End of Freemium?. A conversation about a Infinut decision at Linkedin

All this is related to a hard discussion in the linkedin:

https://www.linkedin.com/nhome/updates?topic=activity%3A5986641279243542528&activity=activity%3A5986641279243542528

Related to the Infinut announcement:

http://infinut.com/2015/03/25/the-end-of-freemium/

The End of Freemium?

I am still reading all this and these ideas are resonating in my head:

Talking out about the fact of having eliminated all free versions of a collection of children's apps some people of google plus says:

Deepak Kumar:

“Good products tend to sell well :-) Wish you the best! “

Trevor Sullivan:

“ I agree with Deepak. If you have a good product, your customers will be happy to pay for it. As a consumer (we all are), I can personally vouch for this. ;) ”

Greg Bulmash:

“It is AFTER the professor has been paid and AFTER the students who paid tuition get the benefit of the class that it is shared more widely.”

and:

“Content sharing licenses and freemium apps are the CHOICE of creators”.

And later:

“My volunteer group is hosted by Amazon and we have volunteers from Microsoft, Amazon, Ticketmaster, Boeing, Expedia and others who all donate their time to teach and mentor. Microsoft also donates $17 for every hour an employee volunteers with our group “

And yesterday the ultimate:

“If you can make such outrageous, insulting, and blatantly prejudiced statements, then you need to do some introspection and deal with the poison inside your own soul, because that kind of bigotry and belligerence has no place in civilized discourse”.

And Finally: Deepak Kumar:

“If there was an ignore button I'd be reaching for it now”.

(as a reaction for my: “To me cause I hilarity people who do good deeds during the weekend to make up for what they do during the week, and also these people who dare to give lessons and advices to everyone. Sorry”.

If we look at this discussion imagining we do not know what it is, we seem to be talking about the sale of any product of dispensable luxury. Or something worse.

I think some kind of brainwashing in the field of marketing is seriously affecting these people, or maybe they do not know about what kind of topic we are talking

We are talking about the disappearance of freemium versions of some quality programs made by Ana Redmond from Infinut dedicated to pedagogy and didactics of mathematics. And I talk about the inappropriate applause that this decision has had on the GooglePlus audience.

First I must say that I share the concern of the developers of apps for the lack of profitability of apps in general that will never reward the efforts of programmers. (Modestly I think I'm a programmer too).

And I am also concerned that because of this lack of profitability of apps, good programmers are forced to work in big companies, and having to endure which is hard to bear in the workplace sometimes. Including my seemingly unfair criticism.

In this discussion, I think no one has taken into account is that we are talking about useful programs when teaching mathematics to young children.

Basic and useful teaching resources to teach math to young children, should be free, must not contain advertisements or hidden payment methods of any kind. This applies to apps and web pages, and to everything that is available to the kids.

Making teaching materials to teach maths to children, is a kind of service to humanity. This work is itself one of these good works that some do only some weekends

And no one freelance programmer is forced to make programs that constitute teaching resources. There are many other fields and disciplines in which they can develop free apps, paid apps, apps with ads or apps with payment mechanisms within applications without any problem.

If you do not already know, I think this is the right time for you to know.

And finally, heading directly to Ana Redmond, I would say that surely the "freemium" versions of their programs were not sufficiently accepted by parents of children because they offered on the one hand free games, and otherwise inaccessible games. This is very common and widely used in general in the world of apps, I think this structure has caused a misunderstanding. Parents have logically thought that was a free version to generate a kind of abstinence syndrome of the paid version. To avoid this misunderstanding, it would be necessary in future free versions of these programs don't will announce inaccessible parts or paid parts. Free applications should do what they already announced, and developers must consider that everyone is smart enough to see that, from the same company, there is another and more complete paid version.

Ethically, independent programmers should be a bit better than drug dealers 

located on the doors of schools. 

Education and proper teaching is the best antidote to ward off the madness in our lives.

From the Prinzhorn Collection

Someone might say that insanity is the lack of tools to understand the real world.

Madness, in the discipline of physics for example, could be exemplified by the ignorance of the basic principle of conservation of energy.

A person who does not understand or unknown this principle, it seems a crazy person to the other people with basic skills.

