Artificial Intelligence, Real Stupidity

Artificial Intelligence (AI) is becoming increasingly popular among service providers. This includes banks and search engines, this on the basis that it provides the same or a better level of service at a lower cost. This is all very fine until the AI goes wrong.

I have seen two examples of AI failure in the last 24 hours. These include Twitter permanently suspending a user for saying that he had killed a fly, and one of my own shortened Google links being banned for allegedly pointing to a child abuse web site when it actually pointed to a government web site on protecting children ( and While the impact on the users is annoying in both these cases, there is a significant risk that AI failure will have serious impact on other people, including the risk of death.

In both cases, the AI engines appear to have been working on the words alone. There was no attempt to do a semantic analysis on the text. Had such a semantic analysis been undertaken, neither of these cases would have happened. Semantic analysis tools are available. That the people who implemented to the two AI engines did not see fit to include any semantic analysis shows an obscene failure to discharge their duties.

Unless, and until, those organisations that use AI instead of real intelligence achieve a reduction in the error rates of their AI engines by at least four orders of magnitude, I call a pox of all their houses!

In the Age of Information, Ignorance is a Choice


This post arises from an accumulation of observations of many people for whom an appropriate description would be “willfully ignorant”. I have in the past been described as being “fiercely analytical”. I make no apology for being that way, and it is by being that way that I write the first sentence in this piece.


Teachers have a number of legal, moral and ethical obligations towards those whom they teach. This includes accuracy of the information given, and making plain differences between facts, opinions and falsehoods. Such obligations also extend to anybody who seeks to impart knowledge to others. Search engines have made fact checking very quick and fairly easy. Anybody who fails to avail themselves of this is making a conscious decision to remain uninformed.

“But It’s Only a Theory!”

Words in English can have multiple meanings. The word “set” covers no less than two pages of definitions in the 1973 edition of the Shorter Oxford English Dictionary. The phrase “Theory of General Relativity” appears to be widely recognised. I have yet to find anybody who thinks that Einstein’s work was just a guess, that being another common meaning of the word “theory”. It seems reasonable to expect that any informed individual would be aware of that distinction.

For anybody who is not fully familiar with the theory of evolution, it is a well-substantiated explanation for the diversity of life on our planet. It is accepted as a fact in the scientific community.

The time has come to introduce Mike Pence and Christina Wilkinson, vice-president elect of the United States of America at the time of writing and headteacher of St Andrew’s Church of England Primary in Oswaldtwistle Lancashire respectively. Christina is on record as saying “Evolution is not a fact. That’s why it’s called a theory!”. This caused such a storm that Christina deleted her Twitter account.

Mike Pence is on record as saying in 2002 “The truth is [evolution] always was a theory [not a fact]” (YouTube video at time stamp 2:26). As far as I can ascertain, Mike Pence still holds this position.

Both of these individuals appear to remain uninformed.

Looking Forward

This is not the place to try understand the reasons behind the choice to remain ignorant. It is a question perhaps best left to educational psychologists. The question that does remain is how can educators encourage future adults to take take advantage of the great quantity of information that is easily accessible. I suspect the answer starts with each child’s first day at school.

A Rate of Learning


The inspiration for this post comes from this tweet by Heather Julian (Twitter @mathrules13) and re-tweeted by Jill B (Twitter @jillgrafton):mathrules13


I will take it as a given the readers are familiar at least one set of skill/attainment level descriptors going from “can recognise” to “can exploit”, and agree that different people have different levels of recall for different things. I will also take it as a given that readers are familiar with Maslow’s hierarchy of needs.

This post does not refer to any publications, scholarly or otherwise. It is merely one person’s thoughts, and it is intended merely to provoke discussion.

The Teaching-Learning Equation

There are a number of phrases associated with the acquisition of skills and knowledge from a source outside the learner, each phrase having its own level of acceptability in different contexts. Examples include “teaching”, and “delivery of learning”. My own sense is that such phrases can obscure the dynamics of the teacher-pupil situation. Given the context implied by Heather’s tweet, I propose a scenario where the teacher:

  • has full command of the subject
  • is totally self-confident
  • has excellent communications skills
  • has good empathy
  • has a good grasp of the pupil’s current knowledge base in the subject

(I can hear some of you thinking back to your own school days and thinking “I wish!”.) Also, to do justice to Heather’s question, I think that we need to focus on what is going on in the pupil’s mind (and here I am forced to rely on my own memories of school, as augmented by how some of my own students have demonstrated learning).

