POSTED ON BEHALF OF DOUG

Not just to clarify the finer points of a new lesson but also to motivate students that a new topic/lesson is important and interesting. It need not come first.

Students can be given some triangles to mesure and told to square the sides then add them up and record them. They will “discover” that the square of the hypotenuse of a right triangle is = to the sum of the squares of the 2 adjacent sides.

The teacher can then say “amazing isn’t it but I didn’y figure this out Mr Pathagoras in ancient Greece did.” The teacher can then explain the concept in some detail work out some examples collectively with the class and then assign some problems to the student. I don’t care much if it is cooperative or individual learning at that point some individual homework will ensue.

Discovery learning, teacher directed learning, cooperative learning, individual learning all in 35 minutes.

This is how it generally works.

Mr. Churchill is a fascinating example of someone who learned by the road less taken,  but routinely trod by those who didn’t get it the 1st time, the 2nd time, and yes a third time in his day. I remember a few immigrant students from Calabria who learned English in a similar manner and finished school at grade 8 with a working knowledge of both English and arithmetic. This education proved sufficient to support their passage in a far more practical world, 50 years ago.

In juxtaposition, we have discovery learning, teacher directed learning and cooperative learning techniques which appear to have similar validity.  I won’t dismiss them. However, on a once through basis, which of the methods is the most effective? 

Perhaps neither because of the broad range of learning speeds of the very heterogeneous student population.  It is around the subject of “repeating” that the face of the “social equity” philosophy rears its head, and the least harm principle is set aside to fit the perception of what is most “socially equitable”.  Instead of re-framing the system to accept a longer and a shorter path to the goal along with much more diversity in teaching methodologies, this potential breakout point tends to be frozen into a political battlefield. What ideological nadir lies on the other side of the river “and/both” for the educratic ideologues ?

Better to engage in fighting full pitched battles between artificially polarized teaching strategies.  Instead of recognizing that there are different techniques which work best for different people and more accurately defining these populations to perhaps arrive at a better overall problem solution; we generally see the education system and its symbiotic unionized workers deflect the issue into the simplistic divisive “either/or” formula, rather than “and/both”. In Animal Farm it went “four legs good, two legs bad”. 

POSTED ON BEHALF OF DOUG

The urge to make education more efficient often works to make it less equitible. That is why reforms to streamline education end up streaming education.

The system in Canada today has produced the only society on the planet where more than 50% are getting a post secondary education. You may think that 50% is low as I do. I look forward to the day that it is 70-75%.

Nevertheless, our 50% system means we are better than Shanghai, Korea, Finland, Japan, Isreal, New Zealand and especially the USA.

Postponing streaming as long as possible is good policy as is ECE, small classes…. all of which help us reach forward to 75%.

Doug, your Pythagoras example demonstrates exactly the opposite of your argument. 

The Pythagoras theorem could be the first dip of a toe into an ocean of mathematical beauty.  There is huge scope for teaching Ms Christodoulou’s segments:  Historical (geometry in historical context, the sign over Plato’s school door), Theoretical (prove the theorem, and demonstrate the idea of a proof), and Empirical (perhaps find the distance between opposite corners of the classroom). 

Instead, you would ask students to play with their constructives and ‘discover’ the sum-of-squares rule as an odd, disembodied fact.  How little we expect of our students. 

A pox to Constructivism - If any parent read the following paper, one would learned why the classroom educator are very hesitant in answering your questions. I even found out why they are hesitant to answered the question, why their kid can do the complex, but not the components to the complex. Its how my youngest passed her math tests in the primary grades, just barely but passed nevertheless. Apparently, according to the paper, its due to a poorly instructed lesson…..ergo, the responses from the educators take the form of the child doesn’t want to do simple or the child is doing it on purpose or some other reason that explains poor performance.

” CONSTRUCTIVISM IN THEORY AND PRACTICE:
TOWARD A BETTER UNDERSTANDING “
http://people.uncw.edu/huberr/constructivism.pdf

Of course when one throws in the equity and social justice pedagogy and practices, the child who does not want to do simple, is transformed to a child who is having a cultural identification crisis because the child has not been exposed to mathematics in a way that is culturally relevant to the child. Meanwhile, in the cognitive and learning sciences world, its a pretty good chance the child is suffering from poor instructional practices, and secondary reasons could be a learning disability.

