Tim Knight's musings on online education and math

November 4, 2013
by tdjknight

Edward Frenkel v E.O. Wilson


Edward Frenkel author of Love and Math lecturing

I have recently bought Edward Frenkel’s new book Love and Math: The Heart of Hidden Reality. The article that was sent to me that provoked me to buy the book appeared in the New Scientist and was very interesting but one link that particularly caught my attention was an article written by Frenkel critiquing E.O Wilson’s advice to young scientists about mathematics. Wilson basically says that he did not need mathematics for his scientific career and so young scientists should not worry if they are challenged by mathematics. Frenkel picks this apart and lays bare the grand fallacy Wilson’s position with both precision and passion. And he is right to do so, however revered and loved is E.O Wilson.

The core of the problem it seems is a total misunderstanding of what mathematics actually is. The idea that it is number crunching, algebraic manipulation and advanced arithmetic seems inherent in society mainly because that is about as far as most people got in their mathematical career. Yes, we all have had mathematical careers, even if we left school at 11 years old!

Frenkel explains how mathematics is so much more than that. “The laws of Nature are written in the language of mathematics” as Frenkel quotes Galileo who knew a thing or two about using mathematics to go beyond our the physical limitations of our biology. Charles Darwin spoke of math endowing us “with something like a new sense”. Frenkel discusses three dimensional curved space, a universe with more dimensions than we can see. The fact is that our own biology limits what we can see and experience, and it is if we are looking at our universe through a keyhole, with a view limited by our own physical and cognitive limitations. The only avenue beyond this biology is mathematics. Not only is it beautiful but it is also attainable. The idea of going outside our bodies to achieve a higher plane of understanding is present in many religions. Mathematics has much in common with this goal and it perhaps no surprise that in India, the home of meditation, that  mathematical prowess is respected as in no other country.

So what has this got to do with mathematics in schools? Well, first of all let’s start to listen to top mathematicians about what mathematics actually is. Marcus du Sautoy (and others) conceive of mathematics as the science of pattern. This leads to a neat understanding of why our universe and mathematics seem to match up so well. It a fundamental assumption that the universe we inhabit behaves in the same way wherever we are in that universe, this could be regarded as a definition of being human. This is also the basis of human learning, including when we are babies. We assume that when we knock over a glass of milk the milk will spill, and will always spill. This pattern in the universe is what we see in the mathematics that is the language of science. When we study and understand pattern in the universe we are almost by definition doing mathematics.

Mathematics is moving so fast and the science that accompanies it is following on the same path that by not urgently taking our curricula beyond number crunching and arithmetic we are creating a new illiteracy in society. The few who understand mathematics will control the mass that do not. This is not fair and a society that relegates mathematical insight to a luxury for the few is on a dangerous path.

November 4, 2013
by tdjknight

Online Classes – What do we lose and what do we gain?


In my ongoing (very occasional) series engaging with the “5 criticisms of online education” as laid out in this teacher’s blog post I am moving onto the second of the five. The criticism is that “relationships, connections, and networking are minimized in the rushed online world”.

One of the most surprising aspects of my experience of online education is how well I know my students after quite a short time. Not only how well I know them but how I know each student equally well. Of course the first question to ask is what do we mean by “know a student”. Although it might be that we know a student’s home circumstances, who they are friends with, how well they conform to the school environment and other extrinsic information, the knowledge of a student that counts for me and forms the basis for the work I will do with them is how they learn best, their learning needs, ambitions, motivations, willingness to be challenged, skills, talents, perseverance and general approaches to learning. I would argue that all this key information and knowledge can be seen online. The way the evidence for this knowledge is accumulated online also means that our knowledge of students is more evenly shared across a class without the “kids at the back” that plagues face to face classrooms.

