really interesting article on math and acceleration

[Anonymous]

From 2009, but new to me (referred to in another context by a former public school math teacher):

http://www.aps.org/publications/apsnews/200910/backpage.cfm

It's about how raising state standards in math has lead to more remediation in college because kids "learn" things in a way and at a time that doesn't allow them to develop the kind of mastery and understanding needed to know how to use what they've learned (or maybe even to retain it). Written by a physics professor with kids in Maryland public schools and based on his experiences both as a parent and a teacher.

[Anonymous]

When upper level math is taught is hardly the problem.

A family member is a chemistry professor at a public state university. He had a problem that required two digit multiplication on a test, over half the class got the multiplication aspect wrong...even several who got the chemistry part right. 32x67 type problem!!

The students complained to him that he should have told them there would be math and allowed calculators.

[Anonymous]

I've had kids in both public and private and here's my two cents. The problem isn't the advanced math itself, because some kids actually do well with the additional challenge. The problem is when parents and kids think they *need* to do advanced math but the kids aren't really ready.

Half of this perceived "need" is really status. ("Johnny is in advanced math, how about little Mikey?")

And half of it is a legitimate (I think) parental fear that if little Johnny doesn't get on the advanced track in 3rd grade, then he won't be a candidate for advanced math in later grades (because you can't easily skip from on-grade math to above-grade math). And ultimately he won't get into the college of his choice.

My kid has been guilty of this as well - he pushed us to meet with the head of school to get him into advanced math. I thought at the time, and I still think, it was partly a status thing among the kids because he'd tell us stories about how so-and-so got in so he wanted to be in too. He's now in the Takoma math magnet and getting As, so there was something there, but I'm not ruling out the status aspect either.

[Anonymous]

Until the public school system recognizes their deficiencies some children get around the poor grounding in mathematical fundamentals, problem solving and critical thinking by joining outside math clubs and circles where the focus in on solving really cool, hard problems using a variety of techniques (e.g., trial and error, number theory, algebra, counting and probability and geometry). The only calculator permitted is the brain.

As a Coach of a few of these math teams, and a father of kids that love math, I haven't encountered any of these kids accelerated (by up to 4 to 6 grade levels) in the grade-inflated, superficial and watered down public school math instruction (e.g., MCPS) fail at the College level (in Math, Physics or Engineering). These problem-solving math clubs are part of an extracurricular mafioso that unconsciously corrects the deficiencies left behind by poor math instruction in MCPS ( an unintended consequence since this in not the primary objective or goal or solving fun, cool and hard problems).

Until the private and public schools can solve the general inadequacies of math instruction parents and their children have other options including actively participating for the longterm in a variety of problem-solving math clubs and circles outside of their school sytems. It's just as easy as doing the same in an outside music, swim, lacrosse, tennis or soccer club...and much less expensive.

[Anonymous]

There is absolutely nothing inherently wrong with math acceleration. Some kids will need it. The fundamental problem is math teachers, parents and children have no clue which kids benefit from acceleration and which kids will not. A case of the blind leading the blind.

Athletic coaches understand this concept much better than MCPS math teachers and their constituencies.

[Anonymous]

Parent of a child who did 2 separate 1 year skips (once @3rd and once @5th). And, another child who has done one skip @1st grade.

Kids who accelerate in math are entirely capable of doing the math if it is taught, but my view has come to be that the teaching is extremely weak. Our family has experienced teachers who regularly give incorrect answers in class and on homework, and teachers who teach methods of problem-solving which have more to do with mimicry of a process rather than understanding the underlying math (see article's point 2 above).

It isn't that accelerated kids are capable of understanding, it's largely that they have not been taught the math principles and have not been given enough problems to see the variations and their own tendancies for mistakes. I must continually re-teach certain problem types (fractions, scientific notation, algebraic manipulation, decimals, unit conversion) at home. Other kids in the accelerated class who don't get this re-teaching doubtless have problems in acceleration.

I also agree with PP that calculators are a BIG problem (their use starts in 3rd or 4th grade). There is really no point in having a 3rd grader use a calculator -- it's counterproductive. I forbid calculator use on elementary school homework in our class. If our children want to use the calculator, they have to do the problem first and then check it with a calculator.

As for #3 in the article -- the concepts themselves are hardly developmentally inappropriate. Just as there are some kids who are reading at age 3 (yes, it does happen), others are not fluent readers until 7 or 8. Same goes for math. The problem is that the acceleration or compacted class is usually just pushed straight down without any thought. For example, my 2nd grader in a compacted 3rd/4th grade math class was asked to do mean/average calculations in the 4th grade segment one quarter before division was taught in the 3rd grade segment. Frustrating to say the least. Some thoughtful re-ordering of concepts thru the year would have been more sensible. But, that's not allowed by MCPS (or the teacher isn't clued in enough to do it).

There are other problems w/ what is developmentally appropriate in terms of pencil-skills. A first grader normally doesn't have the physical pencil skills to write arrays illustrating division or multiplication problems with numbers over 20 or 30. But, give that same child a Montessori-style bead array board, and the multiplication and division problems become much more do-able.

And, finally, another problem with "compacted" classes is that the teacher will often just simply not teach the additional material if he/she is running out of time. This means in a combined 3/4 class, the 4th grade material might not get taught in one unit, but the teacher will still move on to the 4th grade material in the next unit as if he/she had taught the last.

[Anonymous]

To 10:53 you said ... " The only calculator permitted is the brain."