A Model of Learning

My own model of learning is constructivism. In the context of numeracy, a grasp of whole numbers is necessary before the idea of fractions can have any meaning, for example, and the rest of this post is written accordingly.

I find the words “truly remember” and “meet our standards” to be thought-provoking, as it raises questions about what level of memory is being envisaged, and whose standards are being applied during assessment. Using the “quadratic formula” as an example, memory may range from recalling “I know that phrase means something” to being able to write it down upon the instant (as well knowing what it is used for), and its consequent relationship to skill/attainment level descriptors.

Extending the words “truly remember” and “meet our standards” to what the learning experience means for the pupil can also be revealing. Again from personal experience at high school, I was in one cohort where everybody was expected to learn lines of poetry and recite them in class. I learned what I needed to in the preceding 48 hours, recited, and promptly forgot them one hour later. In terms of the teacher’s expectation that we should all enjoy poetry, it was for me a disaster: his standards were irrelevant to me at a personal level.

At the opposite extreme, and at the same school and at about the same time, I had a number of experiences that I found to be highly relevant. I have room here to describe only one of them. The subject was mathematics. The class had been working though material for a few days, and I was not quite sure of how all the bits and pieces fitted together. Towards the end, the teacher spoke a single sentence and everything suddenly fell into place. That learning has stayed with me for over 40 years, this in stark contrast to the poetry experience.


Teachers may have aspirations for their pupils. Sometimes those aspirations are selfish. At other times they are focused on the pupil. I have memories of both from my school days. It is for this reason that I posited the scenario above.

We are now into the complex area of the teacher’s motives, skills, knowledge and abilities and the interaction of these with the pupil’s motives, skills, knowledge and abilities. I argue that it is this complexity that rules out any simple answer or answers to Heather’s question, and that perhaps we should instead be asking ourselves “What can I do to help this pupil towards self-actualisation in as quick and as efficient way as possible?”.


It’s not an easy job!

A Philosophy of Instructional Design


The inspiration for this post comes from Temitope Ogunsakin and his comment on this post where he asks “What would you say is your Instructional Design philosophy?”. This post is by way of answering his question.


The objective of this philosophy is to make the learning experience as easy and enjoyable as possible for the learner. This has two outcomes. Firstly, it maximises the effective of the learning experience for the learner. It also fulfills part of the social contract between educator and learner, that of mutual respect.

This philosophy uses a number of guidelines as a way of meeting that objective. Discerning readers will notice that I have avoided using the word “rules”, as rules tend to be prescriptive and thereby interfere with reaching the objective.


This philosophy makes a number of assumptions about the learner. At the risk of perhaps stating the obvious, it may be worthwhile making those assumptions explicit, and it provides readers with an opportunity to challenge those assumptions.

All Learning is Built on Previous Knowledge

While the claim “All learning is built on previous knowledge” may seem bold, and it sidesteps the question of how babies start acquiring knowledge, I would argue that it is a useful starting point for discussing later learning. By way of example, the teaching of grammar relies on learners being able to recognise sentences, which in turn relies of the recognition of words. In a similar fashion, the ability to use money relies on (among other things) the ability to recognise and understand the meaning of digits.

Different Learners Learn at Different Speeds

It is perhaps a common mantra that different learners learn at different speeds, so it is worthwhile checking a few sources to see how widespread this view is. A quick search on Google found this from the Board of Studies Teaching & Educational Standards NSW, this from the Australian Curriculum, Assessment and Reporting Authority, and this from the New England Complex Systems Institute, all of which support this view.

Adults and Children Learn Differently

Adults bring a number of skills and personal attributes into the learning situation that can be harnessed to good effect. These include, but are not limited to, life experiences across a wide range of subjects, independent research skills, and a thorough grasp of what they want to achieve from their learning.

