What's a parent to do?

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

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

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

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

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

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