Yvonne I was responding to this point you made earlier:yvonne meyer wrote:Elsie, this is a good example of how you get confused about the point of schooling. TIMSS tests students @ Grades 4 & 8. At these Grade levels, the point of testing is not to see how many students have "advanced mathematical skills" but to see how many students have master the syllabus to a level that allows them to continue to access the syllabus subsequent years.If you think every pupil should have advanced mathematical skills, then Singapore still has a long way to go. If you need around 20% of pupils to excel in this area, then the UK isn't doing so badly.
Those figures are not the same ones as you subsequently quote, and the point you make has changed completely:The latest results from TIMSS (Trends in International Maths and Science Study, 2011)In case you miss the point, Singapore (most schools teach in English) was able to get 43% of its students into the highest level of maths whereas England was able to get a mere 18% of its students into the highest level of maths.Quote:
The five East Asian countries had the largest percentages of students reaching the Advanced International Benchmark. Singapore had 43 percent of their students reach the Advanced International Benchmark, followed by Korea (39%), Hong Kong SAR (37%), Chinese Taipei (34%), and Japan (30%).
Northern Ireland was next with 24 percent, then England, 18 percent, followed by a group of eight countries with 10 to 13 percent.
As I've pointed out before I am not defending or justifying poor maths teaching. However, in English schools the system doesn't work like that. A failure to reach an expected level of attainment doesn't mean students can't 'access the curriculum'. Maths doesn't work like that either. A low score in mathematical attainment in Year 4 doesn't mean the student can't make further progress, nor that they have 'missed the Education bus'. You are now displaying your ignorance about how the curriculum works - and about how knowledge works.At Grade 4, 6% of Singapore students failed to reach the level allows them to access the curriculum in subsequent years.
At Grade 4, 22% of English students failed to reach the level allows them to access the curriculum in subsequent years.So 22% of students in England, by the time they are in Grade 4, have missed the Education bus and will make no further progress in maths without intensive remediation which we know is rarely forthcoming.
Can we clarify something? Above, you said that 22% of English students 'failed to reach the level allows them to access the curriculum in subsequent years'. Now you are saying that 51% of them didn't attain 'high' or 'advanced' levels and suggesting that 'high' and 'advanced' levels involve understanding simple fractions. Are you sure about that?78% of Singapore students reach the 'high' and 'advanced' levels.
49% of English students reach the levels 'high' and 'advanced' levels.
Are you suggesting that 51% of English students are not capable of doing the basic maths required in Grade 4? Are more then half of all English students too thick to understand simple fractions and will happily go through life not being able to divide something in half?
Again, I am not defending poor maths teaching. But the question still remains of what proportion of students should be attaining high levels in Maths. What figure are we all aiming for and why?The results in Grade 8 are even more devestating for England.
By Grade 8, Singapore has 78% of students performing at the highest 2 levels while in England only 32% reach these levels.
No it doesn't.What I was commenting on was Old Andrew's perception of what constituted a 'good' maths lesson - that it would likely involve powerpoint slides, didactic teaching and would probably be boring. He clearly felt the algebra lesson was 'gimmicky' even though it was obviously a perfectly effective way of teaching children about algebraic notation. I think this says more about Old Andrew's understanding of mathematics than anything else.The perjorative language you use to describe effective teacher-directed instruction and the unfounded confidence you have in the 'discovery' method demonstrates your determination to advocate your personal beliefs and to disparage effective instruction.
If that's what Hirsch said, my only comment is that he doesn't understand child-centred education either. That extract is a sweeping generalisation if ever I saw one.Quoted from ED Hirsch
Child-centered schooling. (Sometimes called student-centered education.)
Educators preferring this philosophy believe they should "teach the child, not the subject." They reject the idea of lectures, drills, and rote learning because, according to them, it ignores the "feelings" and "individuality" of the child. Therefore, child-centered educators caricaturize anyone who favors a focus on subject matter as inhumane. Hirsch suggests that "on the contrary, ... children are more interested by good subject-matter teaching than by an affectively oriented, child-centered classroom. The anti-subject matter position is essentially anti-intellectual."
'Constructivism' is a well-established term for a biological phenomenon. It's quite possible that people who use the term in education don't understand it, but since the biological definition encompasses all types of learning (including rote, drill etc) all educational methods are constructivist by definition.Constructivism
This term is used to give progressivist education ideas a "spurious scientific-sounding authority." Proponents of constructivism suggest that the only knowledge worth acquiring is that which a student finds for one's self because it is more likely to be remembered and used. Hirsch recognizes that this kind of knowledge is useful. However, he also claims that "both discovery learning and guided learning" are actually "constructivist," so the term doesn't add anything to the discussion
I think that's what I said earlier. Except that I wouldn't agree about the goals - students often make discoveries they weren't supposed to make, but are perfectly valid discoveries.Discovery learning
This teaching method offers students projects to work on rather than textbooks to read. Teachers feel that students will be more likely to remember what they learn from the experience than they would from reading and regurgitating facts. Hirsh agrees that discovery learning plays a vital role in a child's education, however, he describes two serious flaws in using this method exclusively: (1) Students sometimes miss the discovery they were supposed to make and sometimes even make incorrect discoveries. Thus, a definitive goal must be set in the beginning. If the goal is not achieved, the teacher must use direct teaching. (2) Discovery learning is inefficient. Some students never gain the knowledge they were seeking, and even if they do the process is very slow and time-consuming.
Where did you get these quotes from? Not from Hirsch, obviously.