Math TED lecture...what do you think??

[kathymuggle]

http://www.ted.com/talks/arthur_benj...education.html

I thought it was short but interesting - what do you think?

Do you think schools should adopt this?

If we keep a linear model for schools, then stats and probabilty should probably be the pinnacle. I am not sure math should be seen as linear or mountain-like, but more like a web with a few key concepts (which includes stats, number sense, patterning/balance) at the core.

Kathy

[ollyoxenfree]

Well, I agree that everyone should understand probability and statistics. I absolutely DISAGREE that probability and statistics should be the pinnacle of a K-12 math curriculum, in the way that calculus is now the pinnacle that is reached after basics are taught in earlier grades.

Probability and statistics should be a FUNDAMENTAL part of math from the early primary grades not a summit that is only reached after 12 years of study. It's pretty easy to teach simple probability to young children and to build on those concepts. I recall my kids learning probability in the early grades. They had fun with a lot of the exercises. They did things like flipping a coin several times in a row, pulling black and white marbles out of a jar, rolling dice and making graphs from the results. I wouldn't be happy with a math program that put all of that off until late high school. There's no reason to delay teaching it or at least exposing students to the concepts.

The order of instruction for math and science is interesting. This morning, before DS left for school, he was talking about the 12 grade physics test he's writing today on principles of motion, mechanics, acceleration, etc. Most of the class hasn't taken calculus yet, but in physics they are studying concepts that involve calculus. I can only imagine how frustrating it is sometimes.

[Geofizz]

Prob & stats is part of my daughter's day-to-day math education as it is right now. Calculus is the pinnacle not because it's most important, but because it requires the material the comes before it, including some of the probability material (like, what is a gaussian?). Once you've done calculus, then you can derive the rest of the prob/stat that you can't quite grasp before calculus. Indeed, much of economics is the marriage of probability/stats with calculus. e.g., how does a variable like the DOW index affect housing prices? Also, deriving the meaning of 2 standard deviations above the mean requires integrating a gaussian from -infinity to the mean + 2sigma, right?

I took discrete math, linear algebra, and part of calculus from Art Benjamin. He's a phenomenal professor. : But I'm not sure how much I agree with him here.

[eepster]

I was in an honors math program and got statistics in 8th grade, don't most students cover it at some point in high school?

[Kyamo]

Originally Posted by Geofizz

Prob & stats is part of my daughter's day-to-day math education as it is right now. Calculus is the pinnacle not because it's most important, but because it requires the material the comes before it, including some of the probability material (like, what is a gaussian?). Once you've done calculus, then you can derive the rest of the prob/stat that you can't quite grasp before calculus. Indeed, much of economics is the marriage of probability/stats with calculus. e.g., how does a variable like the DOW index affect housing prices? Also, deriving the meaning of 2 standard deviations above the mean requires integrating a gaussian from -infinity to the mean + 2sigma, right?

I took discrete math, linear algebra, and part of calculus from Art Benjamin. He's a phenomenal professor. : But I'm not sure how much I agree with him here.

[GuildJenn]

I just finished reading The Philosophical Baby and they've found that kids under two years get probability, sort of:

Twenty-month-olds were placed one at time in front of a box full of ping-pong balls — 80 per cent of the balls were white, 20 per cent red. The experimenter took five balls from the box, and then asked the child to give her a ball from some red and white ones already on a table. The children showed no preference between colours if mostly white balls were removed from the box.

“Yet they specifically gave her a red ball if she had taken mostly red balls from the box — apparently the children thought her statistically unlikely selection meant that she was not acting randomly and that she must prefer red balls,” Gopnik writes.

That's quoted from this article: http://www.parentcentral.ca/parent/e...-schools-teach

Anyway I don't think I agree that it should be the pinnacle. We did probability in grade 7 and stats in grade 10, if I remember right.

[Callimom]

Kathy the link won't work for me - it kicks me back to a mothering page and if I cut and paste it shows up as a missing page.
Can you post the name of the lecture/lecturer so I can google it?
thanks!
Karen

[MusicianDad]

What do I think? I think statistics shouldn't be part of the math curriculum. Before you start jumping on me... I think statistics should be part of the science curriculum. Starting early enough that students have a very good grasp of statistics by the time they graduate high school.

As for the math curriculum, I don't see why linear and web like curricula have to be mutually exclusive. Why can't we build a solid understanding of a topic before moving on and revisit these topics over time to keep this understanding solid. I also think we need to move away from the memorization used often in math. Memorization does't stick, not for most people. Once they don't need it any more they forget it, what good is that?

[kathymuggle]

Karen: try googling this:

TALKS | IN LESS THAN 6 MINUTES
Arthur Benjamin's formula for changing math education

Good luck!

I think this whole discussion hinges on what is the goal of math education.

If the goal is to give people math that will be used in there daily lives, then I think data management (stats and probabilty) should be central. I think other things should be central as well under this goal, including number sense.

A true story - I have never studied calculus. My high school ended with trig. If the goal of math is to give people math tools they will need in their everyday life - then calculus should not be pinnacle.

If there is another goal - perhaps the development of thinking skills or to give people all the info they need for further exploration (as a PP mentioned) - then perhaps calculus is the pinnacle.

In any event, I like what the video said about the importance of stats/probability. Upon reflection, I am not overly enamoured with the idea it is the pinnacle - but that is because I do not like pinnacles/linear models in general unless it is one we have chosen for ourself (is that too fluffy a statement for an math discussion?, lol). I am more keen on the web model - with acknowledgments that their are mountains in the web - at both the centre and along the tentacles.

