Excellent Discussion of Math's Future

[Peter Farrell]

Maria tweeted this but didn't MathFuture it:

http://www.sciencefriday.com/segments/how-much-math-should-everyone-know-show-your-work/

She participated in a very thought-provoking (and frustratingly short) discussion on teaching "real," accessible, fun math. Her fellow guests were Andrew "The Math Myth" Hacker and Pamela Weber "Building Powerful Numeracy" Harris.

The guests seemed to be in agreement that there's an artificial division between Real Math, the "sublime activity," and Fake Math, the "set of memorized things."

Speaking of Fake Math, I just got off the phone with a math department head at an expensive private school who wouldn't even entertain the idea of introducing Python programming in her department because "we're strapped for time just to cover our syllabus."

Fake Math is the Bible (even here in Silicon Valley!) and you can't leave out any of the Bible to put in this newfangled techy stuff that won't be on the SATs and AP tests. I worked hard to keep from laughing when she touted her school's use of such cutting edge technology as the TI-84!

More Maria!!

Peter

[Joseph Austin]

I must listen to the audio, but re teaching Python:

Consider the Lego Robot experience.

For many years, we did Lego Robots as an after-school experience with volunteers. For example, we would bring a few college students and robot sets to a middle school.  In my case, it was sponsored by a grant.  in other cases, parents would pony-up for a team so their own kids could have the experience. Or an individual teacher would squeeze a unit into his own course, or start an after-school club.

Eventually, one of the school districts where we were volunteering began to "mainstream" robotics into the curriculum.

I don't know what's going on at your schools, but I was observing teachers in rural Texas offering HS electives in Pascal programming back in the late 90's--the same time-frame that TI was making inroads.

If you're trying to make inroads into the SAT track crowd, you will probably have to change the SAT.  But meanwhile, there should be plenty of opportunities to connect kids to programming.  But you may want to switch to Scratch or Java--something they can do on a tablet or phone.  Or can you actually do apps in Python?

Joe Austin

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[Peter Farrell]

Hi, Joe,

Nothing would please me more than to change the SAT! I may not be humble, but I'm realistic.

You make a good point, the inroads might have to be in after-school programs, like the Coder School where I work. I'm also putting together a Computer Art course using Processing, and math is a very helpful tool for people wanting to do art on the computer screen. As I said in my LinkedIn talk, wanting to make cool stuff is a great motivator for people. Here's something cool I made this morning:

http://codepen.io/peterfarrell66/details/BzXbdo/

Peter

[Joseph Austin]

Cool!

I was thinking, if you really want to influence those private school students,

I'd try taking your pitch directly to the students, or to the parents, rather than the school admin.

After a lego robotics workshop, in which I demonstrated how the kids could program the lego robot with the computer, one parent--whose son had is own robot at home, which he had been programming with the buttons on the brick--came up to me and said he was glad to see his son using the computer for something besides games. 

 

Imagine if the parents found out their kids were actually doing MATH on the computer!

Joe

[Joseph Austin]

I can remember being shocked the first time I read a comment by a student that math was all "memory".

I've never considered myself to have a strong memory, and I liked math because I didn't need to memorize!  (OK, so I counted on my fingers when the teacher wasn't looking.)  But instead of memorizing dozens of calculus formulas, I would just derive them as needed.  Math and science, unlike languages or history, had an internal "connectedness" or "logic"  that distinguished it from merely  a list of isolated, unrelated facts that one could only memorize.

I used to think math was about quantitative relationships,

but lately I'm thinking it's really more generally about patterns,

where I conceive a "pattern" as ordered collection of repetitive or progressive entities.  We use "math" to analyze grammars of languages, sequences of sounds in music, organization of atoms crystals, classification of deformable shapes, and many other "patterns" that are only peripherally quantitative. Math is about discovering patterns, then finding ways to apply that discovery to conclusions or predictions about events that may share that pattern in other places or other times, especially including the future.

Joe

[Joseph Austin]

I was recently reminded of a common question from children: "Why?"

What does it mean that we ask "why?"

I can think of two kinds of answers to the "why?" question:

The first is cause. What conditions are responsible for something happening, or being that way.