All Learning Requires the Sharing of an Idea

With the claim “All learning requires the sharing of an idea” I can see readers saying “But what about psycho-motor learning? And affective learning?”. While subjects such as pure mathematics and philosophy are entirely cognitive, and the claim is unlikely to be challenged in those arenas, I would also argue that “the idea comes first” in both other areas. In the case of psycho-motor skills, the idea is often shared by way of demonstration, and followed by learner practice Examples include how to use a hammer, how to drive a car, and how to use a paint brush. With affective learning, the idea is often first shared by asking a question: “How would you feel if …?”, followed by a discussion. Agreeing the ground rules with a new cohort is another example.

Tasks Analysis

I have designed and used task-analysed teaching material from nearly 20 years, and I have found it to be one of the most effective tools in my educational toolkit. I have found that the ideal length of a learning task is between five and 15 steps.

The Guidelines

  • Audience identification: Unless I have a very good idea about what the learners already know, and what it is that they wish to learn, I have nothing to work with: I have no foundations upon which to present new ideas, and I have no direction as to which ideas I should choose. By way of example, I delivered learning in Microsoft project a group of older people who were experienced project planners using manual techniques and who wanted to learn how to use Project instead.
  • Matching the learning material to the learners’ existing knowledge base: Using the same scenario as above, I learned that my audience were in the business of installing water distribution infrastructure, so examples, exercises and questions about pipe laying, construction of pumping houses and supply of electrical power were obvious choices.
  • Bite sized chunks of learning: My comment on the ideal size of task-analysed activities translates well into other learning activities when it comes to planning the amount of material to be shared between signposts. Even in an extended whole group discussion, the learners themselves can raise such signposts, and the learning goes on to new ideas.
  • Structure: I regard structure as crucial. This is a direct consequence of the idea that learners build their new understanding on the foundation of previous knowledge.
  • Humour: Humour can be used tool, though not all learners seem to recognise it at the time. One cohort only came to understand the significance of a Mr Thread as the CEO of the Brazil Nut and Bolt Company in their coursework once they had finished their exams. Other humour can be injected ad lib while speaking.
  • Personal relevance: Without personal relevance, the learning material is likely to be less effective. The mathematics of the motor car was so interesting to one youth-at-risk that it turned his life around and he became a productive member of society.
  • Relevant technologies: The idea of of using technology as a ploy to engage students strikes me as at best silly. Having said that, I will make heavy use of technology where it is relevant. With the Microsoft Project course, it was appropriate to make the following design decisions:
    • All the learning materials, apart from Microsoft Project itself, were entirely web-based. There were no paper handouts.
    • All learners had individual computers, each with a copy of Microsoft Project already loaded.
    • All learners were invited to bring one of their current projects along with them using whatever technology suited them.
    • All learners were expected to work with both Microsoft Project and the web-based learning materials open on their computer at the same time.
    • All learners were expected to leave the course with a fully functional copy of one of their projects in Microsoft project.

    For the record, the course was extremely successful.

  • Immediate feedback: Some subjects, such a computer programming, Excel and Microsoft Project, have immediate feedback as an inherent quality of the product being learned. Immediate feedback is now normally built into web pages where this is relevant. When I write such pages, I build in such feedback at the design stage.

A Final Comment

I would never present all of the above as a single serving to anybody who was learning about instructional design. Having said that, it would not surprise me if experienced instructional designers read it in less than a minute, and then wanted to add their own ideas to the material presented here.

Maths from a Picture

The inspiration for this post comes from Brian Marks (Twitter: @Yummymath, web site with this tweet:
It seemed to me fairly easy to use that picture as a basis for writing a number of maths related questions, so I produced this document in Google drive. It has 13 questions related directly to the picture, and another 23 questions which use that picture as a starting point. The questions are in no particular order, and cover a broad range of topics and levels. While that document is a response to the question posed, I would hesitate to give it to any but the most competent and confident student of maths at year 11 or 12 level. It also goes well outside the area of pure mathematics, and provides some support in the area of physics. Having said that, it may provide an idea or two to anybody who cares to read it.

I would be very interested to hear your comments.

But What Use Does Maths Have Anyway?