Do you believe that if a child can not learn their multiplications tables (which is true for many dyslexic kids) that they do not belong in your clubs or higher level maths?

[Anonymous]

To 10:53 you said ... " The only calculator permitted is the brain."

Do you believe that if a child can not learn their multiplications tables (which is true for many dyslexic kids) that they do not belong in your clubs or higher level maths?

No, I do not believe the child you describe "does not belong in math clubs or higher level maths." Like with the beginning of the year fitness club memberships, staying power on the math club circuit is similarly driven by discipline and dedication to working through solving increasingly more difficult problems requiring more thinking about the various simple and elegant strategies to a solution rather than brute computation. In this regard, one doesn't need an additional calculator beyond the human brain -- even to tackle mundane standardized exercises like the PSAT and SAT.

I agree with a previous poster. The use and dependency on calculators in primary and secondary school math education has crippled the average student's mathematical skills (computation, critical thinking, and problem solving) and dampened our children's appreciation for the beauty of mathematics.

Calculators in elementary, middle and high school math classes are absolutely unnecessary towards a confident mastery of mathematics, intuition and number sense. In fact, the inappropriate current use of these enabling devices guarantees lack of mastery by high school. I, too, forbid my children from using these devices and they seem to thrive more nimbling than their handicapped calculator keyboarding peers.

[Anonymous]

14:44 - I don't quote because posts get too long.

I agree but I think you lose a bunch of students because they get the big red X on their assignments over simple adding and multiplications mistakes which frustrate them to no return. They could probably move past that stage to a higher form of logic and understanding but the kids that don't finish their 100 problems in 60 seconds aren't invited.

I do not let my kids use calculators but they do have a multiplication table near by so they don't get frustrated by the fact that right this second they can't remember 7x8 which catpults them out of deap logical thinking.

Of course if you went for a fitness membership and they told you you could not move on to the other equipment until you showed them you could run a mile in 7 minutes without your ankle brace because I am sorry you have a weak ankle but we want you to prove you are fit before we move you forward. You explain you are there for the spinning class and what does that have to do with your ankel and running fast. They say - We know it is crazy but it is part of our policies and procedures and there is liability you know. You would probably quit even though you could do it. You don't think kids feel that way sometimes.

Yea - and there are some kids that will run on that bad ankle through the pain - but think of all the kids you lost on the way.

[Anonymous]

What did American kids do before the calculator? While I do not have a PhD in mathematics there were no calculators when I was growing up. In fact, when I got to higher level science the slide rule was the mainstay and I became quite adept at using the slide rule. I do not think my mathematics education suffered because I lacked a calculator (not yet invented). Today, many countries beat the pants off us in mathematics. Many of these countries are poor and their children simply can't even afford one of these devices. It's certainly ironic the explosion of calculators of all colors, hues and shades in our wealthy and rich country also coincides with the abysmal performance of her children in mathematics. The calculator is not the answer to our problems in math. On the contrary, putting this device under lock and key for elementary and middle school kids will go a long way to reversing current performance trends in mathematics.

[Anonymous]

What did American kids do before the calculator? While I do not have a PhD in mathematics there were no calculators when I was growing up. In fact, when I got to higher level science the slide rule was the mainstay and I became quite adept at using the slide rule. I do not think my mathematics education suffered because I lacked a calculator (not yet invented). Today, many countries beat the pants off us in mathematics. Many of these countries are poor and their children simply can't even afford one of these devices. It's certainly ironic the explosion of calculators of all colors, hues and shades in our wealthy and rich country also coincides with the abysmal performance of her children in mathematics. The calculator is not the answer to our problems in math. On the contrary, putting this device under lock and key for elementary and middle school kids will go a long way to reversing current performance trends in mathematics.

[Anonymous]

Of course if you went for a fitness membership and they told you you could not move on to the other equipment until you showed them you could run a mile in 7 minutes without your ankle brace because I am sorry you have a weak ankle but we want you to prove you are fit before we move you forward. You explain you are there for the spinning class and what does that have to do with your ankel and running fast. They say - We know it is crazy but it is part of our policies and procedures and there is liability you know. You would probably quit even though you could do it. You don't think kids feel that way sometimes.

Yea - and there are some kids that will run on that bad ankle through the pain - but think of all the kids you lost on the way.

I think you missed the poster's point. Don't overthink this and fake yourself out. With the new year comes resolutions to get fitter and a brand new gym membership. In January many will come to the gym regularly but as we move into February the eagerness and keenness wears off. We start to slip and gym attendance dwindles. The dedication, discipline and stick-to-it ness simply fails us. I believe this was the simple point the poster was making. Math club activities requires the same level of commitment to get the results desired.

[Anonymous]

Of course if you went for a fitness membership and they told you you could not move on to the other equipment until you showed them you could run a mile in 7 minutes without your ankle brace because I am sorry you have a weak ankle but we want you to prove you are fit before we move you forward. You explain you are there for the spinning class and what does that have to do with your ankel and running fast. They say - We know it is crazy but it is part of our policies and procedures and there is liability you know. You would probably quit even though you could do it. You don't think kids feel that way sometimes.

Yea - and there are some kids that will run on that bad ankle through the pain - but think of all the kids you lost on the way.

Wow!

[Anonymous]

Thank you for linking this article.

[Anonymous]

I have a degree in Math. We programmed all our problems after the elementary levels of Math like calculus, diverential eq and linear algebra.

The idea that advanced Math needs to just be able to do calculations in your head is silly.