slower math students in Singapore

from the Air report on math education in Singapore:

The topic structure in Singapore’s framework is efficient because topics are not taught and retaught as students move through the primary grades. Instead of repeating topics that students have already learned, teachers simply reintroduce them as a foundation on which to build new mathematical content. This practice, however, may not be suitable for students who have more difficulty with mathematics. The Singapore system recognizes that students who have trouble with mathematics may not attain mastery by following Singapore’s regular program of mathematics instruction and that these students may need special assistance to attain competence.

Beginning in grades 5 and 6, Singapore identifies its weaker students on the basis of a general examination of mathematics and language competency. These students receive special assistance and are taught according to a special fifth- and sixth-grade mathematics framework. This special framework mandates that students in the slower track

• receive approximately 30 percent more mathematics instruction than students in the regular track, and

• be exposed to the same mathematical content as students in the regular track, although at a slower pace.

The mathematics framework for students needing compensatory assistance adds review material to strengthen students’ understanding of previously taught content. For example, topics on numbers and geometry taught in grade 4 are repeated at a faster pace in grade 5. The introduction of some new concepts such as ratios, rates, and averages, which are normally introduced in grade 5, are delayed until grade 6 for the weaker students (Ministry of Education, 2001a). What is important, however, is that because slower students spend extra time studying mathematics, topics usually taught in grades 5 and 6 do not have to be completely sacrificed to make room for repetition.6

To support the framework for slower students, Singapore has developed a Learning Support Program to help educators identify these students and provide them with extra help (Ministry of Education 2003c). Mathematics Support Teachers (MST), who receive on-the-job supervision and specialized training to ensure that they are professionally competent, deliver compensatory assistance.

In the United States, we expect all students to meet the standards in state frameworks, but the standards do not help teachers address the needs of slower students. In fact, U.S. standards do not acknowledge that students learn at different rates. No Child Left Behind addresses the needs of failing schools, but it does not directly require that failing students receive help. Although some research evidence supports the belief that students benefit when the curriculum is adjusted to match their ability levels (Loveless, 1999), a distinct alternative curriculum would raise concerns in the United States about potential harm to students from ability grouping. Singapore’s approach differs from traditional ability grouping in that Singapore establishes a framework that requires students to master the same content as other students, not a watered-down curriculum as often happens in U.S. ability grouped classrooms. Singapore also provides extra assistance from an expert teacher.

What the United States Can Learn From Singapore’s World-Class Mathematics System: An Exploratory Study (and what Singapore can learn from the United States)

Apparently teachers in Singapore do not deliver 10-minute mini lessons followed by 40 minutes of one-on-one work with the students who are "struggling."

A really bad idea I hadn't heard of

In today's Wall Street Journal:

Assemblywoman Nancy Calhoun, a Republican of Orange County, introduced a measure mandating that school textbooks of all subjects be authored by current or former New York schoolteachers. The bill memo says that such a law would help "provide equal and balanced learning opportunities for K-12 students" and cut down textbook costs by up to 80%.

No Elephant in the Room With These Laws
by Jacob Gershman
APRIL 25, 2011

A law that would actually make it illegal for New York school districts to adopt Singapore Math.

Or any textbook written by an actual mathematician.

Education in Singapore -- the role of good teachers

I found an adorable video on the Singapore Ministry of Education's page. Blog post and video discussing the role of teachers in education is on Throwing Curves: Education in Singapore - the role of good teachers.

what is ACTION?

What do student leaders grow up to be? It strikes me how national political disconnects and the microcosmic political disconnects within an umbrella student organisation are really quite similar.

One disillusioned leader of a cultural organisation here at UVA told me that student leaders' effectiveness here is judged not on the amount of grassroots organising and day-to-day organisation building they do, but on how many glitzy events they throw for their organisation. Did you help your organisation throw three big parties last semester? Awesome, come join this secret society, dedicated to public service and troublemaking in a cool way (but whose day-to-day activities consist of partying, as I am told).

Meanwhile, the many grassroots leaders who work to strengthen routine, day-to-day connections (e.g. between high school students and undergraduates) or gradually build connections overseas (e.g. those behind ThINK / "There Is Hope In North Korea") get little press coverage.

When we talk about ineffective politicians, programme organisers, or education administrators, we should consider where they come from and what was encouraged/promoted in their youth. Perhaps we should also consider what repels capable individuals of suitable character from public service. Some of it is inherently human nature: it is easier to direct public and press attention to big, one-time events rather than day-to-day work. It is also the way, I suspect it works in politics, from school districts to national governments. Before the US did economic stimulus payouts, this was a routinely Singaporean thing to do to convince Singaporeans that the government was doing *something*.

Consider that the name of the Ministry of Education teacher who introduced bar modeling (among other key innovations) to the Singapore primary math is virtually unknown -- his name can be found on a comment thread in this blog, if you search hard enough. The opinions and the authoritarianism of Lee Kuan Yew are celebrated while the intellectual philosophy of the guy who really helped build Singapore, Goh Keng Swee, is rarely mentioned in current Singaporean political discourse. Among the key members of the Central Committee of the People's Action Party, I feel that Goh Keng Swee was the true George Washington -- he retired from public service in 1984 after having spent four decades in the civil service, quietly building the Singaporean economy and education system. Many Singaporean teachers believe he is the true reason why Singapore went from "third world to first".

