It would be difficult to issue instructions to supplement the curriculum for higher-achieving students, because districts will have already committed to material and training based on the lower standards (and this material is often not enhancable to a higher standard) and will not have the resources to upgrade again.
We believe that DESE will better serve the school districts and the children of Missouri if it adopts HIGHER standards. The material needs to work at the higher standard, and simultaneously, via omissions and slower pacing, at lower standards. The other way has little chance of succeeding.
If the current plan goes into effect, districts and parents will be frustrated, and many parents will be angry, when they discover that their top-achieving students are stuck with material that is designed for the lowest-achieving students. They will rightly protest and demand that high-quality material be made available to all students -- material that can be modified to serve students at all levels.
This normal reaction is wrongly called the "math wars", and is claimed by some to be an unavoidable consequence of trying to improve education for all. In fact, it is not a war at all, it is a justifiable response to an educational system that is unresponsive to the needs of the full range of students, and has tried to force large groups of students to use material inappropriate for them.
Let me offer a brief history of the so-called Math Wars: The original "New Math" of the 60's and 70's focused on material aimed at the 80th percentile student, and did not work well for the 20th percentile student, or for some teachers. It was eventually agreed that something should be done to fix this and there was not much resistance to moving on to other ideas.
In the late 80's and early 90's, the NCTM (National Council of Teachers of Mathematics) and the NSF EHR (the Education branch of the National Science Foundation, separate from the Mathematics and Science branches) started promoting "reform" math education programs, based on “inquiry” learning (also known as “student-centered” or “reform” math ). These programs were advertised as egalitarian, let us say “aimed at the 20th percentile student”, but did not work well for the 80th percentile student, or for some teachers. It was widely but not universally recognized starting in the late 90's that these programs had serious problems, but there was and continues to be enormous organized resistance moving on to other ideas. The unresponsiveness and obstinacy of the system to the excesses of this particular swing of the pendulum have engendered the current "math wars".
How can Missouri avoid the Math Wars that are plaguing many other states? By being responsive to the needs of ALL students. For the 80th percentile university-bound student, this responsiveness includes legitimate input from university mathematicians at major Missouri institutions, with more input from these individuals in higher grades. Instead, the writing group has rewritten the introduction to try to prevent exactly this, and to bolster the its own credentials.
Missourimath.org is maintained by Jan Segert, Associate Professor & Director of Graduate Studies, Mathematics Department, University of Missouri - Columbia