Teaching kids real math with computers/calculators

[compsystems]

From rockets to stock markets, many of humanity's most thrilling creations are powered by math. So why do kids lose interest in it? Conrad Wolfram says the part of math we teach -- calculation by hand -- isn't just tedious, it's mostly irrelevant to real mathematics and the real world. He presents his radical idea: teaching kids math through computer programming.

This talk was presented at an official TED conference, by Conrad Wolfram brother of the creator of MATHEMATICA Stephen Wolfram

link
https://www.ted.com/talks/conrad_wolfram...discussion


.

[Garth Wilson]

I must heavily disagree with him. If the student can't do it on paper, they can't do it in their heads either, which means they will have no idea if wildly wrong answers come from the computer because something was entered wrong.

One commenter at the link said many people will enter fields where they have no need of math. I say it doesn't matter. Life needs math. The woman next door went to a swap meet and saw some T-shirts she liked that were $3 each. She thought that was too much. The merchant, sensing her—um, how can I put this kindly—lack of understanding, said, "Ok, I'll make you a deal. Three for $10." She thought that sounded better, and she bought them. It knocks my breath out. Somehow she graduated from high school without learning 3rd-grade material.

My wife and I are involved in a kids' program Wednesday nights. There's dinner before it starts; and last year one of the leaders, just for fun, said to a bunch of fifth- to ninth-graders around one of the tables, "Ok everyone, what's ten divided by six?" Their eyes all turned glassy. Two of them had the idea to reach for their smartphones to try to find a calculator ap, but still didn't come up with an answer. I was absolutely stunned. Our schools today are not much more than babysitting and political indoctrination centers.

[EugeneNine]

(06-26-2017 02:16 PM)compsystems Wrote:  From rockets to stock markets, many of humanity's most thrilling creations are powered by math. So why do kids lose interest in it?

Because of the way it is taught. All kids are different, yet the school system expects them to all be the same. My son can do complex math in his head and get it right every time but low eye hand coordination makes it take much longer when he has to show every simple step of work.

One of the common core methods the school was forcing my daughter to learn, I looked it up and the reason for it was "some students have problems with method x so we suggest method y. Some was bolded by me, the school was forcing all students to use method Y even if they were not the some that it made more sense for. if they were in the some that method X worked better for they were screwed.

Rocketmath is the other mistake the schools are doing. Start in the early grades (1st and second) and have the student work problems as fast as possible and grade on time. Then when they get in the habbit of working too fast expect them to slow down and be more accurate. Completely backwards, doesn't matter if they are learning math, music, or a "sport" they need to start slow and work their way to fast.

Our education system has really suffered in the last few years, we have to employ tutors because while we can get the right answer we can't teach the over complex methods in use now.

[Dan]

The idea of teaching kids "real maths" is an old one, the most recent attempt introducing CAS and expecting kids to learn algebra by getting a machine to do it for you. Here is my response to a similar post about a fortnight ago:

Interesting discussion. As a teacher of mathematics for the last 10 years, my 2 cents worth:

Memorization of times tables an absolute must. As someone mentioned, expecting students to fill in the gaps in their knowledge with a calculator does not work. e.g. 99,000/4 student says 396,000 and doesn't bat an eyelid (pressed * instead of /). Or (6+4)/2 = 8 (enters it left to right with no consideration of order of operations). You are laughing but I see this ALL THE TIME.

A 12-year old I am tutoring took over 10 minutes to do his timetables when I started with him. (used a HP50g program to time him). A girl around his age was doing it in under 3 minutes, I've got him now doing it in under 4 minutes. We are doing fractions now and if his timetables skills were still bad if would be impossible to teach. 3/4 + 1/3, "well you find the lcd and find equivalent fractions. How many times does 4 go into 12?" I've had students stare at me blankly. "O.K. use you calculator". 3! "O.K. multiply the numerator by 3" (goes for calculator again). "Now do the same for 1/3". The student keeps going for their calculator, gets lost in the steps, asks "hang-on what are we trying to do?" It's ridiculous. When we get to algebra they are completely lost.

People thought CAS was the answer, focus on problem solving instead of tedious algebraic manipulations but it doesn't work like that.

[AlexFekken]

I think this goes much deeper. Teaching the general public some basic logical thinking, which would come with teaching proper math, would undermine the possibilty of fooling, and not really educating, most people most of the time...

For example, isn't it amazing how few people pick up that not being able to "fool all the people all the time" is totally irrelevant...

[Paul Dale]

I think that some rote memorisation is required.

The trick is teaching someone to think for themselves.

[Csaba Tizedes]

Hi, I want to teach programming my kids using Processing (later Java and after then Android programming, because I hope they will be billionaire programmers when they will grows up - and they will buy me a lake with a little wooden house with superb internet access )

So, paralelly with this I want to teach calculator programming, and they can understand the limitations and they can solve programming examples on a small system.

