Columbia Parents for Real Math

Thank you!

2008-09-25T06:03:00.001-05:00

District decides to go back to traditional math

A huge number of people have worked long and hard to put the math back in math education at Columbia Public Schools. Thank you!

Michelle Pruitt
Columbia Parents for Real Math

Columbia Public Schools ACT scores show differences in Integrated and Algebra pathways

2008-06-11T19:42:00.000-05:00

CPS Secondary Math Curriculum Coordinator Chip Sharp provided average ACT scores reported by course enrollment which are used in the figures below. Plotting the data in several ways gives food for thought regarding the differences between algebra and integrated math pathways offered at CPS.

The data don't distinguish between which students are sophomores, juniors or seniors when they take the ACT, which students may have repeated courses or what year they started the pathway (7th, 8th or 9th grade). But it does give some idea of how much math "preparation" each course pathway provides at least for the years for which data is available.

The average ACT score is highest for students in the honors algebra pathway. Note that the average ACT score of students in the regular (non-honors) algebra pathway is higher than the average ACT of honors integrated math (IM) students, with regular (non-honors) IM students having the lowest scores. But the year-to-year increase in ACT scores is similar for the algebra, honors algebra and honors integrated pathways. The increase for the regular IM pathway is less from year 2 to 3, but similar for year 3 to 4.

Looking at how much ACT scores change year-to-year in the course sequence suggests where students might have a difficult time moving up to higher level math. For example, regular IM students that try to take either of the AP Calculus courses may struggle since the jump in ACT scores is quite big. (As a matter of fact, very few regular IM students enroll in AP math courses.) Honors algebra pathway students may not be adequately challenged by AP calculus AB (one semester of college calculus in a year-long high school course) since the average ACT score actually drops from precalc to AP calc AB; they should likely be encouraged to enroll in AP calculus BC (one year of college calculus in a year-long high school course).

Another way of looking at the data shows that after four years in regular IM, ACT scores are about the same as students with just two years of algebra pathway coursework. Although students in 2nd year IM have higher ACT scores than 1st year algebra students, after four total years of IM coursework, their ACT scores are lower than algebra students with just three years of coursework.

Comparing ACT scores of groups of students that start algebra and integrated pathways in the same year and with similar Terra Nova scores in 8th grade would likely make clear whether one pathway or the other provides better preparation for the ACT and potentially give some guidance for math placement.

Investigations fall short of NCTM Focal Points and National Math Advisory Panel recommendations

2008-06-10T22:46:00.001-05:00

Non-standard techniques, inadequate practice and low expectations lead to poor conceptual understanding of mathematics

In Fall 2006, the National Council of Teachers of Mathematics (NCTM) released a Curriculum Focal Points document. Pearson Scott Foresman, publishers of the elementary mathematics textbooks Investigations in Number, Data, and Space 2nd edition subsequently released a document claiming Investigations is aligned with the NCTM Focal Points.

First, a word about the Investigations 2nd Edition materials. Each teacher receives a box measuring 12" x 14" x 14" containing nine Teacher's Unit Guides, a three-ring "Resources Binder" containing student worksheets for photocopying, and an "Implementation Guide." Students receive a workbook "Student Activity Book" and the "Student Math Handbook." The nine units have catchy names that obfuscate the mathematical content they purport to contain. For example, the unit on addition and subtraction is called "Thousands of Miles, Thousands of Seats;" the unit on multiplication and division is called "How Many People? How Many Teams?"

Focus on Fractions

Since reliable research indicates that algebra is key to post-secondary academic success (Answers in the Toolbox, 1999) and fractions are key to algebra (National Math Advisory Panel report, 2007), I will focus on the NCTM Focal Points that directly relate to fractions. The Investigations unit on fractions is called "What's That Portion?"

The first NCTM focal point regarding fractions is:

"Understand fractions and fraction models to represent addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators."

Contrast the language of the NCTM document with the Grade 5 mathematics benchmarks published by Achieve, Inc., a national consortium of state governors and business leaders:

"Understand how to add and subtract fractions.

Specifically: Add fractions with unequal denominators by rewriting them as equivalent fractions with equal denominators.

Understand and use the general formula

a/b + c/d = (ad + bc) / bd

Note: There is no need to find a least common denominator. The easiest common denominator of ab and cd is most often bd."

