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 = pK_a + 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 H₃O⁺ by calculating the -Log,

pH = -Log[H₃O⁺].

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

K_a = [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 A_i, B_i, A_f, and B_f. (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 pH_f - pH_i

ΔpH = pH_f - pH_i

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 (B_{f *} A_i)/(B_{i *} A_f)     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.

Linear Thinking and Hub 4 CIS^2

In his book "The Biology of Belief" Lipton does a great job shifting the paradigm of nucleo-centered biology to membrane-centered biology and uses quantum physics as a powerful tool to argument for the shift. (For a Youtube video of this book click here) The importance of this new way of looking at how cells function is that it gives the environment a critical roll in the behavior and development of cells and organisms in general. Environmental stimuli are critical in the way we think. In a similar way John Medina in his book Brain Rules tries to articulate principles that explain why the mind works the way it does. (To see the rules click here.)

When one thinks about how to learn something or how to teach something we normally assume many things and ideas that should not be assumed. For instance the fact that we are all different, we are different at the nanoscopic, microscopic, and macroscopic levels, meaning that there is a genetic, organic, and environmental difference. Paradoxically we all -at the same time- aspire to unity, homogeneity, and similarity. How can we work with this paradox in education? It really looks like the old nature versus nurture dilemma but it is not. This paradox provides with an integrative approach to understanding how we survive and thrive in our work, family, and society in general.

Changes require changing, as I belive Yogi Berra would say, so what kind of changes do we have to do in order to have a positive influence in the changes that inevitably are going on.
So far linear thinking has guided us here. In many ways our society is based on linear thinking, but that is not longer (maybe hasn't been for some time!) the case. We need to thing more organically. We need a non-linear -web like- way of doing things. The Internet has proven the efficiency of this model. But has also opened possibilities for wrong doing. This is where there is a very important role of education in guiding the changes that are occurring.
 
I have developed an idea for a setting; an idea for a context and an environment. I call it Urban Hub 4 CIS². Urban Hub for Creativity, Innovation, Sustainability, and Stewardship. In this Hub 4 CIS² people will join others in their pursuit of learning. Means and attitudes will be there to help all who want in the achievement of their goals. Including of course academic and vocational counseling to those who need it as some will need some help in defining their goals, objectives, and aptitudes to accomplish them. Students will flourish as they find their strengths and institutions will prosper as they increase the efficiency in which they serve their constituents. It is a win-win-win proposition. The individual wins as s/he becomes more involved, aware, and engaged with is his/her (hir) success. The institutions win as they become more effective, solid, and sustainable. And, of course, we all -society- wins as it becomes more just and equilibrated.   

More Trust

It has been a long time since I posted on this blog, and it was about Trust. In it (click here to review) I mention how leadership is based on trust. But then I was not thinking so much about institutional trust, the trust that people have on institutions. Indirectly of course there is a relationship between personal/individual trust within an institution and the trust that refers to the institution. Now I want to address how trust in the institution affects the way we trust each other. In particular the trust that is necessary between educators and students to guarantee student success. (If there is any way to guarantee student success it is through trust.)

As we live in a continuous changing world we have to be aware of types, and areas where these changes are taking place. This analysis and awareness is difficult because the orthodoxies of life give the impression that there is some stability and the Status Quo dominates our actions, behaviors and aspirations. There is a strong inertia in our ability to read history and to understand who we are based on were we have been. Specially when, regarding education, there are norms established by accreditation institutions.

At the forefront of changes in education is the one related to science. STEM not only has fed changes with a lot of energy but in a way it has guided the direction in which these changes have occurred. Changes in medicine, energy, transportation, communication, and in general how we relate to our environment. We can't continue teaching science in the same way we have been teaching for the last 300 years. There are some paradigms like the definition and use of the scientific method that can and should continue to be adopted, but the delivery of these paradigms might (most like shouldn't) be different.

