Tracking Math Students in Elementary School

In Uncategorized on November 25, 2008 at 12:57 pm

I am not philosophically opposed to “tracking” in the elementary schools, provided it does not occur too early.

I am aware, for example, that in Singapore, each student whose individual performance in a math test administered at the end of the third grade reveals an insufficient grasp of mathematical concepts and basic skills for that level is identified and subsequently “tracked” during fourth and fifth grade. This ensures that by the time the tracked students reach the end of fifth grade, they are on par with their non-tracked classmates in math. In other words, when the whole class moves on to sixth grade, virtually nobody is suffering from a deficit of knowledge or skills. Everyone has an opportunity to move forward with confidence and pride.

Admittedly, the questions naturally arise: 1) How is such “tracking” handled?, and 2)Won’t “tracked” students miss out on certain things that non-tracked students receive in terms of non-math instruction?

In answer to the first question, I understand that the “tracked” students experience a 4th and 5th grade math curriculum that involves a relatively heavier emphasis on repeating and reinforcing math concepts, both with respect to such concepts as are covered in earlier grades, as well as new math concepts that are appropriate to the grade they are currently in. By contrast, the non-tracked students spend a proportionally smaller amount of their time in math instruction. The net result is that by the end of 5th grade, the tracked students have completely caught up to their non-tracked classmates in math.

The answer to the second question is apparently “yes”. But since the remedial program experienced by the “tracked” students is spread out over two years, the differential in terms of exposure to non-math subject matter is kept to a minimum. The people of Singapore have clearly decided that the most costly deficit from which a child at the elementary school level can suffer is in math conceptual knowledge and basic math skills. They have molded and shaped their overall elementary school instructional program accordingly.

In my view, Singapore was particularly wise to do this. It has set itself up for success by taking the early steps necessary to provide as many students as possible with the valid option to pursue educational paths leading to financially rewarding and intellectually stimulating careers in science, technology, engineering, and math (STEM). Most of us in the U.S. who never opted to pursue a STEM career are easily convinced that early preparation and diligent practice is essential for musicians who will eventually seek a fine arts degree in instrumental performance, just as much as such behavior is critical for the success of budding professional dancers, or for aspiring collegiate athletes. Why it it that so many in this country resist coming to a similar concluson when it comes to students who will eventually pursue STEM careers? This is a problem that only time and patient argumentation can overcome.

The challenge faced by elementary students worldwide in aquiring critical mathematics concepts, and in developing automaticity with important math facts and processes (like the Standard Algorithm), is well documented. At the same time, premiere public school districts in the U.S. seem particularly unwilling to address this problem head-on. I am beginning to view this as a dysfunction that has its origins in a misplaced concern for egalitarianism. Administrators seem loathe to take specific action to address deficiencies in math instruction, fearing that if they do so, they will be seen by district parents and teachers as regarding non-math subjects as less important than math. Based on my experience thus far, I would say that the Ridgewood administrators are suffering from this syndrome in spades.


  1. As smart a plan as this is, it will never be adopted in Ridgewood. I can think of 10 reasons off the top of my head. The first is this:

    In Regina’s Brave New Math World there is no “standard algorithm.”

    That, sadly, is the nub of the problem. If you can’t agree what math is, then how can you ensure that it is properly taught?

  2. Our BOE will never admit that a tiny country like Singapore could and should be the model for math education in the USA.

    They will give every excuse in the book as to why it can not apply to us, as did Bob Hutton at a BOE meeting last year.

    The phrase bandied about so freely by our administrators and the BOE, “thinking out side of the box,” is only for public consumption not something these folks actually do.

    The irony in all of this is, that they like to believe that they are “progressive.” When in reality, they are very rigid in their thinking.

