explicar l'esperança de vida / Explicar la esperanza de vida.

Els desenvolupadors de gapminder han preparat un PPT molt xulo per explicar l'esperança de vida, que és un indicador fonamental del nivell de salut d'una col·lectivitat. Utilitzen una comparació entre 5 nounats burundesos i 5 suecs, que representen la mitjana dels cinc quintils d'edat corresponents ordenats dels que falten primer als que arriben a més majors, i em pareix que resulta molt clara per als estudiants, des del rigor i la bellesa de les dades. Com que està sota llicència Creative Commons (thanks, pals) m'he pres la molèstia de traduir-ho al castellà i al català, i de pas l'he passat a OpenDocument, de tal manera que qualsevol pot no només baixar-se la presentació, sinó també el programa per exposar-la, per exemple a Libreoffice.

Presentació en català.

Presentació en castellà.

Qualsevol millora o comentari serà ben rebuda. Ja sabeu, difon la idea. Per suposat es pot emprar, modificar i/o transmetre sense més límits que mantindre l'atribució als autors.

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When GDP is not a good indicator (and why)

This year our outcome is just 2 chickens... I eat them both. None for you. GDP will say we have 1 chicken per capita. goo.gl/lz9EA
— Kepa G. de Latorre (@KepaGdeLatorre) 30 de maig de 2013

GDP is widely used as an indicator of development. As a matter of fact it is the main indicator mass media, economists and politicians use to show how an economy is performing, and we rarely see other figures. However, GDP is not always a good indicator, taken alone. In this post I intend to demonstrate why not. I can advance that we'll find two issues: average and market dependence.

To begin with, we need to explain what GDP actually is. The standard definition is that Gross Domestic Product, or GDP, is the total market value of all final goods and services produced in a country in a given year. It is to say, it's the sum of total consumption, investment and government spending plus the difference between exports and imports.

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We could more generally say that it is what an economy have produced in a given period, so GDP will roughly tell us the size of an economy, any given year. If we want to compare between different countries then, because countries can have very different number of citizens -think about comparing China and Sweden: there are 142 Chinese for every single Swedish-, we need to calculate the GDP per person, just dividing the total GDP by the number of citizens. That’s called GDP per capita -and it's also known as per capita income. Finally what matters most for checking how we are doing is not the static volume of the GDPpc, but its growth (or decline), because the GDPpc tells us where we are but not where we are going or how we’ve done recently.

The first problem with GDPpc as an indicator of performance is that it is an average, what means it gives you an information that can be hugely misleading if we don’t take into account the distribution of wealth. Imagine that you and me were a very simple closed economy ourselves, and we produce chicken. This year our outcome is just 2 chickens... and I eat them both. None for you. Now GDP will say we have 1 chicken per capita.

If this example feels too simple to you we can take the leap to the real world. There is an index (we may talk about it in another post) inspired by the Nobel-prize winner Amartya Sen and developed by the Pakistani Mahbub ul Haq named Human Development Index (HDI), which is used by the United Nations to calculate development bearing in mind not only income but also two more dimensions: health and education. Small oil-producer countries such as Qatar, Kuwait or the United Arab Emirates typically rank very high in GDPpc -being Qatar the richest country in the world. However, when we also consider these other dimensions, they fall to positions 30 to 40 in the HDI. Qatar ranked 36 in 2012. How come? That's because they are fairly unequal countries and GDPpc is overrating their average development: some Qatari are extremely rich and, as the country is small, they push up the average significantly -and also to some extent because their spectacular growth has happened in the last 30 years or so and it hasn't fully translated onto the other indicators, but that's another story. I'd suggest to take a minute to compare these two indexes in the map below:

Back to our question, the other big issue with GDP is that it only takes into account what comes through the market. Imagine now any economy which have a beautiful forest. We can decide whether we cut down the trees or we preserve the forest. If we decide to preserve the forest GDP would go unaltered.

We won’t be making any profit through any market and therefore, from a GDP point of view, our economy is not growing at all. But if what we do is cutting the trees down then we are paying wages to the lumberjacks and the truck-drivers, we are selling the timber itself, we make furniture with it and pay designers, retailers and management, during the whole process -hopefully- we pay taxes, we have been using (and paying for) energy, generating and processing waste... GDP is growing a lot.

But are we now -after destroying and selling the forest- richer or poorer than with the conservation option? From a GDP point of view there’s no doubt, we are much richer. As it does not exist a market for the environmental value of conserving the forest it simply has no room in the GDP indicator. Instead it only becomes valuable when we bring it down. But that is, of course, wrong. The forest has many values in its own right, even "merely economic" values: just think about the tourists that visit us for our beautiful environment, the soil and moisture that is kept thanks to the trees, the animals living within, the clean air, the real estate increased value of living close to it and so on and so forth. It's only that there is no market for them -they are (positive) externalities, a concept I'll talk about in another post. In this category of not-market (or not visible through the official markets) goods and services we can find other sound activities that are not reflected in GDP: for instance, housekeeping and black economy might amount to a great deal of (hidden) economic activity.

As it does not exist a market for the environmental value of conserving the forest it has no room in the GDP... goo.gl/lz9EA
— Kepa G. de Latorre (@KepaGdeLatorre) 30 de maig de 2013

Summarizing, GDP may not be a good indicator of performance when taken alone. Specifically when we face large inequalities and/or large externalities it can be really misleading. The United States' GDPpc has grown quite a lot in the last century, at an average 2%, nevertheless you can check in this website of the Economic Policy Institute how that growth has been distributed. I'd recommend to play with the tools it provides to check the trends in three periods: before the World War II, 1945-1980 and 1980-nowadays. Of course very different economy policies were taken place -further on we ought to talk about Keynes. The meaningful question that arises is: does the increase in GDPpc reflect a better life for most of today's Americans -namely 90% of them- than their parents had enjoyed?

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Fer que els Mercats funcionen per als Pobres (M4P)

Un altre mercat és possible?

