Britain is talking about teaching higher math only to the most capable students and teaching “functional” math — “maths that would equip students with basic numeric skills, such as percentages, measurement and estimation” – to less able students. But the test czars haven’t created a “functional” math test to go with an easier curriculum, complains John Crace in The Guardian. Students still struggle to learn algebra, even if they’re just not smart enough.
Or perhaps teachers should abandon their racist, patriarchal, monocultural insistence on right answers.
Paul Ernest, a professor at Exeter University’s school of education and lifelong learning, argues that traditional teaching methods disadvantage ethnic minority pupils, girls, students with special needs and those from poor backgrounds, and that considerations of social responsibility should be applied to maths teaching.“I disagree with people who think that mathematics is neutral and value-free,” he says. “It is human made, therefore culturally influenced, and this makes social justice central and relevant in mathematics.
“We need to think of different ways of contextualising maths to take multi-culturalism, racism and sexism into account. Students need to see that everyone owns maths, and that many countries have had their roles in the development of the subject downplayed. We need to make maths more democratic and discursive, so they are not afraid to suggest wrong answers.”
Not afraid? They’ll be guaranteed to suggest wrong answers if they’re taught multicultural mush instead of math. “Functional” math is starting to look good. At least it’s math.
Education Gadfly’s response is Bollocks!
Nearly every student can learn nearly everything if given the time to do so. The standard should not be lowered. However, students who struggle (research does support this) do best when they remain in at level curriculum, or even “above level,” “advanced,” with additional time to learn the material – either through a program like AVID or with a competent teacher in a guided study hall, taken concurrently with the at or above level course.
Sending kids “back” to remedial will likely garner the same results because the reasons they didn’t learn the higher level skills still exist; it’s not the material, nor, GOD FORBID, changing the answers (?), but modifying the instruction.
I’m embarrassed for educators at this insane “reasoning” out of Exeter. It’s ironic that the most logical of subjects, math, should be approached in such an illogical manner.
Paul Ernest, a professor at Exeter University’s school of education … “I disagree with people who think that mathematics is neutral and value-free,†he says. “It is human made, therefore culturally influenced, and this makes social justice central and relevant in mathematics. … We need to make maths more democratic and discursive, so they are not afraid to suggest wrong answers.â€
This is proof once again that a School of Education is an oxymoron. Paul Ernest is not an educator but rather an ideologue. The only result of his Leftist ideology will be to guarantee that minorities will not be able to succeed economically in society.
Thirty years ago I was the object of a tirade about the imperialism of mathematics by a nut-case Math Ed graduate student (that is, a graduate student in the School of Education specializing in mathematics education). She had long resented my presence at a lunch-time seminar run by the psychology department and one day she snapped. I was the only “hard science/math” person there, and one of the only males, so I felt pretty nervous when she started yelling, but fortunately the woman running the seminar told the young woman yelling to “Shut up”.
I’ll probably always remember this incident because it passed through my head that this crazy woman was going to go out into the world and spread her nasty, stupid ideas, and by golly, the ideas have spread. I felt like a mini-John Galt at that moment, except that I figured that if people actually listened to this woman, the world would stop itself…
Richard – deciding to judge all schools of education by one person makes as much logical sense as Ernest’s suggestions regarding math instruction. Some schools of education are oxymorononical in nature, and as is the case in many institutions (whether they be of the private or public sector), metaphorical inbreeding creates environment perfectly calibrated to in turn breed genetic ideas destined to fail. That being said, penicillin came from mold. Every problem contains its own solution, and most solutions – whether from you or Ernest – are not going to come from gross over-generalization, however justified the frustration they represent may be.
AN environment. Must proofread before posting. There’s a logical idea we can all agree on.
Z,
There’s plenty of evidence that schools of education are largely intellectual wastelands. Habitat for Stupidity is headquartered in them thar hills.
