LiveCode Forums.

Strange, someone seems to have deleted yesterday's post of mine about a stack I uploaded to RevOnline. My post did not constitute any commercial endorsement of anything, it just announced the publication of a self-made RunRev stack.

With that stack, you can practice the "Trachtenberg Speed Method of Basic Mathematics". You can practice UT (units-tens-) training as a prerequisite for fast multiplication, multiplication of large numbers, NT (number-tens) calculation, and fast division with remainders.

The training stack lets you choose how many problems you wish to answer, takes the time you need and calculates a score. It also keeps one highscore in every training area. Over time, your calculation skill and speed will improve greatly!

The training software does not give you explanations on the how-to of the Trachtenberg speed method. You will have to read the details for yourself. To do so, you might consider borrowing or purchasing a copy of the book "Trachtenberg Speed System of Basic Mathematics", or collect some of the information needed as it is scattered over the web.

Jakow Trachtenberg, the inventor of this speed math method, had the misfortune to be enprisoned by German Nazis in a barbaric concentration camp, and that is where he invented his method. There is an entry on Jakow Trachtenber on the British Wikipedia.

Regards

ukimiku,
there was a spam attac last night and this morning almost all posts were gone so I guess Edinburgh had to revert to a backup and the latest posts were lost.

I looked at your "Trachtenberg" stack and find it quite impressive the way you handle skinning. I have not the slightest idea how I could use this stack to improve on my math but that is my fault since not even my math teachers had an idea how to improve on my math.

Once I managed to throw an exeption when I set divisor and everything else to 1 it went into debug mode.

Obviously you managed to get into Revcoding quite fast, so congratulations.

regards
Bernd

bn wrote:ukimiku,
there was a spam attac last night and this morning almost all posts were gone so I guess Edinburgh had to revert to a backup and the latest posts were lost.

I was equally shocked to find out about this one... When I just logged in to revForums awhile ago, I was like, WTF!!??, then after a few hours, everything went back to before almost like nothing happened.... And I was like, am I lacking any sleep?? But then anyway, glad, rev had backups of the forum!, Dunno what I'm gonna do without all the useful infos that I can find here...

ukimiku,

I too am disappointed that your post was removed as I wrote a lengthy response to your post that was also removed, which I am sure you would have enjoyed.

To summarise: I really enjoyed your stack. Your stack is a nice example of using irregular shaped windows, and is well focused on the math (doesn't hide the math in some flimsy adventure game, or behind some smiling cartoon character).

I taught myself Trachtenberg a very long time ago, and your stack was a great reminder. It doesn't leave you once you know it. I can still piss off those around me by doing complex math in my head, particularly the method for multiplcation using eleven is a priceless time saver (and good party trick).

Trachtenberg's story should be on the big screen. I have been playing your game off and on all afternoon - ha ha - pushing for a personal best.

Once again thanks for posting.

Kind regards, Andrew

Hi Bernd,

thanks for your kind words. Actually, I had never heard about the Trachtenberg method until only a month ago, but now I am eager to get to terms with its concepts, thus the training. Also, I am rather disappointed about the fact that so much of my time back in school has obviously been wasted - when they could have taught me this really fast method but instead stuck to the old school of calculating the tedious way.

Unfortunately, although I'm a math teacher myself, I don't have the slightest idea on how to improve your math. But since you are in programming, you don't appear to be a hopeless case

Thanks for the bug report. How can I understand that you "set the divisor and everything else to 1"? Do you mean that you chose a length of 1 for the divisor as well as the dividend?

Obviously you managed to get into Revcoding quite fast, so congratulations.

Thanks, but RevTalk is extremely easy to learn in my opinion. I have a background of extensive RealBasic programming and have ever been fond of learning new scripted languages and interpreted languages in general. I find RevTalk is a very productive programming environment, very well suited for rapid prototype development. About the cross-platform benefits I am not so sure yet. Yesterday, I employed the Trachtenberg stack on a Mac, and the baseline of the font ("Arial") had moved, moving the digits out of their rectangular boxes. Bah. So extensive cross-platform testing seems to be necessary even for the simplest display aspects.

Regards,

Hi dickey,

thanks! I have known this great method only for a month now, but have already begun to teach some aspects of the method in the classroom. When the students are 12, 13 years old, they are still eager to learn some "tricks of the trade", and the older ones (around 17 years of age) are glad to have a few moments diversion from the "Analysis" part of the course.

Kind regards,

Bernd,

I could reproduce the exception being thrown. Thanks for pointing that one out to me.

Regards

ukimiku,

These methods are great confidence boosters particularly for students whom are otherwise struggling with math, and need to come at the basics from a different angle. The basics of math are usually taught straight up (single method). When I help students with math (as a volunteer) I show them at least 3-4 methods of performing the same task and usually one will stick, and help them to excel and gain confidence. Teachers claim it is confusing, but it is in reality empowering students with choice, and teaching self reliance. It is cool to ask them to complete the same problem using several different methods which is also great for cross checking.

Take basic addition...

Eg 246 + 197
If you throw Trachtenberg into the mix you gain even more ways to foster understanding, of the basics, but more importantly strategies for completing problems entirely mentally without the need for complex workings, which is often where disorganised students fall down.

Have a great day.

Kind regards, Andrew

ukimiku,

I am the perfect beta-tester for math applications: I just click around without the slightest idea of what is going on

But since you are in programming, you don't appear to be a hopeless case

well, I solve my math problems by iteration, but please don't tell anybody. 1+1+1+1
regards
Bernd

Bernd,

yes, perfect! And very helpful, too!
Maybe you should carry out your iteration in binary, you might become even faster (according to Moore's law, math program testers get twice as fast every 18 months).