Vaja per davant que jo sempre sospite dels "mercats", així en general i dels apòstates dels mercats en particular. Perquè habitualment sota la retòrica pro-mercats hi trobem gent que el que en realitat demana, ho sàpiga o no, és que els mercats no funcionen com suposadament haurien de funcionar, és a dir, demana que es liberalitzen i es desregulen. O siga, que es deixe camp obert a que els actors amb més poder dintre del mercat generen situacions d'oligopoli o de col·lusió implícita, facen trampa, s'apropien de l'excedent del consumidor, carreguen les seues externalitats en la resta d'agents socials -presents i futurs-, eliminen la competència, aprofiten les assimetries d'informació en el seu favor, exploten els treballadors sense trabes i obtinguen beneficis extraordinaris de la cerca de rendes. Tot això és negatiu per a la societat i per al funcionament de l'economia. I per supost del mercat, entés com s'enten en Introducció a l'Economia. Aleshores es dóna la paradoxa que els defensors dels mercats, generalment, aboguen pel malfuncionament dels mercats. El que cal no és menys regulació sinó millor regulació. De fet és paradigmàtic que els països que han progressat d'una manera contundent durant l'última dècada (Xina, Latinoamèrica, Sud-Est d'Àsia) ho hagen fet gràcies a una economia de mercat que controla de manera efectiva el mercat, allunyats del Consens de Washington i de les recomanacions, no sempre inocents, dels fans dels mercats "lliures". Però. Però ho han fet, al capdavall, mitjançant el mercat.

Pobresa i Mercat

Les poblacions empobrides depenen del mercat per a quasi tot. Hi depenen per a la seua supervivència perquè és on hi venen el seu únic actiu, la seua força de treball. Hi depenen per a proveïr-se de béns i serveis, fins i tot aquells que a l'Occident estem acostumats a rebre per altres mecanismes: educació, sanitat, fins i tot l'aigua -sovint porta a porta. Llevat de pocs casos exitosos (Cuba i darrerament Veneçuela) aquesta dependència del mercat és molt més marcada entre els més pobres que en cap altre estrat social. L'imatge que hem de tenir, perquè és la realitat generalitzada, és la d'uns Estats amb una capacitat fiscal molt limitada que no és capaç d'arribar de manera efectiva, o en absolut, a capes molt amples de la societat i la presència d'ONGD internacionals que estan molt atomitzades i que tenen criteris sovint divergents.

Poc importa, llavors, si hom està "a favor" o "en contra" dels mercats per se -si és que aquesta posició no resulta ser igual que estar a favor o en contra de l'aire, de les mans esquerres o dels diners- perquè la realitat és que els mercats estan ahí, afecten els pobres d'una manera dramàtica, i és dintre del mercat on hem de buscar els mecanismes i les institucions que perpetuen les situacions d'exclussió i pobresa.

Si es preten actuar contra les causes i no els efectes de la pobresa és imprescindible una anàlisi potent dels mercats que marquen la vida de les poblacions objectius. I en aquest cas quan dic mercats vull dir Sistemes de Mercat, o siga no soles el nucli del mercat (diguem la clàssica oferta i demanda) sinó les normes -formals o informals-, les institucions, les funcions de recolzament -que són, a la seua vegada, altres mercats per dret propi-, la tecnologia, etcètera.

Sostenibilitat dels Projectes de Cooperació

Un dels majors handicaps de la cooperació és aconseguir la sostenibilitat, que en aquest context no és més que la permanència dels canvis una vegada finalitzada la intervenció. I hem de reconèixer que s'està fent, en general, malament. Massa sovint les intervencions generen dependència i són insostenibles, i el motiu principal és que es decideix actuar directament proveïnt un servei o un bé que es considera necessari -i de vegades ho és- sense plantejar seriosament com la societat receptora el podrà mantenir una vegada detès el finançament extern. No he vist cap projecte de cooperació que no parle de l'apropiació per part dels beneficiaris i de la sostenibilitat una vegada finalitzada la intervenció. Però escriure en una proposta és molt barat i les formulacions són agossarades. Si l'agència o ONG ha proveït directament el servei... qui el continuarà proveïnt després? I si hi ha un candidat clar a ocupar eixa funció, per què no se l'ha recolzat i preparat des del principi de la intervenció i ha sigut ell l'agent del canvi en lloc de l'organització externa?

La cosa és que massa vegades els projectes no tenen una incidència a llarg termini i quan la tenen aquesta pot perfectament ser negativa. No cal anar a casos d'elefants blancs -hotels en el no-res o pous que cal tancar perquè són un perill per als xiquets i una font d'infecció-. També poden tenir una incidència negativa perquè destrueixen estructures anteriors -que per molt informals o poc adaptades a la ideologia del cooperant en qüestió que siguen, funcionen- o senzillament impedeixen el desenvolupament de noves iniciatives endògenes.

M4P

Per tot això em pareix molt interessant l'estratègia Making Markets Work for the Poor (M4P) proposada per l'Agència Suïssa de Cooperació i altres iniciatives similars, com els Mercats Inclussius del PNUD. La clau per a mí està en un coneixement rigoròs i profund del sistema de mercat on es preten incidir, dels seus constrenyiments i de les seues millores potencials des d'una perspectiva pro-Poor. I altre gran avantatge és que en lloc de prendre un paper protagonista dintre del nucli del mercat es recolza i facilita des de fóra, incidint en els agents que ja hi éren o els potencials nous participants locals. Un parell d'exemples: FIT-SEMA en Uganda va treballar amb les ràdios locals per garantir que la programació era de major qualitat i més útil per als oïents -programes sobre productivitat agrícola o preus dels productes, informació per altres tipus de negocis, etcètera. En lloc de comprar espais i insertar els seus programes com feien la majoria d'ONGD ells van recolzar la capacitat de les ràdios locals per produir-ne els seus propis orientats a les necessitats dels oïents. Resultat: més de 7 milions de nous oïents que reben una informació útil en les seues llengües i produïda per compatriotes seus. Katalyst en Bangladesh, front a l'escasa productivitat agrícola per pràctiques incorrectes i un ús inadequat dels insumos agraris, que tenia conseqüències directes en els ingressos i en la seguretat alimentària de la població, en lloc de fer els clàssics cursos de formació als llauradors locals, etcètera que tenen una incidència necessàriament petita i són poc sostenibles -una vegada finalitzada la intervenció no es pot arribar a nous beneficiaris-, va decidir recolzar la capacitat dels proveïdors de productes agraris -o siga, anant més amunt en la cadena de valor- per a que feren cursos a tots els seus agents, venedors de les xicotetes tendes locals, per a que estos, a la seua vegada, donaren informació i consell als llauradors que els hi compren els productes. D'aquesta manera l'impacte és molt major -1 milió de llauradors- i, una vegada les empreses proveïdores s'han apropiat del model, la sostenibilitat queda garantida.