As fascinating as Ernest’s thoughts are, here is something at least as good:
Anna Sfard‌
Division of Science and Mathematics Education, Michigan State University, East Lansing
The interpretive framework for the study of learning introduced in this article and called commognitive is grounded in the assumption that thinking is a form of communication and that learning mathematics is tantamount to modifying and extending one’s discourse. These basic tenets lead to the conclusion that substantial discursive change, rather than being necessitated by an extradiscursive reality, is spurred by commognitive conflict, that is, by the situation that arises whenever different interlocutors are acting according to differing discursive rules. The framework is applied in 2 studies, one of them featuring a class learning about negative numbers and the other focusing on 2 first graders learning about triangles and quadrilaterals. In both cases, the analysis of data is guided by questions about (a) features of the new mathematical discourse that set it apart from the mathematical discourse in which the students were conversant when the learning began; (b) students’ and teachers’ efforts toward the necessary discursive transformation; and (c) effects of the learning—teaching process, that is, the extent of discursive change actually resulting from these efforts. One of the claims corroborated by the findings is that school learning requires an active lead of an experienced interlocutor and needs to be fueled by a learning-teaching agreement between the interlocutor and the learners.
It’s stuff like this that makes me want to find a billionaire backer and start my own school…
“It’s stuff like this that makes me want to find a billionaire backer and start my own school…”
Great idea! But are there any? Don’t the Wal-Mart heirs have 17 billion to spend on education as mandated by the late patriarch?
Big-money foundations seem to have fallen for the constructivist cult, e.g. Gates http://instructivist.blogspot.com/2007/11/radical-transofrmation-of-high-schools.html
Richard – deciding to judge all schools of education by one person makes as much logical sense as Ernest’s suggestions regarding math instruction.
One person, Zuzuzpetals? Indoctrination of students is part and parcel of the (re)education of students at schools of education. Trying doing a google search and you will see that it is not just one person or one school of education where this occurs.
Indoctrination, Not Education: Rampant Radicalism in the UCLA Graduate School of Education and Information Studies
http://www.bruinalumni.com/articles/gseis.html
Brooklyn College’s School of Education has begun to base evaluations of aspiring teachers in part on their commitment to social justice, raising fears that the college is screening students for their political views.
http://www.nysun.com/article/14604
“Dispositions†theory, increasingly in vogue in education programs, requires professors to evaluate their students’ commitment to concepts such as “social justice†and “diversity†in conjunction with their actual scholastic achievement.
http://www.thefire.org/index.php/article/7274.html?PHPSESSID=
The cultural left has a new tool for enforcing political conformity in schools of education. It is called dispositions theory, and it was set forth five years ago by the National Council for Accreditation of Teacher Education: Future teachers should be judged by their “knowledge, skills, and dispositions.”
http://ed.stanford.edu/suse/faculty/displayFacultyNews.php?tablename=notify1&id=439
The problem is idealogues, not whether they’re right or left. That was my point. You sound like Ernest, Nieporent, just shouting from the other side of the field.
“…We need to make maths more democratic and discursive, so they are not afraid to suggest wrong answers.â€
Fine and dandy, but that fool better hope the mechanic who works on his car’s suspension or the carpenter who works on the addition to his house both have a good working knowledge of the practical geometry involved. Otherwise, “wrong answers,” no matter how democratically arrived at, likely will be disastrous.
Bill
Nearly every student can learn nearly everything if given the time to do so.
Poppycock! Half of all children are below average intelligence, and all the teaching methods in the universe + time can help them only so much. See site
Does saying that you will die if you jump from an airplane without a parachute make someone an idealogue? What about saying that children don’t learn what they haven’t been taught?
I’m still choking on the supposition that “less able” does not mean “stupid,” although it’s proposed that the “less able” should only be offered “functional math,” whatever that means. As a cynic, I could assume that it means that great swaths of children are going to be assigned to a second-rate education, based on judgements made about them at a very early age. So much for education being the great equalizer.
I also suspect that in this new arrangement of pupils, “less able” will more or less mean “ethnic minority pupils, girls, students with special needs and those from poor backgrounds.” As a girl, I never had any difficulty with math, but then, no one tried to shunt me off into a separate track with low expectations. Of course, it seems that the upper classes, and many of the affluent middle classes in Britain have already fled the public system to private schools.