NCTM focal points do not provide examples of the type of problems students would be expected to solve. But disregarding the problems with the NCTM Focal Points, Investigations fails to meet even these nebulous standards. The publisher claims that Investigations meets this focal point with several activities in Unit 4: What’s that Portion? specifically:

pp. 95-96 “Introducing Adding Fractions”
pp. 96-98 “Clock Fractions”
pp. 98-100 “Adding Clock Fractions”

In these activities, students learn to mentally visualize “familiar” fractions on a clock face to add them. If sufficient drill is provided in class, this technique might work for problems with special denominators easily represented on a clock face (fractions with denominators that are factors of 60, although this particular fact is never pointed out in the Investigations lessons), including:

12 (5 min), 10 (6 min), 6 (10 min), 5 (12 min), 4 (15 min), 3 (20 min), and 2 (30 min)

A typical student reaction is presented in the teacher's guide: “I’m starting to remember halves, thirds and fourths. Like I know 1/2 is 6, 1/3 is 4, ..." However, this technique would be useless for adding other simple fractions with denominators that are not factors of 60 like 7, 8, or 9 for example.

The concept of common denominators is specifically delayed for “later grades.” On page 100 of Unit 4: What's that Portion? a note to the teacher states: "One useful strategy students encounter in later grades for adding and subtracting fractions is finding equivalent fractions with a common denominator.”

The "clock face" activity and fraction tracks are not just examples of activities used to teach adding and subtracting fractions; these are the only procedures presented for adding and subtracting fractions in 5th grade Investigations materials.

No universally applicable, accurate and efficient procedure for adding and subtracting fractions is ever presented in the Investigations lessons. Instead a hodge-podge of short-cut methods and estimating techniques displace fast accurate calculations.

Decimals

NCTM Focal Points also state:

"Apply understanding of decimal models, place value, and properties to add and subtract decimals."

Investigations claims to meet this standard with several activities in Unit 6 entitled "Jeweler's Gold" (p. 93-97). During the “Jeweler’s Gold” activity in one full hour of class time, students solve exactly 1 problem:

.3 + 1.14 + .085

The majority of class time is spent making a poster to explain their solutions. If students finish quickly, another problem is suggested for “an additional challenge”:

2.05 + 0.76 + 1.3

The next section covers "Strategies for Adding Decimals" p. 98-104. During one more hour of class time, students order the decimals .625, .025, .3, .8, .75 and then add together the three largest:

.8 + .75 + .625

using a “hundredths grid” if necessary. Nowhere do the Investigations materials discuss alignment of the decimal point for stack-and-carry addition.

A "Teacher Note" on page 133 of Unit 6 states: "Often students are taught 'rules' or 'tricks' to add decimals, including lining up the decimal point." The professional development notes go on to likewise dismiss the value of filling in blank spaces with zeros. Students are never let in on these "tricks."

Failing to provide adequate practice with calculations is as bad as failing to cover essential concepts; lack of repetition masquerades as “deep thinking.”

Standard procedures for adding and subtracting fractions and decimals

NCTM Focal Points also states that students should:

"Develop fluency with standard procedures for adding and subtracting fractions and decimals."

Investigations claims to meet standard 3 with:

• Unit 4: What’s that Portion?
pp. 102-103 “Roll around the Clock” game
pp. 105-106 “Writing Fractions Problems”
p. 108 “Subtracting Fractions”
pp. 122-123 Activity 1
pp. 129-131 Discussion 1
pp. 132-134 Math Workshop 2
• Unit 6: Decimals on Grids and Number Lines
pp. 105-106 Activity 3
pp. 108-109 Activity 1

Investigations never presents "standard" methods for adding and subtracting fractions; therefore, it is baseless to claim that Investigations develops "fluency" with such methods.

Summarizing Investigations 5th grade lessons on subtracting fractions, we have:

- “Subtraction Fraction Equations” chart (A list of subtraction facts like: 8/10-3/10=4/8 presumably to be memorized since no explanation of how they are calculated is given.)
- Using a clock face (discussed above)
- Playing the "Fraction Track" game (Students move between zero and one by fractional amounts; they use premarked number lines with denominators up to tenths but have no way of determining if one fraction is greater or less than another except by using the track as a measuring stick.)

These are not standard procedures nor are they universally applicable. Without the concept of common denominators, students can not even compare simple fractions. For example, on page 51 of the "Student Math Handbook" (textbook), the fractions 7/12 and 4/10 are placed in order on a number line by noting that 7/12 is a "little more than 1/2" and 4/10 is a "little less than 1/2" so therefore 7/12 must be greater than 4/10. However, could students order 8/9 and 9/11 using any method presented in the Investigations materials? No; the "fraction tracks" provided don't have denominators greater than 10, and the denominator 11 is not easily represented on a clock face. This is just one example of how problems that are not cherry-picked to be solvable by Investigations' methods are ignored by the curriculum, yet this is supposedly the way to make children think critically about math.