Meanwhile, Lee Kuan Yew (who loves the limelight) frequently goes on radio and television to tell us how Western liberal democracy is inappropriate for an Asian nation with Asian values, or to make shocking comments about what he thinks about Indians and Malays compared to Chinese, or how Chinese dialect use should be actively suppressed in favour of Mandarin.

With that in mind, we should also beware dismissing those leaders who do real behind-the-scenes work but get little attention for what they do, while unwittingly promoting those leaders whose success has been built by the flashy.

Yet still.

---

During spring break, I (with two dozen other members of above-mentioned cultural organisation) went to UPenn to attend conference aimed at Asian-American activists, leaders, grassroots organisers, et al. which occurs every year. 1400 students there, all for noble aims (in addition to fun). The workshops reinspired me to recommence initiatives that I had gotten discouraged to pursue, and one workshop facilitator (spoken word artist Kelly Tsai) was very good at intimately connecting with participants, even with 30-40 people in the room. She is the type that would make a good teacher -- it goes beyond extrovertedness, as mentioned in the recent NYT article.

However, there were a lot of organising hiccups. The "grassroots" feeling was lacking; the organisers felt distant and unapproachable; my group was shut out of the Irvine Auditorium where the massive opening ceremony was being held, because they had run out of seats and the unionised Penn staff would not allow for standing or even use of the upper balcony. There was little visible effort to maximise what we took away from the workshops, e.g. foster post-workshop discussion after the workshops themselves ended.

Having 1400 students from dozens of schools ranging from MIT to Johns Hopkins to University of Florida in one place -- some of them graduate students already involved in teaching in low-income areas, immigration law, racial discrimination issues, etc. -- is a big opportunity! It's an exciting chance to build a really strong and effective grassroots network. But there were little efforts to mix up the cliques. 500 participants alone must have been staying at our hotel (we squeezed 8 people a room). Apparently when you pack 80 active, passionate youth leaders into a hotel lobby at a time, the thing that should dominate discussion as you wait for the elevator is what room the party is at, who's getting the alcohol, or which frat you are going to hit.

There are always hiccups in every event. But this is an annual event that has gone on for nearly 30 years (albeit at different schools). At the closing ceremony, the organisers spent 15 minutes making speeches congratulating themselves ("To the 20 members of the X&Y Committee, it wouldn't have been possible without you!") and how the Penn chapter had worked on this for two years. Which is fine, I guess. It would have been nice to have sounded more receptive to feedback -- I totally did not get the "tell us how we can improve!" vibe from the ceremony.

Why are some leaders or teachers effective, even "miraculous"? I believe it's their constant search for self-improvement... a trait a Teach for America consultant has noted as well. They are always looking for problems or hiccups to fix.

But I wonder how many conferences go on similarly to the one I attended, even when they aren't student-run. Take teacher workshops -- if you brought 1400 teachers from all over the country into one place, what could they achieve? But what do they achieve, usually?

A Singaporean perspective on Singapore Math

I recently came across an online article by a Singaporean named Justin Lee, the founder of two education businesses in Singapore. In reaction to many articles "fussing about Singapore Math on the Internet," Lee writes:

While many authors bemoaned or even whined about the difficulty American kids had with Math, it made me at times sympathetic or even amused. You see, Math in Singapore was highly enjoyable in my time and we dreaded other subjects like English and Science instead. Why is this so?

One reason, Lee points out, is that, for about 50% of the Singaporean population, English is not the native language. As a result:

Math in primary school (for 7-12 year olds) was one of the easiest subjects to ace. It did not involve language application as extensively as Science. Although the word problems in Math papers still involved the English language, it required us only to write one-liners as conclusions. Many friends of my age then scored above 80 marks out of a 100 in Math on a regular basis. Being able to score so highly in Math (as opposed to barely passing English or Science) easily made Math our favourite subject in school!

This, of course, makes me think of all the language impaired math buffs who suffer under Reform Math's much more language-intensive "story problems" and verbal explanations requirements.

Lee goes on to lament a development in Singapore that is taking math standards in Singapore in the opposite direction as that which American math standards have followed. Apparently, "there has been a rising trend of schools setting impossible-to-pass Math tests and examinations in the late 2000s." Instead of parents being upset that standards are too low, Singapore parents are upset that standards, which have long been higher than ours, have now risen too high.

Lee proceeds to describe how he and his classmates found Singapore math to be easy and enjoyable, with plenty of time left over for fun:

It is true that the Mathematical concepts are built year upon year and concepts that have been taught are not taught again, but merely revisited briefly. This is as opposed to the slightly incoherent system in the US, where kids can sometimes wonder why they are doing the same things again. While this arrangement may appear to be harder on Singapore students, I actually felt it was very easy on us. In fact, we felt that it was a gift from heaven to be able to do fractions at primary 6 again, right after we learnt something similar the year before.

