California Educators and Government Officials Joined Together to Raise Mathematics Standards in the State
New Math Content Standards Are Rigorous
Components of State Accountability Ensure Compliance
New Math Content Standards Are Rigorous
A SNOWBALL OF CRITICISM BECAME AN AVALANCHE
About the year 1995
, more and more Californians----math professors, parents, concerned citizens---- were looking into the declining achievement
of California students in mathematics. They learned that there had been criticism and controversy raging among small groups in different parts of the state for many years, and the controversy extended well beyond California.
Although there is relevant history before 1989, it is a good starting point because in that year the National Council of Teachers of Mathematics (NCTM)
promulgated new math standards. These are usually referred to as “national” standards because of the name of the teachers’ group; the "national" standards were not promulgated by the federal government.
These NCTM standards were criticized for numerous reasons, but one main reason was the presumption that from kindergarten onward a student would have access to a calculator so mastery of math facts was not critical. Articles
criticizing the NCTM standards can be linked to from here.
Thereafter, California adopted state standards that strongly mimicked the NCTM standards. Most California schools used math programs described as "constructivist," and they were criticized more for what was not in the programs than for what was. Criticism
included their lack of textbooks, failure to require children to master math facts, elimination of teaching and practice of the long division algorithm, reliance upon calculators and lack of testing.
Teacher's manuals and summaries of these criticized programs stated what was omitted and what was covered. For example, the authors of one math program
state very clearly that all children are expected to have access to calculators at all times, and they also explicitly list subjects that are covered in a “traditional” algebra program but omitted entirely from their program.
Not all California schools altered their program to follow these new controversial standards or teaching strategies. Some schools
had simply stayed with math programs with textbooks that had strong practice and mastery components, and did not follow "constructivist" teaching methods.
CONTENT AND TEACHING STYLES IN K-12 CLASSROOMS DIFFERED DRAMATICALLY
One of the first surprises learned by those interested in figuring out what was going on in K-12 classrooms was the dichotomy between two different styles of teaching math. At one extreme was “constructivism” which meant simply that children learn what they discover for themselves, not what they are directly taught. In a purely constructivist classroom, a teacher is a facilitator and direct instruction does not take place. At the other extreme from the purely constructivist classroom, is a classroom where only direct teaching takes place. In that classroom, the teacher instructs and the children are repositories of the information imparted by the teacher. While one might assume that most classrooms combined the two teaching styles, those investigating K-12 California math education found that where classrooms were using “constructivist” programs, knowledge of mathematics and math skills had plummeted.
Separate from teaching strategy, is the issue of math content and standards. On one end of the spectrum are very high standards, often referred to as “college preparatory.” With these standards, children are prepared for college level mathematics or Calculus in the twelfth grade. On the other end of the spectrum are math standards that remove some of what mathematicians believe and what has been historically necessary for college preparation for higher mathematics. Standards that removed some of what has historically been in a college prep program are referred to as “math for all” because they purport to have standards that “all” children can master.
It is very important to note that teaching strategy and content are separate issues
. A math program could employ a purely constructivist teaching style to “college prep” math content or “math for all.” On the other hand, a purely direct teaching style could be used to teach to either “college prep” standards or lower “math for all” standards.
CALIFORNIA ADOPTED RIGOROUS NEW MATH CONTENT STANDARDS
In 1996, things really began changing in California when math professors teamed up with other community activists and educators to bring California back into a competitive sphere.
Legislation was passed that required new state math standards. The legislative goal was to prepare California students to compete in a global economy. Legislators were well aware of national and international testing, and the poor showing of California youth in mathematics. An excellent summary of the chronology that followed is in California Standards and Assessment
by R.James Milgram and Veronica Norris.
After the Math Commission presented new draft math standards
to the State Board of Education, they were reviewed by math professors and math professionals. It was reported that about 100 errors were found
. There was also deep concern that the document's drafters did not have strong, professional mathematics and teaching background.
In response to this criticism, the draft standards were given to a team of math professionals who revised the Math Commission's draft by taking out math errors, eliminating instructional strategy recommendations, and rearranging the order so that basic skills were learned before the skills that rely on those basic skills.
Reaction to the Math Content Standards has changed over time. Members of the education establishment who were set to ignore the standards
now support them. Math faculty at universities and colleges acclaim them as a giant step towards educating California children.