L'estratègia té límits. Per exemple no pareix que siga la més indicada per a tractar temes de gènere, perquè des d'una perspectiva de mercat és difícil incidir-hi. El mateix pot passar amb temes ambientals, encara que això és menys clar -Soles cal pensar en els mercats de CO2-. A banda de que és una qüestió que ratlla la metafísica o si voleu, la ideologia, el fet de considerar que els Sistemes de Mercat ho abasten tot, o quasi, com els defensors de l'M4P proposen. Però la realitat és que els mercats estan molt presents a la vida dels pobres, i un enfocament que pose als mercats a funcionar per als pobres és clarament una aportació molt útil al debat, sempre acalorat, sobre la incidència, adequació i sostenibilitat de la cooperació.

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Teaching Pills 4 - Applied Financial Maths: the implicit grant of the ICO student loan

Many overgraduate students in Spain have applied during the last 4 years to a new kind of student loan, called ICO Renta Universidad, in order to complete their studies with a Master's Degree. This is pretty new in the Spanish system, despite being very common in other Western countries, specially in the UK and the USA. In this particular case the loan had quite favourable conditions: a 3 years grace period (up to 6 years, under certain circumstances), a 0% interest rate and 10 years to be repaid.

Some of my fellow friends, who meet the conditions to defer either one or their first three years of payments, have asked me whether it would be better to do so or not. Of course there is not a general answer for that, because each one of them would have different current situations and, more determinant, future expectations of income and, besides, there are some other uncertainties such as the internal devaluation in Spain, the labour market dynamics and the prospects of inflation. Thus I give NO advice. Nevertheless it tourned out to be a nice sample to explain how financial maths work. I'll take a made-up case study and I'll do some assumptions about unknown variables: I'll suppose Spain keeps up within the euro -nobody knows what could happen with these loans otherwise- and inflation will be low, but not negative*. I'll take inflation rate in a 2%, which is commonly accepted as the usual target for central banks and quite consistent with a depressed economy with an extremely high unemployment**. Finally, I'll take a 15.600€ loan, amount very frequently applied for, since it was the maximum amount for a one-year master's degree.

The three options they face are:

A) Regular payment. Starting in the year t to t+9 and paying 130€ monthly:

130 (€/month) *120 (months in ten years) = 15600€.

B) Defer one year. Starting in the year t+1, paying 130€ monthly every year up to t+8, and 260 €/month the last year, t+9:

130*96 + 260*12 = 15600€.

C) Defer three years. Starting in the year t+3, paying 130€ monthly the first four years and 260€ monthly the last three years:

130*48 + 260*36 = 15600€.

By all means it's the same NOMINAL amount because it is a 0% interest-rated loan. Does it mean that they are just indifferent? Absolutely not. Here is where inflation shows up: the same nominal money today is not worth the same 10 years afterwards -in terms of the goods and services you could buy with it. As most of us can intuitively deduce that means that, provided we face any positive inflation and with a 0% rate, it would be better to delay the payment as long as possible but, how much benefit would we take of that strategy? As I said, it depends on the actual inflation rate which we can't know beforehand, but supposing this 2% average inflation rate for the whole period and that it keeps constant during the period -this is a strong condition but it allows us to calculate and it's impossible to foresee any trend in advance. You should take it as an average- the figures would be:

B) 130*12/(1+0.02)^9 = 1560/1.195 = 1305.34.

It is to say, the money we don't pay in the year t and we pay in the year t+9 is worth 1305.34 in terms of real (year t based) money. 1560-1305.34 = 254.66€, or a 19.5% saving of one-year's part of the total credit for that deferred year (therefore for a 1/10 of the total amount, an extra overall saving of 1.95%).

C) 130*36/(1+0.02)^7 = 4680/1.1487 = 4074.22.

In this case the money we don't pay in the years t, t+1 and t+2 and we pay in the years t+7, t+8 and t+9 respectively, is worth 4074.22 in real money (years t, t+1 and t+2 based) instead of the nominal 4680. So far, so good. Now if we want to put them all in the same base-year (we should!) we need to financially move the gaining of the years t+1 and t+2 to the year t (that's called discounting when it's backwards and capitalizing when it's forwards) -> for t+1: (4074.22/3)/1.02 = 1331.44; for t+2: (4074.22/3)/(1.02^2)= 1305.33. And for the year t the deferred payment was worth 1358.07 (No extra calculations needed, it's already expressed on the base year). If we consider the nominal payment was 1560 every year we have: 1560*3 - (1358.07+1331.44+1305.33) = 4680- 3994.84 = 685.16€ That's the overall gain of the option C expressed in real terms, taking t as the base year. It means an extra 4.4% overall saving.