Paradoxically it looks like some of the changes that are occurring appear to move backwards. To some kind of original intent in our society. For example it looks like we are going back to the idea of personal prestige rather than the prestige of the institution. We have never lost the personification of some institutions as we clearly identify individuals with some corporations. More so if this institutions are of recent creation, say Microsoft is clearly identified with Bill Gates, but with older institutions where their founders are long gone is not that easy. Who can identify a person with GM, GE, Ford, MIT, or Harvard? If you are not in that area of business for sure you will not know who is in change of these macro-organizations. Who knows who control Twitter, PayPal, Uber, Airbnb, or the WWW? Again if you are not in the business you will not know. But... For sure you know what these are and what do they do, as most likely you are one of their users. (Note that I didn't mention Facebook!)

A recent TED talk by Rachel Botsman (Jun, 2016) discuss the implications of technology on the way that we trust each other, the way in which we grade and evaluate each other, including services provided by institutions. This is having a direct impact on the way we learn and teach. We now have institutions providing information and knowledge that in some cases is certified through MOOCs. These courses and certifications are from well established (accredited) institutions such as MIT, and others through their own systems of delivery (MIT OpenCourseWare) or through independent delivery systems such as edX, Coursera, and others.

Now, the question is how can we be ready for these changes. As an academic my interest has been on how can I be a better teaching professor? What kind of organization is better to confront the challenges of today? How can I be part of the strengthening of the organization? The answers to these questions are complex, and require deep analysis. But most importantly the answers require a sense of hope and optimism.

As an organization we have to become in many ways what Brown-McNair et al. in their book "Becoming a Student-Ready College".

A body of people focused on serving a diverse population of students.

Trust

Over the years humans have developed ways of relating that is chemically based on hormones of love, compassion, gumption, and trust. Oxytocin has been identified as the chemical produced in response to the feeling of safety and protection one get when living in a community where the leader is satisfying their needs.
In the classroom we have a similar situation when learning something that is challenging. The leader, in this case the teacher, has to make sure that students are aware of the value, the 'worth' of their education. Teaching science is specially challenging due to the complex nature of its language, not only math is involved but particular nomenclature and vocabulary that comes from an intricate historical evolution.

In his book 'Leaders Eat Last' Simon Sinek explores the importance of understanding the relationship between how one feel in some environment (like work) based on the behavior of the leaders of that environment. Underlying this behaviors are chemicals (Endorphins, Dopamine, Serotonin, and Oxytocin) generated by our body. For a short version of his book have a look at his presentation in Youtube
 https://www.youtube.com/watch?v=ReRcHdeUG9Y

So why am I thinking about this in relationship to my teaching?

It seems clear to me that when students come to class are in search among other things of a leader. The teacher as a coach has to be dependable and more important has to be a leader. A leader that has gain the trust of their students.

New Ideas for The New Academic Year

Over summer I had the opportunity to read a lot about teaching in general and in particular about higher ed. The two main areas in pedagogy that made an impact on my thinking are: constructivism and individualism.

The first one, constructionism (constructivism), refers to the idea de we learn building on top of other ideas. As more complex phenomena is understood based on the relationships that it has with simpler experiences.

The second one, individualism, is based on the idea that we all are different and thus have our own ways of learning new concepts. This last area has to be viewed within the context of the similarities that we have just because we are humans and our brains basic functions are the same. The subtle differences then come not from the basic functions but from how this basic functions relate.

The problem is that these relationships are non-linear and in our organizations we have a lot of linearity like the way we design courses in the 100, 200, and higher levels. One may assume that the 100 level is for nomenclature development, while the 200 level allow for the solution of problems that require quantification. Higher levels will introduce the synthesis and analysis beyond quantification but including it.

As I am teaching General Chemistry at the 200 level and Organic Chemistry at the 300 level, I can put into practice these ideas and as I move along I will write about it giving specific examples.

Do you have any examples of these ideas.