Another is purpose: To what end or use is the object or event?

Why math?
We can ask how it evolved, or came to be part of the human experience.
Or we can ask what we can use it for, or perhaps better: what else can we use it for?

I think the latter question is more likely to lead us to a better understanding of math, and of our world.

Joe Austin

[Andrius Kulikauskas]

Thank you, Peter, for the link. That's a major show on public radio!

It was nice to hear Maria's voice. Also, she showed several of her
strengths. She was able to look for positive ground with guests who
represented quite different, seemingly opposing views. Also, she opened
up a lot of positive possibilities. In particular, she gave a nice
example of how 5 year olds can relate to calculus, building starships
(Millenium Falcons) and asking how a circular shape could be built out
of rectangular legos, and how the shape would grow more circular if the
legos were smaller, etc.

It was nice to hear the host say there would be more such shows. Excellent!

Andrius

Andrius Kulikauskas
m...@ms.lt
+370 607 27 665

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[michel paul]

On Sun, Aug 28, 2016 at 9:54 PM, Peter Farrell <peterfa...@gmail.com> wrote:

Speaking of Fake Math, I just got off the phone with a math department head at an expensive private school who wouldn't even entertain the idea of introducing Python programming in her department because "we're strapped for time just to cover our syllabus."

Yep. ​I cannot begin to tell you how ​deeply infuriating that kind of reasoning is. It was my life. I was surrounded by it. You can never get any kind of traction with it. No matter how amazing the things you demonstrate, no matter how deep the parallels you can point out between programming and mathematics, no one cares. It just doesn't matter to them at all.

Fake Math is the Bible (even here in Silicon Valley!) and you can't leave out any of the Bible to put in this newfangled techy stuff that won't be on the SATs and AP tests. I worked hard to keep from laughing when she touted her school's use of such cutting edge technology as the TI-84!

Yep. The 84. ​There was a time when I could still laugh, but after awhile it's no longer funny.

Like when a student came up to me after the first year of my computational math course to say thanks for doing this, that this was without doubt the most valuable course he had taken in high school, and he was glad he had done so despite his teacher telling him not to. I was puzzled, and he said, yeah, his teacher last year was telling all his students not to take Mr. Paul's computational course, because his ideas were just too different and had nothing to do with Calculus.

That's when it's no longer funny.

--

​ Michel

​

===================================
"What I cannot create, I do not understand."

- Richard Feynman

===================================
"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
===================================

[Peter Farrell]

Thank you for the input, everybody!

Joe, I'll take your advice and pitch my Computer Art class as an after-school activity first. But the convo made me think of ways to address such resistance. Then I read Michel's post! 

Andrius, you're so right: it was a fascinating discussion that deserved a lot more than 17 minutes! Was it a coincidence that the guest who sounded the least negative doesn't work in a school?

Michel, it's so unfair that teachers are overworked and have no time to innovate or improve their approach. Many of them are just spinning their wheels until retirement. Anybody coming around with new ideas (well, different ideas) is going to have to talk to the brick wall. 

Don Cohen got out of the system and did his own thing for 40 years. 

Peter

[Maria Droujkova]

Thank you for listening! I am reasonably happy with how the segment turned out. 

On the subject of computer science as a subject, this report is of interest: http://services.google.com/fh/files/misc/searching-for-computer-science_report.pdf

Turns out parents, teachers, and admins involved in schools overwhelmingly agree computer science would be great and useful (something like 90% of people agree) - if only it counted for college entry like other standard subjects do. 

Which brings me back to the point I made on the radio: that we need more choice and diversity in what counts for our math.

Cheers,

Dr. Maria Droujkova

NaturalMath.com

Make math your own, to make your own math!

-- .- - ....

--

 

[Joseph Austin]

Maria,

Thanks for sharing that report.

I first learned to program a computer over 50 years ago, by reading a book and having access to a computer.

A year later, I took my first class--an after-hours training class.

By the time my school offered a credit course in computing, I could have taught the course.

We must break our mindset of thinking that education can only happen in the classroom.

If parents and the community support students' natural curiosity, they will learn.

When I started, a programmable computer system cost $100,000 (in 1965 dollars).

