New Years resolutions slowly engaging

Mental Calculation, Mathematics, and Puzzles
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Life and work have had me busy (and still do) but it’s time to reengage.
So…

Back to basic mental calculation

  1. Mental Multiplication… I was spending quite a bit of time with difference of squares and had gotten to 3 digits when I ran out of steam. I think I am going try focusing a little more time on just getting my 01-99 multiplication nailed this year. It is extremely handy and extends to much of the other mental manipulation. I will keep up the two digit difference of squares but till I really get comfortable in two digits stretching in larger numbers of calculations is not all that beneficial right now.

  2. Soroban… My understanding is children start with about 3 years of abacus practice prior to starting flash Anzan. I have dusted off my abacus and I’ve installed BlueStacks on my PC so that I can practice using the various android apps for abacus practice out there. ( as an aside I think getting very fast with complements will help the mental calculation, I find I stumble here pretty regularily )

  3. Major System… I have played with this a few times but not really embedded it into my thinking. My working memory is about average ( no special talents ) so the ability to manage longer strings of numbers/calculations is going to take a memory system. - This year I would like to get the basic hundred pegs fluid in my head and apply them when doing calculation to reduce my fuzziness.

  4. Slide Rule… Occasional dabbling into estimation and logarithms… I know this is one of Kinma’s areas of interest. I will probably spend a little time this year becoming familiar

→ My understanding is there are 15 kyus/levels of prescribed exams for Soroban. Can anyone point me at curriculum / testing standards. It would be nice to give myself some structure in practice.

  1. Back to Khan Academy - I would really like to get my math up to a undergraduate university level so that I can begin to understand Physics. I really enjoy the lectures for the general public but it would make me feel better to be able to understand how the world works if not why.

  2. On the side I have been practicing machine stenography daily for about 6 months now and while I show no special talent I am improving with each sleep. … Real Time Court Stenographers are tested to 225wpm and there are stenographers that can type into the 300wpm range. I practice 7-10 hours per week currently.

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Great list. How do you practice the 2-digit multiplication?

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Previously I gen’ed random 2 digit multiples and simply practiced while learning as many “tricks” as I could find. I got pretty good coverage but found my calculations where I use complements pretty weak and that outside of practice session my skills tended to crumble fairly easily.

This year I am going to take a different approach.

I am fairly comfortable with my times tables to 22 right now.
For the next two weeks I am going to drill them exclusively both for the sake of memorization to reduce calculation time AND to practice as many different calculation strategies with them as I can to improve my calculation ability ( I am out of practice)

February I will add 23-31 so ( 1-31 )
March ( 1-41 )
April ( 1-51)
etc…
Boring, simple and achievable with the intent to have 1-101 extremely crisp by the end of the year.

I think that an extremely strong 2x2 without conceptual gaps is the key to my being able to successfully get to doing 8x8’s (in combination with a good memory system to keep the intermediate factors). 4x4 should be doable quickly without a memory system if 2x2 is really strong ( I think ).

It’s not really an end of itself but more an exercise in becoming as mentally comfortable with numbers as I am able. Lots of other fun objectives this year so rather than boil the ocean I thought I might lock a specific skill in this year to the point where is sticks in long term memory rather than simply fading as soon as I chase the next squirrel.

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There are some great Vedic mental maths techniques I’ve been dabbling in. It all looks like good fun, provided you can keep the motivation up!

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I’ve been dabbling for a few years. Motivation comes and goes. Unlike some of the more long term obsessive folk here I’m hoping that committing smaller chunks to longer term memory will pay off for me better than trying to learn everything at once and having it fade quickly when I get distracted by life. I find that if I can get into practice mode for 6-8 weeks I can generally maintain a good level of practice until some important life event bumps my priorities.

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There has been a lot of content written during 2017 about this.

I have written about how to automate calculating with complements using the soroban I think about half a year ago.
Long story short; once you automate calculating using the soroban, you kind of automatically start to use them.

Indeed, I love it. Helps to quickly estimate answers to difficult questions.

I remember reading about the standards somewhere and I am currently unable to find it.

However; not exactly an answer to your question, but try this:

https://www.abacusmathslearning.com/course/index.php?categoryid=2

Also; checkout this:

One of the best sites about the soroban is this:
http://webhome.idirect.com/~totton/abacus/pages.htm

Great to see you back here and, as always, ask questions and I will do my best to give my take on things.

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Just a little update… I’ve been playing with 1-20 in the evening almost entirely through mental rehearsal rather than any kind of software. It’s a small set but I’m quite enjoying rediscovering difference of squares, the mental short cuts for multiply numbers in the teens and other old tricks relearned, decomposition, and just changing grouping.

I have been doing the most basic of soroban practice using my old chinese soroban (5 earth bead) and an android app (know abacus) to do the drills. I’ll be order a japanese soroban next month

Interestingly, the idea of not just 10’s but 5’s complements is entering my thinking with multiplication in general. And although my mental subtraction (under practiced) is not improving my use of complements is starting to make sense and for the first time multiplication with 9’s is starting to allow me to skip the subtract/add step mentally.

I suspect there are plenty of complements methods that will become obvious to me as I continue to play with soroban and with Arabic numbers in my head.

While x5 is trivial by multiplication or mentally halving the number the idea of applying double/double/plus the number with more steps is also kind of interesting. Using an approach like this has more steps but trivial memory load and very simple calculations.

Imagine the challenge conceiving these ideas with Roman numbers. The Arabic abstractions really are a neat invention. I’ve never looked but it makes me wonder about other abstractions for thinking about numbers and what their strengths might have been. Are there other ways of thinking about numbers that I simply have never heard of? 0, 1, 2, 3, 4, 5, 6, 7, many. I can only really conceive about that many things in my head. If I mentally group shapes; 2d squares, triangles, rectangles, lines and similar 3d shapes of numbers I can visualize numbers more than 7 (i.e a 3x3 cube is 27). A geometric number system seems more natural than a “base” system although probably not nearly as easily communicated. I also have no strong idea how you manipulate it but it’s fun to think about.

The idea of reducing the problem domain down to trivial sets of numbers appears to be fruitful. The “memorization” of the trivial numbers is mostly a by product of familiarity with mentally playing with them and the small set leaves time to actually think about their relationships rather than drilling 1000 discrete calculations without taking time to stop and look at them.

… Which is too say I have started to think about numbers again a few minutes each night and it feels good. Children playing with sand.

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Ordered a nice soroban. Will probably take a month to arrive. In the meantime, it’s time to start playing with the 20’s.

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For android, I use Simple Soroban:

Great app!!!

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My Soroban has arrived.

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