I heard a story once about Albert Einstein, who, after a hard day’s work revolutionizing physics, left the university and went on his way, but ended up lost and confused, unsure where to go. It was like his brain had been working so hard that he couldn’t find his own house anymore; the supreme difficulty of whatever thought process Einstein was engaged in at work meant he had almost nothing left in his gas tank for the performance of even the most simple mental tasks, like recalling a piece of information he used every day. There’s no evidence that this story is true, and it’s about as extreme an example as you can get, but the phenomenon of cognitive load is clearly real and relevant to those of us who are interested in education.

Cognitive load is like the mental energy we use to perform difficult tasks. This can take the form of  solving  a mathematical problem, forcing ourselves to do routine household chores when we’d really rather watch TV, or biting our tongue when somebody annoying is provoking us. Apparently, all of these tasks take the same kind of mental energy. It’s effectively the same thing as stress; all of these situations act like a work-out for our brains. Just like you need a rest between physical resistance exercises if you want to avoid damaging your muscles through over-training, your brain can only take so much mental stress before its performance drops and the effect on your development becomes negative.

There are a number of strange phenomena which seem to be related to this concept. Apparently, if people are put in a difficult situation and have been making stressful ethical decisions, for instance making sacrifices for the benefit of others, they are less likely in the immediate future to resist their impulses. It appears that putting yourself second for a long time makes it harder for you to do the apparently ethical “right thing” next time. This works the same if you were doing some other kind of mentally difficult thing, like trying not to eat a tempting sugary treat, working on a complex intellectual exercise, or waiting for something. In any of these situations, people were less likely to exhibit restraint if they were tested immediately afterwards.

So it looks like our brain only really has one gas-tank, and it fuels pretty much any difficult thing we do. This relates to how much effort it makes sense to put in each day. It seems like today’s society glorifies the state of being busy, the rushing from one engagement to the next. Our lives are over-scheduled and we’re expected to be productive much of the time. It looks like our genetic heritage might not be entirely suited to this. Our brain can probably only manage about four hours of useful work a day, for most of us, and the rest of what we do is largely on autopilot. It’s important not to over-exert ourselves mentally, and to save our energy for the important stuff so we don’t get drained working on all those other things that take up our time and cognitive capacity. A healthy balance is required, such that we experience sufficient stress to promote growth, and we exert effort in areas which will reinforce our learning and help us continue to develop, but without imposing expectations on ourselves which could end up being counter-productive.

Over the last month I have been doing a few different experiments, with the Raspberry Pi and Mathematica, to develop a number of different lessons/experiments for our students. I don’t have much time  for educational theorists so I take an empirical approach to teaching and believe it is important for teachers to be counted among “those who can do”.

Theory often motivates many changes to the educational system in this country. Consider recent changes to the New Zealand Maths Curriculum, which introduce more emphasis on statistics. The changes seem sensible. Students now gain a better understanding of the statistical process and the variability inherent  in sampling and data.

Nevertheless, there are problems with the implementation of this new approach. The usual problems of NCEA , where teachers spoon-feed students and teach directly to the  assessment they deliver, are common. Technically speaking, it seems that students gain the understanding that  Statistics is a narrative activity (a form of story telling). I  am not in favor of the narrative  approach, since many flaws in statistical reasoning are caused by our tendency to tell stories and  join the dots. I encourage my students to withhold judgment, unless there is strong evidence, and to also consider base rates when making  inferences. Story telling seems particularly prevalent when it comes to time series analysis.

Maths and statistics students should develop a maker mentality and that means they need to code. Essentially, code is maths brought to life. While report writing and analysis has it’s place, it is  a bureaucratic activity, while  making  and experimentation leads to new ideas, technology and growth. The thoughts detailed in this video do match my experience when it comes to using maths.

My post,Wi Fi to the Beehive and Raspberry Pi,in the Wolfram Community shows how running a few experiments leads to some interesting new ideas.

Hi, my name’s Tobias and I’m the new English tutor here at Emerson Willard. My job is mostly to extend students’ writing ability and go beyond what they learned in the primary course. By now they hopefully have a functional level of spelling and grammar and so I focus on a combination of revising these basics to find problem areas, and trying to get the students to write. That second part is actually most of the program.

