Friday, June 15, 2012

Math follies

And you thought it couldn't get any worse!

The weak, Everyday-Math based, math program at our kids' school has been a major complaint for a decade or more. Our soon-to-be 7th grader spent 8 years under this program, and only got into a good junior high/high school because we had taught her a lot at home. Any change would be an improvement...or so we thought...

Near the end of the school year a letter came from the school (aka: Dot School), saying that they were changing the math program. There really was much rejoicing. They are moving from the pure-constructivist EM, to the practice-to-mastery-based Singapore Math. This is a massive improvement. Singapore is really a strong program, and their "Singapore Bar Method" is an amazingly powerful system. It allows kids in 5th and 6th to do complex algebra and ratio problems which would otherwise have to wait until later.

Then the details of the school's switch started to become apparent. First of all, next year, the only change will be at the lowest grades: the kindergarten and 1st grade classrooms. For 2nd-5th the transition will happen the following year. For the middle school, it will only begin to change as next year's 4th graders move through 6-8th grade. The full roll-out, therefore, won't be complete until the 2016-2017 school year. It also means, that the incoming 5th graders will never see the improved program.

Guess which grade our kid will be in next year?

We protested loudly. We wrote a detailed almost-four page letter detailing our dislike of EM and preference for jumping on the SM bandwagon immediately. That letter is here (names have been changed to protect the guilty):

In your prior e-mails you have said that K1 will transition to Singapore Math next year and the rest of the school the following year and the junior high program will change as the kids who have transitioned to Singapore Math reach 6th grade.  This means that next year's 5th grade class would stick with Everyday Math and the current junior high math program through 8th grade.  You have done a thorough review of these programs, so I am sure that you know more about it than we do, but here are the reasons why we prefer the Singapore program.
Spiral vs practice to achievement.

While some math skills have no prerequisites, for the most part, math builds on earlier knowledge.  Everyday Math’s spiraling curriculum means that topics are repeatedly gone over lightly, and there is no attempt at making sure one concept has sunk in before progression to the next skill.  Without fully building the foundation, subsequent topics don’t make as much sense and are harder to grasp.  With Singapore Math, you do not progress until you have spent sufficient time to master a skill.  That is a key difference: repeated, light coverage vs. practice to mastery.

In addition, the Everyday Math books were designed to work with a public-school calendar of roughly 180 school days. Dot School’s calendar is six weeks shorter, and Dot School kids miss many other days of math class for special events.  Because the experiential learning activities in Everyday Math take so much class time, it is difficult to compress the curriculum into the shorter school year, and about one-third of the material in any given year is never covered.  This is deadly in light of the spiraling nature of the curriculum—it means many skills are not presented enough times and in enough detail to really sink in.   At least with Singapore, if a previous year’s teacher doesn’t get to the end of the book, it is very clear where the class left off, and what skills they need to work on to make up the gap.

Standard algorithms

Everyday Math presents multiple algorithms for solving arithmetic problems.  For multiplication, four different methods are presented.   The program does not emphasize standard algorithms, so these are not mastered.   Singapore instead focuses on one or two algorithms, and then takes the time to ensure the student achieves mastery.  Using too many methods leads to a great deal of confusion.   Many of the algorithms taught (lattice multiplication being a prime example) are not robust enough and do not scale to more difficult problems.  Try doing a lattice multiplication problem with four or five digit numbers, or with decimals; it quickly devolves into a mess.  Using the classic algorithm for such problems—or even harder ones—is straight forward, and you don’t have to waste time drawing the lattice.  The Everyday Math Teacher’s Reference Manual actually states that the lattice method was originally added for its “recreational value and historical interest,” not it's mathematics value, and that, “It is not easy to understand exactly why lattice multiplication works.” (K-3 Edition, 2001, pg 107.) In other words, it’s something to play with, but is hard to understand and not worth spending the kind of time that Dot School spends on it—time which could be spent actually working to master a robust algorithm. Obviously, Singapore doesn’t teach this at all.  I won't even talk about long division, the problems with Everyday Math are well known.

Level 5 Everyday Math still does not emphasize the standard multiplication algorithm.