Today you can get one for $50.

We may need to do a better job of matching supply to demand,

but there's really no essential reason why a willing student can't learn computer science.

If you know one, send him/her to me.

Joe Austin

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[Maria Droujkova]

We have to be careful not to confuse access with support. 

When you started, Joseph, most people had no access. The quest of that time was to give access to tech to everybody. It's not quite done yet, but your generation made awesome progress.

Now that most people have access to tech and learning materials, it's clear that for many, that is not enough to learn. They also need support.

The current quest is to figure out how to provide enough quality support for everybody. 

Cheers,
Dr. Maria Droujkova

NaturalMath.com
Make math your own, to make your own math!

-- .- - ....

On Thu, Sep 1, 2016 at 7:45 PM, Joseph Austin <drtec...@gmail.com> wrote:

Maria,

Thanks for sharing that report.

I first learned to program a computer over 50 years ago, by reading a book and having access to a computer.

A year later, I took my first class--an after-hours training class.

By the time my school offered a credit course in computing, I could have taught the course.

We must break our mindset of thinking that education can only happen in the classroom.

If parents and the community support students' natural curiosity, they will learn.

When I started, a programmable computer system cost $100,000 (in 1965 dollars).

Today you can get one for $50.

We may need to do a better job of matching supply to demand,

but there's really no essential reason why a willing student can't learn computer science.

If you know one, send him/her to me.

Joe Austin

On Aug 31, 2016, at 9:56 PM, Maria Droujkova <drou...@gmail.com> wrote:

Thank you for listening! I am reasonably happy with how the segment turned out. 

On the subject of computer science as a subject, this report is of interest: http://services.google.com/fh/files/misc/searching-for-computer-science_report.pdf

--

 

[Andrius Kulikauskas]

I wanted to add how amazing it is personally to discover how much the
opportunities to learn math have changed in my own lifetime.

I got my Ph.D. in Math in 1993 from UCSD. My real interest was to
study math as a tool for philosophy, and I was fortunate to take some
classes in syntax, Kant, automata theory and do a lot of independent
study on my own philosophy. I really thought it would be best for me to
have, say, a four year encyclopedic course in advanced mathematics, but
instead had to do rather specialized research for my Ph.D. thesis.

At the time, the options were to take a class or read a textbook. I
don't think I ever had a teacher who really made math intuitive for me.
And so the classes ended up seeming quite obscure. There was absolutely
no big picture. The alternative was to simply pick up graduate level
textbooks and plow through them, doing the exercises. My high school
didn't offer calculus, so I managed to teach myself from a book one
summer. But I couldn't find sufficient motivation to do that for, say,
Fourier analysis or other disparate subjects.

Today with the Internet there is a world of difference.
* I can read thousands of Wikipedia articles on the most advanced math
subjects and concepts. I may not understand very much, but I can hop
around and around, and keep coming back. I don't have to study in
sequence. Which means that I can focus on subjects that seem most
central to the big picture.
* I can watch video lectures by accomplished teachers from around the
world. On a recent day I marveled that I watched Tadashi Tokieda of
Japan/France/US/UK teach Geometry and Topology in South Africa; Norman
Wildberger teach Universal Hyperbolic Geometry from Australia; T.E.
Venkata Balaji teach Algebraic Geometry from India; and Fredric Schuller
teach Geometrical Anatomy of Theoretical Physics from Germany.
* There are many online graduate textbooks or survey papers available as
PDFs for free. That removes a big obstacle. And https://arxiv.org is a
repository where many mathematicians publish. I can publish there, too,
and perhaps be read and found.
* I can ask questions and watch others ask questions at
http://mathoverflow.net and https://math.stackexchange.com Indeed, I
think I can build up a reputation there and become known without
publishing any papers. Some of the most accomplished mathematicians in
the world are active there. In a sense, it's possible to see
mathematicians think and to interact with them.
* There are some amazing bloggers like Joan Baez and Terrence Tao who
really make it seem possible to have an encyclopedic view of the big
picture in math.
* There is software available with which to do research on math
problems. And also to share results. It has become, I think, easier to
write in Latex, and I imagine, to create videos.
* There is the Math Future discussion. :)

Andrius

Andrius Kulikauskas
m...@ms.lt
+370 607 27 665

>> <mailto:drou...@gmail.com>> wrote:
>>
>> Thank you for listening! I am reasonably happy with how the
>> segment turned out.
>>
>> On the subject of computer science as a subject, this report is
>> of interest:
>> http://services.google.com/fh/files/misc/searching-for-computer-science_report.pdf

>> <http://services.google.com/fh/files/misc/searching-for-computer-science_report.pdf>

>>
>
>
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[Joseph Austin]

My point is that we can't expect the public schools to be pioneers.

