Can someone explain the Discovery Method?

[overthere]

It's not a case of this strategy or that strategy: teachers need to use them all because they all have their purpose.

Correct.

Gold star for you.

Unfortunately, Education Alberta insisted on the discovery method as the sole means of teaching elementary age children the basic math skills that will serve them their entire lives..

Fortunately, experienced teachers ignored(as usual) the dumb shit routinely promoted by people that should really know better. In the serenity of their classrooms, they employed a variety of methods to make sure their kids learned what they needed to know. Children learn in different ways, so good teachers teach in different ways to different kids in their classes. Imagine the horror of 'curriculum experts' at this notion!

[Big Guy]

But memorization is worthwhile for its own sake. Sort of like pushups.

For you math fans out there, there are other “fun” systems to the approach of mathematics;

There are other methods. For example;

Multiplying by 6

Rule: to multiply by 6: Add half of the neighbor to each digit, then, if the current digit is odd, add 5.

Example:

357 × 6 = 2142

Working right to left,

7 has no neighbor, add 5 (since 7 is odd) = 12. Write 2, carry the 1.

5 + half of 7 (3) + 5 (since the starting digit 5 is odd) + 1 (carried) = 14. Write 4, carry the 1.

3 + half of 5 (2) + 5 (since 3 is odd) + 1 (carried) = 11. Write 1, carry 1.

0 + half of 3 (1) + 1 (carried) = 2. Write 2.

It is an example of the “Trachtenberg system” ;

http://en.wikipedia.org/wiki/Trachtenberg_system

I played around with this system many, many years ago, surprising high school teachers and later winning a few glasses of milk in University pubs.

[socialist]

Memorization is a waste of time for anything higher than single digits.

It is far more practical to break larger numbers into smaller calculations that you can easily perform in your head. For example:

12 x 17: (10 x 17) + (2 x 17) = 170 + 34 = 204

or

7 x 23 = (7 x 20 ) + (7 x 3) = 140 + 21 = 161

So simple that even Pliny could do it.

Except, actually understanding the math (ie, the distributive property in this case) is harder for dumb-kids than memorizing stuff.

And dumb-kids go home to their dumb parents who don't understand the distributive property either, and their dumb parents get on Twitter and say "Look at this ridiculous 'new math' they are teaching Jimmy at school! What's wrong with memorizing the times tables? #whateverhappenedtothe3Rs" and pretty soon you've got a bunch of dumb old-people complaining about how stupid modern education is and how they were way smarter back in the day because they memorized the times-tables (but can't remember them anymore.)

-k

Exactly. Also take big numbers and multiply. For example 867 x 383. Do this to prove understanding.

800 x 300 = 24,000

800 x 80 = 64,000

800 x 3 = 2400

60 x 300 = 18,000

60 x 80 = 4800

60 x 3 = 180

7 x 300 = 2100

7 x 80 = 560

7 x 3 = 21

Add them all up and you get 332, 061.

[Mighty AC]

I just learned something new about standardized tests in Canada. 1) The tests conducted by each province are not even close to the same level of difficulty. 2) In Ontario Developmental Education students are exempt from the EQAO tests for obvious reasons, but are still tallied in the results with a score of 0, So schools with dev ed programs end up with lower scores.

[Michael Hardner]

This is the tired old "is our children learning ?" meme... which we've been hearing since the in-depth exploration of youth rebelliousness "The Wild One" was released just 61 years ago.

If it bleeds, it leads - the article references an elementary school slippage of 71% to 67% success, while downplaying an increase in success with high schoolers.

Yawn.

[cybercoma]

I just learned something new about standardized tests in Canada. 1) The tests conducted by each province are not even close to the same level of difficulty. 2) In Ontario Developmental Education students are exempt from the EQAO tests for obvious reasons, but are still tallied in the results with a score of 0, So schools with dev ed programs end up with lower scores.

Those aren't the same tests that are done by the OECD with PISA, afaik.

[waldo]

looks like Discovery may about to be, uhhh... concealed in Alberta! Those wascally Neo-Cons!!! What's a young socialist to do now? (I kid, I kid, hey socialist)

Edited September 20, 2014 by waldo

[overthere]

looks like Discovery may about to be, uhhh... concealed in Alberta! Those wascally Neo-Cons!!! What's a young socialist to do now? (I kid, I kid, hey socialist)

That one has been dead for a while, glad to see the coffin lid being nailed shut. The sanctioned demise of this initiative was rumoured about a month ago, before the Prentice ascendancy. In reality, it was DOA from inception.