Which kind of calculator is best for this purpose?!

Any manufacturer acceptable. The availability, lowest price important and remember, they are kids, therefore they will throw it into their bags, into the corner, spill with water when use it. Maybe dig it in the garden. therefore the 71B or 41CX is not suitable.

I have an idea, the SENCOR has very good clones of CASIO calculators which are programmable (SENCOR SEC103 == CASIO fx-3650P, but the price is 1/4 of the CASIO).

Any idea?

[Maximilian Hohmann]

Hello,

(08-26-2018 09:07 AM)Csaba Tizedes Wrote:  ... and remember, they are kids, therefore they will throw it into their bags, into the corner, spill with water when use it. ...

maybe you should teach them first that things can have a value and need to be treated accordingly? Most kids can understand that concept :-) Our son took part in a project at school were they got introduced to CAS calculators early in secondary school, around age 11. We needed to buy him a Ti Nspire then because this is what the school decided upon. I explained him that this thing is worth as much as two birthday presents and one Christmas present together and if he broke it it would be on him to get it fixed at the cost of all those presents... The calculator made it's way through school with hardly a scratch. But it didn't get him interested in programming languages either.

Earlier on we had bought him a kit of Lego Mindstorms as an introduction to programming. He liked that much more than the calculator and actually played with it and did some programming.

Regards
Max

[Csaba Tizedes]

(08-26-2018 11:33 AM)Maximilian Hohmann Wrote:  maybe you should teach them first that things can have a value and need to be treated accordingly? Most kids can understand that concept :-)

Of course, they can understand it. But I don't want they use these calculators too carefully. These equipments are not eggs. The main goal is the joy of learn. If they will care these units like their skateboards, I will very satisfied. That will not a problem if they fills up with graffiti or coloring with marking pens. The main goal is a calculator which capable to learn the programming basics. And cheap and available now (in store or eBay).

And I do not want graphics calculator, because they are not really handy units.

Thanks,
Csaba

[SlideRule]

A modest suggestion [attachment=6250]for pedagogical edification.

Quote:There are many ways to talk about why mathematics and its applications matter. You will hear expressions such as “mathematical literacy” or “quantitative literacy.” They mean, essentially, that math is important. It is important because
knowing it can make your life easier. In other words, it can help explain how your world works. We created this course and this book because we know that not everyone looks at mathematics in this way.
In school, you spent a great deal of time learning the tools of mathematics—how to manipulate symbols and how to solve equations. In this course, you will spend time learning about the power of mathematics, which helps us understand many different parts of our everyday lives and the world itself. We hope this exploration will give you a broader sense of the subject and why we wanted you to take a math course every year you were in school. It’s “for all practical purposes” because, in a sense, you’ve learned to hammer nails and saw wood—and now we’re going to build houses.

from the Preface pg. xv.
BEST!
SlideRule

[Csaba Tizedes]

(08-26-2018 12:07 PM)Csaba Tizedes Wrote:  The main goal is a calculator which capable to learn the programming basics.

The real question what is the minimal requirement (for programming)?

At least:
- registers (min. 6, better: min. 10)
- Multiple program storage (more program slots or LBLs or LBL"name" or simple "name", etc at the beginning of each program)
- LBL/GTO (min. 10 / programs)
- LBL/GSB/RTN (subroutines nested at least main+level1+level2)
- IF/THEN (better if THEN has END: 1+ instruction after THEN)
- I/O from keyboard/to LCD: INPUT/PRINT (better if "text" available)
- at least 0.5~2kB program steps memory

Better:
- variables (name 1 character)
- arrays or variables can be addressed as array elements (like on CASIOs: A=A[1], B=A[2], etc...)
- looping (ISG/DSE, maybe FOR)
- structures (WHILE/UNTIL)
- at least 4kB memory

Much better:
- variables (register number up to memory limit or name 1+ character)
- 2D, 3D, nD arrays
- indirect addressing of variables
- indirect addressing of program labels
- boolean variables, strings
- formatted output
- at least 16kB memory

Much more better:
- expandable memory
- backup/recovery from PC
- accessing memory (PEEK/POKE or something similar)
- assembly programming
- CALL of system/user routines
- redefineable charset
- well documented hardware
- accessing to HW / I/O from program

etc...

Csaba

[grsbanks]

Maybe you want to invest in something that's built like tank and will be able to withstand a certain amount of bashing about. Combine that with some education relevant to the value of items as suggested by Maximilian Hohmann, then go and get a machine that's worth a bit more than your average cheapo Casio such as a DM15L. It's durable and feature-wise is ticks most of the boxes you enumerated in your last post.