The inspiration for this post comes from Lee Finkelstein (Twitter: @leefink) with a tweet that resulted in the following exchange:
and it raises the question of why mathematics is taught in schools. The rest of this post shares my ideas on this question.

Assumptions Revisited

It seems to me that one of the purposes of schooling is to equip students with the knowledge, skills and attitudes to function effectively as adults once they leave school. It also seems to me that different students have different aptitudes and interests, and this has impact both on their performance at school and their learning. There is also the observation students will be “going into the world” where there will be jobs that do not exist at the time of their schooling.

Using Lee’s cri de coeur about why his 11th grade daughter needed to memorize things about the unit circle as a starting point, it is worthwhile commenting that every subject at school has relationships with other subjects, even though they tend to be taught in isolation from each other at high school. By way of example, mathematics is an essential component of the high school subjects chemistry, physics and engineering drawing. Mathematics is also an enabling tool for vast numbers of jobs in the workplace. Similar comments apply to the study of language its relationship with the workplace.

Speaking from personal experience, there were subjects that “bored me rigid” at school. It was not until well into my own adult life that I developed an interest in some of those subjects.


The above raises the thorny and perennial question of what, and perhaps to a lesser extent when and how, educators (and by this I include non-teachers as well) should decide what should be learned. I have no answers to this question. All I can do in this context is to mention ideas and raise issues for other people to ponder and perhaps come up with their own answers.

It now seems appropriate to offer some personal experiences. When it comes to mathematics, its relevance to me was that I found it engaging for its own sake. There were three areas in particular (quadratic equations, linear algebra and statistics if you must know) that proved to be invaluable 20 years later, and saved my then employer in the region of US $10M/year. I found history and geography to be as dry as dust, and it was not until I explored the countries of western Europe as an adult that what little I had learned as a child served as an invaluable basis for learning about, and more to the point understanding, what it was that I was looking at.


I must now leave it for you, dear reader, to respond with your comments below. I look forward to hearing from you.

A Twitter Convention Observed

Introduction and Allegro

If you are familiar with my presence on Twitter (@philhart) you may have observed that I tweet on a range of subjects including Australian politics (#auspol), education (#edchat), mathematics (#mathchat) and security (#security), and I will sometimes tweet public replies with the intention of amusing the recipient. I have noticed that some people follow me for obvious reasons (they are educators, for example) and others for no reason that I can discern (but that is their privilege). Of particular note is people who add me to a special list on the basis of what seems to be a single tweet, with mathematics seeming to be the main cause for this. The risk that such people run is that they may be deluged by my tweets on other topics. To that end, I have abandoned convention and now commence my tweets with the relevant hashtags, leaving the content to follow, this with the hope that readers will know what I am tweeting about before having to read it all. I have noticed that some other people are doing the same thing. In light of this, I ask the following question:

Is it a practice that you agree with?

Is it a practice that you think should be promoted?

I look forward to reading your comments.

Maths Wars


The inspiration for this comes from Lina Zampichelli (Twitter: @micky_lina) with her post in the FS Teach Facebook group. (It is a closed group, so no link, sorry.) It links to an article in Canada’s National Post headlined “Math wars: Rote memorization plays crucial role in teaching students how to solve complex calculations, study says“.

I have been conscious of the recent shift towards “exploration learning” of mathematics, and I have felt uneasy about it, which unease I put down to a sense of nostalgia. Reading that article has made me re-appraise my unease, and the time has come for me to put my own viewpoint about how mathematics might be effectively taught so that it can be effectively learned.

I expect that I might upset a few of today’s younger teachers.

My Use of Mathematics as an Adult

Before describing my own experiences of learning mathematics, it might be useful for me state how I use mathematics in daily life. I do so as a matter of routine, and it is for on a par with reading, writing, speaking and listening: I could not function effectively without my skills in mathematics.

I use my estimation skills when shopping. I do so to check the reasonableness of the total payable. People “behind the counter” sometimes make mistakes, and I will discuss this when I think that I am being overcharged or undercharged. The estimation skill also applies when planning a major expense: what are approximate balances on the credit cards and bank account, what roughly is our monthly income, and what is the cost of the proposed expense. I can then make a yes/no/defer decision.