A lesser cause was pushback from parents and some education pros, but the main reason was that teachers just refused to get behind it. Many continued to teach to the student and not adopt the 'one size fits all' mandated program. Of course, better teachers have always done this.

These fads happen all the time in primary education, though less often now in Alberta. Klein put limits on the % of funding that could be spent outside schools. This severely limited the endless bouts of 'curriculum development' at school boards. Although school boards (and individual schools) in AB have considerable autonomy, there are far less HQ buildings choked with far fewer deputy superintendents looking for something, anything to do.

[Keepitsimple]

If discovery was working as it should, kids should be able to be better at basic math - not worse. I learned "short math" only because I knew my tables. For example 51 x 19 might seem hard to do in your head but break it down like this and you'll have the answer in seconds:

51 x 10 = 510

510 x 2 = 1020

1020 - 50 = 970

970 - 1 = 969

Basically doing 51 x 20 and then subtracting one of the 51's. That's a much more "discovery" method......learn your tables and then discover ways to do "Short Math".

[Argus]

this one cries out for lil' socialist!

Wouldn't a teacher be better?

[Argus]

Rote learning is a waste of time. Long division is a waste of time.

Arithmetic is the foundation of Mathematics. If you can't do basic arithmetic (without a calculator) you're going to have some serious damned problems with Math.

Education in the modern day is about engaging students.

Education is about educating students. I'm not surprised you fail to understand this, though.

Engagement which does not succeed in educating is a failed endeavor.

the discovery method allows students to learn at their own pace.

Generally a slow one, evidently.

Memorizing times tables doesn't lead to understanding.

It leads to the ability to do numerous basic arithmetic problems quickly in your head.

Many of you are stuck in the way thins were done in the 50s.

Successfully, you mean? Yes, success generally does garner support. Just as the lack of success of modern teaching methodologies garners considerable criticism.

Too many people on here comment on education and think they are experts because they once went to school. That's like saying I'm a highway constructing expert because I drive on highways.

"Hey, Joe, your bridge just collapsed and fell down... again."

"Are you an engineer like me!? Then don't you dare criticize!"

"But your bridge collapsed."

"I'm a professional, damn it! You ignorant people can't begin to understand the complexity of my skilled expertise!"

"I understand the bridge fell down, you moron"

[Argus]

But learning happens in all sorts of ways and some people learn better by figuring things out themselves. It's kind of ridiculous to pose it as a Math War when a competent teacher would recognize that rote memorization has its place for building your thinking power just like abstract thinking does.

Wait, what? Are you saying Socialist isn't a competent teacher!?!?!?

[Argus]

Memorization is a waste of time for anything higher than single digits.

It is far more practical to break larger numbers into smaller calculations that you can easily perform in your head. For example:

12 x 17: (10 x 17) + (2 x 17) = 170 + 34 = 204

or

7 x 23 = (7 x 20 ) + (7 x 3) = 140 + 21 = 161

I do that all the time, naturally. But it requires the basic, almost instinctive by now grasp of the times tables I learned when very young. I.E., if you don't know immediately that 10 x 17 is 170 then breaking it down to that is rather pointless.

12 x 12 is 144. I don't even need to think about it. 6x7 is 42. It's virtually instantaneous. That makes it very quick and easy to break things down.

[kimmy]

Successfully, you mean? Yes, success generally does garner support. Just as the lack of success of modern teaching methodologies garners considerable criticism.

"Hey, Joe, your bridge just collapsed and fell down... again."

"Are you an engineer like me!? Then don't you dare criticize!"

"But your bridge collapsed."

"I'm a professional, damn it! You ignorant people can't begin to understand the complexity of my skilled expertise!"

"I understand the bridge fell down, you moron"

And what again is causing people to conclude that modern teaching isn't successful? Students have to learn a heck of a lot more nowadays than the old cranks who talk about "back to basics!" as if learning "the 3 Rs" and cursive writing were enough to prepare you for a career doing anything more than operating a cash register in 2014.

I do that all the time, naturally. But it requires the basic, almost instinctive by now grasp of the times tables I learned when very young. I.E., if you don't know immediately that 10 x 17 is 170 then breaking it down to that is rather pointless.

