The Purpose of Education

There are a few different views of what an education is for with varying degrees of popularity. Some people support the idea of a "Classical" education. Others support a more modern or "Progressive" education. Some use the word "Traditional". I personally do not like to operate at the level of labels and insist on getting into how different people define these words and what they actually mean when they use them. For example, to most economists 'inflation' means rising prices. To others, it means expansion of the money supply or credit. If the supply of money increases while at the same time prices decrease, you will see people on television arguing with each over something which you would think would be a simple matter of fact: that there is inflation or there is deflation. The argument will go on without resolution, all without the audience being informed that different definitions of the word are used by the opposing talking heads. This is not productive.

Whether someone argues for "Traditional" education, "Classical" education or "Progressive" education, it seems these days most agree that the purpose of education is to better the whole student: body, mind and soul. In any case, this is what I believe. I believe education is more than just vocational training (though being prepared for future jobs is also very important). I believe a large part of education should effect training of the mind, development of virtues such as reflecting how we should live our lives better (including staying in good health) and the evolution our students into creative learners and critical thinkers. Education is not filling a leaky vessel, but setting alight a soul.

Knowledge and Learning

When scientists cannot explain something, they have a ‘problem’. Their current explanations are not good enough. The way scientists learn to be able to explain new things no one has ever explained before is by guessing at the new explanations. They simply guess based on their hunches. Only then do they calculate predictions based on those guessed-at explanations, then run experiments to see if they defy those predictions or not. When observations defy predictions, they refute the explanations off of which those predictions were based. In this way, the guesses scientists make – their new explanations, come to better and better describe reality as it is with each new problem they face. Today, science progresses relentlessly. But it is a process; each of its problems takes years to resolve and it is an engine which works by making productive use of courageous guesses and learning-moment failures. Both are fuels to the growth of knowledge and learning.

When a young person learns a concept they do not yet know, but that is known by others, it is no different for them than for the scientists who are at the forefront of the human effort to understand what is not yet known. Each student ultimately must guess at their own way of understanding what is being presented to them. This is because understanding is non-transferable, but must come from within. Learning for understanding is a fundamentally creative process.

Nothing can be stated perfectly clearly – that’s not a thing. The content of a sentence is not only in the words that compose it, but in the system of interpretation inside the mind of the listener or reader. And these are more unique to humans than our fingerprints. Explain something to 10 people with the same words and you will have 10 people with 10 different ways of understanding what you just said to them. Passing off knowledge with language with this high of fidelity is not possible. It takes repeated attempts at guessing how to understand. I know of no other way for learning to occur. Still, through a process of trying, error-correction, and two-way feedback our understandings can come to converge over a period of time and through a series of trials.

The Role of the Teacher

A teacher must keep in mind how learning actually works and what the purpose of education really is in order to fulfill his or her responsibility. The teacher must try to help students find interest in the subject matter and allow students the chance to learn creatively. And the teacher must strive to engender a culture that elevates the students and that allows for collaboration and learning.

Because learning is a process with failure as a impetus, a teacher must allow for students to try things and fail at first, so these failures must be recoverable and not be allowed to have a chilling effect on students' willingness to try and guess. At the same time, accountability is one of the virtues that must be developed in students. As students construct their understanding, they will get some things right and some things wrong and it's appropriate that they tinker with their models and their projects not only to get them to work but to better understand what makes them work and what makes them fail. Sometimes the example of a "near miss" is more illustrative to what the working principle actually is than a working example. These help students define the requirements that make something work.

To help with interest, it is best to allow, as much as one can, students to have choice and options in how they approach learning something. The phrase "low floor, high ceiling" is sometimes used but that is not enough. There must also be "wide walls" to enable engagement, interest and creativity. This helps students become curious and invested in their own learning.

It also should be the goal of the teacher to engender virtues of a good student such as trust in the culture of the classroom: that ideas can be shared and criticised in good faith and that everyone is respected even in disagreements. A friendly competition can be healthy, but collaboration must be encouraged.

Aspirations

I believe technology could fuel learning in math classes (and even help integrate math applications into other courses) but only if done right. Other than presentations I have shown to my classes, the math courses I have taught have not involved much technology use by the students. I hope to develop new learning experiences and activities which leverage technology in the math curriculum in a smart way that I believe would improve and augment the traditional approach. I believe this would require coordination across the whole curriculum to do properly.

Pitfalls

The proper use of technology in non-technology courses should be intentional, specific and limited. There is a difference between digital literacy and digital dependency. The use of technology in math education should leave students with a stronger understanding and not leave them helpless without the computer to do things for them.

Also, insofar as this use of technology involves programming, there are concerns with adding learning requirements outside the scope of the already jam-packed math curriculum and of testing only the students' math skills on assessments independent of their programming expertise. So, I believe it's better to integrate math applications into technology courses and teach students about scientific programming than to integrate programming lessons into math courses. Think pre-requisite or co-requisite courses rather than units within the math course. At the same time, students in math courses can be allowed to use what they already know about programming within math classes.

Finally, schools should also be concerned about their student's privacy while using cloud-based apps and be very aware that many "free" apps use addicting psychological traps to both stimulate and hyponotize users to keep them using and coming back. Advertisement, for example, are often designed to trigger primative aspects of the mind which rely more on emotion than on critical thinking. This is disruptive of learning and must be avoided. Not all apps are created equal!

Opportunities

I know first-hand that technology can be a powerful tool to build intuition and explore your own questions about a mathematical topic or quantitative relationship in the real world. Allowing students to play with variables in the context of an interesting problem enables a deeper understanding of the phenomenon being studied and also of the nature of mathematical modeling. This is something I think about a lot and I love to talk about it!