Basic counting along with addition and subtraction skills can be a time-saver, particularly in shops. At shops where I am known, rather than having to scan six or more items with the same bar code, or wait for the shop assistant to count them, I simply tell them the number, this saving time for both parties. When it comes to presenting cash, I often find that it is quicker and simpler to present money with the cents and low dollars value to the amount where I can receive a single bank note in return. Presenting $20.70 for a total of $10.70 means that I have less metal weighing down my wallet, and the giving of change is also quicker. (It also often brings a smile to the cashier, some of whom seem chronically short of change.)

When it comes to photography, the numbers associated with shutter speed, aperture and focal length always come into consideration when I compose a shot. Here we have gone away from simple counting, and moved into the areas of multiplication, division, and geometry.

Stepping up another gear, a grasp of statistics means that I am able to move from “average care” given by my local doctor, to “better care” with my doctor’s support. Whenever I consult him, I turn up with a printout of all the relevant data presented in statistical form, which allows him to make much better informed decisions. It also allows me to adjust my own medication very rapidly to respond to changes in my own body. A bout of influenza had a very strong impact on some of my vital signs, and ceasing one of my medications for the duration made my life a lot more survivable.

Raising the ante yet again, I use something called “vector matrix algebra” to solve problems with real-world impact. There is a bank of mains power outlets on the island bench in our kitchen. That bank looks a bit like a toblerone chocolate. The quickest and most effective way to find out which angles I needed to use to cut the pieces of wood was by using vectors. Anybody who writes software to display three-dimensional objects effectively on a computer screen needs a thorough understanding of vectors and matrices.

Pulling Out the Bones

In the examples above, as well as in other scenarios, I use the following skills as easily and as unconsciously as I read and write:

  • Counting
  • Addition and subtraction
  • Fractions in all their various forms: a/b, percentage, 12.3456
  • Multiplication, division
  • Geometry, both Euclidean and spherical
  • Trigonometry
  • Time, whether measured in femtoseconds or billions of years
  • Logarithms and exponentiation
  • Algebra and power series
  • Equations
  • Imaginary numbers
  • Base 2 (binary) and base 16 (hexadecimal) numerals
  • Statistical presentation and testing for statistical significance
  • Vectors matrix algebra
  • Calculus

At the bottom of all this lies my ability to count (1, 2, 3, …) which I was taught at a very young age. It was at about this time that I also noticed that not everything could be measured in whole inches, which lay the basis for my later grasp of fractions. I have a very clear memory of learning how to add double and triple digit numbers. Later came the rote learning of times tables, and I am very grateful for having been taught them. Procedures for long multiplication and long division soon followed, whence the concept of a remainder built on my observation of fractions of an inch. I was introduced to simple geometry at about the same time, this built on the concepts of space and measurement. At high school, these ideas were generalised into algebra, which itself served as a basis for learning calculus and the real-world applications thereof. Algebra was also used as the basis for learning vector matrix algebra, as was statistics.

What we have here is a structure of learning that was built on a foundation of a few simple concepts (counting, space, time, and observation) that my teachers helped me to assemble.

Putting this into a historical perspective, I have been the beneficiary of mathematicians whose efforts go back to the ancient Egyptians. The Arabs are credited with the idea of zero as a digit, but this is predated by its appearance in India in about the fifth century CE. Isaac Newton and Gottfried Leibniz are jointly credited with inventing calculus. More recently, vectors came about as the result of about a dozen people over 200 years. Let me put it another way:

If it had not been for the efforts of such people, I would still be counting by using pebbles on the floor of a cave.

Back to the Battlefront

The idea of “discovery-based learning” in mathematics strikes me as being fundamentally flawed. In my view, what is needed is a thorough discussion on what mathematical skills today’s children might want to use in their own adulthoods, and how best to equip them with those skills. Given the developmental benefits described in the article cited at the top of this post, I think it would be madness not to use rote learning to teach times tables.

A Foray Into Learner Experience Design


The inspiration for this post came from Joyce Seitzinger (web site:, twitter @catspyjamasnz) and her leadership in the arena of learner experience design.