It might appear as though a Singapore student would have had to spend many hours poring their beady eyes other Math textbooks and Math problems to acquire such ‘astounding’ proficiency in the subject. The truth is, the pace of learning was rather fine. I could do quite well in school without having to attend extra lessons (tuitions), and school only lasted from 730am to 1pm, Monday to Friday. There was still ample time for monkey business after 1pm.

To sum up, I am positive that Math in primary school was enjoyable for most students in the 1990s. This may not be so after internal Math examination standards were revised upwards in the late 2000s, but we shall address this issue in another article.

I look forward to more! In our self-absorbed, American-exceptionalist country, the Singaporean perspective, which should be a key element in the debate over math reform, is all too often overlooked (le radical galoisien?).

a math class of 41 pupils

Ms. Sherry Tai, my young Singapore primary school math teacher (I think she was in her mid-20s) formed a personal bond with each one of us 41 students. 40+ students is a pretty typical class size at the primary and secondary school level. She was also our science teacher, our form teacher and our PE teacher, though plenty of other teachers taught our same class.

I remember her well because I was a "problem student" (partially because of my harebrained personality, partially because I had come from American middle school...) and she frequently confronted me about my performance.

What was her math class like? Ah, I remember sometimes she would be marking workbooks (and we'd be doing some other work, like practice problem sets), and she'd call people up individually about their work.

Being the problem student, I would be frequently called up of course. Being called up was annoying and sometimes intimidating because she'd be like, "why did you do this problem wrong?!" and you'd be like, "huh? I don't see what I did wrong?!" but then you'd be hushed with her explanation and sent back to your seat to redo the problem.

I'd feel sort of smug when the prefects and class monitor and monitress (and other model students) would get called up, and I wouldn't. Ahh, incentive for doing good work! As I got the hang of Singapore Math, I found myself being called up less and less. The dreaded 5-point word problems became less like monsters and more like delightful challenges I tackled with confidence. One thing that didn't seem to go away however, was my tendency to forget to bring some little thing to school (like say, a worksheet, an arts and crafts item required for that day, sometimes stationery, like correction pens...). A problem I suffered in American elementary school. A problem also suffered in college.

And oh yeah, correction pens. Let me tell you about those. In Singapore, stuff is often done with three sorts of pens. You need to bring a blue/black pen, a red pen, and a green pen to school. This colour requirement caused me endless grief initially (after moving from America) because I would have a knack of losing pens, or just not bringing all of them. But why this colour scheme?

Well, let's say you're doing a math workbook. You do the problem in blue/black ink. Your teacher (or your classmate) marks it in red ink. Sometimes, you do the marking for others, so you also need a red pen. If you get a problem wrong and receive it back, you're supposed to do the correction in green pen. (This scheme also readily applies to science and language work...) You do this for workbooks, worksheets, mock exams, real exams (after you get them back). You even do it for group work (dun dun dun). The colour scheme helps you keep track (and organise) about what you did wrong, and what you did right.

When I moved from America of course, I was not used to this system, so often I'd return marked workbooks without doing all of the required corrections, or I'd do the green pen corrections wrong, which usually resulted in a sharp call for "John Soong! Up here please!" every math class for the first few weeks. Yes, the corrections are supposed to include your working. (Didn't know that at first.) Yes, doing corrections in green ink for a 5-point problem you got 4 points off of was tedious.

Now, I actually have little idea what "rapid formative assessment" is supposed to mean rigourously. We had plenty of "assessment books" though, and as the PSLE approached, she made us buy additional assessment books on top of what the syllabus required, just so she could have the enjoyment of marking more of our work. Oh, and she would schedule remedial classes afterschool. For all 41 of us. ("Unless you had a 100 on your CA2 [no one did], you have to attend.") And by now, I'd faithfully do the problems, the working, the corrections (which became fewer) ... but forget things like the $2.50 I was supposed to bring to pay for the extra book, some parent's signature required for the remedial or the Edusave form. I think in one term (about two and a half months) I'd generally accumulate ten infractions.

None of the classwork was really graded. I can't remember the exact breakdown, but I think it's like the 2 CA exams account for like 30% of your grade and the two SA exams account for 70%. And the infractions ... well, other than being embarrassing, they aren't really life-changing. (What happened is that the group with the least amount of collective infractions at the end of the term won some sort of reward.) So I guess all those workbook problems were "formative assessments", sort of? Sometimes even one of the major exams (the CA1) does not have an impact on grade or has very low weighting (like 5%).

Does Singapore education have a cultural component? Prolly. But it's actually rather simple:

a) The work isn't graded. But teachers will nag you about it if you don't do it correctly. Incessantly. Even if you're only one out of 41 students.
b) It doesn't matter that the CA1 doesn't impact your final grade that much. It's just something you don't want to do badly on. Not only will the teachers nag you about bad results, so will your parents. And it goes on your report book. In fact your end-of-year grades don't affect your GPA, because GPA doesn't exist in primary and secondary school.

If you have a "bad home environment", your parents might not nag you about your performance, but there's still plenty of reprimand to face at school. In fact, my single mother almost never made me do my homework. My teachers did.