Investigations vs. Singapore Math

Investigations students will be drawing pictures of clocks in 5th grade while Singapore students will be solving problems like these presented on the Singapore Math web site 5th grade placement tests:

•Find 32% of $96.

•Express 8 5/8 as a decimal correct to 2 decimal places.

•Express each as a percentage:

(a) 0.47
(b) 6
(c) 215 out of 500

Investigations' non-standard techniques, inadequate practice and low expectations lead to students having a poor conceptual understanding of mathematics and poor problem-solving skills as reflected in dropping test scores in 4th and 7th grade at Columbia Public Schools.

CPS TerraNova scores drop five percent after TERC Investigations adopted

2007-11-12T20:05:00.000-06:00

The MAP (Missouri Assessment Program) 4th grade mathematics test includes nationally normed multiple choice items from the TerraNova assessment from CTB/McGraw-Hill (p.2 in the MAP examiner's manual at the Missouri DESE web site.) Columbia Public Schools students' median national percentage rank dropped five percentage points on these items after TERC Investigations was adopted. The adoption was phased with Fairview Elementary adopting TERC in all grades for the 2001-2002 school year and the remaining elementary schools adopting TERC for fourth grade in 2003-2004.

According to Resendez and Manley (2005) cited on the U.S. DOE website the TerraNova CTBS is a reliable and valid standardized test that offers broad coverage of the mathematics content in most textbooks and reflects the National Council of Teachers of Mathematics (NCTM) standards.

According to Assessment Standards For Missouri Public Schools on the Missouri DESE web site "the advantages of these items are: 1) they are effective in measuring students’ breadth of content knowledge; and 2) a large number of these items can be administered and scored in a short amount of time."

A major criticism of TERC materials is their inadequate coverage of standard mathematical content like definitions and terminology, a criticism which is clearly supported by CPS test results.

Comments to the National Mathematics Advisory Panel

2007-09-20T19:35:00.000-05:00

COMMENTS addressed to the National Mathematics Advisory Panel, September 6, 2007:

I represent a parent group in Columbia, Missouri. Our community is a microcosm of the national math debate, albeit perhaps a late blooming one. All the players are assembled for yet another season of "mathematics on the verge of a nervous breakdown."

The math education department at the state university located in Columbia is heavily funded by the NSF to promote teacher development using particular math curricula. Many of their graduate students earn master's degrees by participating in the implementation of these curricula in the public schools. The local public school implemented these curricula in 2001, in part to gain access to MU graduate students for CPS classrooms.

But who evaluates the effectiveness of these curricula? It goes without saying that public school administrators like to present student achievement in the best possible light. Students and faculty at MU's math education department have published numerous papers, not surprisingly, supporting the effectiveness of their own efforts; however many of these same papers have been found to lack sound research by the What Works Clearinghouse.

At the same time, nationally-normed, standard assessments of student achievement are being ignored. An eight-year record of CPS student scores on the Iowa Algebra Aptitude Test spanning the period of implementation of CMP seems to indicate a significant drop in algebra readiness but has not been carefully examined by the school district or university researchers. ACT test scores have dropped and remedial math rates of students attending state universities have escalated since adopting these math curricula.

Parents are justifiably concerned. Many parents who work at the University of Missouri in the math, engineering, food science, economics, psychology, and other departments have signed a petition opposing the current math curricula used in the public schools. These scientists, engineers, mathematicians, technicians and physicians know intimately the demands of a career requiring mastery of mathematics and they are speaking up to say the local public schools are failing students who have aspirations to follow a STEM career path.

Likely, this script is is all too familiar to the panel. You have been tasked with advising the President and Secretary Spellings "on the best use of scientifically based research on the teaching and learning of mathematics."

I conclude with one important point, the cliffhanger for the season: how best can evaluations of effectiveness and assessment of student performance be separated from and independent of development and implementation of curricula? The basic tenet of slightly adversarial, peer-reviewed research is lost when researchers are paid by textbook publishers and administrators play dual roles implementing curricula and assessing their impact.

I thank you for the crucial and urgent work you are doing on behalf of our students, families and nation.