  3. I agree with making math a more important subject in schools but our schools claim they are just trying to produce “well rounded” citizens (the average Joe) with nothing special about them. This, however, is just an attempt to make everyone equal in outcome as if everyone is your “average Joe” no one will become scientists and mathematicians but just another person working your average 9-5 shift earning 40k per year. I don’t think Euler, Gauss, or Ramanujan was your “average Joe”. Nothing against your “average Joe” as they are certainly needed in society but shouldn’t our children be taught to aspire to achieve more than your common person? If they fail to do so then so be it but we shouldn’t put such holds on them and discourage them from trying. By the time kids are in high school they have already bought into the idea that they will grow up to be your “average Joe” and will no longer entertain the idea that they will become the next Einstein or the next Gauss. This is just another example of public school brainwashing. At the core of the public education philosophy, is a huge flaw.

  4. All this is just another reason to scrap the failed, outdated model of education know as our public school system.

    It is time to seriously consider privatizing all education and fund it from public trust. The net effect will drive down costs and improve quality. It will create niche schools for those special children either in need of more help or those who are exceptional.

    It will allow for schools to compete in a marketplace for students and the dollars attached. Those that fail the task will perish and those that succeed will flourish.

    But most importantly, all children will have access to the very best in education.

    The marketplace is unforgiving of failure and its discipline needs to be enforced upon public education.

  5. We can’t solve the nation’s education deficits here on this blog, nor here in Ridgewood. We can’t wait for the system to die and for the marketplace to take over. We must make the best of what we have in the short term as we build up steam for the long term salvation of public education.

    Focusing on fixing weak math is key to making rigor a general necessity across other disciplines in our schools.

    Although it may not look like much, we are making headway toward that goal. The fact that we, free citizens, are having this conversation is a huge thing facing our own local monopoly. Monopolies do not like to be held accountable. Any hint of a demand for accountability is like a stab wound in its gut. Eventually, it will determine that its interests lie in some form of compromise with its detractors.

    We are at this point and we must focus our energy and input on shaping that compromise. We may not end up with the best math but we will end up with some iota of improvement.

  6. 2:51 PM,

    Not good enough. It is like being a little bit free. Either you are or are not. There is no in-between.

    The Monopoly must bend to the will of the people or cease to exist.

    I’m so glad you were not around in the late 1700’as as we established our independence from the crown.

  7. Hi this is 10:24 (the person advocating for AOPS all the time), I myself am of chinese descent (yes the arms race comment was simply to notify you of how deep the math crisis really is, not to invoke any animosity between the two countries) and was brought up in America. The chinese school structure is different from what we have here. As some of you have mentioned tracking as a solution, how about applying to middle schools and high schools like we do for college. The best students get into the best schools (Renmin was one of the top 2 schools in the city (the other one being Beijing 4th). No one is knocking on our university system as it is sucessful for the most part, why not emulate it?

  8. Look,

    Do not worry about elementary tracking. Once our precious will be in the middle school they will be taking Connected Math, same wonderful program that is taught in Newark, Passaic …

    and is standards based.

    The same standards the state put in place for Newark, Passaic and … Ridgewood.

    Take heart, the state DOE is satisfied. Are you?

  9. 3:18 we did not “establish” our independence from the crown. We fought long and hard for it. Blood and guts lay in the fields for years before our independence was won. Short of blood and guts, there would be no winning, nada, none.

    A monopoly is as dictatorial as the crown, so are you advocating that we take up arms? Prior to fighting for independence, even the staunchest Colonialists sought to make an accommodation with the crown and its Loyalists. Remove the odious taxes and we’ll find a way to get along. But the crown would have none of it. Hence the fight.

    The BOE for all its faults has signaled a willingness to address the issue. It also could be just a ruse as they stack the decks to their constructivist side. But any decision that appears pre-arranged to reformist ideals will not be accepted. A strum and drang will ensue.

    Are we there yet? By May we will know if battle lines need to be redrawn or if our swords may need to be shielded. If we’re going to have a bloody battle, then let it be after they have thrown down the gauntlet. To draw blood beforehand will be self defeating.

  10. “…we must focus our energy and input on shaping that compromise.”

    The operative word here is “compromise,” 1:29.

    That is my point. Compromise didn’t gain our freedom, bloodshed did.

    There was no compromise with the crown. And there can be no compromise with the BOE on math.

    Are you OK with just an average math program, one a little bit better than what we have now?

    I’m not. I refuse to compromise for something a little bit better than what we have now when there are far superior programs available.

