Can someone explain the Discovery Method?

[Boges]

Because apparently Ontario are doing a crappy job doing it to students.

http://www.thestar.com/yourtoronto/education/2014/08/27/ontario_students_still_struggle_with_math_latest_tests_show.html

Ontario elementary students continue to struggle with math, new results on provincial standardized tests show. The scores come at a time boards are focussing their efforts on the subject in a bid to boost achievement.

The Peel District School Board announced Wednesday it’s launching a big push to help kids with numeracy and improve teaching methods. The aggressive plan will make math the focus of all of its schools and all teacher professional development.

For parents, the Peel board has ditched its annual literacy conference to instead host one dedicated to numeracy next spring.

On Wednesday, the Education Quality and Accountability Office, or EQAO, released test results from the 2013-14 school year, showing that despite gains in reading and writing in the elementary years, the percentage of students meeting math standards has dropped.

What's wrong with memorizing the times tables?

Edited August 28, 2014 by Boges

[Boges]

Look at the graphic in this story.

http://news.nationalpost.com/2014/08/21/math-wars-rote-memorization-plays-crucial-role-in-teaching-students-how-to-solve-complex-calculations-study-says/

Gold Star to the first person that can explain this.

It shows the carry over method we've all learned in school. But what's the other crap for? Why is 2<3 relevant?

Edited August 28, 2014 by Boges

[waldo]

this one cries out for lil' socialist!

[socialist]

Rote learning is a waste of time. Long division is a waste of time. Education in the modern day is about engaging students. the discovery method allows students to learn at their own pace. Memorizing times tables doesn't lead to understanding. Many of you are stuck in the way thins were done in the 50s. Sorry, but this is the 21st century where collaboration is more important than memorizing useless facts. If I need to regurgitate facts I will consult my smartphone.

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.

[bush_cheney2004]

Consulting a smart phone is not education. It's just revenue for the service provider who actually got an education.

[Boges]

Rote learning is a waste of time. Long division is a waste of time. Education in the modern day is about engaging students. the discovery method allows students to learn at their own pace. Memorizing times tables doesn't lead to understanding. Many of you are stuck in the way thins were done in the 50s. Sorry, but this is the 21st century where collaboration is more important than memorizing useless facts. If I need to regurgitate facts I will consult my smartphone.

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.

Teachers in Ontario are doing a bad job with collaboration then.

If it's a "better" way then it should be easy to explain how to come up with a simple math equation using the method.

I'll hang up and await your explanation of the method.

7x3=?

Discovery method please. CHOP! CHOP!

Edited August 28, 2014 by Boges

[socialist]

Teachers in Ontario are doing a bad job with collaboration then.

If it's a "better" way then it should be easy to explain how to come up with a simple math equation using the method.

I'll hang up and await your explanation of the method.

7x3=?

Discovery method please. CHOP! CHOP!

You draw 7 circles and place 3 dots in each circle. This shows understanding, not useless, baseless memorization. Teachers are doing a great job despite all the adverse conditions that hamper our jobs like underfunding, which is happening in BC.

[Boges]

You draw 7 circles and place 3 dots in each circle. This shows understanding, not useless, baseless memorization. Teachers are doing a great job despite all the adverse conditions that hamper our jobs like underfunding, which is happening in BC.

We're not talking about BC, we're talking about Ontario.

Why wouldn't drawing 3 7's suffice? 3x7 is essentially 7+7+7.

You can understand that 8x7 is 56 without having to count 56 dots in circles.

[socialist]

We're not talking about BC, we're talking about Ontario.

Why wouldn't drawing 3 7's suffice? 3x7 is essentially 7+7+7.

You can understand that 8x7 is 56 without having to count 56 dots in circles.

To have a full understanding of what multiplication is, kids need to draw pictures. Your lack of knowledge on the latest educational research astounds me, yet, doesn't surprise me.

[Boges]

To have a full understanding of what multiplication is, kids need to draw pictures. Your lack of knowledge on the latest educational research astounds me, yet, doesn't surprise me.

I understand the theory fine. But once you understand it, what's wrong with teaching way to make it more efficient?

What about the image I posted with subtraction. What's wrong with the carry-over method? Why is 2<3 relevant?

If this method was so great then we'd be seeing result. It appears Alberta is going back to the good old method.

[Mighty AC]

I understand the theory fine. But once you understand it, what's wrong with teaching way to make it more efficient?

If this method was so great then we'd be seeing result. It appears Alberta is going back to the good old method.

New methods for teaching math were introduced years ago, by several nations, because students could perform calculations but struggled to explain what they were doing and to recognize math concepts in the real world. A simple example would be to ask a primary student what an odd number is. A common response was to list a string of examples like 1,3,5,7,etc, but most could not articulate what makes a number odd or even.

So now rather than just having kids memorize that 3x7 = 21, we also have them prove they know why. Students don't have to draw pictures, but the circle and dot example Socialist gave would be one way for students to prove they understand what they are doing rather than just regurgitating memorized answers.

As a result of the changes, student mathematical literacy or the ability to recognize and explain math concepts has improved. However, efficient computation, which is simply checking for the most right answers on timed tests, has dropped. This is what we primarily test for, so it appears are kids are struggling in math, even though they are really doing alright.

The best solution is not to throw out inquiry or discovery based learning but rather tweak the teaching methods to also work on efficiency. It is probably also a good idea to improve our standardized tests to also diagnose student understanding and numeracy skills along with the speed at which they compute right answers. There is nothing wrong with memorization, if students actually understand concepts first.