I keep saying an extra gaining. Why? Because either way or even not delaying any payment we are already benefiting from the 0% interest rate, provided any positive inflation, and we are, therefore receiving a covered transfer from the government or the bank, whoever is covering the rates -I guess it must be the government, banks are not known by their philanthropic approach to lending. We could, for instance, calculate what's been the actual gain of the grace period for the first payment year, because we know the actual inflation 2.989% (2010), 2.377% (2011) and 2.868% (2012). Supposing someone who had the loan approved on the 1st January 2009, the grace period has supposed, so far: 1560 / (1.02989)(1.02377)(1.02868) = 1560/1.0846 = 1438.31. -> 1560-1438.31=121.69€ (year t based) or 8.46% saving for the first year of payments. In conclusion, the money he or she asked to finish the studies has received a sort of 8.5% grant, so far (for the next years we'll need to multiply this discount factor by (1+i)^t+n, being i= real inflation and n= number of years). Obviously this "implicit grant" will be higher as times goes by, provided positive inflation (for the 13th year, taking a 2% average inflation rate it would be 1.02^13 = 1.2936 -> a 29.36% "implicit grant": the 1560€ you have to pay then would be worth roughly a 30% less in real money than when you got them, given this inflation rate). The higher real inflation during the period the higher implicit grant you get, and vice versa. Whether it is fair or not has nothing to do with financial maths (although I can't help saying that I'd rather go for a public and affordable -ideally free- university system and a proper grant scheme for the poor, which allows everyone to get the education they want, regardless of their current or future income and their lower or higher opportunity costs. But this is another story).

I have only exposed the differential figures between option A and option B and C, which was the relevant information to make a decision in this case. Thereby year t is the year you start to pay the loan and not the year you received it, which would be the proper "year zero" to know the total amount of the implicit grant. It is indeed interesting to calculate the global gaining of the loan -to know which percent of it is a sort of implicit transfer- and if you feel curious, given a 2% inflation rate it would be  roughly a 19-23% depending on the payment option you choose, and in our study case it would represent an implicit grant of 3.000€ to 3.800€, but we can't infere the actual inflation rate and such long term predictions are rather unreliable. We know, however, that given any positive inflation we'll have this implicit grant and that the higher inflation the higher grant. Now we just need to patiently wait until 2023 to check which the actual grant will have been***.

So, in conclusion, the decision about paying now or delaying the payments depends, as I said at the beginning, on unknown factors such as the prospects of inflation, the risk aversion of the lenders and their future employability and/or other income resources. The figures are based on crucial and strong assumptions, specially referring to inflation, but it may be worth and it's always interesting to take a look to what numbers have to say.

*deflation is a real danger, though, if the crisis carries on for very long, Germany is still sickly obsessed with inflation and/or more bubbles burst, but this is another point (macroeconomics and economy policy issues) and one of the reasons I DON'T give any advice.

** It is true that inflation in Spain had been traditionally high and we have quite a dysfunctional economy able to sustain high unemployment and high inflation at the same time (a phenomenon known as stagflation) but the amazingly huge unemployment suggests it won't be the case the following years: before the crisis it reached an average 3% and the last 3 years it's been constantly over 2% (2.99%, 2.37% and 2.87%), while at 2008 and 2009 it was only 1.4% and 0.8%. The slowdown of global markets, the decreasing GNP, the still overpriced housing sector and, specially, the unbearable 26% unemployment rate suggest it won't raise any more than 2%. Finally, I've taken into account that the loan is for a total 13 years and, hopefully, the depressed conditions won't last that long, so considering deflation for the next 13 years seems just unreasonable. A 2% will do.

*** And I found a way of writing a future perfect somewhere ;)

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Teaching Pills 3: teaching through ICT

"In God we trust; all others must bring data" Dr. W. Edwards Deming

In my last TP post I wrote about how you can teach with almost no material resources and in this one I'd like to show just the opposite, how you can use in a sensible way some of the huge amount of resources currently provided by the ICT. There are many websites, blogs and even apps which may help you to prepare materials, to decide teaching strategies and to support your work. The few times I have had the chance to teach myself I have relied heavily on powerpoints, dynamic graphs and maps. I have also made internet research about the subject (no matter I had it very clear in my mind), keeping an open-minded approach not only because I am a novice (which I clearly am) but because you may find extraordinary tools. Today I'm speaking just about two sites I've already used. However, before starting I'd better say two important things: firstly, these resources are a support to your lessons, but they can't substitute the teacher, it's important that you prepare yourself properly for every lesson and that you don't rely too much on your PPT or your internet connection. Questions will be asked and you ought to be ready to clearly explain them. Secondly, it's important that you adapt the resources you find to your objectives and to the stages you are working with, because a messy explanation may be worse than no explanation. Once these two warnings have been issued, let's go to the resources:

Gapminder.org: the beauty of stats

Gapminder is a website offering very nice resources. In my lessons of introductory economics to nurses (yeah, I know it sounds weird, it was nice, though) I used them to show some of the stats relating health and wealth, HIV and children by woman. They are very useful to start debates about the underlying causes behind some issues, and doing it from the scientific approach of data. However, they can be used at any level of teaching and they have this beautiful stuff about life expectancy:

We all know what life expectancy means, only that... do we know? Well, we know that it is an economic indicator very often used to measure the health of a society, and thereby, the development level of a country, but most people, specially young students, tend to think about it like if everyone in let's say Rwanda was going to live more or less 56 years, which is their current life expectancy. And everyone in the UK about 80. Of course this is the wrong way to interpret the indicator. Life expectancy is an average and, thus, it rather reflects how hard is to arrive to be old in a country, how easy is to die before your time. The guys in gapminder.org have prepared a powerpoint that explains it very clearly. Highly usable. It's worth to take a look:

http://www.gapminder.org/downloads/life-expectancy-ppt

Worldmapper.org: Put your stats on a map

This is a demographic-corrected UK map

We are used to see statistics in number or in graphics. And we are used to physical and political maps of the world. In the worldmapper website we can find maps reflecting statistics. I really like them, they set a very interesting point of view, specially regarding to international development statistics such as poverty, GDP, health, education... they are somehow impressive when you compare different regions and they give you a different sight of both the world and your surroundings.

An adaptation I made of two worldmapper.org maps to provoke debate among students: the red one is the world sized by GDP, the coloured one is the world sized by people who lives with less than 1$ a day

Of course, this two are samples I knew about because I had used them before to teach. You could also explain the carbon footprint and let the kids calculate their own one; there is plenty of sites with Maths or English games... it's up to you to use these resources and make learning a bit funnier.