Public School is a "commodity" market; they cater to broad demand with broad support from textbook publishers, schools of education, testing and accreditation organizations, etc.  

The CS community hasn't even settled on a language or operating system yet!  

We have three major desktop operating systems on the market and as many more incompatible hand-held systems, to say nothing of a Babel of competing programming languages. Today, if you get any two computer scientists together, you will get three different opinions on what to teach! 

[Research topic: "mathematicize" computer science into a core set of concepts and "axioms" around which a keyboard-type-able notation can be developed as a "universal" math/programming language for instruction.  We've had some early attempts in LISP and APL and Smalltalk and even Pascal--

but noting seems to have bridged the gap between mathematical thinking and keyboard writing.]

Nevertheless, in the era of YouTube, pioneers have unprecedented opportunity to match willing teachers with eager minds.

I'm suggesting we avail ourselves of opportunities that exist, such as you and some others are already doing,

instead of lamenting the slow pace of the establishment.

I suspect that the whole paradigm of "school as we know it" will be replaced soon in any case.

We are already seeing erosion from Charter Schools, on-line instruction, and home-school, and later, industrial certifications in lieu of degrees.

To say nothing of kids teaching each other.

And the "voucher system" offers a mechanism for diverting the public purse to the private pocket to pay for it.

And math education (as we have known it) in particular no longer serves a public need:

all the math the average person needs can be done with their handheld--no need for "everyone" to spend eight years learning pencil and paper algorithms,

much less the "advanced math" only tech experts will ever use.

Other skills such as following and giving instructions [aka. computer programming], foreign languages, and "people skills" are in greater demand and in need of more time and attention.

The success of Minecraft and Legos and computer games generally tells me that kids are still willing and eager to "problem solve" and "construct",

if we but give them the right toys and, as you say, support.

"My generation" has paved the way with initiatives such as Lego Robots and Scratch programming;

I trust the "younger generation" will find creative ways of using the internet and whatever novel thing comes along next.

Joe Austin

[Bradford Hansen-Smith]

Now that most people have access to tech and learning materials, it's clear that for many, that is not enough to learn. They also need support.

The current quest is to figure out how to provide enough quality support for everybody.

Maria, if parents would work with their children from infant on up, as you appear to do with children you work with, by indulging their curiosity and allowing them to discover their own interest for themselves there would be no need for support to get kids to use the tools that are of their generation. I think Sugata Mutra proved a point about the pivotal role curiosity plays in learning anything. The greatest support we can give is access and then leave them alone to discover for themselves out of their own need to know. We already know the child's natural instinct is to learn from everyone and everything around rather than from a curriculum that "knows" what they need to learn. Culturally I think our greatest fear is the idea that we might allow our children the freedom of curiosity to find responsibility for themselves; it might well change our idea about mathematics and a great many other things; that itself is a great fear.  Problem is most children are already conditioned early on to carry the fears of their parents that carry cultural fears for all of us. This is a bigger problem than supporting technology and getting kids to learn math.

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Bradford Hansen-Smith
www.wholemovement.com

[Maria Droujkova]

On Fri, Sep 2, 2016 at 12:45 PM, Bradford Hansen-Smith <wholem...@gmail.com> wrote:

Now that most people have access to tech and learning materials, it's clear that for many, that is not enough to learn. They also need support.

The current quest is to figure out how to provide enough quality support for everybody.