In my online environment what exactly is the  information about students that I use to form my knowledge of them? Much of it is quite pure data such as performance in assessment, page views, discussion posts, blog posts and general engagement in the course. This seems quite cold but this objective sense of a student’s performance is both unbiased and powerful. At the same time we have significant one – one interaction with students by email, messaging and discussions. This puts context on the hard data that is available. My personal sense is that I have a very strong understanding of a student’s attitude, approach, confidence, motivations and ambitions. This was not always the case in face to face schools where although I knew some students very well, others were unknowable,  which was principally the student’s choice. This avoidance of contact between a student and teacher is virtually impossible in an online environment.

It is interesting that often my impression of a student is confirmed when I have direct contact with schools and that in other circumstances a student has been able to remodel their persona in the online environment. A student that is seen as non – communicative or lacking in confidence in a face to face school can leave this baggage behind and attempt communication in a the safe, less socially charged environment of a physical school stuffed with adolescent angst, boundary testing and general tension. I strongly believe that this online experience can help a student cope better with their face to face world and be an important aid to growth.

As usual in order to make the most of an online environment these benefits must be recognized and course design has to be aware that they are important goals in an online class as well as knowledge and skilled based goals. Online education is not subverting face to face schools but actually helping students cope better in the challenging environment of a physical (blackboard jungle was made nearly sixty years ago but the title of the  film still seems ring true in many schools). Schools are places that, whilst more familiar, are much more challenging and complex than online spaces that are relatively very simple. We have to use this simplicity to help students understand how to control communication, come to knowledge for themselves and manage their time to their own benefit. Online is the perfect place to develop appropriate and sophisticated approaches to learning that will benefit a student in their online and face to face world.

It is interesting that the criticism mentions the “rushed online environment”. I think this is probably a fair criticism of many online course that are simply about knowledge transfer and not about student development. Good online courses, especially at the high school level, must have “approaches to learning” built into them. Good teachers “teach the student” they do not “teach the subject”. The same could be said of good online courses.

October 14, 2013
by tdjknight

Measuring Success in Online Learning


“The measures of success are often wrong – learning experiences are far more important than a checklist of standards and objectives.”

This quote above is one of the five criticisms of online education and in this blog post I would like to examine the important point that I think it is trying to express. The first thing to note is that it is difficult to generalize online courses and instead of answering the criticism head on I would like to ask whether the criticism stands on its own terms. Is it possible to classify “standards and objectives” and “learning experiences” as opposed but somehow linked concepts.

Let’s begin with standards and objectives. Let us first deal with  course objectives. This is surely not controversial. A course of study needs objectives, otherwise it would be impossible to write the course. So the problem must be about the standards. The word “standard” has taken on negative connotations, especially in the US.  I personally take standard as meaning the measuring stick against which we measure out success or otherwise of meeting the objectives of the course. This I classify as assessment. Here it seems we are getting down to the essential question of what we are measuring and how we are measuring it. What is a courses assessment policy, has it been made clear and we know what is being measured and by which means. In fact it seems to me the problem with “standards and objectives”in courses (and this applies to ALL courses not just online) is a lack of clarity in learning objectives and subtlety in measuring student and course success against these objectives. I think the critique actually has things the wrong way round, we do not need less “standards and objective” but better and more nuanced versions of the checklists in the quote. We can start to make judgements about the quality of online learning programmes by looking at how they assess. Is there transparency and clarity in assessment? Does it measure the right things? Does it undertake measurement to enhance learning as well as make judgements? How is the data from the assessment used? Does it all make sense?

So let us now move onto “learning experiences”. I assuming that this is about interactions with others in a class involving discussion, critique and improving approaches to learning. I agree wholeheartedly that these experiences are fundamental to education and learning. However, I do not understand how the author of this critique implies these learning experiences cannot take place online. Is this not an issue to do with learning objectives? If as part of our objectives we include the abilities to discuss, interact and collaborate then we can plan to involve  this in an online environment. We would also need standards to assess student progress in these skills. My experience tells me that online can be extremely powerful as an agent to help students make progress in their approaches to learning, self reliance and independence. This can be translated into similar progress in face to face environments.