While, the patient without the most basic knowledge, could spend a lifetime to solve an impossible problem to solve, further worsening their own state.

And besides, could eventually add more and more vicious circles of those who already we have normally in the head

Education and proper teaching is the best antidote to ward off a little the madness in our lives.

I will illustrate this with a drawing of the Prinzhorn Collection.

Part of the therapy practiced in the mental institution run by Hans Prinzhorn, 

( http://en.wikipedia.org/wiki/Hans_Prinzhorn ) was to propose to internal patients to conduct drawings and diagrams in which patients express their concerns, concerns or ideas in general.

http://prinzhorn.ukl-hd.de/index.php?id=14&L=1

The drawing represents one of many attempts of a patient to figure out how to build a bicycle propelled by perpetual motion: I mean that as the bicycle moves, the bicycle exploits a supposed energy power, and the bicycle moves forward and accelerates itself, without help of the bicycle rider.

Some months later: More info about education may cut dementia:

http://www.nytimes.com/2016/02/11/health/education-may-cut-dementia-risk-study-finds.html

Fractions.... ugh !

I have read many complaints online from math teachers.
Specifically on Linkedin [sci Math primary/secondary education]:
http://www.linkedin.com/groups/Fractions-ugh-69765.S.5941088157259800577

I would like much to some expert tell me if I'm wrong!.
There (at the SciMath group of the Linkedin) I wrote this:

I'm not an expert, and surely I am wrong in thinking that I will develop.
Anyway I'll try, and I'm sure I will not say anything new, but I'd do at least a
little humor:

I think we are talking about the understanding of the fundamentals of elementary
mathematics:
If you have not settled well the fundamentals of elementary mathematics, when it
comes to fractions can not understand anything. (And I'm not oblivious to this
state)
The difficulty of the fractions is that it requires an understanding of the
division.
And the division, requires an understanding of subtraction, and ultimately of
the sum.

Electronic calculators that are available to all people, both children and
adults do not differentiate between operations: all are on the same level
represented by a key with a painted sign. But conceptually, the knowledge
necessary to understand each of the elementary operations should be
superimposed, and with a particular order. (Although sometimes, as a first
track, in some calculators the sum key is larger)

First we must become familiar with numbers, identified and recognized.
And it seems that we are forced to choose the base 10 by a consensus not really
know where it came from.

From this point, propose a specific order to teach children basic
operations:
As is evident, we must begin by the sum.
But the next step, not subtraction.
The next step is multiplication.
That is, from knowledge of the positive integers, to play with them.
And games and experiments can be the sum, or multiplication.
The amount is usually depicted as a line, that is a dimension, although not
mandatory.
Multiplication games, involve working in two dimensions.
Squares and rectangles: Here, as a game that takes place in a plane or a sheet
of paper should work both multiplication as operation.
I think it's important vision of multiplication as an array of big dots in a
plane.
Here you should begin to explain about numbers that can be obtained from a
multiplication: it should be clear that there are some numbers that can not be
the result of a multiplication.
At this point, children know and can recognize all the numbers perfectly, and
can clearly see that there are numbers that can not fully populate a square or
rectangle.
I think at this time of learning the knowledge of the concept of prime number is
as important as knowledge of multiplication tables. (The prime numbers are the
numbers that you never will find as a result in any multiplication table, and at
the same time any number can be obtained by multiplying prime numbers between
them). The prime numbers are the basic bricks of the complete construction of
the numbers building.

And then I think you have to start again:
We must expand the knowledge of numbers.
In our world, we are used to seeing positives and negatives:
Are protons and electrons, positive and negative charges, matter and antimatter,
attraction and repulsion, money in the bank and debt (currently precisely, more
debt than money), in the old photographic culture negative film, and copies
positive, and finally even the worst example: positive and negative
temperatures.

After familiar with the expansion of natural numbers to integers, you can begin
to explain a new operation: subtraction.
And the rest can use all the analogies offered by nature to experience:
But there is one that is best suited: Matter and antimatter.