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Teaching pills 2 - Fractions: Learning by playing

We are increasingly getting used to see our kids having access to a whole set of sophisticated (and expensive) tools designed to helping them study: laptops, next generation tablets and mobiles, digital blackboards, very advanced and complicated software, internet and so on. Nevertheless, I believe that the most important thing still is, and will always be, a passionate teacher and the will to learn of the students. You can encourage learning without any of these gadgets, and you can be very effective in breeding knowledge and attitudes with a pencil, somewhere to write on and a bit of creativity.

Two years ago I went to Nicaragua with an education Spanish charity and I had, among other goals, the objective of working with the local teachers in maths pedagogy. Specifically we had to work about fractions equivalency and operations, and we had to bear in mind not just the national curriculum but also the difficult conditions they face every day, almost without material means or support of any kind. That's the main reason the charity worked there. Because of the students' age, which was rather diverse, from may be 6 to young teenagers of even 15 -this is only one of the difficulties these teachers have to deal with, if you believe your job is tricky you should go there and see how they manage to teach in these conditions. Well, I wanted to focus it as a game, and one with different levels. After some weeks of thinking and reading about the question that's the game I proposed for learning fractions equivalency:

You need something to write with (say a pencil) and something to write on (say a paper). You don't need anything else. Not even a blackboard and not for sure a maths book, which they did not have most of the time. Then you make cards, or better, the kids make their own cards, and in these cards you (they) write fractions in different forms: 1/2, 2/2; 1/4, 2/4, 3/4, 4/4.... for the whole game you write percents: 25%, 50%..... numbers: 0,33; 0,4; 0,5; 0,66; 0,75....... and there is no rule saying you need to stop in 1, you can make fractions above the unit: 6/4; 12/6; 20/5........ and percents and numbers as well: 150%; 300%; 1,25; 2,5; 4............ and even mixed numbers: 2 1/4; 1 1/5....... The amount of cards you'll have at the end is up to you. It depends on the number of kids you are working with, the deepness you need to work and so forth. I like to have many, hundreds of them. You can also repeat them, make some sets, which will help you to work in groups.

And what can you do with these cards? Everything.

I proposed them 4 or 5 different games, but they could (and ought to) work out their own games with them: the more the kids played, the more used they'd get to the fractions equivalency, and the equivalency between fractions, real numbers and percents, and operations with fractions like adding and substracting. My idea was the kids working in groups -because they improve their social skills- but you can also do it individually if you believe that fits better with your conditions. Some of my proposals were: Giving a whole set of cards to each group and a) classify the fractions that are actually the same (like 2/4; 1/2; 5/10) -fractions equivalency-; b) find a number by adding fractions: (find 2? one group find it by adding 1/2 + 4/4 + 2/4 another group can use another cards 4/3 + 2/3...); c) and d) You can repeat these games with fractions and percents and numbers all together and so one can find 2 by adding 0,5 + 100% + 50/100, for instance. And in the game c they'll have a little mountain where 6/3, 4/2, 200%, 50/25 and the number 2 will be together representing the same amount. Another little mountain with 1/3; 0,33; 33%; 3/9, 2/6..... Nice, isn't it? The more they play, the better they'll understand what fractions actually mean. A second session of games, once they are used to the cards (which may as well be in the third or fourth lesson or later, depending of their rhythm) would be giving them an incomplete set of cards, and every group a different one. So, now you can create two new kind of games: 1) negotiation games, where to get to the result they'll need to negotiate with other groups to get the cards they need, while offering the cards they don't need. Interesting introduction to trade, bargain and so on -there is a sort of introduction to David Ricardo and trade theory here, eh?- and working a lot of social skills. 2) You can introduce substracting (and even other operations) to arrive to the goal number.

As a matter of fact you could make up many more games with these cards, focusing on different needs (discover the hidden card -intro to equations-; games to identify prime numbers, and so on). They'll pick it up very quickly, though, and the main target of the cards, let them get the hang of the fractions, will be achieved in just one or two sessions. Besides, they have made the game themselves, and they have learned all this while having fun, challenging their minds. You don't need  more than your will and a pencil.

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Teaching pills 1: Primary Maths. The easy way to multiply

What I love of maths teaching is that you are, may be more than in any other subject, teaching a way of thinking. To be honest I don't really know how multiplying is usually taught in the UK, but in my country in most cases it's still regretfully taught as a memoristic skill, with tables from 1 to 10 that children need to memorize and repeat until they automatically can throw up the result of any single-digit multiplication. In my opinion this is not only a rough and boring way of learning something, it also denies the opportunity of logical and deductive thinking to the children and spoils a chance to reinforce their self-confidence and their understanding of how maths work, the relationship between adding and multiplying, substracting and dividing, and so on. In short, wrong way of multiplying teaching. Moreover, it is hard, takes time and can create an ugly -and mistaken- impression that maths are boring. I bet I can teach any kid who pays attention to multiply in just one session and making it fun. I have tried it before with kids in Nicaragua, kids who had a fairly large lack of previous knowledge -which might have been good, at the end- and most of them got it quickly and, with a few hours of practising, were able to do it by themselves. Of course I haven't "invented" (though "discovered" would be more accurate) this teaching strategy, I am sure it's broadly used, with subtle differences, all over the world. Twenty-five years ago I was taught to multiply with part of this at my school Aire Lliure, which used to be -at least at its origin- an impressive education cooperative, a school based on a sort of libertarian pedagogy, teching how to think instead of what to think. I became a fan and I have just completed it.

Here it comes: My easy way of multiplying that promotes deductive thinking is based in two well-known mnemonic rule -the 9 and 5 rule- which most teachers use to teach to multiply by 5 and 9; the natural ability of mentally adding few times (up to 4); and memorizing just two multiplications: 6x6= 36 and 7x8 = 56. Once you know this, and supposing you are able to add and substract, you have all you need to mentally deduce any single-digit multiplication. Children don't need to memorize anything else and, more important, they'll feel good every time they deduce an unknown one, reinforcing their confidence and their maths liking, which may be really useful for their future.