I learned to be an English teacher in Prague, at the Edua Languages TEFL course. My trainer there, an American, was talking about the basic approach required to help people learn English. Most of his student teachers were already university graduates, and some of them even had master’s degrees in certain disciplines, and so most of us thought of ourselves as able speakers and writers of academic English already. But John asked us, “If you were a baseball coach, would you get up in front of your team and say ‘Look how many home-runs I can hit?’ Or would you try and get the players swinging the bat for themselves?”

Most of the task of being an English teacher was eliciting content from the students, while maintaining an actual language goal in mind for them to develop. Maybe that day you wanted to work with them on the difference between “had had” and “had,” or difficult verb tenses like “will have been.” Whatever it was, the important thing was being able to engage the students and get them thinking about the language goals you had for them.

After gaining my qualification as an English teacher I promptly went on to never work as a TEFL teacher, ever again. I’d given several practice lessons throughout the course of the four week program in order to gain my qualification, but after that I eventually left the country and came back to New Zealand. Apart from that brief stint in the TEFL world, I’ve also worked as a physics demonstrator and a private tutor for university students. As a physics demonstrator, my job was to show university physics students how to perform experiments and then to help them when they had trouble and mark their work when it was done. As a private tutor I spent most of my time with students from Saudi Arabia, going over their written essays and finding the obvious mistakes and opportunities for stylistic improvements, while at the same time helping them with whatever course material they were struggling with. This often involved taking the subject matter from their prescribed texts and processing it into bite sized chunks to help their comprehension during test preparation.

In all of this and the course of my own academic studies, I’ve found that the most powerful revision and memorization tool is the essay. The process of writing an essay requires not only the recall but the organization of a disparate array of facts and concepts to form a coherent and easily readable argument. The essayist must take items scattered throughout their conceptual space and render them into a one dimensional string, putting one word and one paragraph after another. At the same time they have to exercise theory of mind, and understand how the reader will approach the text they’re creating, how to make it engaging and comprehensible. They need not only to present the facts but get a point across, and there are few other techniques which bear these complementary features.

This isn’t just my hunch, either. A 2011 study, published in the journal Science showed that using essays as a form of retrieval practice was one of the strongest techniques for encouraging the memorization of information, out-performing rote memorization or more modern techniques such as mind-maps. This process required that students write an essay based on material they had learned and that in the act of writing they attempted to recall what they had studied, rather than looking it up again. This meant the essay writing acted as a form of retrieval practice, and the process of manipulating the information as well as actively recalling it helped to cement the information in the learners’ brains while also establishing rich connections to multiple areas due to the necessity of fitting the information into a logically structured text. This wasn’t limited to the arts, either, as the original study was carried out with students a week after reading brief passages about scientific concepts.

The surprising applicability of tools from the English department in studying scientific topics is of particular interest to me. My academic history covers a wide range of topics but right now I’m working on a degree in English and mathematics. The double major isn’t just because I’m a glutton for punishment but because the interdisciplinary approach has always been attractive to me. The areas that interest me the most are the so-called formal sciences, the overlapping set of disciplines including linguistics, mathematics and philosophy from which more specialized areas are developed. At the core of all this are the questions of how information works, how it can be communicated and how it is understood, from which such disparate areas of study as psychology, computer science, physics, and language all draw much of their theoretical underpinnings. Some of the deepest and most intractable unexplained problems in science today are the questions of consciousness, cosmology and comprehensibility. In short, what is the mind, why is there anything and why does any of it seem to make sense? These questions, esoteric as they may seem, are all related by concepts drawn from areas such as information theory and abstract mathematics, and the most recent and promising answers to many of them come at times from unexpected quarters. The current consensus in physics, for instance, is moving towards the ideas of the “mathematical universe,” the universe as an abstract mathematical object, and the holographic principle, the idea that our apparently three dimensional world is really the projection of a two dimensional space.

These developments are as exciting as they are intriguing, and I hope to be able to convey something of my passion for knowledge to my students. Another interesting development is that student-directed learning is one of the most powerful educational paradigms, in that when allowed to direct their own course of study students tend to learn more than when a course is imposed upon them from above. While my approach involves a fair amount of simply pushing the student to achieve a greater level of understanding and fluency in their writing, I also hope to be able to engage students’ interests from a wide range of subject areas and find topics which appeal to them, using the process of learning to write as an opportunity to learn about other concepts as well.