[Mighty AC]

I stumbled across these animated gifs recently that kind of help illustrate my point in my previous post. Check them out they are very cool

http://www.iflscience.com/brain/math-gifs-will-help-you-understand-these-concepts-better-your-teacher-ever-did

I wonder ho many previously understood the demonstrated math concepts as clearly as they are shown in the pictures? I expect that most of us were trained to memorize/use formulas to solve trig problems for example but very few were made to see the big picture or taught to the point of mastery.

[Boges]

I stumbled across these animated gifs recently that kind of help illustrate my point in my previous post. Check them out they are very cool

http://www.iflscience.com/brain/math-gifs-will-help-you-understand-these-concepts-better-your-teacher-ever-did

I wonder ho many previously understood the demonstrated math concepts as clearly as they are shown in the pictures? I expect that most of us were trained to memorize/use formulas to solve trig problems for example but very few were made to see the big picture or taught to the point of mastery.

Teaching the method to understand is fine. But it's not practical at all to expect a student to keep drawing from that method every time they're doing the equation. It's putting more importance on the method than the result.

[Mighty AC]

Teaching the method to understand is fine. But it's not practical at all to expect a student to keep drawing from that method every time they're doing the equation. It's putting more importance on the method than the result.

It's not a method that is taught to students, it's just a way of learning through inquiry. The process of demonstrating understanding just applies to new concepts. Once a concept is mastered it is just used as a tool and new concepts are explored.

Current education is often trashed as being 'a mile wide and an inch thick', so the goal here is just to teach concepts to a greater depth or thickness. The new(ish) focus on understanding is more time consuming and the transition in teaching style has exposed some holes that need to be plugged. Part of the problem is that, like most of us, many primary teachers were just taught surface level math as well. Helping kids actually visualize and understand concepts in greater depth is more difficult when teachers were never taught that way. The proper solution is to plug those holes through professional development and improved best practices. The wrong approach would be to revert back to the old method because of limited evaluations that only test computational speed.

[Mighty AC]

Gold Star to the first person that can explain this.

It shows the carry over method we've all learned in school. But what's the other crap for? Why is 2<3 relevant?

Since 2 is less than 3 you have to 'carry over' from the tens column....leading to 12-3 = 9 This graphic isn't depicting inquiry or discovery based learning, it's just an illustration depicting the thought process involved with the 'carry over method'.

Edited August 28, 2014 by Mighty AC

[The_Squid]

To have a full understanding of what multiplication is, kids need to draw pictures. Your lack of knowledge on the latest educational research astounds me, yet, doesn't surprise me.

Astound

verb (used with object)

1.

to overwhelm with amazement; astonish greatly; shock with wonder or surprise.

LOL

You frighten me, but that doesn't scare me!

Hahaha

[Remiel]

Did anyone here have to use a dictionary to compile their post?

[Wilber]

You draw 7 circles and place 3 dots in each circle. This shows understanding, not useless, baseless memorization. Teachers are doing a great job despite all the adverse conditions that hamper our jobs like underfunding, which is happening in BC.

I carry a pencil and paper around all the time so I can draw dots and circles for simple multiplication. What's the matter with the rest of you?

[BubberMiley]

The graphic is just a meaningless piece of clip-art the National Post added. It's not supposed to demonstrate a new way of doing math.

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

[WWWTT]

LOL I'm a construction expert because I drove on an highway?!?!?!

No sorry Socialist, maybe we know something about education because we spent like 20 freekin years sitting in a freekin classroom listening to a freekin teacher buddy!

I'd like to see you go to China and work the same pace as the Chinese teachers!

You wouldn't last five freekin minutes buddy!

WWWTT

[kimmy]

What's wrong with memorizing the times tables?

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

Edited August 29, 2014 by kimmy

[Bob Macadoo]

It's not a method that is taught to students, it's just a way of learning through inquiry. The process of demonstrating understanding just applies to new concepts. Once a concept is mastered it is just used as a tool and new concepts are explored.

Current education is often trashed as being 'a mile wide and an inch thick', so the goal here is just to teach concepts to a greater depth or thickness. The new(ish) focus on understanding is more time consuming and the transition in teaching style has exposed some holes that need to be plugged. Part of the problem is that, like most of us, many primary teachers were just taught surface level math as well. Helping kids actually visualize and understand concepts in greater depth is more difficult when teachers were never taught that way. The proper solution is to plug those holes through professional development and improved best practices. The wrong approach would be to revert back to the old method because of limited evaluations that only test computational speed.

Exactly. You have rote learning teachers, teaching a language they never learned. Just like in high school when you had the gym teacher fill in for French......mon dieu.

The main hole to plug is the context/explanation to jump from theory to efficiency. Teachers expect kids to figure that out on their own....its a difficult bridge and kids fall behind because they are trying to apply discovery methods on a test. They weren't given time to move to efficiency in class, and if its not driven at home.......you get a kid who understands concepts but can't apply the quickly; smart kids dropping to the bottom.....if not out.

[BubberMiley]

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

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

[BubberMiley]

Teachers expect kids to figure that out on their own....its a difficult bridge and kids fall behind because they are trying to apply discovery methods on a test.

I think in practice, the expectation would be that they would have practiced enough before the test that they would be done discovering, or at least be fast at it, by the time they write the test.

[Mighty AC]

I think in practice, the expectation would be that they would have practiced enough before the test that they would be done discovering, or at least be fast at it, by the time they write the test.

It's possible that the effective but time consuming inquiry based techniques are leaving too little time to work on problems and become efficient. This will get sorted out with Professional Development, experience and improved practices.