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All these experiments involved rote learning, but Rohrer and Pashler have also found similar effects with more abstract learning, like math. This is particularly troubling, the psychologists say, because most mathematics textbooks today are organized to encourage both overlearning and massing. So students end up working 20 problems on the same concept (which they learned earlier that day) when they should be working 20 problems drawn from different lessons learned since the beginning of the school year. In brief, students are wasting a lot of precious learning time.
That's Saxon.
30 problems a day, no more than 2 on the same skill or procedure.
Day in, day out.
Extreme mixed review.
Which reminded me to get out my mixed review books:
Middle-Grade Math Minutes: One Hundred Minutes to Better Basic Skills
Doug Stoffel Creative Teaching Press 2000
www.creativeteaching.com
Mixed Skills in Math
ISBN: 1-56822-861-9
These are both for middle school, but you can find mixed-review books for all grade levels.
overlearning overrated?
how long does learning last?
shuffling math problems is good
Saxon rules
Ken's interval
same time, next year
remembering foreign language vocabulary
5 comments:
I had planned on doing Fast & Fun Mental Math (Grades 4-8) which covers the basics without being tedious. But now I'm left wondering if that will be enough to supplement a math curriculum based entirely on Singapore Math material. I'm definitely still sold on Singapore Math but if there's a way to make learning more efficient, I'm all for that.
I've just read the article -- I don't think this is "hard."
The article has a ratio for spacing study sessions (I'll post, but I also sent it to you).
I've also just pulled Rohrer & Taylor's "The shuffling of mathematics problems improves learning"
I do think that Primary Mathematics alone probably isn't enough, given Cassy T's comments about Singapore parents & society, as well as the comment left by a person who said parents provide their kids with a lot of drill and practice.
My guess is that there's quite a lot of distributed practice being provided outside the classroom.
(Cassy & knowledgeable others - if you've got time to chime in, please do!)
In fact, 20 (not so) different problems using "variations on a theme" can get quite tedious and boring, and afterwards you can just rush through the entire homework assignment (for you to forget the next week).
Catherine: Uncannily, that has also been part of the criticism by locals of the Singaporean system. Not criticism per se, but whenever the government boasts of what a good education system it has, or when someone defends the status quo of the curriculum, the rebuttal is often, "but there's so much tuition! How do you know it's the curriculum [govt success] and not us [parent success]?"
However, I'm a person who went through the system with barely any tuition whatsoever, and did quite well. I think I also have peers who don't take that much tuition (if any at all) and they do quite well too.
Of course, since I didn't take any tuition, I can't say how much tuition helps in general. Tuition isn't extreme, and sometimes students are hurt by tuition (because of incompetent tutors).
There is also peer culture: peer tutors and peer assistance. In primary and secondary school, in between staying afterschool to eat and play soccer, in between gulps we also copied each other's answers. (Which I think was mostly constructive since we showed each other how to do problems.)
Implementing a culture of tuition is possible if your school already has such a thing as a "Learning Lab" (as my high school does), then you can have an equivalent. In my opinion, paying a tutor 40 dollars an hour is unnecessary compared to the just-as-effective afterschool tutoring facilities that schools can bother to provide.
Teachers keeping blogs and requiring students to participate in them (like the Eat Your Maths blog I linked the other time) is also a very good way to continue practice afterschool.
I find blogging to be a medium of teaching that has yet to be even exploited. My friends in Singapore often keep blogs where you can share test answers (after they have been graded, of course) and homework answers, etc. Blogging is real-time where active communication can take place afterschool. (i.e. you don't have to wait till the next day to receive help on a problem)
My friends and their teachers often keep blogs where teachers and students often communicate with each other afterschool, if not with posts, then comments. I can see so many possibilities with this and I see it relatively unexploited even in Singapore, but there are so many ways you can be tutored via the internet.
And I don't mean that fishy "learn your degree online" sort of tutoring, since you maintain communication with people you will meet physically the next day.
So schools in the US can do a lot to replace Singapore's component of tuition.
Often I wonder what the effect would be if my high school simply opened the canteen afterschool for more than just a snack (it's open for a few minutes only afterschool). In Singapore, students stay back because they can eat first before they leave. Because so many stay back, soccer games can be organised, homework discussed, etc. Because so many stay back, the school has little problem in organising afterschool remedials.
So something as simple as food can impact something as fundamental as learning culture.
(Also the Singaporean schools usually employ a system of eight competing stalls, so the American complaints of not-so-good cafeteria food are not known here, because each stall competes for the student market, as well as specialises in each type of food. Some stalls are halaal, some serve drinks, some make roti prata and curries, etc.)
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