If the alpha in/out is vital then go for a DM41L.

Disclaimer: I am involved with Swiss Micros but not financially. I do not stand to gain anything by recommending their machines.

[Csaba Tizedes]

(08-26-2018 02:05 PM)grsbanks Wrote:  go and get a machine that's worth a bit more than your average cheapo Casio [...] ticks most of the boxes you enumerated in your last post.

Hmm, maybe a TI-83/84 or a HP39gs fullfills these points and the price is much better than a SwissMicro calc - or if I want to hit them into the deep, I will power up my 12Cs. I have lot of them - and easy to buy a spare. Unfortunately the scientific functions are missing.

I have 15C, but I think at the beginning no need a too complicated stuff. Much more applicable a calculator which can be fits to their studies. For example on a 15C you cannot use the fractions. But on a CASIO you can show the result of a program calculation as a fraction. (Eg. a program which finds a well estimating fraction of a real number or the roots of a quadratic equation as a fraction.)


Csaba

[Albert Chan]

I think teaching math with calculator or a computer is a mistake.
Students need to be able to do it in their head.

Only *after* that step is solid, should calculator is used (to save time)

One time I was in a supermarket, the cash machine was broken.
The cashier math skill were so bad, the change I get back is *more* than I paid her !

[Csaba Tizedes]

(08-26-2018 03:46 PM)Albert Chan Wrote:  I think teaching math with calculator or a computer is a mistake.

Yes, but I want to use them PROGRAMMING. OK, they can do it on a cheap EeePC or any similar netbook, but these computers too big to use on a bus or underground when they commute to school. And a calculator is not a "bragging" stuff.

The real problem is the following:

- They can learn programming on a tablet or on a smartphone, but these has no keyboard. And no /limited support of any programming language.
- They can learn programming on a netbook, but these has no connectivity if required and too big computers and easy to spot by the "hard guys".
- They can learn programming on a HP200LX or PSION, but these has no any today favourite programming language support (and C is too early for they).
- They can programming on a calculator, but a calculator only a calculator and on these they can learn only the basics and very hard later implement in another programming language.

The real question is that, what is a good programming language for kids?

[John Keith]

(08-26-2018 04:22 PM)Csaba Tizedes Wrote:  The real question is that, what is a good programming language for kids?

Nowadays I would suggest Python. It is simple enough for beginners to learn the basics easily but powerful enough to be used to build real applications later.

[Thomas Klemm]

(08-26-2018 04:22 PM)Csaba Tizedes Wrote:  The real question is that, what is a good programming language for kids?

The question is not only which language but what they want to achieve with their programs. Maybe you ask them.

---

Clojure

Maria is a coding environment for beginners.
Creating graphics gives them immediate feedback and a feeling of achievement.

---

JavaScript

Another possibility is using JavaScript with Canvas in Chrome (or Firefox):

• To start the developer tools use key F12 and switch to the tab Sources → Filesystem.
• Create a folder on your desktop and add it to the workspace by dragging and dropping it.
• You have to give Chrome access to do so.
• Now you can create new files from within Chrome.
• Make sure to use only the good parts of JavaScript.
  

The HTML file graphic.html must be loaded from the browser and just contains these lines:

PHP Code:

<!DOCTYPE html>
<html>
  <head>
    <meta charset="UTF-8">
  </head>
<body>
 
<canvas id="white-board" width="800" height="500" style="border:1px solid #000000;">
</canvas>
 
<script src="graphic.js"></script>
</body>
</html> 


Note:
You can set width and height differently.

The JavaScript file graphic.js contains the code. The function clean clears the canvas and moves the context ctx to the center of the canvas:

Code:

const canvas = document.getElementById("white-board");
const ctx = canvas.getContext("2d");
const W = canvas.width;
const H = canvas.height;
 
function clean() {
    // clear canvas
    ctx.setTransform(1, 0, 0, 1, 0, 0);
    ctx.clearRect(0, 0, W, H);
    // move to center
    ctx.translate(W/2, H/2);
}
 
clean();

Now you can use the Console and make experiments by writing code snippets.
Once you have something meaningful extract it into a new function in the JavaScript file.
Documentation: HTML Canvas Reference

You have a debugger which allows to set breakpoints and step through the code.

---

Raspberry Pi

• Google Coder: A Simple Way to make Web Stuff on Raspberry Pi
• Scratch
• There are tons of projects often with excellent documentation. Most of them use Python which I consider a good programming language to start with.
  

Personally I would advise against using calculators to start learning programming.

Kind regards
Thomas

[burkhard]

(08-26-2018 03:46 PM)Albert Chan Wrote:  I think teaching math with calculator or a computer is a mistake.
Students need to be able to do it in their head.