    Accepting anything less, is failing our children.

    P.S. I guess my subtlety of choosing the word “establish” went over your head. It is implied that our freedom was paid with blood. And for the record, there is no long term salvation of Public Schools only its slow painfully expensive death.


  11. The BOE for all its faults has signaled a willingness to address the issue.

    I have not seen any honest attempt at this by the BOE.

  12. Hutton’s wife was a substitute teacher one day this week at Travell.

    Call me naive but isn’t that a conflict of interest…?

  13. The only way we can truly get kids to perform to their abilities is to get rid of these stupid statistics about how people aren’t ready to think on a high level until adulthood and other trash like that. This belief is simply a way of controlling the masses and providing jobs for statisticians(stat is a load of BS). We must also overthrow the current perception of what math really is as most people still think it is following a set of rules. When most people think of math they think addition, subtraction etc… nothing about proving fermat’s last theorem etc… Finally we must be patient with our kids and realize math ability will not develop overnight. Math builds upon itself. Math is a set of truths that exist in nature therefore cannot contradict itself ever therefore many problems in Algebra has some connection with Geometry and vice versa. For example the formula nCr + nC(r+1) = (n+1)C(r+1) can be proven with polynomials(algebra) and using combinatorics(probability and counting). To truly understand the formula above, one must understand how Algebra relates with Probability. Knowing and memorizing it and being able to plug into it is not enough.

  14. There are so many more “influential” folks or “people of notice” that have relatives working in our school district.

    The list is long. Very long. It is political favoritism born of the the corrupt nature of our political structure.

    Who is to be held accountable when there are no political parties in our village. Who?

    With a structure of friends and factions running our village, is it any wonder that our taxes are so high. We get the government we deserve ans we pay for it dearly.

  15. 7:56

    Okay, you’re naive. And dopey.

  16. Hutton, Johnson, Seavers, Lorenz – there might be more, but these are the ones that I know are working in the district.

    Is it nepotism, I don’t know. You be the judge.

  17. Nepotism and Unions, perfect together.

  18. Children in Ridgewood used to be tracked, that is until parents decided that even their below average kid was above average and had to be treated that way. The parents, though, had a good point as tracking was not used to the best advantage of the struggling students, who were just the inheritors of weaker curriculums and lower expectations. Tracking when done well allows for gifted children to excel to their potential and provides an environment for less gifted children to reach theirs. Sadly, public education is on a political mission first, and an education misson second. The political mission is to reach minimum expectations of public schools. Since those expectations are falling every year, the job gets easier and easier and can be done by less talented and experienced teachers and administrators.

    On a graph, this would be depicted as a pretty straight line downward. Not a good sign for the future of that socialist enterprise.

  19. P.J.:

    Halfway through reading the brilliant article associated with the following link, I began imagining that its author would be very impressed with your free speech efforts in Ridgewood generally, and the impact and effectiveness of this blog in particular.


    Before you managed to kick into high gear the process of subjecting elected public officials and other local public employees of importance to your particular brand of scrutiny and accountability, there was literally nothing that an ordinary Ridgewood resident could do to peek behind the curtain and get some sense of what was really going on in town with the ‘powers that be’.

    The fact that things are different now is a result rightly to be cheered. Some who are new to this format may get squeamish, or hung up on the notion (quite overblown, IMHO) that there is an overall or prevailing ‘air of negativity’, but for every one of these people who successfully resolve never to visit this blog again for that reason, there has to be nine or ten who break that pledge in time and are drawn right back in.

    Let’s face it–for the time being at least, you are the only game in town. If they don’t like your style or that of your regular commenters, they can start their own blog for heaven’s sake. (Let’s just hope that at least some of them have the guts to put a face behind the blog like you do, rather than offering up some goofball image of anonymity like someone wearing a paper sack on their head with holes cut out to see through, reminiscent of the possibly late, and certainly unlamented, “Unknown Comic.”)

    Anyway, in this high political season I just wanted to wish continued good luck to you. Please keep up the great work that you are doing, and we will all keep reading and chiming in like usual.

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