Over on another blog, “So how have we got to the puzzling situation where many modern progressives have aligned themselves with ultra-elitists in restricting high culture to the elite? It’s too simplistic to laud ‘traditionalists’ and blame ‘progressives’. The puzzle of how knowledge became toxic is better explained like this: it’s postmodernism, with all its scepticism of the value of truth and knowledge, rather than progressivism, that is the culprit.” - See more at: http://www.guerillapolicy.org/education/2013/06/16/which-ideas-are-damaging-education/#sthash.GFOqHK7n.dpuf

To which, as Doug has stated, efficiency makes it less equitable, and to which, since my youngest has been a victim of this type of thinking - its called, ‘Let us all pretend we have equal abilities and skills’, but since efficiency cannot entered the classroom, only the best and brightest will have a decent education. Then Doug, is using Ontario data, and implying it to all of Canada, and I do think its a honest mistake. In Ontario, 30 % of students are entering university, and another 20 % into the colleges. No data for the skilled trades, but in reality across the provinces, close to 75 % of grade 12 graduates are entering post-secondary,  for the reason most jobs now require some type of certification. The grade 12 diploma is rapidly become worthless, and as such something should be done.

At the Cumudgeon blog - ” I believe that mathematics should be taught, not collaboratively explored; algebra and geometry are better than a vague course of Integrated Math; spiraling doesn’t work nearly as well as learning it properly the first time.”  He writes, “
She’s pretty much nailed it. Here’s my take on it.”
http://mathcurmudgeon.blogspot.ca/2013/07/seven-myths-of-education.html

A PDF file entitled - Myths About Direct Instruction. It starts off - “Critics have damned and demeaned the Direct Instruction philosophy…..........”  Its pretty good example of how the progressive public education stakeholders treats the cognitive and learning sciences of the 21st century. Oops, can’t have the whole class learning and steadily achieving can we now??
http://www.nifdi.org/pdf/ch3_engelmann_adams.pdf

Another paper, “Ten Faulty Notions about Teaching and Learning that Hinders the Effectiveness of Special Education.” Here again, the progressive public education stakeholders slaps the cognitive and learning sciences out of the classroom, and in comes some type of constructivism so everyone will equally share space at the bottom of the achievement charts.
http://www.updc.org/assets/files/professional_development/uspin/RS-2012-Heward-Artlce.pdf

Lastly, a blog called Pragmatic Education.  It gives some hope, that there is educators out there plugging away….............  http://pragmaticreform.wordpress.com/

Nancy provides a useful list of citations arguing that Direct Instruction should be more effective than Discovery (thank you). 

Here’s a paper that tested the proposition empirically:  “We found not only that many more children learned from direct instruction than from discovery learning, but also that when asked to make broader, richer scientific judgments, the many children who learned about experimental design from direct instruction performed as well as those few children who discovered the method on their own. ” http://pss.sagepub.com/content/15/10/661.short

The learning is effective in either method for successful learners, but the proportion of successful learners is much lower for Discovery.  That difference becomes a yawning chasm of cascading failure when the next lesson tries to build on the current one.

Read it for yourself, a pre-print of their paper is available at http://citeseerx.ist.psu.edu/viewdoc/download?rep=rep1&type=pdf&doi=10.1.1.137.8094

Can anyone know of empirical evidence to support Discovery?

I have never run across any empirical evidence to support the discovery approach.  What I have run across, and scads of it, within the public education ivory towers that the processes of discovery learning is far more important, then the outcomes of students.

My child, like the majority of children need the knowledge-building components for effective and consistent learning to occurred. How could the public education stakeholders be so against the instructional methods based on the science, that virtually benefits all students.

ugh, discovery.

How can I in good conscience set up my grade 9, 10 or 11 students to discover concepts that took the great minds of science decades to put together?  And the great minds of science were building on some strong foundations while still
working on ideas for years ..

Science students in high school need foundations and then an opportunity to apply those foundations in a lab setting.  This discovery nonsense was packaged by and for people with no understanding of how learning works .  A bit like the Daisy girl with her contrived anecdotals   masquerading as data driven science.

cheers. Mirka