Activity I Dear friends, The Variables are an a interesting subject for our lives! And a very interesting subject for me and the students. We are doing a special experiment for Felipe's proposal with the 14 year old students. All Romanian children between 7 and 18 years old get a monthly allocation from our government: 50,000 lei (Romanian currency). That means 0.60 US$ (60 cents). The parents of the students get the money until the children are 14 years old. After 14 years (when the student have an identity card), they can take their 50,000 lei directly from a Bank. I proposed this experiment to my 14 year old students because is the year they receive their identity cards and they become real "citizens." Here is the situation in our country. Two weeks ago, our government raised the price of petrol more than 50% for "national budget equilibrium." We decided to make a theoretical experiment using variables. All Math Team students from School No 10 calculated and manage their little "budget." First we did a simple calculation. We considered 2 situations: before and after the moment that petrol became more expensive and chose 2 prices: for one standard bread and for 1 liter milk. We asked: How much bread and liters of milk we might buy using our allocation before, and after the increase in petrol price? Next, we calculated the cost of petrol in prices of food (preparation, transportation). We decided that in most cases, that should be only 10-15%. The problem:We studied the new prices for bread and milk and they did not reflect this percentage.The new prices are too high. The percentage [of increase in the price of petrol] should mean only a raise of 10-15% [in the price of bread and milk], not 40-55%. Maybe all traders want some quickly advantages. My intention was to put the students in a real situation: to be witness to a difficult period - the transition to a new life. Dear friends, we are looking forward your suggestions: What could be the best way for us to change this situation? Have a good day! Petru and Math Team

Last week our class developed an activity on this subject. We suggested the following Math problem: The students from the 4^th grade class have planed to go on a trip in April this year. We will invite all our brothers and sisters. The price/ person is about 10 $, 140,000 lei, "leu" is Romanian currency, 14,000 lei means 1 $.

There are 16 families with only one child, 21 families with 2 children and 3 families with 3 children. How much money will pay to the travel agency for the trip? How much money will each family pay in case they have only one child? What about a family, having 2 children? What about a family has 3 children? We used "a" for the trip price/ person.

The payment deadline is the 1^st of April. We should have paid:

(16+ 21* 2+ 3* 3) *a = 67* 140,000 = 9,380,000 lei.

Since 1991 the prices in Romania are changed to US dollars. I need a larger sum of "lei" to buy one dollar every time inflation "raises its head"! That is a real drama for Romanians, because their salaries are not correlated to the dollar increase. The salaries are decreasing over and over. This week has been full of surprises from this point of view. One dollar has increased with 2,000 lei Wednesday and this is a real shock for our trip plans. The travel agency called and informed us about the price increasing.

How many "lei" I need for the new price/ person in case one dollar means 16,000 lei? We use the same "a" from the first table and "b" for the additional sum of the trip price/ person. (20,000 lei)
 

	Money spent by each family category	Total money/ family	Total each family category
LAST WEEK
16 f 1 child	a	140,000* 1=140,000	2,240,000
21 f 2 children	a*2	140,000* 2=280,000	5,880,000
3 f 3 children	a*3	140,000* 3=420,000	1,260,000
T o t a l l e i			9,380,000
THIS WEEK
16 f 1 child	(a+b)*1	(140,000+20,000)*1=160,000	2,560,000
21 f 2 children	(a+b)*2	(140,000+20,000)*2=320,000	6,720,000
3 f 3 children	(a+b)*3	(140,000+20,000)*3=480,000	1,440,000
T o t a l l e i			10,720,000

We compared the both situations from the last and this week. Unfortunately, this statistics obliged us to cancel to our trip plans, because the students' families have other priorities.