Instead, it rehashes partial-products (which does have a great deal of value when just beginning multiplication…in third grade,) but it doesn’t scale well to large problems—they become unwieldy.  A simple 3X3-digit multiplication problem leads to 9 lines which have to be added together—and for kids, this means keeping their columns very straight, which many have a hard time doing; while the standard algorithm gets it done in 3 lines.  In addition, the partial products method gets much more confusing when you start throwing in decimal points, and are multiplying hundredths by hundreds.

Level 5 Everyday Math also continues to emphasize the lattice method, which is mathematically confusing and of little mathematical value.  If the idea of favoring partial products, as Everyday Math does, is so that kids are always remembering that the digits stand for hundreds and thousands, etc, then the lattice method throws all that out in favor of a party trick.


Much of Fifth Grade is taken up by fractions, including multiplying and dividing them.  Instead of teaching that division is the opposite of multiplication and introducing the idea of a reciprocal, Everyday Math skips teaching fraction division entirely, believing that the subject is too confusing, and teaches kids to reach for a calculator instead.  It is hard to understand why Everyday Math skips over this, as fraction multiplication and division is so much easier than fraction addition and subtraction.

Algebra requires students to be able to work fluidly with fractions, including fraction division.   It is difficult to find the square of a polynomial which includes fractions, if the only way you know how to do fractions is to reach for a calculator.  Math skills build on one another, and skipping this simple, yet crucial, bit of fraction arithmetic handicaps Everyday Math-taught kids as they advance.  Singapore Math does cover fraction division and doesn’t (ever) emphasize reaching for a calculator.


On page 14 of the Singapore Math Primary Mathematics 5A workbook, there are already problems with exponents.  Our girl wasn't taught anything with exponents until 6th grade.  Again, this is a very easy thing to learn—especially squares and most cubes—yet it is missing from Everyday Math.  Just as multiplication is introduced as repeated addition, so too can exponents be introduced as repeated multiplication.


Everyday Math, at least as our kids have both experienced it at Dot School, doesn't get around to the properties of circles until very late.  When our boy talked with his table mates about "pi", he was derided and asked if there was also a number called "cookie."  This was near the end of fourth grade, and most of his class had never heard of pi.  Our girl's class this year covered volume and surface area of cubes, rectangular boxes and pyramids, which is covered earlier in Singapore math.  Being able to calculate the volume of a rectangular prism—not to mention cylinders and spheres—is actually a useful life skill, yet this, again, seems to be missing from Dot School's current math program.

Mental Math

The mental math aspects of Singapore are great, adopting ways of thinking about problems that speed calculation, increase accuracy, and emphasize the meaning of numbers.  These are the sorts of skills that a student will use for life.

Singapore Bar Method

The Singapore Bar method is a powerful tool.  Using it, kids in early grades learn complex algebraic concepts and study ratio problems that they would otherwise have to wait years to get to.  It is really an impressive system, and of great value.  Obviously, Everyday Math doesn’t use this at all.

Junior High and Beyond

The standard college prep math track leading to Calculus in 12th grade would start with pre-Algebra in 7th grade and Algebra in 8th grade.  The Chicago Math program uses a slightly different sequence.  In order to allow students more time to learn Algebra, first year Algebra is split into two years and sandwiched around Geometry which is taken in 8th grade instead of the traditional 9th grade.  To get to Calculus in 12th grade, pre-Algebra has to be taken in 6th grade.  The sequence looks like this;

                6th grade:  Transitions (pre-Algebra)
                7th grade:  Algebra
                8th grade:  Geometry
                9th grade:  Algebra
               10th grade:  Advanced Algebra/Trig
               11th grade:  pre-Calculus
               12th grade:  Calculus

Dot School uses the pre-Transitions book in 6th grade.  This book is mostly a review of 4th and 5th grade math.   A full two trimesters are spent reviewing addition, subtraction, multiplication, division and fractions.  The new material covered, mostly ratios, statistics and geometry, are covered in earlier years in Singapore Math.  Dot School kids have to transition to another school in 9th grade and will not have received an Algebra curriculum comparable to kids moving from other schools, because they will have made it through only the first year of the three year Algebra sequence in Chicago Math.  Presumably, if basic math skills are mastered in grade school and ratios, statistics and basic Geometry are learned earlier, as covered in Singapore math, students will be prepared for Transitions in 6th grade or the school will switch to the Singapore junior high curriculum. 

