Education Matters

In a fairly recent post, I had mentioned how many of Bangalore’s lakes are being killed. But nature is extremely resilient, and given the slightest chance it will bounce back. And some of Bangalore’s lakes are wonderful examples of urban wetlands that are priceless treasures.

I’d recently visited the Hulimavu lake, a fairly large lake just half a kilometre from Bannerghatta road, one of the busiest roads in the city. This road is filled with apartment complexes and office blocks, with traffic that usually moves at 5 miles an hour on good days. Not surprisingly, this lake is under severe stress. There is plenty of legal and illegal construction all around the lake, and much of the lakebed has been encroached. Many of the other construction sites nearby use the lake as a convenient dumping ground for excavated earth. Along one channel, untreated sewage is slowly being discharged into the lake. A whole lot of people seem to use parts of the lakebed like a public toilet. And there are roads running all around the lake, on what clearly was the lake’s spillover bed. As is sadly the case in most Indian cities, the local residents are either unaware or unable or unwilling to do anything about this.

In spite of this, there remains an incredible diversity of life in and around the lake. We decided to take our binoculars and see what birds still inhabit the lake. I was more than pleasantly surprised at what we saw. There were plenty of brown pariah kites, and a few magnificient copper and white brahminy kites (and we were also able to follow a couple of them to their nest, on a nearby eucalyptus tree). There were also plenty of cattle and little egrets all around the lake. In addition, we saw a couple of grey herons in statuesque stillness, waiting for their next fish or frog to swim by, and a good number of moorhen pottering around the wetland. In the lake itself there were a good number of Eurasian coots swimming around, as well as a few snake-necked darters out hunting. These were just the confirmed sightings in a span of about 15 minutes of standing by the lake with Salim Ali’s indispensible handbook, which makes it more than likely that many more waterfowl inhabit the lake.

Urban wetland management unfortunately is not much of a concept in most of India. Yet this lake is just one example of the kind of diversity and richness of life in lakes around the city. It is also a fine example of a lake that could easily be made into a city nature park. To do that, only a little needs to be done to protect the wetland. Obviously, preventing encroachment around the lake would be a priority, as would be stopping the flow of untreated sewage that is choking the lake would be an obvious other step. In addition, the usual mismanagement of “lake development” that most city authorities eagerly embrace should be avoided. Usually, the city decides to build a big “garden” around lakes, which means manicured lawns, paved paths, lots of flowers and trees that don’t usually grow in wetlands, and a complete destruction of the wetland around lakes. This usually ends up slowly killing the lake. Most of these birds live and nest amidst the reeds that grow in lake wetlands, nurturing a rich ecosystem that supports frogs, breeding fish, small reptiles and small insects. Unfortunately, “beautifying” or “developing” lakes by building parks only breeds mosquitoes (by killing off fish and dragonflies that eat them, and breed in the reeds). The Yediyur lake in Jayanagar was a thriving lake that was killed off by just this effort of “development”. First came some lawns, and then there were motor boats and motor scooters, and now it is just a little swamp that breeds mosquitoes.

Instead, if the city could declare some of the lakes of Bangalore protected wetlands, and then spend a pittance on preserving the wetlands, we would be left with wonderful city parks where children and adults alike could spend evenings or weekends observing a diversity of birdlife and plant life (in addition to perhaps small amounts of regulated recreational fishing). It would be a chance to educate and enrich our own lives, and reconnect with nature in the heart of a stressful urban environment. A fond memory of mine is the environment around Lake Washington, in Seattle, right by the magnificent Husky Stadium. The wetlands around the lake are now carefully protected, and there is a beautiful little nature trail, with a description of the flora and fauna around the lake, as well as the importance of wetlands for human survival. People relax here now on weekends, paddle in little canoes, or walk around the unpaved nature trails, or spend lazy sunday afternoons trying to fish (with a permit). Yet this wasn’t always so, and the lake and wetland had nearly been killed in the sixties, and a massive restoration effort of over twenty years revived it. Here, we have wonderful living lakes in the midst of a massive metropolis. Do we need to sacrifice them in the name of “development”, or can we learn to live with them, and allow them to make our lives so much better?