Only *after* that step is solid, should calculator is used (to save time)

One time I was in a supermarket, the cash machine was broken.
The cashier math skill were so bad, the change I get back is *more* than I paid her !

Our four kids are homeschooled and even for the eldest (entering 6th grade) calculator use is really limited to only "special" activities that occur on occasion. We want fluid numeracy in head, with requires some rote learning of things like the multiplication tables. There's really no way around it, I think.

Albert's story was funny. I have another. A few years back, I was at the local home center store which has a gardening department. It was late in the summer and the remaining plants had been marked down once already and that day were getting another mark-down as the store attempted to clear out the seasonal inventory. I attempted to buy several shrubs which already had been marked "50% off" their original price. That day there was a sign out among the plants which said "starting today, reduced another 50% !"

Well I took the shrubs up to the counter and the cashier (late teens, early 20s, not long out of school herself) was completely flummoxed. She kept telling me that couldn't be right because it would mean I'd be getting the items for 100% off. She had the calculator out and sure enough, 100% off meant everything was free! I desperately tried explaining to her how percentages worked, but she eventually needed a manager.

[Thomas Klemm]

(08-27-2018 05:01 PM)burkhard Wrote:  We want fluid numeracy in head, with requires some rote learning of things like the multiplication tables. There's really no way around it, I think.

Start with:

 1  2  3  4  5  6  7  8  9
 2  4  6  8 10 12 14 16 18
 3  6  9 12 15 18 21 24 27
 4  8 12 16 20 24 28 32 36
 5 10 15 20 25 30 35 40 45
 6 12 18 24 30 36 42 48 54
 7 14 21 28 35 42 49 56 63
 8 16 24 32 40 48 56 64 72
 9 18 27 36 45 54 63 72 81


Show them that multiplication is commutative: \(a\times b=b\times a\)
Thus we can forget about the lower left triangle:

 1  2  3  4  5  6  7  8  9
 2  4  6  8 10 12 14 16 18
 3  6  9 12 15 18 21 24 27
 4  8 12 16 20 24 28 32 36
 5 10 15 20 25 30 35 40 45
 6 12 18 24 30 36 42 48 54
 7 14 21 28 35 42 49 56 63
 8 16 24 32 40 48 56 64 72
 9 18 27 36 45 54 63 72 81


The first line is trivial. I assume they can count:

 1  2  3  4  5  6  7  8  9
 2  4  6  8 10 12 14 16 18
 3  6  9 12 15 18 21 24 27
 4  8 12 16 20 24 28 32 36
 5 10 15 20 25 30 35 40 45
 6 12 18 24 30 36 42 48 54
 7 14 21 28 35 42 49 56 63
 8 16 24 32 40 48 56 64 72
 9 18 27 36 45 54 63 72 81


Multiples of 5 are easy so off they go:

 1  2  3  4  5  6  7  8  9
 2  4  6  8 10 12 14 16 18
 3  6  9 12 15 18 21 24 27
 4  8 12 16 20 24 28 32 36
 5 10 15 20 25 30 35 40 45
 6 12 18 24 30 36 42 48 54
 7 14 21 28 35 42 49 56 63
 8 16 24 32 40 48 56 64 72
 9 18 27 36 45 54 63 72 81


Multiples of 9 are easy as well: first comes the factor decremented by 1 and then the difference to 10.
Or if you prefer: the digits add up to 9.

 1  2  3  4  5  6  7  8  9
 2  4  6  8 10 12 14 16 18
 3  6  9 12 15 18 21 24 27
 4  8 12 16 20 24 28 32 36
 5 10 15 20 25 30 35 40 45
 6 12 18 24 30 36 42 48 54
 7 14 21 28 35 42 49 56 63
 8 16 24 32 40 48 56 64 72
 9 18 27 36 45 54 63 72 81


Thus we end up with 6 + 9 + 6 = 21 essential multiplications.
However the multiples of 2, 4 and 8 have a lot in common.

So you might show them that 2 × 6 = 2 × 2 × 3 = 4 × 3 = 12.
And that 4 × 6 = 4 × 2 × 3 = 8 × 3 = 24.
So they learn the associative law. And see some of the results appear multiple times.

Thus we end up with a few multiples of 3 and 7 that they still have to learn by heart.
Show them the diagonal: these are the squares.
And teach them the powers of 2 until 2¹⁰.

Best regards
Thomas

[Albert Chan]

(08-27-2018 05:01 PM)burkhard Wrote:  I attempted to buy several shrubs which already had been marked "50% off" their original price.
That day there was a sign out among the plants which said "starting today, reduced another 50% !"

Maybe the cashier was right, and we were wrong ? I am OK with 100% off

I came from Hong Kong, and figuring out discounted price is very simple.
There is no such terms as x% off, only discounted to y%.

Multiple discounted price = y1% * y2% ... of original