Thursday, May 11, 2017


Painting can be a metaphor for teaching. The painter start with preparing the surface on which the paint is going to be applied as students have to be prepared for the instruction and knowledge the teacher is going to administer.

Recent discoveries in Psychology pioneered by Kahneman and Tversky (Prospect Theory) have shown that the way we think is modulated by our emotional state. The old metaphor of the personality being a horse carriage where the horses were the acting emotions and the logic intellect (the mind) was the guiding influence in our behavior was displaced by a new metaphor of an elephant and its rider. An eloquent account of this new metaphor was clearly articulated by Jonathan Haidt in his book "The Happiness Hypothesis." We now know that controlling emotions is like threading water, like guiding and elephant. This is a critical aspect of the teaching-learning dichotomy in the context of a classroom that has been set based on the old paradigm.

Students come to class with a variety of feelings, from excitement for a new experience to apprehension for the unknown and their previous negative experience in the classroom. Over all there is the pressure that students have based on the grading scheme used in today's system of education. Grading which is supposed to be objective and in reality has a big component in subjectivity. This subjective aspect is based on the reality of the behavior of both teacher and student. These of course will be, as mentioned before, highly emotional.

The metaphor of painting as education allows us to think about the steps taken during the class to impart information, and educate students to be able to acquire the knowledge for the subject of the course. The learning has to be done by the student, not by the teacher. The teacher is there to guide the process by which the student learns, so it is imperative that the teacher is somehow aware of the emotional state of the student. This is where priming comes.

In art priming is the process by which a surface is prepare for the painting. Paint layers that will bring not only a new appearance to the object that is painted but will give that object a new meaning. A canvas becomes a piece of art. Painting is more than just adding paint. Painting is transformation. This is the whole idea of education. This is where the metaphor makes sense!

So when a painter is ready with an idea and a canvas the first thing she does is to prepare the canvas, to prime the canvas. This is done by applying a special coat of special material, the primer, that will bring the surface of the canvas to be ready for the paint. Two aspects in the "ready for the paint", one is to protect the underlying surface and the other is to remove any imperfection.

What would the priming look like in the class room? How would this priming prepare the students and remove imperfections?

What I have tried is the following. First address the mood by being happy beyond a simple greeting, happy in the recognition that is always a blessing to be able to learn, to be in a situation where peace and safety are guaranteed. I use candy and birthday celebrations to make students feel welcomed and aware that they are now in a new setting. In Dr. T.'s classroom.
Second. They take an attendance quiz, which is a review of topic covered in the previous class and will not only remind them of the subject but remove any lack of understanding (an imperfection) that imperils their ability to continue learning.
After it is clear that students understand the questions on the attendance quiz, I mention the importance of the subject matter as it relates to their lives. We work on their use of calculators and relevant math to help them feel confident that they can solve this problems. Building confidence becomes one of the main purpose of the priming. A secondary benefit of this kind of priming is that the attendance quiz which returned the following class can be used as a guide for taking exams.

As the primer is not paint, in class the activity chosen for priming might not be related to the lesson. For instance (happiness) blowing bubbles changes the mood, singing "happy birthday" to someone celebrating changes the mood, or just a piece of candy will do it too.

If you have any ideas about priming in class, will you please share them with me?        

Tuesday, May 2, 2017

The T equation

In science we have many numbers, constants, equations, formulas, laws and principles that have the name of someone who invested a long time studying the phenomena related to the former. It is hard to know how long they stayed looking and learning about what they were studying. In most cases it doesn't matter. When dealing with pressure we have the unit Torricelli (torr) in honor of Evangelista Torricelli who invented the barometer. I don't know but it is not hard to think that the invention took many long hours to take place and to improve until he was able to have a working instrument. While he was doing this he was also thinking about pressure. How can it be defined? How can it be related to the forces involved? How can it be related to the area? et cetera. [By the way the pressure of the atmosphere at sea level is about 760 torr.] So the names associated to these constants, units, laws, et al. are in a way a representation of the effort of those individuals and the societies where they lived.

There is also the fact that naming things makes it easier to remember. It has been studied that when someone is presented with two individuals, one named Baker, and the other being a baker. It is easier to remember the fact that one is a baker rather than the name of the other. If you want to know more about this read the excellent book by John J. Medina "Brain Rules".
One very useful equation in buffer chemistry is the Henderson-Hasselbalch equation:

pH = pKa + Log(Base/Acid)

that relates the pH of a solution made with a weak acid or base and its conjugate acid or base. As it is known in chemistry by definition the mathematical operator p stands for the -Log.
So the pH can be calculated from the concentration of the Hydronium ion H3Oby calculating the -Log,

pH = -Log[H3O+].

The Ka or equilibrium constant for the acid base reaction is calculated from the concentrations of the products and reactants in equilibrium using the following relationship:

Ka = [H3O+][Base]/[Acid] with this relationship and using the properties of Log functions such as Log (AxB) = Log A + Log B. One can derive Henderson-Hasselbalch equation.

Now, traditionally when one is trying to calculate what is the change in pH when a small amount of acid or base is added to a buffered solution one calculates the pH before and after the change occurred, it easy to do by using Henderson-Hasselbalch equation twice, and calculating the change by difference.
I have developed a shortcut by doing the following: First I make the point that I know both concentrations, the initial and the final concentration of both acid and base. I will call them Ai, Bi, Af, and Bf. (The final concentrations of course can be easily calculated as we know the initial concentrations and the amount of acid or base added to the solution. Let's not waste time here with an example of how to do it.)
The change on pH of course can be written as the difference between pHf - pHi

ΔpH = pHf - pHi

If we use the Henderson-Hasselbalch equation twice in the previous equation and use the properties of Logarithms we can get to the following condensed equation to calculate the change in pH:

ΔpH = Log (Bf * Ai)/(Bi * Af)     This is the T equation!

This very simple equation states that the change in pH is the Log of the product of the final base times the initial acid divided by the initial base times the final acid. Even though we should be aware of the values of the initial and final concentrations the fact of the matter is that as long as we have the acid and base cross multiplied, i.e. if the base is the initial the acid must be the final, the only difference if we do them vice versa is that the sign of the difference will change from negative to positive or vice versa. Which in reality doesn't matter because we normally want to know the absolute value of the change in pH. We know that if we add a base the pH will increase a bit, and if we add an acid the pH will decrease a bit. But what we are interested is in the absolute value, the magnitude of the change.