Everybody knows that matter and antimatter destroy each other.
And simultaneously, you can create equal amounts matter and antimatter at the
same time from nothing (they can not humans, but somewhere in the universe
happens: To be clear I'm doing a simplification that would make hair tip to a
physics expert)
Imagine games where positive numbers are eliminated with the negative, or the
creation of equal amounts of positive and negative elements from nowhere, with
no any change in the effective amount of all elements above board (the sum of
all them).
Even I have examples in software made by me some years ago.

And I think this is the time to speak of zero. Zero is both "nothing" and also
an undetermined but equally positive and negative elements or matter and
antimatter, pennies in the pocket and debt.

I think the point where we are, the films they have seen children, and games
that will surely develop or imagine, no child will miss in a reflection that use
matter and antimatter as imaginary tool for learning.

At the same time, we could start with the mechanics of operations as it has
always has been done: Subtraction with borrowing and the usual mechanics to
solve these operations.
But with the confidence that the result will always be within the set of the
known numbers. Because we are familiar with a result of both matter and
antimatter, money or money we owe.

We know to add and multiply, and we know subtract.
All the way I'm trying to go, we must never forget that mathematics is a fun
game, and a place to experiment:
Although not essential not think it be reflected by any curriculum, we must not
forget that we have not tried the multiplication of positive and negative
numbers, separated, or mixed. As representable integer multiplication above a
plane, the results are evident. And I guess as a fun game, yet I believe I can
assure you that with correct results guaranteed, although I can understand the
discomfort that may feel a teacher, helpless in front such unusual
situations.

And when we got here, we are ready to face the division.
The result of a division is a sharing out, it is also a proportion.
We're not prepared to afford the mechanism of decimal division.
We would have to broaden our knowledge of numbers:
At this point, we only know the positive and negative integers: natural
numbers.
Before starting to split, one must know the integer division: the sharing
out.

At this point, the division is the inverse operation of multiplication.
When we have the result of a multiplication in one plane (a rectangular matrix)
we can see directly the result of two divisions simultaneously. A square
displays the result of two splits. A square, the same sharing out twice.

Experimenting with splits that to make it easier, at first by simplicity should
be positive numbers, you can reach to see a problem with the distributions of
numbers that are not the result of a multiplication already met the first heard
of multiplication: the prime numbers.
Therefore, we must expand for the third time knowledge of numbers. Must
integrate rational numbers, the fractions.
Each fraction is the representation of a new kind of number: A number that needs
two numbers, one above and one below (or where you want to put). And are both as
a ratio and the description of a sharing out. But in the educational process
should be clear that they are a new type of number: which allows to get the
result of the inverse operation of multiplication for numbers that we could not
arrive until now.

I'll stop my thoughts here.
The explanation about fractions extremely lengthen this already too long
letter.
And I will not do. From now just do a sketch, but I think I managed to
substantiate the basis necessary to prepare the fractions with a little more
comfort than detected in this dialogue so interesting:

At this point, with the basis described, we would have the ability to understand
a little better the fractions, equivalent fractions, the role of prime numbers
in simplifying fractions, and the ease with which we have faced the positive
numbers and negative, integrate them into reflections on fractions, if only to
play but to see also that mathematics is a solid and coherent construction that
which is far from being threatened by the antics that can devise a kid.
And then face the complex world of operations with fractions.
And I think we should stick with the same order we have followed so far:
The sum of rational numbers, multiplication, subtraction and division.
And once experienced this, or at the same time addressing the division with
decimals.
The decimal number as a result of a division is somewhat flawed alternative way
of expressing a rational number also called fraction.

Greetings, and thanks for the opportunity to participate in this dialogue.
This dialogue has been very useful, because it gave me the necessity of
writing, and writing it, I think I have clarified my thoughts a bit. Thank You.
And thanks for the patience if you arrived here.

Adding unit fractions +

 New Android app:  Adding Unit Fractions +

4/5 

The app proposes 21 challenges to overcome.
Obtaining the proper fractions listed at the top of the application, 

adding two or three unit fractions.

Each proposed proper faction has a variable number of solutions.
And different levels of difficulty
You can not repeat unit fractions with the same value.
In the app you'll find a button to delete all the solutions found in the current problem, and to start from scratch.
The littlest unit fraction used in this app is 1/28.
The program is designed to show the usefulness of the subtraction of fractions in solving such problems.

