Trachtenberg Speed Mathematics Trainer on RevOnline

[ukimiku]

Hi Andrew,

thank you for your kind feedback.

On the latency: this is caused by the Runtime engine. On my (rather new) Windows computer, there is no noticeable latency with the buttons. On a Macintosh (2 years old), there is no noticeable latency after clicking a button, either. On a different Windows machine (3 years old) running XP, it takes some time initially to draw the buttons on the alpha channel background image, but after clicking the buttons, there is no delay/latency at all. What kind of computer are you using (age/OS)?

The scoring in the UT/NT sections differs from that of the multiplication/division sections. In the UT and NT sections, the number of correct answers is squared and then divided through the elapsed time (in seconds) and multiplied with a fixed factor. So, indeed, the faster you are, the more points you get. And the more answers you get right, the more points (going up quadratically even). Maybe it would be better to have a more linear scoring system, thanks for pointing me to this.

In the multiplication/division sections, the points you get for a correct answer depend on how long (number of digts) the multiplicand and the multiplier have. Their numbers of digits are multiplied, because the effort you have to perform mentally grows quadratically, too. And: the faster you are, the more points you score. Basically, the score in these sections is roughly proportional to the product of the numbers' lengths, and inversely proportional to the time it takes you to enter correct answers.

I myself am new to the Trachtenberg method, and find myself doing at least 300 UT problems and about 30 multiplication problems (multiplicand 2 to 7 digits, multiplier 2 to 3 digits) every day. I find it amazing how much is happening in the mind then, as it is pushing aside old methods and approaces, sometimes even some kind of resistance. Interesting!

A great day to you, too!

Kind regards,
Michael

[dickey]

Hello Michael,

What kind of computer are you using (age/OS)?

ASUS EeeBox Intel Atom N270/1GB/80G/802.11a/Windows XP Home (ENG) - less than 12 months old - however modest spec... unit.

I did not notice the latency today - could it be a case of only happening the first time you download and play it, as I had just re-downloaded it yesterday when I noticed the issue.

Actually, I like the scoring in the UT/NT sections as you have explained it. You either go spectacularly well as you gain momentum from each successive correct answer, or you go downhill fast. It is hard but fair. Now that I understand it, I would (if I were you) be reluctant to change it.

300 UT problems and about 30 multiplication problems (multiplicand 2 to 7 digits, multiplier 2 to 3 digits) every day

Ha, ha - burning more calories than a run in the park with that practice regime. I have probably done similar, but you must agree you do improve very rapidly. It is all down to practice though, and if a student kept up the practice for say 4-6 weeks they would be travelling pretty well.

sometimes even some kind of resistance

Resistance is the absolute right choice of words to describe the condition where your mind fights against it's excess baggage of more conventional methods. Most of my errors to date on UT/NT have been as a result of that resistance. You just get sucked in, particularly if the T result is less than 10 sometimes you add it to the U result when the T result should in fact be zero. It is quiet amusing. In UT speed comes from freeing your mind from the whole answer just concentrating on the U or the T as the case may be. For example: when doing the T in problem 27 * 3 (rather than thinking 3 * 7 = 21 just thinking twenty-something (and not completing the units section in your mind). There are probably lots of strategies to gain more efficiency.

I will continue to practice over the next few months, to see if I can regain the speed I had when I was a teenager.


Kind regards, Andrew

[ukimiku]

Hi Andrew,

I am a bit unsure actually as to whether I should change the scoring in the UT and NT sections. Now you get "rewarded" by an almost-exponential increase in points if you choose to complete, say, 500 problems. Which is good from a didactic perspective, but at the same time makes comparing of scores from one "player" to the next unfair if they chose different numbers of problems. Well, I think I'll just leave it at what it is for the moment.

I have observed that my mind has deduced the following rules for calculating quickly the UT product:
xy * 0 = 0
xy * 1 = x
xx * 9 = 9 (xx denoting the same digit)
xx * z (for z other than 9): digit-sum of (x*z). I know the basic multiplication tables by heart, so there is only one addition necessary. I notice that I tend to see the products from the basic multiplication tables before my inner eye, and adding is almost instantaneous.
xy * 2 = 2x except when y >= 5 (in that case, add one more)

and some rules for the cases in which x equals 5 or the multiplier equals 5.

Did you notice anything similar with you?

Kind regards,
Michael

[dickey]

Hello Michael,

I can confirm all your observations are correct.

When it comes to systems of fast mental arithmatic for me there are only two worth considering Trachtenberg Speed Mathematics and Vedic Mathematics. If you aren't familiar with Vedic Mathematics it is an Indian system that pre-dates Trachtenberg by around half a century. Vedic Mathematics has 16 main sutras (Indian for precepts, tenants or rules, and 13 sub-sutras). It is similarly fast to Trachtenberg.Trachtenberg probably has the edge on very large numbers. I get the feeling working my way through the program at present it may be easier to teach from a younger age than Trachenberg. The Chinese I believe have it right for early school education K-2, with the use of the abacus as a practical (physical and visual) tool for a basic understanding of numbers + - x /. I am reading a book on Vedic Math at the moment, and aim to order a more detailed text when I digest the first volume. You can pick up a good book on the subject for about US$10.

In the best of all possible worlds, children would all learn one or both methods - but that won't happen. Each method seems as different as they are similar. As a parent you would hope that the next generation would shift the bar on achievement a little higher than that reached by their parents - alas I simply see no evidence to support that desire. I feel that there is a worrying trend of 'dumbing down' of syllabi to the lowest common denominator of achievement which makes students and parents: 'hopeless, but happy'.

Michael, it has be great to chat to you on these very interesting subjects.

Kind regards, Andrew

[ukimiku]

Hi Andrew,

thank you for your tips on reading. A friend of mine has independently discovered Vedic mathematics and pointed me to it. Becoming immersed in the Trachtenberg method, however, I have not yet had time to delve into the Vedic pool of math ideas.

I tend to confirm your observation about a worrying trend of "dumbing down" of syllabi. For instance, students that graduated from my school, say, 5 years ago knew significantly more higher math than current graduates. In general, the government of many of the German Länder are making graduating from secondary schools deliberately easier every couple of years since it is advantageous for them to promise the students' parents that the graduation of their children is almost guaranteed. For a country like Germany, that has no other resources than knowledge and education, this is a pity and a potential future problem. For decades, we have been observing a steady decline in patents, in the number of engineers, the number of students taking up technical subjects...

I found chatting with you very rewarding, thank you.

KInd regards,
Michael