The California Department of Education had posted a list of numerous endorsements on its website. Jaime Escalante, the Garfield High School teacher of “Stand and Deliver” fame whose low income minority students succeeded in A.P. Calculus, and John Chambers, CEO of Cisco, were among them. The President of the State Board of Education sent a letter to the State PTA President asking for PTA support.
The California Math Content Standards have received national acclaim.
The well-respected Fordham Foundation
evaluated math standards used within the United States and Japan and gave California standards their highest ranking
. That California math content standards have become the new “gold standard” was visible when William Bennett, former U.S. Secretary of Education, announced the formation of a company to provide U.S. children with a challenging K-12 online curriculum
. One of the few specifics his website provides is assurance that the math program will provide "(a)n early foundation in basic arithmetic, based on a highly respected math curriculum and the rigorous California math standards."
Components of State Accountability Ensure Compliance
STATE OFFICIALS CONSTRUCTED AN ACCOUNTABILITY SCHEME
State officials recognized that for the California Math Content Standards to have any impact they must reach the classroom. So the State Board of Education along with the governor and the legislature created an accountability scheme to ensure compliance by local districts
so that higher standards reach all children in California, not just those living in high socioeconomic communities.
There are slightly less than 1000 school districts in California. Among these districts are kindergarten through eighth grade districts, ninth through twelfth grade districts, and kindergarten through twelfth grade districts. Among these types, districts vary dramatically in size. Very large districts like L.A.U.S.D. contrast with very small districts like Whisman with only three schools.
Local districts control content and curriculum in their classrooms. However, the state can make it lucrative for districts to comply with state standards by offering financial incentives and by paying for instructional materials, testing and teacher training.
As described below, the highlights of the state accountability scheme include Frameworks that describe significant math standards and suggest instructional strategies, textbooks that align with the standards, teacher training so teachers can teach to the standards, assessments so children, teacher and parents have information as to how children are faring compared to their national peers and with respect to the California standards, the Academic Performance Index (API) that rewards improvement, and the high school exit exam that requires knowledge of solid elementary school mathematics and Algebra.
The California Department of Education website
contains much information about standards based reform in California. The state accountability scheme described in the paragraph above is part of this standards based reform.
MATH FRAMEWORKS PROVIDE GUIDANCE CONCERNING MATH CONTENT STANDARDS
In December 1998, the State Board of Education adopted Math Frameworks
that go along with the Math Content Standards. The Frameworks highlight significant standards
, and describe instructional strategies. One of the criticisms of the Math Content Standards were that they did not include instructional strategy or detail the relative importance of each standard. The Frameworks address this criticism.
INSTRUCTIONAL MATERIALS ALIGN WITH MATH CONTENT STANDARDS
New math standards could not succeed without new instructional materials. After the Math Content Standards were adopted, an emergency textbook adoption was authorized.
Textbook publishers submitted for adoption, and a list of textbooks was approved . This is the A.B. 2519 list
, and the textbook adoption remains good through 2003.
However, it was not a complete adoption, and many textbook publishers did not have time to improve their instructional materials to align with the state content standards. In January 2001, the State Board of Education adopted new programs, and this textbook adoption is in force through 2007.
Before the January 2001 vote, the textbooks up for adoption went through a lengthy process. After publishers submitted to the state, the textbooks were reviewed by a Content Review Panel (CRP) and an Instructional Materials and Assessment Panel (IMAP). The Content Review Panel is made up of mathematicians, persons with subject matter knowledge, and this panel reviewed the submissions based upon a specific set of criteria. At the same time, IMAP committees, made up of 50% classroom teachers, reviewed the materials based upon a separate set of criteria, looking specifically as to how teachable the programs are. The CRP and IMAP recommendations went to the members of the Curriculum Commission who independently reviewed the textbook submissions based upon specific criteria. The Curriculum Commission voted, and the approved and recommended list of programs were forwarded to the State Board of Education whose members will made a determination this January, 2001.
TEXTBOOK FUND PAYS FOR STANDARDS ALIGNED MATERIALS
The state has made it possible for local districts to purchase textbook series that align with the Math Content Standards by establishing the Schiff-Bustamante funds
. Prior to the establishment of Schiff-Bustamante, a district had the use of monies from the Instructional Materials Fund (I.M.F.)