I have developed a range of different materials for different subjects since the mid 1990s. In terms of generating a positive emotional response, the most successful of these was a paper handout where learners had to puzzle out for themselves how to assemble fragments to computer code to achieve a required outcome. The responses ranged from quiet, but still audible, expressions of satisfaction to loud exclamations of success. But for all the materials that I developed the concept of learner experience design was something of an assumption: I was too focused on producing material that was concise, complete and accurate. The time has come for me to turn this around and produce something focused primarily on learner experience design, and treat the subject matter as a given. (The result of this exercise can be found here.)


I wanted to design and build something completely from scratch. This immediately eliminated all existing learning management systems and other software aimed at creating interactive learning experiences. This had a downside: learners would not have a record of their progress.

There then came the issues of the target learners, and the subject matter. My own work with adult learners immediately suggested this group, and my own familiarity with mathematics suggested the topic of fractions.

The criteria for success came next. I chose the following:

  1. How well did the result reflect the expectations and background of mature learners?
  2. Did the result strike an effective balance between visual monotony and visual overload?
  3. How well did the material draw on experiences that mature learners are likely to have?
  4. How easily would learners be able to navigate their way around the material?
  5. Was the material chunked logically?
  6. Was each chunk of an appropriate size for the concept or concepts that it contained?
  7. Did all the material make a coherent whole?
  8. Were there opportunities for self-assessment?


My original intention was to provide a complete guide on working with fractions (addition, subtraction, multiplication, division, and simplification) and designed the front page accordingly. When I came to writing material for each of the chunks, two things became very apparent. The chunks were in the wrong order, and there was too much material for all the navigation points to be shown on a single display. This failed two of the success criteria: navigation, and logical chunking. Being as I was both a content creator and a subject expert, I took the decision to omit multiplication and division from the result. I also discovered that I needed an extra chunk to precede the multiplication and division chunks that I had not thought about when I first chunked the material. While the original order might have made sense from the viewpoint of keeping related ideas together, it would have been a disaster from a pedagogical viewpoint.

The choice of what examples to use also arose. My own experience of materials about fractions left me feeling somewhat jaded: just how often are pizzas divided into equal segments in these materials? I used examples and photographs of items in my own house: coins, a lemon, a box of eggs, and an empty avocado tray. I also produced a graphic of a fuel gauge.

I had a very particular idea of how I wanted fractions to be displayed. All the usual packages failed to match my requirement, so it was a case of write my own application to do that, and use GIMP to process the images into something suitable for display on a web page.

Criticisms of the Result

While the result could be described as “adequate” when it comes to the success criteria, the following observations could be made:

  1. The result will not work on mobile devices: the required display size is too large, and the result has no mobile equivalent.
  2. The learner requires an HTML5 web browser.
  3. The use of an avocado tray in the context of an avocado farm probably lies outside the direct experience of most people.
  4. Some learners may find the style too terse.
  5. The chunk on simplifying fractions properly belongs to the (non-existent) pages concerned with multiplying and dividing fractions.
  6. The result has not been trialed.
  7. The result is not compliant with standards such as SCORM.

Lessons Learned

The next time that I prepare such material, I will be able to do so with a more informed perspective.

An Essay on Instructional Design


I thank both Jo Hart (Twitter @JoHart, blog and Michael Graffin (Twitter @mgraffin, web site for inspiring me to write this post.

On Learning About Instructional Design

When Jo mentioned instructional design in conversation, I realised that while I was acquainted with the term and that it was to do with designing and building educational experiences for learners, I was quite ignorant of exactly what it is that constitutes instructional design, and I regarded this as a quite unsatisfactory state of affairs. A little bit of research soon threw up the following resources:

As I worked my way through these articles, I realised that I had been here before 40 years ago, though in a different context. I was looking at how systems are first analysed, and then designed.

On Analysing Systems

In the business context, the phrase “systems analysis” means producing a model of how part or all of the business works, usually with a view to improving the way that the business operates. This is then followed by “systems design” with the outcome that existing systems are modified to meet the current business objectives, usually increased profits in the case of commercial business.

Translating this into the educational arena, this means producing a model of how education works at the classroom level, and then designing educational experiences to meet the current educational objective, to wit better educated people.