Some hints: 

In the Rhindt Mathematical Papyrus (RMP) in 1650 BC the scribe Ahmes
copied the now-lost test from the reign of the king Amenemamhat III .

The first part of the papyrus is taken up by the 2/n table.

The fractions 2/n for odd n ranging from 3 to 101 are expressed as sums of unit fractions. 

In this app you can build some of the Ahmes  decompositions ( 2/3 , 2/5,2/7, 2/9 ) and 

the discarded ones by him also.

The app allow to decompose also: 

3/4, 3/5, 4/5, 5/6, 3/7, 4/7, 5/7, 6/7, 3/8, 5/8, 7/8, 4/9, 5/9, 7/9, 8/9, 3/10, 7/10, 9/10.

You can use the knowledge acquired solving the 2/X decompositions to solve the rest of the problems

.....   

At first glance we can try the most elementary mechanisms: Subtraction of an essay:

2/3:

2/3 - 1/2 = 4/6 – 3/6 = 1/6; 2/3 = 1/2 + 1/6.

2/3 - 1/4 = 8/12 - 3/12 = 5/12; 2/3 = 1/4 + 5/12 = 1/4 + 4/12 + 1/12 = 1/4 + 1/3 + 1/12.

2/5 – 1/3 = 6/15 – 5/15 = 1/15; 2/5 = 1/3 + 1/15.

2/5 – 1/4 = 8/20 – 5/20 = 3/20; 2/5 = 1/4 + 3/20 = 1/4 + 2/20 + 1/20 = 1/4 + 1/10 + 1/20.

2/7:

2/7 – 1/4 = 8/28 – 7/28 = 1/28; 2/7 = 1/4 + 1/28.

2/7 – 1/6 = 12/42 – 7/42 = 5/42; 2/7 = 1/6 + 5/42 = 1/6 + 3/42 + 2/42 = 1/6 + 1/14 + 1/21

2/9:

2/9 – 1/6 = 4/18 – 3/18 = 1/18; 2/9 = 1/6 + 1/18.

To solve the basic problems of the 2/n table, Milo Gardner 

in the Wolfram's Math World suggests this basic rule first published in 2002:

2/(p*q) = (2/A)*(A/(p*q))  where A=(p+1)

Rule applied: 

2/(3*1) = (2/(3+1))((3+1)/(3*1))= (1/2)*((3/3)+(1/3))=(3/6)+(1/6) = 1/2+1/6.

2/(5*1) = (2/(5+1))((5+1)/(5*1))= (1/3)*((5/5)+(1/5))=(5/15)+(1/15) = 1/3+1/15.

2/(7*1) = (2/(7+1))((7+1)/(7*1))= (1/4)*((7/7)+(1/7))=(7/28)+(1/28) = 1/4+1/28.

2/(9*1) = (2/(9+1))((9+1)/(9*1))= (1/5)*((9/9)+(1/9))=(9/45)+(1/45) = 1/5+1/45

2/(3*3) = (2/(3+1))((3+1)/(3*3))= (1/2)*((3/9)+(1/9))=(3/18)+(1/18) = 1/6+1/18

From the basic 2/n table, we can afford easily the solution of the other problems:

3/4 = 2/4 + 1/4 = 1/2 + 1/6 + 1/4

3/5 = 2/5 + 1/5 = 1/3 + 1/15 + 1/5.

4/5 = 2/5 + 2/5 = 2/3 + 2/15 = 1/2 + 1/6 + 2/15 = 1/2 + 5/30 + 4/30 = 1/2 + 6/30 + 3/30 = 1/2 + 1/5 + 1/10.

5/6 = 4/6 + 1/6 = 2/3 + 1/6 = 1/2 + 1/6 + 1/6 = 1/2 + 1/3.

3/7 = 2/7 + 1/7 = 1/4 + 1/28 + 1/7.

4/7 = 2/7 + 2/7 = 2/4 + 2/28 = 1/2 + 1/14.

….........