. Monies from this fund are allocated to the districts on a per pupil basis of about $28.00 per student. Only thirty percent of I.M.F. funds can be used for textbooks that do not align with current standards. Seventy percent of I.M.F. money must be used to buy current, standards aligned books.
In contrast, Schiff-Bustamonte funds, which are allocated on a per pupil basis, albeit differently than I.M.F, allocate about $48.00 per pupil. Schiff-Bustamante funds can only be used for instructional materials that align with the current state standards.
TEACHER TRAINING IS IMPERATIVE
Teacher training is needed if the new materials and content are to be presented to children. Teacher training funds are available directly for training, and also to districts that apply for grants. See, for example, A.B. 1331
. Just recently, the news media reported additional legislation will be introduced to create teacher training funds.
TESTING ALIGNED WITH BOTH NATIONAL AND STATE STANDARDS
The STAR Program's SAT-9 Provides a National Comparison
Since spring of 1998, California school children have taken the SAT-9, a nationally normed, standardized, multiple choice test. It is called “nationally normed” because a sample group of children took the test in 1995 before the test was even given to anyone. The raw scores of this group were normed along a bell curve with the mean and the median measuring the 50th percentile. This means that a range of raw scores falls within the 50th percentile. Every time the test is given, the percentile ranking is measured against the original normed group.
Depending on their average raw scores compared to the original sample of children, California children could average higher or lower than the 50th percentile. The test is not re-normed after it is given.
There are a number of publishers of nationally normed tests. Some of the tests are more challenging than others. For example, the Educational Records Bureau
(E.R.B.) offers a test called the CTPIII
(archived, now CTP 4
test). This test purports to begin its bell curve at about the 80th percentile of a national normed bell curve. What this means is that a child might have a raw score that places the child at the 99th percentile nationally but only at about the 60th percentile compared to the independent school group.
The only test results available as part of the SAT-9 STAR program are nationally normed results. These results are available to the public on the California Department of Education
website and on the Ed-Data site
. District and individual school scores are available. One can easily compare SAT-9 results from year to year and discover how many students tested above the 50th percentile. School profiles are available for comparison purposes.
The STAR Program Also Assesses Children Against Higher State Standards
The second part of the STAR program
, “augmented” multiple choice questions, assess how well children are mastering the material in the California Content Standards
. On a grade by grade basis, the state gives an annual assessment to test student's knowledge of this material. Although this portion of the test is referred to as “augmented,” these test questions are an integral part of the state's STAR program. A current blueprint for each grade level will be available on the Department of Education website after January 19, 2001.
Thus far, school districts and individual schools have only received the average percentage correct on the “augmented” portion of STAR testing. In the future, the state will change the reporting and use the same demarcations as NAEP uses: Below Basic, Basic, Proficient and Advanced. The results will not be nationally normed like the SAT-9 because the test is not given nationally. The state plan is described in this EdSource primer on STAR Test Scores
THE ACADEMIC PERFORMANCE INDEX REWARDS SCHOOLS THAT IMPROVE THEIR ACHIEVEMENT TEST SCORES
Academic Performance Index
is a financial reward system
that rewards districts that increase their API by a certain percentage in a year's time. The kindergarten through eighth grade API is made up of 40% math SAT-9 percentiles and 60% Language Arts percentiles. The high school API includes additional subjects. Schools that increase their API, by increasing their SAT-9 results, are financially rewarded. In the future, the API will be measured against children's mastery of the state content standards. The EdSource informational bulletin
contains a simple explanation of this program.
THE HIGH SCHOOL EXIT EXAM TESTS KNOWLEDGE OF ALGEBRA
The high school exit exam
is new, and there is great fear that large numbers of students will not pass the exam because it requires a solid grounding in elementary school mathematics and tests a student's knowledge of Algebra
. In the past, Algebra has not been a state requirement for graduation, and many local districts also did not make Algebra a graduation requirement. The high school exit exam changes this dramatically , since many questions on the math portion of the high school exit exam require a knowledge and facility with Algebra.
THE CONTROVERSY REMAINS
The controversy surrounding NCTM standards and the math programs that align and follow these standards remains strong, not just in California, but throughout the United States. NCTM standards still find support among educators at all levels of government, even in California.
NCTM has revised its standards in 2000, but criticism of the new guidelines remain. The 2000 guidelines, PSSM , are not standards in the sense that they are a grade by grade description of what a child should learn. These new guidelines have been subject to similar criticism