Rethinking Math Curriculum

by Olga LaPlante

I am very interested in math, I love it, in fact, but have no intimate knowledge of the ways it's taught in the US. What I have seen - quite superfluously - has done little to excite me (for one thing, your long division order is backwards, and ever more confusing) about the prospect of my son getting excited about it either. I have heard many a time from people of various levels of education that they "hate" math - around the world, not just in US - and have always been perplexed by it.

The talk I have highlighted here appeals to me - and resurrects the appeal of math to a wider audience. Given that in many schools, the wise solution to "raise test scores" is simply longer hours of teaching math using the same textbook in the same classroom of kids with the same teacher using the same strategies, I wonder if the success is guaranteed.

I have also read a number of posts on this blog about the math curriculum (Everyday Math being one of the most memorable) and math core standards (somehow, Everyday Math was mentioned in that post, too, hmmmm...) and wonder if the more experienced and knowledgeable persons would kindly offer their insight about Dan Meyer's attempt to teach kids about math.

Common Core Math Standards and Everyday Mathematics

By Pam Kenney

I spent much of last weekend reading and critiquing the new Common Core Math Standards (K-6 only) for the National Coalition for World Class Math. I must say I was surprised at and pleased with their thoroughness and rigor. My primary assignment was to analyze the standards’ sequence of skills. I had several suggestions to facilitate learning (teaching students to count by 5s and 10s, for example, before requiring them to count money), but for the most part the standards are presented with their delineated skills building on each other from grade to grade in a logical progression. I love the standards that require children to use mental math, the kindergarten one that ensures students are able to begin counting in the middle of a number sequence instead of always starting at 1, and the strong emphasis on understanding the “whys” of math. They require the memorization of math facts (although I’d like to see mastery at earlier grade levels than these standards mandate) and the use of the standard algorithm (again my preference would be for its introduction more quickly after understanding is achieved than it is now). The timetable for the mastery of concepts isn’t as clear as it could be, and I hope that need will be addressed as the comment period continues this month.

As I read the standards, I made an unexpected discovery. From the outset, I began noticing something interesting: Many of the skills and their attendant requirements reflect those taught within the Everyday Mathematics curriculum. At the fourth grade level, for example, standard #6 under “Number – Operations and the Problems They Solve,” states, “Compute products and whole number quotients of two-, three- or four-digit numbers and one-digit numbers, using strategies based on place value, the properties of operations, and/or the inverse relationships between multiplication and division; explain the reasoning used.” EDM is famous for, and often criticized for, the many methods (lattice, partial products, and partial quotients, e.g.) it expects children to learn to facilitate a thorough understanding of the “whys” of multiplication and division. This standard and many others like it throughout the standards document continue that emphasis. The new standards differ from EDM, though, because they include basic fact fluency requirements, the use of the standard algorithm, and at least an attempt to set mastery levels. What is not clear is how much of the spiraling that is peculiar to EDM will be eliminated if they’re adopted, and that is an important facet of the standards that needs to be analyzed.

I have been a critic of the Everyday Mathematics curriculum for years and have written about its shortcomings on this blog several times. However, I’ve amended my position somewhat after working with a fourth grader on her EDM assignments throughout this school year. I’m finding it increasingly difficult to fault EDM’s basic goal, which is to help students understand what they are doing when they solve problems and why their answers to problems are reasonable or make sense mathematically. EDM is very good at helping children develop math reasoning skills. I still have problems with its de-emphasis on basic facts, its delayed use or elimination of the standard algorithm, and its spiraling of concepts that doesn’t pinpoint mastery expectation points. It appears that the Common Core standards have addressed fairly well these problems, as well as the vocal criticism that has stemmed from them from parents and teachers, and have provided a more balanced approach than EDM does.

Questions still linger, though. Here are two: Why are these national standards so reflective of Everyday Mathematics? What input into the development process, if any, did the University of Chicago Mathematics Project or the EDM publisher, Wright Group (a division of McGraw-Hill), have? I have read comments from a variety of sources stating that classroom teachers should have had more say than they did in the creation of the Common Core Standards. My hope is that their input didn’t get squeezed out by that of textbook publishers.

Coming soon: Part II – Common Core Elementary Math Standards and Teacher Competence

The Nation's Report Card - Math

By Pam Kenney

The results of the 2009 National Assessment of Educational Progress (NAEP) Trial Urban District Assessment (TUDA) in math were released December 8, 2009. 18 school districts across the country participated in the study, and the scores allow the public to follow over time the progress of our students' math achievement.

At Nation's Report Card, you can view national, state, and district results for grades 4 and 8. The graphs and tables are excellent and allow you to compare scores from 1990 through 2009. You can look at the information adjusted according to gender, race/ethnicity, type of school, family income level, student disability status, and English language learners. Also, there are links to a press conference about the TUDA Mathematics report card and a narrated presentation on the major findings.

Everyday Mathematics is credited by Washington, D.C. public school teachers and Chancellor Michelle Rhee as one reason why students there have made significant gains in math achievement at both the 4th and 8th grade levels since 2003: "... an increased focus on the use of games, calculators and written responses -- to help students demonstrate their reasoning in solving a problem -- helped drive the gains in scores in the national assessment, known as NAEP." While I agree that deepening children's concept grasp and understanding of problem-solving is vital to success in math, I continue to be unsettled by the relative unimportance of practice and mastery in "reform math" curricula like Everyday Mathematics. My questions, then, are these: Are schools, such as those in D.C., using supplemental materials to fill in the gaps in EDM, thus contributing to the rise in scores? Or - are tests like the NAEP also so focused on the "whys" of math that even studying their results won't tell me whether my fourth grader knows 6*7=42? I don't know the answers to these questions, but I'm going to find out.