Touch Natural Numbers

In February 2010, the magazine "Scientific American" ISSN 0210136X number 401 in the Mathematics Games section, published the article of Agustin Rayo (philosophy professor at MIT) on: "bricks, locks and progressions." http://www.investigacionyciencia.es/files/3486.pdf There are specific items on the RSA encryption method.
And on the Theorem of Ben Green and Terry Tao
The article touched me.And what attracted me was the beautiful graphics representing natural numbers in the form of combinations of spheres and worms were colored graphic representation of primes. (See  Scientific American article in *.pdf cited above).At nummolt.com, I spent many years trying to graph the numbers. You can see my work from 1997 that I mean: http://www.nummolt.com/nummolt/numdown.htm
It is an old tool, based on the reflections made from quotations by Barbara Scott Nelson and others, read online about children's learning when to add and subtract with borrowing. 
But while it is easy to graphically represent the addition and subtraction of natural numbers is however much more difficult to make a simple representation of the multiplication, the amount of calculations involving multiplication algorithm that are used and taught in schools, after memorizing the "multiplication tables".There have been many attempts to make graphic representations of multiplication multiplication Mayan eg: Mayan Multiplication video. 
And myself, I also made my attempts in my programs.But the mere fact that prime numbers as the basic bricks which are built from all natural numbers, had not ever considered. 
When I read the article, I sent a letter to Agustin Rayo to tell him that I had really liked the article, and I naively I asked if the graphs corresponded to any investigation being carried out.
 
He politely replied that the drawings he had done in the best way that he had come to illustrate the article, and do not corresponded to any investigation. 
At this point, I already had developed for years with Wendy Petti program for Mathcats "Place Value Party": http://www.mathcats.com/explore/age/placevalueparty.html In this program we tried to show the value of the position of the numbers from birthday cakes with candles.A few years after,  Ulrich Kortenkamp published the Place Value Chart: Seeing Ulrich Kortenkamp program I wrote to MathForum saying that this program was a lesson for me, and I congratulate the author:http://mathforum.org/mathtools/tool/181488/ 
Few years later, talking with Joan Jareño about a game with primes, from Creamat they warned me about the existence of a poster with primes:
http://esquemat.es/algebra/factores-primos-por-colores
In reference to the original from John Graham-Cumming:http://blog.jgc.org/2012/04/make-your-own-prime-factorization.html 
At this time (2013), I understood that I had all the pieces to build a tool that I dreamed.
When I was looking at the internet to address program development, in addition to the well-known Ulam spiral, I had knowledge of the parabolic sieve: shown by Yuri Matiyasevich  and Boris Stechkin form the Steklov Mathematical Institute of the Russian  Academy of Sciences. 
There's an explanation for this, here: http://plus.maths.org/content/catching-primes

The first had to do was to assign a color to each prime number.Because the app is dedicated to the children, I decided to give the three basic colors first three prime numbers, and intersperse the following numbers.Therefore, red is 2, green 3 and 5 is blue, 7 yellow, magenta 11 cyan and 13. And from there, putting the colors go.The purpose of this distribution is that the resulting color of the product color is the sum of the colors of the prime factors or filtration of colors of the prime numbers.Thus, the color corresponding to 30 (2 * 3 * 5) will be white, and the color corresponding to 1001 (7 * 11 * 13) will be black.

Having decided this, the work was left to do was clear:Show prime numbers as small circles within a larger circle, usually corresponding to a composite number.Removing prime circles from the circumference, equals to divide.Add a prime circle, equivalent to multiply.In parallel, the the app displays numbers in a place value format, but in vertical, as in the  Mathcats "Place Value Party" program.

And adding the display parabolic sieve, and all the numbers well placed within the Ulam spiral and the representation of the module number.
In the end, the program Touch Natural Numbers is a small laboratory that can be studied composition and numbers, and make elementary operations within the set of natural numbers.
And never there is a division that is not resulting integer.
Nor has there ever the possibility of subtraction with a negative result.

Hope you like it, and especially useful for teaching math in elementary school.