Further Comparison

There are many formal systems for undertaking systems analysis in the business context. This matches the plethora of models of how people learn.

There are many systems design methodologies in the business context. Again the same is true in the educational context: one has only to look at the differing viewpoints in the five links above.

As one trainer in systems analysis and design once said to a class of which I was a part, it is about having a toolbox of methods, and choosing an appropriate method for the situation that you are currently looking at. I think the same holds in the educational context.

The Author’s Toolbox

The concept of instructional design is relevant to all three domains of learning: affective, psycho-motor, and cognitive. However, due to my limited experience in two of them, I address only the cognitive domain.

The model of learning that is presented below results from using the following tools:

  • Observing how learners succeed, and how learners fail, when going through a learning activity.
  • Observing learners’ emotional responses to a range of learning environments and learning activities.
  • Observing the differences in knowledge between different learners in the same cohort.
  • Observing the different rates at which different learners learn.
  • Observing the different different types of question asked by learners of different ages.
  • Observing how students react to different styles of presentation.
  • Observing group dynamics
  • Observing how learner motivation changes over time, and considering what might be causing those changes.
  • Observing how understanding of high school mathematics is dependent on understanding previous concepts.
  • Observing similarities and differences between academic endeavour and commercial endeavour.
  • Observing change of subject matter over time.
  • Asking questions.

A Model of Learning

I claim to have some learning in the areas of mathematics and of information technology, and I use both contexts in what I am about to say.

It seems to me that it is impossible to have the concept of a fraction until you have grasped the concept of a whole: there is a whole cake, take a piece out of it, and you have a fraction of a cake. The same applies to information technology: until you are acquainted with spreadsheets, the term “cell address” is meaningless. In both cases, understanding the second idea is crucially dependent on having a good grasp of the first idea. This is a constructivist approach.

There is also the question of “Why bother to learn?”, this addressing the issue of student motivation. This plays a crucial part when it comes to designing delivery activities and materials.

Relevance of information also plays a part. Applied mathematics changes very slowly, while practice in information technology changes very rapidly. Information that was relevant 10 years ago may be entirely irrelevant today: the floppy disk serves as a paradigm for this. This has implications not just for the professional development of educators, but also for the materials that they use.

The way that learners prefer to study also differ. At one extreme, there are learners who much prefer to work through a learning activity on their own. At other extreme, some learners need a lot of support from their teachers and peers.

Devices for Developing Learning Activities and Materials

The ideas offered below are neither complete nor prescriptive. They again come from my toolbox. Readers must decide for themselves which of those ideas are relevant to their own context.

  • Identifying goals, sub-goal, and sub-sub-goals until you end up with something small enough to be a single learning activity. Verifying that the sequence in which the material is going to be present is logical. This is an iterative process that continues until the summative assessment, if any.
  • Project management:
    • establishing existing levels of knowledge in the learners
    • identifying which learning goals will be achieved by when (aka scheduling)
    • identifying the human resource implications (crucial if you happen to be team teaching)
    • identifying costings where appropriate.
  • Identifying the resources needed for any learning activity, and either locating same or preparing your own.
  • For every planned learning activity, checking the following:
    • relevance
    • completeness
    • correctness, particular for task-analysed activities
    • unambiguousness
    • accessibility
  • Incorporating feedback from the learners into existing and planned learning activities.

In light of the increased use of information technology in learning activities, it is perhaps worthwhile going into some detail about making online learning activities more accessible. At the risk of stating the obvious, merely converting an existing printed document into an online form does nothing to increase the accessibility of the material being learned. The advantages of an online learning environment include, but are not limited to:

  • Immediate feedback on assessment tasks
  • Access to live data
  • Increasing or reducing the challenge presented to the learner on the basis of the learner’s answers (adaptive assessment)
  • Opportunities for independent research
  • Choice of route towards a learning objective
  • Audio and video material
  • Being updated for new information – current news stories are relevant here
  • Being updated for correctness

The choice of route towards a learning objective takes on an even bigger role in online learning. While printed material tends to very linear, online learning lends itself to having multiple pathways, so signposting becomes very important.

An Invitation

Please add your observations and additions in the Comment box below. Thank you.