While I appreciate that numerous posters have said their child is doing stats/probability (which is very much why it should not be a pinnacle - in some way it is a life skill and as such belongs at the centre of the web), I do not think they are only early elementary or even high school skills. I remember university students taking stats and really struggling with them. I have met numerous adults who really do have trouble sythesizing stats in a way that is useful to them. It is a skill that should be started in elementary school, but it is hardly something that is an elementary school skill.

Last thought: it is interesting that math is often seen as a mountain. In other disciplines, the web analogy is more used. Example: science. We have a core science knowledge - and then we branch off into other areas. I am sure these areas overlap - but few put biology, physics and chemistry in a mountain and say you must do this one before this one and that one is the pinnacle.

Kathy

[eepster]

Originally Posted by kathymuggle

A true story - I have never studied calculus. My high school ended with trig. If the goal of math is to give people math tools they will need in their everyday life - then calculus should not be pinnacle.

I think this a one of the big reasons that calculus is treated as a pinnacle, b/c not everyone makes it to the top of a pinnacle. In fact many many people don't.

I never made it all the way up to calculus, even though I was a great math student. At the end of my sophomore year in high school, I transfered to a boarding school with a very unusual math curriculum. I never finished at that school anyway since I dropped out do to illness and took my GED (there isno calculus on the GED.

I definitely see math as only semi-linear. Yes, certain concepts build on each other, but not necessarily in a linear way. If you look at how geometry is taught, you can see the progression clearly.

• In pre-k and kindergarten, very basic geometry is started. Students learn shape recognition and classification. They learn to sort similar shapes by size.
• In early elementary school students begin to calculate area for squares and rectangle. They start to classify shapes in more complex ways learning about other types of quadrilaterals, and such. To do this the students need to use arithmetic, which is a different field of mathematics. They learn how to use a compass and ruler to make basic shapes.
• In late elementary, they start to look at angles. They learn to calculate the area of more complex shapes such as triangle. They now need to be able to calculate using fractions. They learn to calculate volume of basic solids such as cubes. They learn to use a protractor.
• By middle school, they should be able to calculate the volume of any shape as well as most solids. They often learn to use a compass create right angles and other similar "tricks."
• Finally in high school, they start to prove why certain rules hold true, such as the Pythagorean theorem. To do this properly students should have learned logic. (Most commonly though, they are unfamiliar with logic beyond Volcans on Star Trek, and instead rely on memorizing formulas and proof they don't really understand.)

Of course one wouldn't call geometry the pinnacle, it is learned in parts and then revisited over and over. Though many students never go beyond highschool geometry, it isn't the end of the road. Interested students then use what they have learned to do in highschool geometry and apply it to other math subjects, just as they used arithmetic, fractions, and logic while working on geometry.

Calculus isn't so much a pinnacle, as it is the subject that one happens to cover in many advanced 12th grade math classes.

[ollyoxenfree]

Originally Posted by kathymuggle

While I appreciate that numerous posters have said their child is doing stats/probability (which is very much why it should not be a pinnacle - in some way it is a life skill and as such belongs at the centre of the web), I do not think they are only early elementary or even high school skills. I remember university students taking stats and really struggling with them. I have met numerous adults who really do have trouble sythesizing stats in a way that is useful to them. It is a skill that should be started in elementary school, but it is hardly something that is an elementary school skill.

I agree with you. I think some concepts can be introduced at a fairly early stage in primary school. The statistics curriculum can continue to build throughout elementary and high school and on into university. I don't think regression and multivariate analysis are elementary school skills, at least not for 99% of the population .

Data management has always been a fairly significant part of the math curriculum for my kids. I think that's common from what we've experienced in different cities and countries. In early primary, they graph data and use pie charts to examine class birthdays and rainfall over time etc. Once they learn some multiplication and division, they learn about mean, median and mode. It continues to build from there. It just seems that Benjamin doesn't realize that data management is part of standard public school math curriculum - or maybe it isn't where he is. I think he's right that it's important and should be developed further.

Originally Posted by kathymuggle

Last thought: it is interesting that math is often seen as a mountain. In other disciplines, the web analogy is more used. Example: science. We have a core science knowledge - and then we branch off into other areas. I am sure these areas overlap - but few put biology, physics and chemistry in a mountain and say you must do this one before this one and that one is the pinnacle.

Kathy

I think many math curricula use a spiral approach, at least through the elementary years. Students spend time on basic arithmetic and number sense, which is incorporated into daily math like using measures (weight, volumes) and managing currency and figuring distance and time and velocity. They also study geometry and algebra in increasing complexity every year. Practically speaking, I think this is somewhat similar to a web concept, unless I'm misunderstanding. Students are introduced to various branches of math and different applications over the course of each school year.

For advanced math though, I think it makes sense to establish certain skills before you can build on earlier concepts. I'm not sure how a student would manage differential equations before s/he understood simple algebraic manipulations. There is a somewhat linear progression in some areas of math. I think continuing a spiral-type curriculum throughout high school, covering geometry, functions, calculus and statistics in increasing complexity is a good idea.

Regarding calculus in everyday life - in my earlier post I mentioned that DS had a physics test yesterday on principles of motion and acceleration. Last night, while we were driving he was joking about his physics teacher. It seems Mr. S. had said that he'd know he was getting through to them when they started observing everyday phenomena and thinking about the physics behind them. DS said he suddenly realized that he was watching the moving vehicles and thinking about the physics - their apparent and actual velocities relative to our car and relative to the stationary objects like the pavement. DS groaned a little about it, but he laughed too! He didn't need to understand physics to drive home, but understanding physics gave him a deeper insight and appreciation to a pretty mundane daily activity. The fact that the physics was actually involving calculus didn't escape him either.