Understanding and Managing Math Anxiety

Have you experienced math anxiety? Most people have. It’s not unusual for most of us to experience it. Even practicing mathematicians experience it. We will probably never liberate ourselves of it, but we can minimize its effect on us by understanding its origin and learning how to manage it.

Symptoms of Math Anxiety

When confronted with a problem involving mathematics, we experience

Nervousness in class or even at home by ourselves

Helplessness/hopelessness during exams and homework

Panic in the form of brain freeze during exams and homework

Origins of Math Anxiety

Anxiety about mathematics has its origin at the same place that anxiety about many things do.

We experience anxiety when we have little or no information about something new we are to experience. Our anxiety about this new experience can even be heightened if we think we will be exposed to it alone.

We might get anxious when we travel to a new city by ourselves and don’t know exactly how to use the transportation system.

We might get anxious when we go to a dinner with a group from work and don’t know many of the people.

We might get anxious when we come along with a new girlfriend to meet her friends.

We might get anxious when we enroll in a photography class when we have little or no experience with cameras.

We experience anxiety when we are exposed to activities or events that are new to us, that we don’t understand well, and that we feel we have little control over. We feel less anxious about things we understand and our anxiety about them lessens as we understand them more. We typically do not feel anxious over things we can control.

Managing Math Anxiety

We can decrease our anxiety about mathematics if we can get to the point where we think we can understand what mathematics is and can gain some control over it.

A big problem in our mathematical education is that we have rarely been told what mathematics is and what it does. Do you know what algebra is and what it does? Do you know what calculus is and what it does? Probably not. You’ve probably not been told. So of course we are anxious about it, we don’t even know what it is we are about to do. Let’s find out now what mathematics is and what it does.

People look for relationships between things. When we find them, we study them. We write expressions that describe how the things are related to each other. Then we use those expressions to extract information about the relationship.

Here are a few relationships we might explore:

There is a relationship between the population of a city and the average speed at which people walk in that city. The higher the population, the faster people walk.

There is a relationship between the diameter of grains of sand on a beach and the slope of that beach. As the diameter of the grains of sand increase, the slope of the beach increases.

There is a relationship between the length of a thin metal cable and the temperature of the air around the cable. As the temperature of the air increases, the length of the cable increases.

There is a relationship between the demand for a commodity and the price of the commodity. Generally, as the price increases, the demand decreases.

I think of mathematics in the following way.

Mathematics is the art of expressing relationships and manipulating those expressions so as to extract information about the relationships.

To help decrease anxiety you might feel whenever you start any mathematical endeavor, think first of the big picture. This may help you understand what it is you are doing.

Big Picture

Think to yourself: In mathematics, we study relationships between things. I am about to study the relationship between this thing, call it Thing A, and this thing, call it Thing B.

Keep thinking: Since the two things are related, there must be something between them that expresses the relationship. The something between them is a set of computing instructions that takes an individual number from the Thing A box, and maps it to an individual number in the Thing B box.

To help manage any anxiety you may feel,

Keep thinking: I am going to work with the computing instructions to
1. Use the computing instructions to extract information about the relationship between Thing A and Thing B, or
2. Manipulate the computing instructions so that I can extract information about the relationship between Thing A and Thing B.

Two major activities of algebra

There are two major activities in algebra. (There are more, but these are the two major ones in my view.) They are evaluation and equation solving.

Evaluation is the activity of using the computing instructions and the order of operations to produce an output value from an input value.

Evaluation: Given and input value, get an output value.

Equation solving is the activity of using the computing instructions and the order of operations “in reverse” to produce an input value from an output value.

Equation solving: Given an output value, get an input value.

Example

In our time/weight example, suppose time (measured in months) and the weight of a tumor (measured in grams). We might wish to predict the weight of a tumor after a certain number of months after is detection.

The various values of time are represented with the letter t.
The computing instructions are represented with the letter w.
The output values of weights are represented with the symbols w(t).

Summary

Calculation is but a small part of mathematics. In an algebra course we spend a lot of time manipulating symbolic expressions so as to make evaluation efficient and to put the symbolic expression into a form that we might recognize. If we recognize the form (linear, quadratic, exponential, etc), we can used procedures that mathematicians have developed to solve an associated equation.

Next Post

In the next post, we will look at naming schemes and how those names are used in algebra.