Sincerely,

Michelle Pruitt
Columbia Parents for Real Math

TERC tea party in New Jersey

2007-09-11T20:31:00.000-05:00

Contributed by Joan O'Keefe

I am from the Village of Ridgewood in New Jersey. So you may say I am a villager with a pitchfork. That American Gothic image of the farm couple, they would not send their children to your schools. They would demand a practical math education for farmers - needing to learn how to multiple and divide dozens of eggs. But lest I be called a "shopkeeper," let me also invoke the image of our professors of mathematics who will refuse to let their children learn reform math because they know as teachers of mathematics that reform math does not provide the proper foundation for higher level mathematics, the sciences or engineering.

My friends you may not know this, but you are witnessing the first shot of the revolution. With this speech, I begin the revolt of the parents of the children in your schools against all forms of reform math.

I am here not to petition you or to plea with you, but to tell you , I/We will refuse to allow our children to be taught in this ridiculous way. I/We will not be intimidated by your PhDs in Education, I represent the thousands of parents who have achieved great success with traditional math education and are the generation of proof that it works. We will begin to send back your silly TERC books, filled with only simple answers derived using standard algorithms. We will instruct our children to refuse to draw pictures, not to write math stories and to call it an "equation" with symbols rather than the silly "math sentence." If you have the audacity to chide them for using REAL math, we will come down to the school en masse and picket with large signs that say NO MORE BAD MATH or JUST SAY NO TO TERC, MATH IS A TERRIBLE THING TO WASTE.

You can decide to allow reform math to continue, but you will find us, your customers and clients, no longer cooperative. We will throw out the TERC2 and CMP2 workbooks and send our children in with traditional texts. Our children will become so smart, they will teach the teachers.

When in the course of human events it becomes necessary for parents to dissolve the ties which have connected them with their child's public school a decent respect to the opinions of mankind requires that they should declare the causes which impel them to the separation.

We will boycott Pearson Publishing and its subsidiaries until its salespeople stop pushing reform math programs on our schools based on weak and laughable research. We will boycott the schools that use reform math and we will inform every minority group that they are getting substandard mathematics education compare to their contemporaries.

Welcome to history, welcome to the beginning of the parental revolution, welcome to the beginning of the day when the public was put back in public education. Let this be our declaration of independence and the start of our revolutionary war.

We hold these truths to be self-evident, that all children are created equal; that they are endowed by their Creator with certain unalienable Rights, that primary among our children's rights is the right to an adequate and true education. Within that right, there shall be included a strong mathematical education.

A math education defined by mathematicians rather than educators and includes the following tenets. 1) Our schools should focus on math programs on the basis of their content and from hereon pedagogy will driven by the clear detailed well documented mathematical content. 2) A math program should include a logical sequencing of topics, honoring the scholarly subject entitled mathematics. 3) A quality math program will not include for any grade other than Kindergarten the use of scissors, glue, paperclips, M&M or any other object that is now defined as a manipulative and acceptable for exceeding assessment benchmarks. No, our children will have the high and honorable goal of a math program desiring them to use the abstract symbols and language of mathematics. 4) A quality math program will emphasize the learning of necessary math facts & standard algorithms. 5) The math program should use the proper language of mathematics and not invent new unnecessary or watered down terms.

We the parents of the children in the public education system are not happy. These are our children whose educational fate you decide. Shame on those of you for not including the educated parents of this country in this debate; shame on those of you for having 48 speakers and only three of them parents; and shame on those of you for ignoring parents concerns, for it is OUR children who will be known as the LOST Mathematical Generation, OUR children who will not be able to make change without a calculator, OUR CHILDREN who in their elementary years are being limited in their future by reform maths limitation of its teachings. It is our children you doom and it is done without even giving a PARENT THE CHOICE FOR THE CHILD.

Thomas Jefferson's vision of public education would NOT have included drawing circles to add and subtract. Jefferson would be angered when he saw mathematics taught with scissors and glue. Jefferson would be irate when he saw that educators dismiss the outcries of parents. Jefferson would weep at the thought that his dear United States of America would lose an entire generation of its educated society because a British publisher wanted to make more money selling manipulatives with programs like TERC and CMP than selling real textbooks. Just as patriots broke open tea chests and heaved them into Boston harbor, with other patriots at other seaports following that example and staging similar acts of resistance, so too should parents be be throwing TERC2 and CMP2 workbooks into a harbor or river or recycling bin - our very own Boston tea party.