Dot School is not an island, isolated from the schools and students in the surrounding communities.  When Dot School's students leave, whether in 8th or 6th, they will face competition with students from around the city.  Many of Dot School’s peer-schools begin tracking students as early as fourth grade and Dot School's current curriculum leaves many students struggling in their next school.   As math is a foundation for the physical sciences, students will struggle in subjects like physics and chemistry as well.  Dot School kids have to choose between struggling to catch up and retaking Algebra in 9th grade.  Because high school AP Calculus is now all but a requirement to study STEM and related fields at competitive colleges, the latter option makes it unlikely that students will choose these career options.

Schools that have adopted Singapore Math often see tremendous gains in achievement in the first year, and the fifth graders next year would benefit tremendously from it.  You already know the weaknesses of Everyday Math and the strengths of Singapore Math better than I can point out.  I know you are aware of the lengths parents are going to supplementing math outside of school and what students go through preparing for the ISEE.  You know the perennial and vocal protests from parents about Dot School’s math program—you were on the receiving end of some of that anger at the math meeting a few months ago.  You have already determined that Singapore Math is the better program, but you are telling next year's 5th grade parents that our kids can't have it.   Please reconsider.
Yesterday, my sister met with the head of the  elementary school to discuss trying to get the boy placed in 6th grade math. He, Mr. H, said it would not be "developmentally appropriate" for him to advance beyond his classmates, and that it would be damaging to allow him to actually learn something new in math next year. And, since 6th grade math is pretty much a review of 3rd-5th grade math, they have no intention of teaching him anything new until he gets to pre-algebra in 7th. By that time, hopefully, he will be departing the school and mooning them on the way out.

Instead of learning something new, the boy will be presented--by virtue of being advanced from many of his peers in math--with "leadership opportunities" in the classroom. We have been down this road before. That is exactly what they told us when he was 5 years old and we wanted him in kindergarten; they wanted him in pre-school. It would be good for him to be in a class with kids who are barely verbal, they said, because he could develop leadership skills! Instead, he spent a lonely year, with no one to talk to, and almost no one on his level to play with; all the while, watching his former classmates actually learning something in kindergarten. What he learned that year wasn't leadership. The school taught him that he was too stupid to go up to K with his friends, and he learned to hide behind potted plants in the hallway when the K classes walked by.

But, I forgot to mention, they are going to change the 5th grade math curriculum next year! Yay!

They are going to make it worse!

Instead of learning something from their institutional embrace of Singapore Math, and asking themselves what makes that program better (direct instruction and practice, practice, practice,) and applying that to the handicapped EM curriculum that they insist on using, they are doing the exact opposite.

They are taking the constructivist EM curriculum to new, never-before seen heights. They are going to ditch most classroom instruction completely in favor of a student-discovery, centers-based classroom! This is the same centers-based system that was used at the school in kindergarten, so the kids will be familiar. That means that there will be about four stations every day for the kids to cycle through. The goal of this is to keep them unfocused and increase the frenzy and distraction in the classroom. The more movement and noise, the better kids will learn math! The student-discovery aspects will mean that kids won't have a clue how to do some of the work; which is great, because they don't really want to do it, and the teacher doesn't really want to teach them anyway! Win-Win!

Yesterday, I tried to find any evidence that the fad of "project based learning,"  which is what they are calling this at the school, is a good way to actually teach, impart knowledge, and to get kids to achieve. Guess what? There is no significant evidence for this method. There are a handful of month-long demonstration projects that showed some improvement, but there has never been a quantitative, random assignment, long-term, longitudinal study of this method. In other words, a couple classrooms have used it temporarily, and they liked it! However, it should be noted that studies have also shown that any change in a curriculum--whether it is eventually proven beneficial or harmful--improves things in the short-run. Enthusiasm over the newness goes a long way. Real studies require long-term quantitative results, not quick "we liked it! we really liked it!" studies. There is no such research approving "project-based learning."

So, we're tearing our hair out...and spending the summer teaching him real math.

My sister has written another letter. Beautifully snarky. I'll see about posting it after the school has seen it.

1 comment:

Anonymous said...

You need an educese - English translator.

"Not developmentally appropriate" = it would make us work harder.

"Leadership opportunities" = he will bring up class average test scores.

"Expand his repertoire of active listening strategies" = shut up.

"Learn how to share his understanding" = do what the bullies say.