Bada Bing, you need to get on the phone QUICK. Sylvan, Huntington, and every private tutor in the country needs to be made aware of your brilliant insight. While you’re on the phone, you may want to call our local community college and see if they can do something about the scores of students who, for the last six years, have been obtaining their associates and then going on to obtain their masters with a guided study program. They began this program six years ago, based on a small group study of two years. Three groups, all pegged as incapable or unmotivated learners (how did you put it, below average intelligence?); one in remedial, one in at level, and one in at level with an additional guided study hall to assist with learning strategies. Guess which group had the largest percentage, by far, earning credit and continuing on? The third group … the one that was simply given more time in a structured manner to learn the material. Before you quit notifying all these slow learners who are unteachable, you might shoot at least an email over to the folks at AVID who have been employing this strategy successfully for years.
Finally, there’s a math guru in our state – first name Doug, who’s revolutionizing the way math is taught in high school. His motto is that kids don’t need remediation/simplified or dumbed-down instruction, they simply need more time with the same material. I’ll get his info because I know you’ll want to let him know how wrong his supposition is.
I cannot help but wonder what YOU do when you don’t understand something the first time you hear it or read it … but I’m sure with your sharp mind, that never happens to you.
No, Barry, saying that you are destined to die if you went to public school and ever go up in an airplane, because you know, anyone educated in public school wouldn’t have the sense not to jump from an airplane without a parachute. That would make you an idealogue. Saying that homeschooled children cannot be taught well because their parents are all crazy right-wing ultra conservatives would also make you an idealogue. The problem remains: idealogues with their own agendas which often have little to do with educating as many children as possible at the highest level possible.
Thanks for the correction, Zuzu. Given enough time at level curriculum with a competent teacher in a guided study hall, nearly every student can become an Einstein, Mozart or Newton. Got it.
Z,
Why do you claim that Richard Nieporent, BadaBing and Barry are all ideologues?
You may disagree with any or all of them, but so far you haven’t actually rebutted what they say.
I think you mean well, so I hope you’ll take these comments in the same spirit.
R,
Why I claim they are ideologues:
humorous explanation:
http://redwing.hutman.net/~mreed/warriorshtm/ideologue.htm
dictionary support:
http://www.m-w.com/dictionary/idealogue
I imagine I forget the most important rule of all, though, which is something about wrestling with a pig. For the record, I did rebut some of the statements in some of the posts, but I didn’t learn very much in the process, which is the worthwhile reason for coming to this site.
Point taken.
badabing,
given time at level and good teacher contact, yes, virtually student can learn physics and music. One confuses solid baseline material and genius breakthroughs at one’s own peril: one can stand on the shoulders of giants without being a giant oneself, as Newton Himself pointed out in the 1670s. Just as almost everyone can be taught to read, not just those in the upper 50%.
Your argument echoes a local superintendent who attacked a new school calling it discriminatory because there weren’t enough failing juniors. He ignored that outcome that the students who started below average were simply taught well.
I have seen the program that Z refers to called AVID. I observed an algebra 2 class. At least it was called that. The assignment for the day was to use the internet to do research on bridges. There was no formal algebra lesson. I suppose given enough time with some solid direction from the teacher and a good textbook, they might have gotten around to learning something called algebra, though whether it qualified as an algebra 2 class remains uncertain.
I have much research that I’ve read that I can refer you to regarding discovery learning versus direct instruction. I have also seen the results of very bad math programs. I do have my opinions and see nothing wrong with having them, particularly when they are informed by research.
I understand Z’s point about wrestling with pigs and it was therefore with some reluctance that I chose to write this entry.
Chris,
I think it’s clear that some people can understand more difficult concepts more quickly than others. For brevity I’ll call this “intelligence”, without getting into the details of verbal and quantitative measurements, and possibly others as well.
I suspect, mutatis mutandis, that not only will the more intelligent learn more quickly and go farther than the less intelligent, the less intelligent will also find that there are things that they cannot, practically speaking, master.
In other words, I doubt that learning is linear. I don’t think that the less intelligent, given enough time, can get to wherever the more intelligent are. I think that the difficulty of learning things increases very quickly once you hit your limit, so to speak; and this limit exists for all, whether your IQ is 90 or 150 or 200.
I want to be very clear that I don’t think that more intelligent people are “better” in any sense of the word.
Finally, a side point: Learning music is not the same thing as being Mozart (actually I would have chosen Beethove, but…).