12 x 12 is 144. I don't even need to think about it. 6x7 is 42. It's virtually instantaneous. That makes it very quick and easy to break things down.

Yeah, but the point is that at some point memorization isn't practical anymore and understanding the underlying mathematics has to take over.

-k

[Topaz]

What I heard on the news , is that the Catholic kids, did better than the Public School kids, but they both, did poorly in Math. It was also said, part of the reason is the WAY the kids of today get the answer. So I'm thinking too many on depending on a calculator than reasoning it out on paper. The saying, "if you don't use it, you'll lose it" seems to be alive and well in schools.

[socialist]

Most of you have no clue; none.

Memorizing times tables, and forcing kids to complete drill and kill worksheets stymie creativity. Some of you need to walk into a modern school.

This is the future of math.

http://curriculum.org/secretariat/justice/index.html

Edited September 21, 2014 by socialist

[Argus]

And what again is causing people to conclude that modern teaching isn't successful? Students have to learn a heck of a lot more nowadays than the old cranks who talk about "back to basics!" as if learning "the 3 Rs" and cursive writing were enough to prepare you for a career doing anything more than operating a cash register in 2014.

How about personal acquaintance with high school grads? No, too narrow?

Well, the origin of this discussion is the math testing which showed that Canada's score slipped -- again. I think this is the third straight time, is it not? There are powerful movements of parents in numerous provinces screaming at their schools and governments that their kids aren't learning how to do math. I believe Manitoba has already responded to this. And I'm pretty sure the same complaints have been made about English.

http://news.nationalpost.com/2013/09/13/frustrated-professors-convince-schools-to-step-back-from-new-math-and-go-back-to-basics/

And if you listen to John Manley it's a national emergency.

http://www.theglobeandmail.com/news/national/education/canadas-fall-in-math-education-ranking-sets-off-red-flags/article15730663/

[Argus]

Most of you have no clue; none.

Memorizing times tables, and forcing kids to complete drill and kill worksheets stymie creativity.

Perhaps, but it also teachers them how to do math.

[Guest]

How about personal acquaintance with high school grads? No, too narrow?

Well, the origin of this discussion is the math testing which showed that Canada's score slipped -- again. I think this is the third straight time, is it not? There are powerful movements of parents in numerous provinces screaming at their schools and governments that their kids aren't learning how to do math. I believe Manitoba has already responded to this. And I'm pretty sure the same complaints have been made about English.

I wasn't involved in this thread as I didn't know the issue, having fully grown kids now, but I happened to listen to conversation among indignant parents on this issue just the other day. It would seem that the consensus is that it is most definitely the wrong way to teach math skills, and petitions are being organised to try and force a change in the system. I think parents resent their kids being guinea pigs

[Michael Hardner]

The sky is falling and our children are idiots... said every generation of parents and adults since the 1950s.

[WestCoastRunner]

The sky is falling and our children are idiots... said every generation of parents and adults since the 1950s.

CRAP!

[Mighty AC]

Those aren't the same tests that are done by the OECD with PISA, afaik.

You are right the EQAO tests are not used for PISA results.

[Mighty AC]

Let's say students are more engaged in math, identify more math concepts in the real world, show a deeper understanding of math concepts and problems, report reduced fear of the subject and a higher level of enjoyment, yet take longer to produce solutions on standardized, timed tests. Are these students actually declining in mathematics?

How should we proceed? Should we scrap inquiry based methods and returned to the old way, that left roughly half of students feeling they 'hate math', for political reasons? Maybe inquiry based teaching methods for math will continue to improve with time, familiarity and professional development. Maybe we could continue to tweak math ed teaching methods to achieve the best of both worlds.

The fact that students are forced to tackle far more advanced concepts, far earlier than we were is reason enough for adults to stop calling for a BS 'return to basics'. This is like calling for a return to vacuum tubes in electronics; the old way has been quite thoroughly surpassed.

Edited September 22, 2014 by Mighty AC

[Michael Hardner]

CRAP!

Yes, that is what I'm saying.

[Argus]

The fact that students are forced to tackle far more advanced concepts, far earlier than we were is reason enough for adults to stop calling for a BS 'return to basics'. This is like calling for a return to vacuum tubes in electronics; the old way has been quite thoroughly surpassed.

How about university math professors complaining about all the students coming into university whose math skills are so deficient they require remedial training? Are you going to tell them they don't know math as well as you do?

Edited September 22, 2014 by Argus