We, the parents, will ultimately triumph because it is Our children, not children of the state or education system. And for OUR children, their education is more important and held more dearly than any social, political, economical, or ideological agenda.

It is on the shoulders of parents across this nation, that a generation of children will not be lost in their math education. And those that recognize this and stand in recognition will provide to the future of this great nation, mathematically capable citizens to lead us throughout the 21st century. And that success will be none for reform math.

Written by Joan O'Keefe of the Village of Ridgewood, New Jersey and published here with her permission. She is a member of a parent group opposing TERC and CMP in her child's school district. Their web site is http://www.vormath.info/. Her opinions are her own and we welcome discussion of the issues she raises.

Universal language or joke?

2007-09-04T22:24:00.000-05:00

Contributed by Alexander Koldobsky

The quality of the secondary math education in the United States has long become a standard joke among mathematicians around the world. It is very painful to see how the most powerful country trails behind European, Asian and third world countries in the level of mathematical
skills of high school graduates.

To my opinion, the major reason is that, unlike many countries, algebra is not included in the middle school curriculum in the United States. Algebra was invented a few thousand years ago as the universal language of mathematics, allowing to avoid lengthy word explanations of mathematical procedures and making mathematical studies logical and connected. It is
essential that the students start learning algebra as early as in the 5th grade, which brings mathematical formulas to them naturally later in their lives. It is still possible for the best students to start algebra in the 8th grade and be successful, but in general American students continue looking at mathematics as a foreign language. I think the switch to starting algebra in the 5th grade must be made as soon as possible, by adopting a system used in one of the countries like Russia, France or Germany. American students are as smart as anybody, and they and their teachers will quickly adjust to this system.

The so-called Connected Mathematics Project, Integrated Math and other recent innovations are even worse than the "traditional" American system. They further water down the curriculum and leave the students largely unprepared for college mathematics. Instead of bringing our children back to the level of "ancient Greeks playing with stones on the beach,"
American math education must quickly switch to the most advanced methods of mathematical learning.

Alexander Koldobsky is a math professor with fifteen years of experience in teaching mathematics at the college level in the US and a parent of two children who went all the way through the American educational system. His opinions are his own, and we welcome discussion of the issues he raises.

What's a parent to do?

2007-06-28T22:00:00.001-05:00

Maybe you thought that since your student was getting good grades in math, you could relax. The experiences of many parents who have signed the CPR-Math petition should at least make you wonder:

"My husband was amazed to discover that our daughter who has consistently received A’s in Math courses and can not do long division as a freshman in high school."

"My child is in the gifted program, but didn't know basic arithmetic."

"My children received A's & B's but are now 2 years behind their peers in districts in which this math isn't taught."

What can you do to make sure your child will be prepared for the real world after graduation, whether that means college or a job? For a start (and probably a shock) learn about the expectations the Columbia Public Schools have for your child's math skills.

Standards?

CPS curricula are subject to several layers of "standards." The Missouri state standards are a mishmash of several documents, including a new draft document which was released April 24 this year. But you can cut to the chase and look at CPS' elementary instructional program guidelines to see that they fall short as measurable and as standards.

For example, by the end of 5th grade, CPS students are expected to:

Explore properties of regular and non-regular polygons, particularly triangles and quadrilaterals.

Compare that to this excerpt from the California elementary math standard for 5th grade:

2.2 Know that the sum of the angles of any triangle is 180° and the sum of the angles of any quadrilateral is 360° and use this information to solve problems.

That's S.M.A.R.T. --Specific, Measurable, Achievable, Relevant and Timely, an acronym many in the business world will be familiar with.

Did you expect your child to master multiplication and division of fractions by the end of elementary school? The goal of CPS is rather more modest. Referring again to the CPS' elementary instructional program guidelines, fifth graders are only expected to:

Represent fractions, decimals and percentages and order fractions and decimals using landmark numbers of 0, ½ and 1. [emphasis mine]

Manipulating fractions shows up in the new draft standards for Missouri in grades 5-7 with these rather strange wordings:

demonstrate fluency with efficient procedures for adding and subtracting decimals and fractions (with unlike denominators) and division of whole numbers (Grade 5)
multiply and divide positive rational numbers (Grade 6)
apply all operations on rational numbers including integers (Grade 7) [Why mention integers since they are a special and simpler case of rational numbers?]

These proposed standards seem to at least be higher than CPS standards. The Fordham Foundation gives Missouri standards an F for being vague and consistently below grade level.