I’ve addressed this “math is just a social construct” crap on my own blog. There’s a far left group out of Milwaukee, Rethinking Schools, that pushes this tripe, and I’ve “deconstructed” (actually fisked) their arguments at
http://rightontheleftcoast.blogspot.com/2005/07/math-for-social-justice-part-1.html and again at
http://rightontheleftcoast.blogspot.com/2005/07/math-for-social-justice-part-ii.html
Zuzuzpetals, since you seem to be so interested in the meaning of words, go look up ad hominem.
in a modest modern physics class, a below average student could learn, apply and be fluent in things that Newton never considered. (granted much less so for music and Mozart — or Beethoven, Ragnarok)
but they couldn’t take that class if they never progressed that far in science by being placed in the “less than 50%” track.
Certainly some students will learn the material faster, but that’s not reason to triage access or to dumb down the material. Long ago perhaps only the top 5% of people could read: no reason to keep old standards unexamined nor to think that they can’t be improved. The argument isn’t one of linearity, but a challenge to have good curriculum, good teachers and good support. It’s not rocket science.
ad hominem. What Southern cooks do to almost everything. AKA grits.
Barry, AVID is a program that teaches study strategies and makes sure that students who say they want to go to college actually enroll in college-prep courses. It provides tutoring and monitoring as they go through school. I’ve never hear of students taking AVID math or AVID English. They take the regular college-prep courses offered by the school. AVID has been quite successful for students who start ninth grade prepared to take algebra, which is the minimum level required. Sadly, many Hispanic and black students for whom the program was designed do not qualify as algebra-ready in ninth grade.
Long ago perhaps only the top 5% of people could read
I think you made that up. Of course, at some point in history, only a select group were able to read, but only because they were taught and the rest weren’t. They weren’t necessarily the “top” of anything, except luck. The ability to read really isn’t related to intelligence. Even kids with Down Syndrome can learn to read, although their comprehension will never equal that of someone with normal intelligence.
RN – I am fully aware of the connotative charge words like “leftist” and “ideologue” carry as well as “indoctrination.” I’m not sure I’m understanding your penchant for self-flagellation, though.
Can some us admit fear that whole classrooms of students of wide-ranging abilities are going to be slowed down to the least common denominator?
Without requiring some students to spend potentially large amounts of time outside of class, the only way to accomodate a wide variety of pacing levels would be to reduce the amount of material covered–which may be okay but then the superfluous material becomes enrichment for the fastered-pacing students and aren’t we right back where we were before?
The article concerns the UK, not the US. It outlines proposed changes to the UK math curriculum, to track students into an academic or a “fundamental” math stream. The argument seems to be, if a child will do poorly on the math exam given at the ages 14-16, why not teach them “fundamental” math instead?
The trouble, for me, is the sorting of children into academic and non-academic streams. I think the middle class children, and upper class children, will not be sorted downwards, because they’re the ones most likely to bolt the public system. It may be harder for the children of working class parents to persevere through to university, but I don’t think that they should be denied the chance to learn.
Chris,
I think you’re missing my point.
What’s important is the gap between the high-IQ and low-IQ students, not the difference between the stuff being taught today and the stuff that was taught a hundred years ago.
In a world with limited resources, triage is a necessity. (Streaming is more accurate than triage because it allows for more paths, btw).
You can give a low-IQ student the best coaching possible, but he’ll still do worse than a high-IQ student, mutatis mutandis. That’s nature – ain’t good, ain’t bad, it just is.
There is one exception to my thesis that high-IQ students will do better than low-IQ students; in ed-school circles, the reverse is immutably true.
Ragnarok,
I understand that you think I’m missing your point — that is what worries me. My point is that there is a need for far less triage (streaming) than currently occurs. With classroom structure that works, the strong student can and will excel … but the weaker student doesn’t have to be denied access. Moreover with good teaching and support, that weaker student can reach objective measures of competency. (even as that stronger student sails even higher)
Access doesn’t mean that all students are consigned to move as a convoy at the speed of the slowest student. Quite the opposite, especially with decent differentiation and strong professional support.
Sister Howitzer .. I absolutely did make up that number — debated whether to include the disclaimer in my earlier not that I don’t have accurate stats for the Middle Ages, despite reading Tuchman’s Distant Mirror long ago: 1 in 20 may even be generous. But you did peg the argument correctly: it’s very hard to learn what you’re not taught. Many skills, like reading, are broadly accessible to students — not just the upper half.