I guess most of you have got it straight away, but I'm going to explain it with a bit more of detail just in case anyone studied laws -sorry, solicitor and lawyer friends, I know the truth can be painful. First, the mnemonic rules: You all know multiplying by five is easy, just the half ten (v.gr. 8x5 = [the half ten of 8] 40). Most of you might also know that multiplying by nine is very easy indeed, just the previous ten and what's missing to get to nine. It is to say: if you want to multiply, for instance, 6x9, you take the previous ten of six (5, fifty-something), and the unit is what's missing to make nine: 4. So, 6x9= 54. This works. Ok, we've got every single number multiplied by 5 or 9. Then, adding up to four times can be done mentally without effort. So, we have deduced every single digit multiplied by 1 to 5 and by 9. Now we have these two ops, 6x6=36 and 7x8=56, which we'd better memorize (we could eventually add them but I have realized it's a bit tricky for children) and now we have a supporting point to get to every single-digit multiplication directly or by just adding or substracting the number once. Think about any single-digit multiplication, let's say 6x7? the child mental process would go: Ok, I know 6x6=36, so if I add 6 I'll have 6x7! 36+6=42. Good. 8x3? Ok, eight and eight, sixteen, and eight twenty-four. Easy. 8x6? Humpf, well I know 8x7=56, so if I substract 8 I'll have 8x6 -> 56-8=48. Or either I know 6x6=36 I add six twice and I'll have 8x6 -> 36+6=42 +6= 48. And so on, and so forth.

 It's a perfect system, and despite it may look a bit complicated in writing it's very easy indeed to do mentally. What I love of this teaching strategy is that it focus not in memoristic learning but in deductive abilities. It relates multiplying to adding, which is nice, and to substracting also, which is even better because it gives the child a more comprehensive understanding of mathematic relationships, but the important point is that it reinforces a lot their self-confidence and transforms the maths in a deductive game, something that is worth and fun. As it should be.

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Good (and bad) practice among advertisement in Charities / International Development

A short time ago I saw an AWESOME advert, which had been deployed as part of a campaign on safe water supply by UNICEF Sweden. As this and the following are all public advertisements I have felt free to reproduce them here:

I really loved the advert for many reasons and I would use it with no doubt as an example of good practice in charity advertising whether I had to give a lesson about the subject (hopefully some day, why not?) or explain to a friend what I believe should be done in such cases. In my opinion it has a perfect sensitization approach, it is indeed shocking as it must be, while being very simple; it is far from taking any advantage or making an unfair use of the beneficiaries; it is also far away from the moral blackmail that still today is regrettably used sometimes -bombing the tired eyes of the audience with unbearable extreme situations-; technically is perfect; and besides it makes you mull over your preconceptions about which actually are the most harmful dangers the children in empoverished countries face, so, it raises the awareness of the people.

Sensible people might think that among the charities should be a strong commitment with these values, that they'd be specially careful when using pictures or messages, for they are not typical companies trying to fight for customers, they are rather social agents engaged to sensitize the population. To be honest, most of them are aware of that and create nice examples like the bad-water one. Some of them do not. There seems to be an increasing competition between them to get the confidence (and the money) of the largest possible part of the goodwill market -instead of spreading this "market" (sorry for the word) and, therefore, they appear to forget the awareness role and have a competitive approach based on the market rules- say almost-no-rules. Thus, they'd fight to take the money to their projects, and make use of any mean. I'll ilustrate my opinion with two samples.

Please, bear in mind that the following examples have been found after barely one hour of internet research and that I don't intend to critisize any individual charity, but only the way they have tried to advert themselves in this specific poster. I'm sure we could have found adverts alike from many other organisations and good adverts from these ones. I must also thank my fellows and friends Dinka Acevedo and César Jiménez for their contribution.

 First sample: it is incredibly easy to find campaigns making a reproachable use of the beneficiaries, even children, to advert the NGO.

This little girl has eventually become the Hussain Bolt of the medical aid, and the sponsors wanted to be sure their logo was clearly readable. The smile of the lifeguard could also have been used in a toothpaste campaign. I am sure they were able to promote themselves without having to use a child in this rough way. For my standards this is an unfair use of her, even though I have found people thinking otherwise. Anyway, we can do it better than that.

Then, we can find the moral-blackmail-strategies. This would generally consist of appealing to your feelings of guilt by bombing your eyes with dreadful pictures of abject poverty, sickness, misery or hunger. We all have seem them, since they were very tipical in the 70s and specially the Ethiopia's famine was widely used to raise funds. I don't argue that the funds were needed and getting them fastly by any means could eventually have a positive effect in the short term, but they used these kind of pictures far too much and this overuse became in a mental block of the donors (no bother they call them partners, it is part of the marketing). We can find more subtle or imaginative samples though, and I have found one that I believe illustrates exactly what I am trying to explain. It's in Spanish and, even though the picture is quite expressive by itself, I can't help translating the text. It reads: "One of them has got house, food, water, education and medical care. Guess who?" and underneath "Help us to change it". I sincerely hope that this poster has meant one or two sacked people either in the NGO or in the publicity agency. I don't know what annoys me more, if the small child or the glowing dog. This sort of adverts try to steadily blackmail the audience and this is ethically unacceptable and should never be done. It is not giving any useful information, nor raising awareness, just guilt-feeling.

I think that the charity advertisement should be conceived to change attitudes more than raising money, or at least change them while raising money. They must be carefully designed to present the utmost respect to the objective population and to the audience at the same time. They should move to actual actions, for small they were, which help change things for good. In this respect there are indeed many actions we can perform from here to change things, such as ethical shopping, political lobbyism, voluntary involvement or reducing our consumption (of goods, energy). We should be showing far more of what we can do and a lot less of what we can't avoid to happen, since this is counterproductive. And, last but not least, they should avoid creating a perverted picture of the truth. To illustrate what I mean and to finish with a thoughtful smile, another awesome brand new campaign, now on video: Africa for Norway, RADI_AID!!!