Everyday Math Revisited: Parents Stand Up

By Pam Kenney

About three weeks ago I posted a commentary on this blog critical of the math curriculum Everyday Math. I was prompted to write it because I was receiving an increasing number of calls for help from parents whose elementary-age children were struggling in math classrooms using Everyday Math, and parental attempts to assist them at home were frequently not successful. The post generated more than 20 comments from both parents and educators. From the strong feelings expressed in those comments and from subsequent independent reading and research, I have become aware of a grassroots movement among parents anxious to become an integral part of the debate about how math is taught in our schools. For the first time in many years, parents are so frustrated by and angry about the trend by our nation’s school systems to adopt “reform” math curricula, they have banded together to stand up and fight for the kind of elementary math instruction for their children that will provide the concept grasp and computation skills necessary for success in math at high school and college levels.

One group, the United States Coalition for World Class Math, is made up of “an ever-growing group of state coalitions comprised of mathematically literate parents, many of whom are scientists, engineers, mathematicians, and educators who want nothing but excellence in Mathematics Education for the students of our country, the United States of America.” The focus of its mission is to urge each state’s department of education to develop core curriculum content standards in math, using as guides the curriculum standards from countries with the highest scores on international math tests as well as those from the U.S. states with the highest math rankings. Calling for standards that will prepare children for success in college and beyond, it recognizes the importance of input from research mathematicians and university math professors as well as from K-12 educators and professors of math education.

There is now an active state chapter of the national group, the Maine Coalition for World Class Math. Maine parents who are concerned about their children’s progress in math and the suitability of the math textbooks chosen by their school districts will find not only a sympathetic ear at this site, but a wealth of information, too. One particularly interesting and thought-provoking link provides visitors with the coalition’s “Design Principles for K-12 Mathematics Standards” that “address the major deficiencies and defects that currently plague far too many of our state mathematics standards.” One pertinent complaint of the Maine Coalition for World Class Math is that today’s math reform movement has led to the widespread adoption of curricula like Everyday Math. Many critics of Everyday Math argue that it attempts to teach children the conceptual “hows” and “whys” of math in such depth and in so many different ways that it fails to do a good job teaching the computation skills necessary to ensure the mastery of basic arithmetic. Its spiral approach (a method that moves from concept to concept and back again without clear mastery goals built in), a scope that is too broad and a sequence that is not logical, an over-reliance on calculators, too many confusing ways to solve simple problems, and little requirement for practice are common criticisms. Parents are concerned, too, that many of the Everyday Math methods have not been explained well to them, and they feel removed from the vital school-parent partnership.

The Coalition for World Class Math has had its share of criticism. Many educators feel it, and other groups like it, are advocating a return to the teaching methods of the 50s and 60s that emphasized rote drill at the expense of conceptual understanding. I don’t believe that perception is accurate, however. What thoughtful parents are desperate for today is a balanced approach to teaching math. They understand well that their children need to internalize the whys behind long division, for example. But they want their youngsters to know instantaneously that 6*8=48, too, and that takes practice. I believe their plea to schools is this: If it helps kids understand the process of long division better, teach them initially using a partial quotients method. But, also, teach them the long division algorithm that they will be required to use throughout their school careers. Don’t do away with drill; require enough basic facts practice to guarantee mastery. Parents know it takes diligence for children to become excellent math students, and they want their kids to work hard.

Please give parents more credit. They, just like teachers, want the best possible math instruction for their children. They are not uninformed or hopelessly out of date. In fact, the parents I work with would love to help schools improve their math instruction. The current reform vs. back-to-basics math debate shouldn’t be seen as an “us vs. them” movement. Parents have a lot to offer, they know their children better than anyone else, and their views deserve to be heard and thoughtfully addressed.

Everyday Math: Yea or Nay?

By Pam Kenney

Over the last few years, many school districts across Maine have adopted Everyday Mathematics as the math curriculum for their kindergarten through sixth grade students. The program's development by the University of Chicago School Mathematics Project began more than 20 years ago, and the first textbooks were published in 1998. Since then it has been implemented, then rejected, in school systems across the country, often because children taught using Everyday Mathematics consistently fail to meet state math standards. Frequently called "fuzzy math", it eschews rote learning and relies on spiraling, a method that introduces children to a concept but quickly moves on to another concept before mastery is achieved. Concepts are re-introduced throughout the school year with the hope that, through repetition, the kids will learn them. Unfortunately, spiraling doesn't work very well. Top math students are bored, average learners are frustrated because, just when they are starting to "get it", another topic is introduced, and children who are struggling in math are overwhelmed and give up in despair.

The seeds of Everyday Mathematics and other programs like it started to sprout more than 50 years ago with the launch of Sputnik I by the Soviet Union and the subsequent realization by U.S. educators that our students needed more difficult math and science courses to help the country excel globally. One result of that decision was that the rote-learning focus of math instruction at the time was replaced by one that emphasized the "whys" of math. "Carrying" and "borrowing", for example, were replaced by lessons on re-grouping and learning about ones, tens, and hundreds. That shift was needed and changed how math was taught for years. The problem now is that we've made the "hows" and "whys" of math so important that we've relegated concept mastery and computing skills to secondary, undervalued positions in some math curricula. Everyday Mathematics is a prime example of the new philosophy, and its inherent spiraling and neglect of mastery have had a negative effect on learning. I think many Maine schools jumped on the Everyday Mathematics band wagon without researching its many drawbacks thoroughly enough; and math programs are so expensive, it will be a long time before these schools can afford to replace it.