Petru Dumitru, Romania

Comments from Felipe Zatarain
Math Educator and Invited Guest to the Connecting Math to Our Lives Project

As someone who lived in Mexico when the Mexican peso was devalued I have seen the impact of hyper-inflation on those least able to protect themselves from its destructive impact. I myself was fortunate enough to work in the United States so the impact was beneficial to me and the other 25% of Tijuana (the Mexican border city in which I lived) workers employed on the United States side of the border. My friends, taxi drivers, carpenters, factory workers, who worked in Tijuana found each week that their hard earned money bought less and less, so life began to revolve around the necessities.

Parents try to lessen the impact of these changes on their children, but the cancellation of a class trip brings children into direct contact with these realities. It is my firm belief that children should examine those realities with mathematics, just as Petru's students have done: this is Connecting Math to Our Lives.

One of my colleagues, Enid Lee, says that numbers can tell only half of the story. The other half is the narrative interpretation of our mathematical results. It is the search for reasons. If math is used to examine social and economic situations what is the story about why this is happening, and the effect of these numbers on people (from those who seem to benefit most to those who benefit least).

Some questions which Petru's students might think about answering are: Why is the lei linked to the dollar? What percent of total family income was to be used for the trip? How did this change when the lei became priced at 16,000 to the dollar? What sector of our society benefits from this change? What sector does not benefit?

I hope other teachers in this project have examples similar to Petru's. Connecting math to student's lives gives them not only a way of learning mathematics, but of understanding more about themselves and their society.

Thank you again for your participation.

Felipe Zatarain

 

Comments from Kevin Rocap
Co-director, Center for Language Minority Educational Research

I truly believe that your students could teach some economists I know a thing or two. Your example of the loss of salary purchasing power based on the exchange rate of the Romanian lei for the U.S. dollar is really central, in my mind, to major theoretical and policy debates taking place now regarding global economics.

The term "convergence" is used by some to talk about the idea that the current high mobility of transnational capital leads to a globalization process whereby individual nation-states (like Romania) may have less and less power to enact policies to protect and support their local economies and their local populations. To oversimplify a bit, nation-states have to subordinate themselves to transnational and global policies and practices. They have to "fall in step" as it were with the global market economy. This is called convergence. Convergence can result in loss of protections for workers, etc.

Others argue that "convergence" is a myth and that countries like France and Germany who put in place strong nationalist policies are proof that convergence is not a necessary outcome of current global economic relations. My guess, as someone who is not an economist, is that the answer is a little more complex and mixed than that. That is, that examples like France and Germany are examples of relatively strong national economies. It is not surprising to me if they have some strength to resist global influences. But the large majority of countries likely are not in a position to resist strong transnational economic forces and are therefore subject to adverse convergence effects.

Some economists would also object to me linking convergence to monetary issues - currency exchange rates, etc. - they would say that convergence is really about things like individual nations being influenced to lower their minimum wage, to provide tax incentives to transnational corporations or to stop workers from being in labor unions. But I prefer to look at outcomes. It seems to me that it doesn't much matter to your students and their families whether their money buys less because their wage has been lowered or because their buying power has diminished. But I am, I suppose, a naive non-economist.

Your example brought important questions to mind for me:

Do you think that students and classes who are able to take greater numbers of trips for learning purposes do better academically? (In the U.S. we refer to these as "field trips"). Good field trips provide increased opportunities to learn in a real world context and can be highly motivating for students.

If students who do go on trips do better academically because they have more opportunities to learn, then are students and classrooms put at an academic disadvantage if they cannot take as many (or any) learning trips?

Thus do fewer learning trips lead to reduced academic success? Does that in turn lead to less success entering and succeeding in higher education? And then less success in getting satisfying high paying jobs? And, in the aggregate, lowered national economic productivity?

I think that your students have opened up quite a critical "can of worms" - some deep and difficult topics to think about. I wonder if there are ways to raise these issues appropriately in classes like yours? I know that my comments are more geared to you as a teacher. It is challenging to think about how to raise such issues constructively with students. Any ideas? Anyone?

Thank you again for your example. If your students don't mind I would like to share their calculations with some economics students at University of California, Berkeley.

Kevin Rocap