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Decreixement, la utopia concreta: Viure millor amb menys

És possible un creixement infinit en un món finit? Podria paréixer una pregunta absurda de no ser perquè la resposta que donen els models econòmics liberals és 'sí'. Com que els mètodes de producció i consum, les normes que els regulen i la mateixa concepció de la societat moderna estan basats en aquests models neoclàssics de creixement potser fóra interessant parar-se un segon a pensar sobre el tema. L'editorial 3i4 dins la seua col·lecció 'Gaia / Pensament global, territori i medi ambient' ens presenta una cuidada edició en català de dos dels llibres del guru del decreixement Serge Latouche: Petit tractat del decreixement seré i En defensa del decreixement. Tots dos s'insereixen entre els moviments post-desenvolupistes i bioeconòmics, els corrents actuals més puixants i influents de la crítica al model productiu i a l'imaginari no sols capitalista sinó desenvolupista i economicista. El primer, de més càrrega teòrica, és una mena de manual decreixentista que pretén servir d'eina de treball per als responsables polítics conscienciats, mentres que el segon està plantejat com un FAQ sobre el decreixement: hi inclou respostes a les objeccions més freqüents, aclariments de punts obscurs del cos teòric, controvèrsies, aparents contradiccions i en definitiva un argumentari concebut segons explica l'autor per armar els partidaris, especialment els joves, que estan menys bregats al debat intel·lectual.

Trencar amb l'imaginari

Arrelat en l'ecologisme polític i en autors de la rellevància de Nicholas Georgescu-Roegen, Ivan Ilich, André Gorz o Cornelius Castoriadis el decreixement, o més pròpiament en paraules de Latouche "acreixement en el sentit d'ateisme", pretén "rompre les ambigüitats dels addictes al productivisme i rebutjar el culte irracional, quasi idòlatra del creixement pel creixement". Latouche, portaveu autoritzat dels objectors del creixement fa una crítica ferotge al sistema productiu mercantilista i la seua lògica perversa producció - ocupació - consum (o en altre nivell publicitat - crèdit bancari - obsolescència programada) que ens abocaria de manera inevitable més prompte que tard al "decreixement [forçós] o la barbàrie". Començant per rebatre la ignorància voluntària que els economistes teòrics neoclàssics han fet de la natura en els seus models -mitjançant el truc d'indiscutible elegància matemàtica de la infinita substituïbilitat dels factors, i valorant les lleis de la termodinàmica que impliquen que alguns processos són irreversibles i que cada vegada el cost en recursos serà més gran i no menys com preferim creure, l'autor considera que estem clavats en un atzucac de conseqüències catastròfiques per a l'humanitat i, potser, per a la vida mateixa al nostre planeta: el creixement és el càncer de la humanitat.

L'abundància frugal

Cal, per tant, abandonar la senda de l'acumulació que s'ha intensificat de manera dramàtica en el segle XX i tornar o reinventar un progrés basat precisament en la frugalitat, en l'autolimitació de les necessitats (per això és fonamental limitar la publicitat i les necessitats creades) i en els béns relacionals com la cultura, la conversa o la participació política que no s'exhaureixen per l'ús sinó que hi creixen front als béns materials, renovables o no. L'abundància frugal implica també una aposta per assaborir la lentitud, com al moviment slow-food que arreu del món té cent mil productors, llauradors, artesans i pescadors que lluiten contra la uniformització de la nutrició i per recuperar els gustos i els sabors. Dóna fins i tot consells per una dieta frugal: més estacionària, més vegetariana i més local. Per a Latouche l'abundància frugal no és més oxímoron que el desenvolupament sostenible, concepte ja àmpliament desprestigiat -alguna cosa està malament si el director general de Nestlé pot emprar el mot sense rubor. Aquesta abundància frugal estaria, doncs, molt relacionada amb la simplicitat voluntària, l'assumpció conscient d'una manera de viure senzilla, que rebutja el consumisme i la falsa ètica del treball obligatori, i que posa l'èmfasi en un humanisme que pot ser més o menys hedonista, però en tot cas vivencial i d'una escala indefugiblement humana.

Retornar al món local

Bona part dels problemes de la globalització o mundialització de l'economia estan relacionats precisament en l'abandonament del món local. En aquest sentit Latouche entronca amb propostes que vénen del sud, com el consum de proximitat preconitzat per Via Campesina i el Fòrum Social Mundial, i reivindica un retorn a allò local, a l'agricultura local i el consum local que garanteixen una sensible reducció de la petjada ecològica, un augment de la seguretat i la sobirania alimentària i la creació de llocs de treball a l'entorn en què s'hi viu. El comerç local front a les grans superfícies implicarà millores en reduir la zonificació, fent innecessari l'abús del vehicle privat i reforçant el teixit social i la cohesió als nostres pobles i ciutats alhora que redueix la pressió sobre els països empobrits, especialment vulnerables als daltabaixos dels mercats internacionals i a l'especulació. Latouche ens proposa un veritable "reteixit" orgànic de l'àmbit local, no tancat en si mateix sinó constituït en una xarxa de municipis a la manera en què ho presentaria Roberto Camagni, que situa l'escala de la vida, de la democràcia, ara sí, participativa i de les relacions a una dimensió més humana i més serena.

Desintoxicar-se de l'addicció a la feina

Front a les crítiques que, amb tot el sentit, indiquen que al si del capitalisme una aturada del creixement -fins i tot un creixement feble- implica una reducció dels llocs de treball i un augment de la desigualtat i de la conflictivitat social, l'autor advoca per compartir la feina i recuperar el plaer del lleure, no tant de l'oci en el sentit mercantilista sinó més bé el plaer del temps recuperat per a u mateix, per al joc, la contemplació i la participació pública. Compartir el treball serà doncs una condició necessària per a reduir el consum de recursos naturals, i junt amb la fi de l'explotació de les poblacions del sud amb la relocalització esmentada adès, garantiria una transició d'un model productivista a un decreixentista. Malauradament en aquest camp les propostes, tot i la seua més que probable utilitat, semblen hui en dia molt allunyades de les agendes, més si cap després del fracàs de la iniciativa de les 35 hores a França.

Quina crisi del pensament?