Regards

Andrew,

thanks for sharing your explanations and considerations. Here in Germany, students learn a variant of the Carries-Above method you spread out so nicely, as they write the carries in small print at the foot of the column in which they are to be considered, not above the whole of the original columns.

I think as a math teacher I am responsible for not wasting the time of my students with ineffective methods, so I am happy about Trachtenberg. Cross-checking is one of my favorites, too, I teach cast-out-nines and cast-out-elevens. Together, these two methods catch about 99% of all mistakes made. Not bad for a couple of seconds of thought...

Kind regards,
Michael

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I saw this thread and was intrigued - now finally I have Rev Online working again I downloaded your stack with interest.

Now I'm baffled - I have no idea what the Trachtenberg system is, so I just looked up on Wikipedia and will play for a while, but my first thought is that whether or not you include any instructions about the Trachtenberg system itself, you should probably add some help on using the trainer. It's not clear (until you've tried it) that the first digit selected always goes in the right-hand box.

More seriously, (or is it just me not knowing what is supposed to be required) there are a number of problems presented where the answer is clearly not feasible in the format displayed. Eg 51 x 9 = _ _ (ie it seemed to be expecting a 2 digit answer, less than 100). Also there were some that just failed me and I'm not sure why - there were some "multiply by zero" answers where selecting 0 as the first digit jumped me on to the next problem, or for 07 x 2 = ?? entering 4 as the first digit got me a fail and jump to the next problem, while 72 x 1 = ?? got me a fail for entering 7 first. So the question is, is there an issue with the verification, or with my understanding of what I'm supposed to try and put in the answer boxes?

This was using the stack in the IDE on Windows. Apart from my bewilderment, it looks very slick and a nice funky interface. On my Windows display it does have a sort of "flat spot" on the outer extreme of each "bubble" and that a little fraction of the main "bubble" stack shows behind the edge of on of the substacks that opens.

I hope that is constructive and helpful.
SparkOut

Hi SparkOut,

thanks very much for your feedback. From what you wrote it seems you clicked on "UT" or "NT" training. These are, despite the multiplication symbol "x", no traditional multiplication problems. Instead, you are supposed to enter the "Trachtenberg UT product" in the UT section of the trainer, or the "Trachtenberg NT product" in the NT section, respectively. They constitute completely new operations that have to be learned.

For instance, the UT product is formed as follows. Example:
59*7.

You might notice the litte "U" above the left-most digit of the multiplicand (the first number, before the "x"). This is a reminder that after multiplying 7 with the first digit, 5, you keep in mind only the unit digit of the result. In this example, 5*7 yields 35, you discard the tens digit of this 35and keep only the 5. Above the second digit of the multiplicand, there is a small "T" which stands for "tens", as a reminder to keep the tens of the next product, 9*7, which yields 63, so you keep the 6 only and disregard the 3 of the 63. Now you have two numbers in mind, the 5 from the first product (units), and the 6 of the second product (tens). Now you add these two numbers together and arrive at 11, which is the correct solution for the Trachtenberg UT product. You click on the 11, and the answer will be marked as correct, and the next problem will be presented immediately (time is running).

The NT product is formed in a similar way, that is: the second multiplication for keeping the tens is performed exactly as above, and again, two numbers are added. The difference, however, lies in the way the first number is calculated: Instead of disregarding the tens of the result, you keep the whole product in mind and then add the tens of the second product. Example:

59*7 (NT style):
step 1: 5*7 = 35. Keep the 35 in mind
step 2: 9*7 = 63. Again, keep only the tens and add the 6 to 35.
Your answer should be 41.

Naturally, these are not the results they teach you to obtain in school. Nevertheless, these products are needed for multiplying quickly (UT product) and for dividing quickly (NT product). I have indicated a proposed order of aquisition by small numbers on the main dispatch interface: you will find a small encircled "1" near the letters "UT", so you should learn that first. The faster you can calculate UT products, the faster you will be able to multiply really long numbers - in your head alone, without intermediate results! No writing - gain in speed! But: the rules for the long multiplication are not explained in the software, I had to get a working version out quickly for my students. Anyhow, since you speek RevTalk, the algorithm is coded in the function "Trachtenberg_product", have a look if you like.

The NT product, in addition to the UT product, is a prerequisite for the fast division.

I have not yet noticed the display glitches you mentioned. On my Windows (Vista), the background image does not deviate from its outer form.

I agree that instructions on using the trainer would come in handy. Anyhow, once (or twice) you enter a result in the NT section, it indeed becomes clear that the right-most digit is entered first. I will probably not be able to provide instructions on the Trachtenberg method as such; the part of Trachtenberg's book that is covered by the training stack spans about 150 pages in very, very easy English (for children's self-study).

Again, thank you very much for your valuable feedback. I hope that you might become even more interested the Trachtenberg speed system, as it is very quick, elegant and quite something with which to show off (if so inclined...

Regards,

Well thanks, I must admit to being very intrigued and I will definitely keep the stack on hand and one day when there's time I will have a delve into finding out how it works and what I can do to train myself up.

Hello Michael,

I am personally using your trainer a couple of times a day at present. It does really get the mind focused.

In reference to the UT exercises (but it might be similar on NT):

I have noticed when you get faster that there is some latency between a question appearing and the buttons 0 through 18, becoming active again.
You might go to click say the button labelled 5 and it is inactive only to wait 1-2 secs before being focusable again. Ha ha, this wouldn't worry me if I wasn't competing with myself.

Just a question on scoring. I assume the longer you take to answer the lesser your score for a correct answer. Out of interest could you explain the scoring a little more.

Have a great day.

Kind regards, Andrew