Continuously Changing Learning Objectives

Teaching science is challenging for a lot of reasons one of which is that learning objectives are shifting with changes in our scientific and technologic reality. Take for instance the development of robots. Robots have been in the mind of futurologist, technologist, and industrialists since the beginning of the industrial revolution (maybe before) mainly to replace humans doing unpleasant tasks.

Reading Diane Ackerman's book The Human Age I am exploring the idea of the possibility of self aware robots.

Image form Amazon

This exploration made me think about the problem of teaching a subject like chemistry that is being transformed by the use of "artificial" intelligence. Computer models that can replicate chemical reactions and gather data that is retrofitted to the algorithm so through many fast iterations a final reactant can be identified as the best. For an example of a computational drug design look at this youtube video 

In this video you can see as the molecule is modified to fit in the dock the enthalpy of the hydrogen bond which is a measure of fitness is calculated and displayed.

Of course these experiments can't be done by someone without basic knowledge of bonding, atomic and molecular orbitals, molecular structures, and thermodynamics. But all of these concepts are there in cyberspace and constitute 'knowledge' that is universally shared. The main problem is that now there is no way we can teach everything that is available in any branch of science, like it was the case a century ago. The issue, for me, becomes how to structure a systematic process where students will learn basic concepts that include how to get the necessary information from the internet. The cloud becomes the hub where students transit for the interconnection of ideas and tests. Hypothesis are explored in this new environment where collaboration becomes the norm and communication (including of course the proper language) the most powerful tool.

So, the question becomes: how much time should be invested in learning and developing searching and communicating skills?

  

What is there in the vocabulary

     One may wonder why is having a broad vocabulary important in science? How would understanding the meaning of a word helps grasp the concept referenced by the word? Is the understanding of the meaning of a term necessary to solve problems where the term is invoked?

     These are not trivial questions, but it appears that they are, based on the fact that we use a lot of terminology which meaning depends only in the context where the terminology is used. For example let's think about the word "attraction". Take a moment and think about the word. Then you realize that in order for you to thing about the word attraction you have to construct a sentence like: two bodies experience gravitational attraction due to their mass. Or, two bodies feel romantic attraction due to their psychological compatibility.

     Are these two examples of attraction similar? I dare to say, no! They are very different with respect to the way that the ideas of force and feelings have completely different mechanisms thus the solutions to the problems presented in each case will have very different results and conclusions. Let's expand this argument for the sake of clarity. In the case of gravitational attraction one knows that the force is proportional to the mass of the bodies involved. Therefore one can write a formula that simply states this attraction as a function of mass like this: Force of attraction between to bodies at some distance is proportional to the product of the masses of the bodies. F(at some distance) ~ m₁*m₂  or F~m₁m₂; where m₁ and m₂ are the masses of the bodies. The next step is to remove the proportionality symbol ~ through experimentation and change the proportionality to an equality like the following where the distance factor is introduced: F = k (m₁m₂/r². The r² indicates that the force decreases with the square of the distance r.

Now let's try to do the same with the romantic attraction. What factors would we use for the 'psychological' feeling that these two bodies experience, can we talk about these feelings like forces?
Or the metaphor will completely get out of hand? The opposite was the case when in the seventeen century Isaac Newton suggested that two bodies 'attracted' each other through gravitational forces. 

The French much given to romanticism were completely opposed to Newtons ideas for many years because they could not come to terms (pun intended) with the idea that inert bodies like rocky planets could have feelings and 'attraction" was before Newton used in the sense of the later example. Now of course we have blurred the line between the metaphorical meaning and the 'literal' when we use the term force to indicate desire, need, or even thought.

So what is there in the vocabulary? Why do we have to teach a bunch of terms in science classes?

How can the lack of understanding of the terminology involved in a particular discipline hinders the understanding of difficult concepts?

The answer to these question surely will lead to better pedagogy of science teaching and learning.

Do you have a term that is you favorite?