Touch Natural Numbers App at Google Play:
http://play.google.com/store/apps/details?id=com.nummolt.number.natural.touch
 

 

Touch Natural Numbers at Youtube:

 

Maurici Carbó

www.nummolt.com

From here I recommend the book "You Can Count on Monsters" from Richard Evan Schwartz, with a similar approach to the natural numbers:

Circadian clock - Google Play

Posted the new "Circadian clock" at: Google Play:

 
The mechanism :
The green outer ring with 5 primary partitions and and 300 smaller partitions gives 59/300 turns per minute counterclockwise: 11.8 turns per hour.
The planetary gear of the seconds, in green color, is driven by the outer ring and gives 59 rph counterclockwise. And in turn, the axis makes a complete turn clockwise, rolling on the inside of the crown of the minutes, by hour.
The hand of the minutes, in blue color, turning on the central axis and linked to the axis of the planetary gear of the seconds, makes a complete turn every hour.
The wheel that rotates clockwise integrally with its base and with the hand of the minutes, make to spin counterclockwise two blue planetary wheels. These two planetary wheels spins counterclockwise a third planetary gear.
The third planetary wheel rotates one turn per hour clockwise and transmits the rotation to the fourth planetary wheel. The fourth planetary wheel spins counterclockwise and progresses clockwise.
The fourth blue planetary wheel gives 2 turns on itself and its axis gives the entire turn around the sphere of the clock every 12 hours.
On the four planetary wheels is mounted the hour hand: a big red triangle, giving rigidity to the structure and indicating the hours and rotating clockwise.
The big red triangle, linked to a freewheel on the central axis, drives the rotation of the three static planetary yellow wheels of the day. Turning counterclockwise about its fixed axis, rotates counterclockwise the yellow big crown that distinguishes the day light hours, of the darkness of the night and makes a complete turn every 24 hours.
The big red triangle, also linked to another freewheel on the central axis, drives the rotation of three static planetary wheels magenta of the week, much bigger than those for the day. Turning counterclockwise about its fixed axis, and spinning counterclockwise the crown magenta indicating the day of the week, and makes a complete turn every week.

Technical drawings for the Circadian Clock:
http://www.nummolt.com/CircadianClock/
© 2014 Maurici Carbó, architect.

 

The circadian clock in action:

 

Circadian Clock: youtube

Notes from the developer:

About the word 'circadian':
The term 'circadian' comes from the Latin 'circa', meaning "around" (or "approximately"), and 'diem' or 'dies', meaning "day".
This app is only a clock, with many layers, showing many overlapped mechanisms, with zoom. The triangle of the hours is manually adjustable, and has an algorithm to reset the clock to the system time after any adjustment.
Nothing concerning the biological circadian cycle.
But one of the layers of the clock represents daylight.

Clarification after some questions:
The Circadian Clock has no relationship with the 'Circassian Circle'.
The Circassian Circle is a dance whose origin is possible in the Circassian people.
The Circassians are a people that was displaced during the conquest of the Caucasus in 1862 and still suffering the effects of the Circassian diaspora:
http://en.wikipedia.org/wiki/Circassian_diaspora

RAE (Real Academia Española): Answer about Quintillón to Centillón

En relación con su consulta, le remitimos la siguiente información:

      Ni el DRAE ni el DPD, ni tampoco otros escritos gramaticales de la Real Academia recogen ningún numeral superior al cuatrillón. El Diccionario del español actual de M. Seco trae uno más, quintillón. Por otra parte cabe decir que tampoco se documentan en nuestros bancos de datos, lo cual es indicativo del escaso uso que tendrían en español. En páginas de Internet pueden localizarse series más amplias de numerales, formados por analogía: sextillón, septillón, octillón, nonillón, decillón, undecillón, duodecillón, tridecillón/tredecillón, cuatridecillón/cuatordecillón, quindecillón, sexdecillón, septidecillón/septendecillón, octodecillón, nonidecillón/novendecillón, vigillón/vigintillón.       Lamentamos no poder ayudarle, pero nuestro cometido se limita a resolver dudas concretas sobre el uso normativo del español, y su consulta se refiere a hipotéticas voces que no tienen ningún uso en nuestra lengua.

     Reciba un cordial saludo.
__________
Departamento de «Español al día»
Real Academia Española

************

Despues de esta carta, pudimos desarrollar:
Calculadora natural


Muchas gracias!!!

Versión inglesa:

How looks a centillion?

Versión española:

Calculadora natural: