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.