Tant si estem d'acord amb les tèsis decreixentistes com si ens trobem perplexos front a una crisi sistèmica que no pareix bosquejar la seua fi, o si, senzillament, hom vol saber més sobre com i per què viure millor amb menys i sobre temes tan interessants com l'equitat nord - sud, el deute ecològic, les recomanacions que el decreixement té per als països empobrits, el caràcter revolucionari o reformista del moviment, què s'amaga darrere de les huit R, la conveniència d'un partit decreixentista, la utilitat d'una moratòria tecno-científica o sobre les propostes concretes del seu programa polític aquests dos llibres de Serge Latouche són una manera estimulant de plantar-li cara al futur amb una mirada revolucionàriament assosegada.

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Llengües amenaçades: en favor de sí discutir per conscienciar

(Nota de l'autor: Altres llengües al lateral -->)

Recentment vaig tindre, en una assamblea mixta de Redolí i la nova fornà de cooperants nascuts de l'inefable IIDL de Castelló, l'oportunitat de tornar a debatre, per moments acaloradament, sobre la nostra llengua, la pretesa imposició que en fem, etcètera, com en una mena de dèja-vu col·lectiu en el què molts us hi trobareu representats. Hui m'he trobat un modest documental del que pensen els maies sobre els maies i com que era gravat a Quetzaltenango, ciutat on vaig tindre la sort de passar un temps i parlar amb mams, quetziquels i altres hereters de la cultura maia, m'ha sorgit escriure aquesta reflexió:

La solució més còmoda sempre és no discutir. No corres el risc de ser malentès, ni de caure-li malament a ningú, ni d'acabar empestat. Saps que la llengua és una cosa tan clavada en la identitat de cadascú que, indefugiblement, el debat pujarà de to i les postures tendiran a radicalitzar-se.

Els de la Plataforma per la Llengua sí que saben motivar

Jo personalment m'estime més discutir. Perquè crec que en tot diàleg, si és sincer, encara que siga fort, hi ha un intercanvi d'idees i que aquestes idees enriquiran a totes les parts. Incloent-me a mi, clar. Les idees són una llavoreta que germinarà potser en mesos o anys però que allà queda. També és cert que els que tenim per costum fer didàctica sobre el tema, ni que siga a martellades, estem molt bregats mentres que els nostres oponents, dignes, intel·ligents i benintencionats, és potser la primera vegada que s'han trobat oposició argumentada i bel·ligerant front a les seues idees monolingües. Per això jo he trobat dreceres, perspectives i exemples que, de tant testar-los al camp de lluita, he anat refinant i optimitzant i aquesta entrada del blog pretén fer una collita, oberta i no exhaustiva, de part d'aquesta munició (dialèctica) efectiva:

- Jo no crec que parlar en valencià siga el meu dret. Jo ho considere el meu deure. I ho explique amb el següent argument: És cert que els filòsofs francesos (diguem-ne Rousseau, Descartes) i els alemanys (posem Schopenhauer, Nietzsche) pensen molt diferent i en canvi es pareixen entre ells, al menys en la manera de construir les idees. Això és clarament perquè pensen en francès o en alemany i és que cada llengua és una manera de veure el món. Contribuir a mantindre una llengua amenaçada amb vida és aportar no als parlants (passats, presents o futurs) d'aquesta sinó a la diversitat cultural del món. A la profunditat del pensament possible. A la riquesa de la humanitat.

- Respecte al requísit lingüístic i la "imposició" del català en determinats àmbits, tres arguments: 1) Si es reconeix que vivim en democràcia (?) i llibertat no té sentit que l'administració no entenga els administrats en la seua pròpia llengua. L'única manera de garantir-ho és el requisit lingüístic per a la funció pública. 2) Les llengues naixen, creixen, de vegades es reprodueixen i, finalment, moren. Una llengua que no és necessària morirà. I com que el bilingüisme és sempre diglòssic, una llengua minoritzada que no troba àmbits on siga necessari d'aprendre-la, està condemnada a morir tard o d'hora. i 3) És que a ningú no se li acut que un professor de matemàtiques anglès vaja a donar classe a Madrid o a Medina del Campo i no li done la gana d'ensenyar-se el castellà, faça les classes en anglès i els alumnes ja s'ensenyaran. És que qualsevol que trobe feina a Dinamarca de per vida ja té consciència de que haurà d'aprendre danès. Aquest tercer argument és útil també quan l'oponent va a terrenys possibilistes del tipus "en un món global la llengua minoritària no em resulta útil" o "és que el valencià el parleu quatre gats". El danès el parlen tres gats (6 milions front a uns 10 del català) i per suposat si anem al món global let's speak English, my dear fellows.

En fi, que tampoc cal perdre amistats ni que et lleven la paraula. I quan es debat sobre llengües apareixen una gran quantitat de sentiments i no tots reconeguts. Per exemple, entre els monolingües honradament progressistes (siguen punkis, cooperants o sociates) hi ha una fosca consciència personal de que s'està col·laborant, ni que siga per passiva, en un genocidi cultural. Això fa que es posen molt a la defensiva, perquè tenen un remordiment més o menys inconscient i els incomoda molt. Cal tractar-lo amb carinyo. I no patim, si més no, apuntaran als seus fills a la línia en valencià :) Després hi ha un sentiment fortament identitari en la llengua. La llengua ens defineix més que cap altra part de la nostra cultura. També s'ha d'anar amb compte, perquè això cega molt i fa que l'agressor real se senta agredit si, per exemple, un desconegut li parla en una llengua que desconeix quan ell pensava que estava en el seu àmbit lingüístic. I li pareix de mala educació el que és ser educat: donar-li l'oportunitat de començar a aprendre la seua llengua. En realitat el que és de mala educació és guardar-nos la nostra llengua per a nosaltres i impedir al foraster accedir a ella.

Per acabar he de dir que al debat hi havia, molt callada, una xica d'Almoradí. Va demanar la paraula i va anunciar que ella soles diria una cosa. Les gotes de suor perlaven el meu front. Ja ve la Vega Baja del Segura, cos a terra. Però la xica va dir, amb eixe característic accent panotxo: "Lo que no puede ser es que haya gente que se vaya a defender el quechua y el aymara y luego vengan a su casa y hagan todo lo posible por exterminar el valenciano." Ole.

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