But a bigger problem than the state standards are the constructivist curricula used in CPS: TERC Investigations in Number, Data and Space at the elementary level, the Connected Mathematics Project in grades 6-8, and Core Plus for the 70% of high school students who take the usual administrative advice and enroll in integrated math.

What Can You Do?

First, find out if your child is at grade level according to a national standard, not your child's report card. Try these practice problems aligned with the California standards for grades 1-8. Placement tests are available from Saxon Math or Singapore Math for all grade levels.

What if your child is already falling behind? At the elementary level, you can likely supplement with "after schooling" using a text like Saxon or Singapore math and still give your child a solid basis that includes basic arithmetic skills and number sense, although the bad habits they develop using TERC Investigations in school may hamper their ability to be neat, fast and accurate. Too much emphasis on verbal skills and manipulatives may actually interfere with the development of mathematical reasoning.

At middle school and above, you may need to hire a tutor at Kumon, Focus on Learning, or Sylvan Learning Center, or find an online program. The Missouri K-12 Virtual Instruction Program (MoVIP) uses the Calvert mathematics curriculum for elementary grades and offers an algebra sequence at secondary level. State funded seats for this fall are already full at the secondary level and nearly full at the elementary level, but tuition paying seats are unlimited.

Next, track your child's progress longitudinally. CPS administers the Cognitive Abilities Test (CAT) in 2nd and 5th grade and the mathematics MAP test includes Terra Nova items which are nationally normed. The Iowa Algebra Aptitude Test (IAAT) is administered either in 6th or 7th grade. (You can see the full CPS assessment plan on the district web site.) It's reasonable to expect your child's achievement to be consistent from year to year. If a score suddenly drops to a much lower national percentile rank, talk to the school and be ready to take remedial action.

The crucial transition period is middle school. You may be worried mostly about your child making new friends and finding her way from class to class on time in a new school, but you also need to worry about making the right choices in class selection so that in 5 or 6 years time, your student will be ready to graduate with the appropriate math credits for his or her post-secondary plans. All CPS sixth graders are enrolled in Connected Math, but as early as 7th grade, options may be available.

A very few students are candidates for "accelerated algebra." If your child had high scores (90th national percentile rank or higher) on early aptitude tests and has done well in school, it's reasonable to think they should be tested for an early start on the secondary math pathway. Approximately the top ten percent of CPS students are given the Iowa Algebra Aptitude Test (IAAT) at the end of 6th grade, and approximately the top 25% of those students enroll in "accelerated" Algebra I Honors as 7th graders. If you do the math, that's only about one classroom of 30 students each year. Starting in the fall of 2007, CPS intends to offer accelerated Integrated I Honors to 7th graders as well.

Algebra or Integrated?

For the vast majority of students, the decision between the algebra and integrated pathways waits until the end of 7th grade or even the end of 8th grade. These students take the IAAT at the end of 7th grade and in part based on those results, most students will be advised to enroll in integrated math. About 30% of students opt for the more traditional sequence of Algebra I in 8th grade, Geometry in 9th grade, Algebra II in 10th grade and Precalculus in 11th grade.

Work with your student to make this decision carefully and be firm. Students have the option of which math pathway to follow. Then pay close attention to homework, quiz and test scores---if your child begins to struggle, act quickly! Spend more time on math homework with your child, talk to the teacher and get extra help if necessary. Math is cumulative and you can't skip some concepts and pick them up later.

And if your child aspires to attend college, start practicing and preparing for the ACT or SAT well ahead of the usual junior year testing. If math skills are weak, studying for the test can actually improve scores, and study guides are available at the public library and at almost any bookstore. ACT and SAT scores may determine whether a student is accepted to the school of their choice and whether or not they receive scholarships.

And finally, continue to advocate for your child at her school. Talk to the teacher and talk to the school principal and talk to the school counselor. Don't expect that escalating your issue to district curriculum coordinators will resolve anything--they are charged with implementing the curriculum, not with assisting students and parents.

ACT scores decline under Core Plus, remedial math rates up

2007-04-17T20:43:00.000-05:00

At their "Parent Math Nights," CPS administrators showed CPS student ACT scores and rates of enrollment in post-secondary remedial math that compare favorably to other districts in Missouri with similar demographics. However, that same data shows a troubling historical trend.

The charts below show the number of CPS students enrolling in remedial math courses at the post-secondary level jumped after Core Plus was adopted in 2001-02. From single digit enrollment rates in remedial math prior to 2001, 20% of Hickman graduates enrolled in remedial math at colleges and universities in 2006. Rock Bridge results are just as alarming.