So, in summary, I think we have a criticism that is not only incorrect but lacks validity in how it has been stated. However, the debate around the quality of online courses in providing rich “learning experiences” can lead us to important indicators of how good an online course has been built. There is a lot going on here and a quality online course requires significant work in defining key objectives, building learning experiences that allow students to progress towards these objectives and intelligent assessment that allow us to measure how well students (and courses) are performing. Not all online courses are alike and it is hard to measure one against the other. However, I think this discussion around “approaches to learning” and “assessment” can helps us understand more the qualities of particular online course.

September 13, 2013
by tdjknight

Five Criticisms of Online Education



Whilst doing some research I came across a blog written by an online teacher who had had enough. Within the blog there were five key criticisms. The comments on the post indicated that in the US especially there seems skepticism about online education due to poor course design and a drive to make money by private companies. As I pointed out in a different blog post online is here to stay but that it can go in different directions.
I believe that online can have a hugely positive effect on general education in our societies, helping students have access to the best pedagogy, liberate them from the walled classroom and improve life long learning skills. However, if it is used to simply replace face to face classrooms at less cost (and benefit shareholders of the online provider) we will undermine general education and create even more inequality in both access to good education and educational outcomes.
I want to take each of the five criticisms of online education given here over a series of blog posts and try and show how good course design, well trained teachers and a broad view of education can make an online learning experience positive. So positive in fact that it can improve a student’s face to face learning experience.

What is wrong with Online Learning – 5 Criticisms

• The measures of success are often wrong – learning experiences are far more important than a checklist of standards and objectives
• Relationships, connections, and networking are minimized in the rushed online world
• Differentiation and personalized learning is lost in the pre-created curricula and assembly line experience of most distance courses and MOOCs
• Motivation and engagement suffer through isolation – we’re seriously becoming ok with virtual science labs!?
• The subject matter (and the learners’ needs) should drive instructional strategies, not technology

September 6, 2013
by tdjknight

Good Writing and Simple Mathematics

Screen Shot 2013-09-05 at 19.09.23

In mathematics education we seem to spend our time confusing students. The saddest thing is that the curriculum in some countries aids and abets this abuse of mathematical power. Mathematics can be very difficult and it can also be extremely simple. However, we seem to place obstacles in the way of children to make mathematics more difficult than it needs to be.  I currently have to relearn long division because my son is in Grade 5. A levels in Maths, Further Maths and Physics, a decent degree in Mathematics from Oxford University and a quarter of a century doing mathematics full time teaching students to university level do not seem to be cutting much ice with my family. “You are a math teacher aren’t you not just some imposter?” seems to be the current refrain in my house! Well, actually I am a Math teacher and I would not do any other job for the world. The thing is that I have not needed to do a long division problem in over 35 years. I have used calculators, estimation and more recently smart phones but never long division.

This would be funny….if it was not deeply worrying. Here is an excellent article discussing the requirement of long division in schools in UK in the new curriculum. The mathematics curriculum which seems the most clear cut of all syllabi in fact can become quite a political entity but as often happens a debate about what our children actually need rather than relating learning to some past epoch seems to hard to achieve. I would suggest that those interested in innovative curricula for younger children should look to the New Zealand math curriculum.

Another article that caught my eye recently was from one of the real up and coming stars of science and mathematics writing, Adam Kucharski. A Cambridge PhD in Mathematics he is also a writer of remarkable clarity and quality. The article that I was particular attracted to is a discussion of how we make Mathematics more complex than it needs to be and the real dangers of this. The key example is how by large portions of the population rejecting mathematics wholesale we can end up with problematic mathematics models that have not been properly scrutinised. This might not seem to be a major issue but actually it is extremely serious. Some background reading of the 2008 financial crisis will show that the major problem was a misuse of algorithms and mathematical models. One of my favourite movies of the last couple of years is called Margin Call. If you want to understand more about mathematics, why so many mathematicians work in finance watch this film.

So in summary, it really matters that the population are not excluded from mathematical knowledge. I would argue it is not the general public’s fault that their attitudes and understanding of mathematics is so poor. We need national and international commitment to understanding, this is a democratic right. Oh…and to start with, save me some family pain and take long division out of the curriculum.

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