Maria, if parents would work with their children from infant on up, as you appear to do with children you work with, by indulging their curiosity and allowing them to discover their own interest for themselves there would be no need for support to get kids to use the tools that are of their generation. I think Sugata Mutra proved a point about the pivotal role curiosity plays in learning anything. The greatest support we can give is access and then leave them alone to discover for themselves out of their own need to know. We already know the child's natural instinct is to learn from everyone and everything around rather than from a curriculum that "knows" what they need to learn. Culturally I think our greatest fear is the idea that we might allow our children the freedom of curiosity to find responsibility for themselves; it might well change our idea about mathematics and a great many other things; that itself is a great fear.  Problem is most children are already conditioned early on to carry the fears of their parents that carry cultural fears for all of us. This is a bigger problem than supporting technology and getting kids to learn math.

Sugata Mitra documented the types of support children needed. That included peer support and also support from "friendly grandmas" - interested, caring adults. There were also issues and limitations he documented. His data and conclusions are quite different from leaving children alone. 

Advanced math is a human non-universal. As in, most cultures never develop most of it. It is a treasure, built piece by piece by many cultures, and it takes a lot of human support to carry on from generation to generation.

Yes, freedom. Yes, free exploration. Yes, moving beyond fear, towards peace.

Also - tons of support!

--

[Roberto Catanuto]

Thanks for such interesting observations. As I see the thing, it seems to me that in most schools/countries students are simply asked to study Mathematics TO pass a test, not to study Mathematics to LEARN Mathematics. It's a problem I personally experience everyday as a Math teacher. 

How to close the gap between true Mathematics-for-learning and fake Math-for-tests?

1. hope that some policy makers change their minds and make curricula for learning, not to pass exams (very unlikely)

2. ignite a grass-root movement from students, parents and teachers to overturn the ridiculous idea that study is for exams' passing and not just for learning

3. spark such a big interest in what Math truly is that students, parents and teachers refuse to obey to ridiculous tests

4. more ideas welcome...

Please, free learning and stop this madness of tests taking.

Thanks Maria for the wonderful contribution you're making to the community.

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[Joseph Austin]

I've read that the current public school curriculum was developed by the British to educate administrators, in days when documents were handwritten and math was also done by hand. Graduates would immediately use what they learned and continue to do so throughout their careers.

Today, in my experience, the educational level most closely tied to actual job performance is technical college (grades 13-14).

When I was teaching in TX there were advisory councils of local employers who would advise the schools on curriculum to prepare graduates for local jobs.  I'm not aware of such a formal school-employer links the the K-12 or college level, but I suspect I'd more likely find them at the MS level than BS or PhD.

So I'd say, if you want students to learn for the sake of learning, instead of just for the test, you must teach what they will actually use;

what they see their graduated relatives and friends actually using. 

For example, spend less time on polynomials and trig and more time on statistics and finance,

less time with pencil and paper and more time with calculator (the one on their phone) and spreadsheets,

less time with "problem sets" and more time with "games" or projects.

If the student doesn't see a need for an answer to a problem, how is she motivated to learn how to solve that problem?

Suppose students were trained to evaluate quantitative results from policy decisions: anything from changing the menu at the cafeteria to changing early-voting hours.  For one thing, students would learn there's more to solving a "math" problem than crunching numbers: they would need to understand what answers they need, what mathematical procedures would give those answers, what data they would need to collect, and how to collect reliable data.

They might also realize that they need to convert their numerical answers into a persuasive presentation, complete with charts and graphs and an emotion-wrenching photo or two, integrating what they learn in math class with what they learn in speech and composition and social-studies class.

In other words, they might discover that they can actually use what they learn to impact their lives,

and in the process, discover what else they need to learn that may or may not be included in the curriculum.

I've often said that, to be considered "literate" in the twenty-first century, a person will need to know how to produce the equivalent of a TV commercial or documentary.  And we must learn to measure and quantitatively compare, not just disclose and decry.  Such goals could form the foundation of curriculum reform, in which "math" and "technology" will play a significant role.  Unfortunately, the "right of free speech" to stretch the truth has been abused to such an extent in advertising, politics, and even supposedly "factual" news reporting, that the rigor associated with math may not be welcome in the public square.

The "powers that be" may not be eager to see a population actually increasing in ability to think!

Joe Austin

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