The original data used to prepare the charts are available at the DHE website here: http://www.dhe.mo.gov/hsgrad2005table1c1.shtml The Missouri Department of Higher Education reports high school graduates' enrollment and preparation at Missouri public colleges and universities for each year since 1996. This includes all students that enroll full- or part-time as degree- or nondegree-seeking first time freshmen at all 2 and 4 year post-secondary institutions in Missouri.

State Representative Ed Robb currently has a bill in the Missouri House that would allow students at two-year or four-year colleges or universities to seek tuition reimbursement from their high schools when they have to take post-secondary remedial courses. Whether you agree or disagree with this course of action, it's clear that the problem warrants attention.

It's no surprise that ACT scores (chart below) also went down during the same time period. These are immediate negative results much like the immediate deleterious effect of Connected Math on the IAAT test scores of 7th graders which we reported on this blog. What is surprising is that the district isn't looking at or reporting these results in its Secondary Math Task Force report to the Superintendent. The historical trend in the results of the Iowa Algebra Aptitude Test was also never examined.

The Columbia school district continues to compare itself only to other Missouri schools, and plans to narrow those comparisons even further by suggesting that CPS should only be compared to schools that use experimental curricula like Core Plus. This despite the fact that in 2005 only 17 percent of Missouri’s 10th grade students scored at proficient or advanced in math according to a Missouri Alliance on Math, Engineering, Technology, and Science Education report.

Why I believe supplementing the Investigations curriculum would be an ineffective and frustrating strategy to improve math education in CPS

2007-04-11T21:49:00.000-05:00

by Tere DeWitt

A well written mathematics textbook is a thing of beauty to the math teacher. It has many layers and nuances that might not be obvious to the casual observer. The components that make up a good lesson will include practice over the new concept, applying the new concept in application problems, an opportunity to be challenged with the new concept by more difficult practice and/or applications, review of previously learned topics to reinforce their learning, and perhaps foreshadowing, to borrow a literary term, or pre-requisite practice of the topic to be learned tomorrow. Truly good texts can layer 2 or more of these components into a single question. They give the teachers, who know their classes better than anyone, flexibility to choose the appropriate content to best further the education of their students. They also allow for different learning styles and provide a variety of means for the teacher to use to communicate the content, so no student is left out of the learning process all the time. This takes a lot of planning and editing and doesn’t just happen by accident.

Now, we are getting some of the school board candidates to speak out for the teaching of mastery of basic math facts and standards in our elementary schools. They have said that they think Investigations should be supplemented.

The Investigations curriculum is not designed to support mastery of basic arithmetic facts. It is designed to support their discovery methods and also the use of calculators. Therefore, the problems in the curriculum would be worthless for the teaching of basic math facts and could actually have a detrimental effect on the learning of basic facts by not being designed to reinforce them and to increase in difficulty as the student progresses.

One of the reasons the traditional algorithms have been used for thousands of years is that they are efficient, with fewer steps than other methods, and therefore have fewer places that an error could occur. If a student learns one of these algorithms and sees its efficient result, they will be very resistant to another, longer and perhaps more tedious method to solve a problem. Likewise, the Investigations curriculum, which is very calculator dependent, will encourage students not to learn the traditional algorithms because the calculator is more efficient than the algorithms and the algorithms become the tedious method. I would not want to be a teacher in this classroom fighting this battle day in and day out.

The Investigations curriculum does not build on previously learned knowledge. Their teachers’ resources say that the units may be taught in any order. We are missing the vital components of review and also of taking concepts to greater depths. They are a one size fits all package without allowing for the difference in learning styles. As a math teacher, I know that there is a lot of math out there to learn. I never get all the information covered in my classes that I want to. To devote six weeks for “discovering” a topic takes time away from developing any depth about that topic and then, to never revisit that topic during the school year, means that for many students that topic is all but forgotten. This is not good pedagogy and we can’t waste that precious time.

For these reasons above, I have come to the conclusion that Investigations is such a weak curriculum, we should replace it as soon as possible. We will have to phase in a new curriculum, because our students will be behind, so even more precious educational time is going to be lost. Investigations has done some good, in that the traditional textbook authors have responded to their methods and the “drill and kill” books are a thing of the past. The new blended texts, as some websites are calling them, include all the components I have listed above and also include discovery learning opportunities, writing to explain math, critical thinking exercises, and non-routine problem solving. Let’s encourage our curriculum review committee to look these resources over and see if we can’t come up with one strong mathematics curriculum. A curriculum that contains a variety of methods to best help the diverse student population of Columbia to learn math to the best of each individual student’s ability.

Tere DeWitt is a math tutor and member of the CPR-Math steering committee. Her opinions are her own, and we welcome discussion of the issues she raises.

Algebra Aptitude Test scores decline under Connected Math

2007-04-09T21:27:00.000-05:00

The Iowa Algebra Aptitude Test (IAAT) is used as a placement test in the Columbia Public Schools and is administered to all students in 7th grade to help identify honors vs. regular math placement in 8th grade. CPS secondary math curriculum coordinator Chip Sharp expressed it this way: “It is a readiness test. This means it was designed to measure how ready a student is to study abstract concepts in the algebraic strand of mathematics."

The chart below shows the percent of CPS 7th graders that scored above the national 50% rank on the Iowa Algebra Aptitude Test (IAAT) from 1999 to 2006. Under the middle school math curriculum in use from Fall 1999 - Spring 2002, 42.1% scored above the national 50% rank. Under the experimental Connected Math curriculum in use from Fall 2002 - Spring 2006, that dropped to 38.4%. A simple statistical test shows that this is a significant difference, and represents approximately 100 additional students scoring below the 50% rank every year.

Important points to note: the Missouri DESE has declared that the MAP test is out for 11th graders and will be replaced with an end-of-course exam in Algebra I by 2009 (http://columbiamissourian.com/news/story.php?ID=2435) so looking at the test results for an "algebra readiness test" makes sense.

Another point: the line between the previous curriculum and Connected Math in this data isn't fuzzy as is often the case with comparisons--students scored lower using Connected Math, and the difference is significant. Connected Math (CMP) was implemented at CPS in 6th grade in 01-02 and in 7th grade in 02-03. Therefore, students tested in 7th grade in 01-02 had used the "old" curriculum exclusively, and students tested in 7th grade in 02-03 had 2 years of Connected Math in middle school. The data represent over 9,000 student test scores over 8 years. The original data is available at the CPR-Math google group pages (http://groups.google.com/group/cprm/files).

Another way of looking at the results:

Math curriculum	Testing Year	How many more students in bottom half than top half each year?	Number students in bottom half-number students in top half adjusted for cohort size
“old”	99-00	178	185
“old”	00-01	186	196
“old”	01-02	151	154
CMP	02-03	262	249
CMP	03-04	245	239
CMP	04-05	295	293
CMP	05-06	260	255
CMP	06-07	285	283

The average number of students scoring in the "bottom half" under the "old" curriculum was 172. That increased to 269 when students studied a Connected Math curriculum as 6th and7th graders. So a simplified way of viewing the results is that on average, approximately 100 more students score below the national 50% NPR each year that Connected Math is in use in the CPS middle schools. NOTE: The IAAT is normed for 8th graders, so the results do not indicate that CPS students score below the national average, but that CPS students are tested earlier than most students.

Math parent groups across the country

2007-03-15T20:54:00.000-05:00

Visit Weapons of Math Destruction in Alpine City, Utah for excellent advice if you're moving to a new school district and want to avoid fuzzy math. They list districts known to use constructivist curricula. If you want to find out what damage has already been done, they list placement tests for recommended math curricula so you can help your kids catch up until the schools respond. Plus, this site features comics that will make you smile even if you want to cry.

The "math wars" may have subsided in New York, but myths about math education are still alive and well in Missouri. Parents, a list of myths you may hear that emphasize methodology over content is available at the NYC HOLD Honest Open Logical Decisions on Mathematics Education Reform web site.

Washington State's Where's the Math? has a list of critiques of math education research. They also offer parents advice on how to talk to your schools administrators and teachers.

And Mathematically Correct which originated in California provides program reviews of math curricula, including the math programs used in CPS: Investigations, Connected Math, and Core Plus (scroll down for links).

Welcome to Math That Works

2007-03-15T20:22:00.000-05:00

We'll use this blog to publish information about math curricula used in the Columbia Public Schools and the school district curriculum review that is currently in progress.

Links to recent media coverage are on the right. Be sure to watch Columbia Daily Tribune reporter Janese Heavin's blog "Class Notes" at http://blogs.columbiatribune.com/education/

Watch the "don't miss" YouTube video: http://www.youtube.com/watch?v=Tr1qee-bTZI