## Minimum spanning trees

In our Young Entomologists classes the children tried the ‘muddy city’ problem from csunplugged.org.They were trying to minimise the paving between a certain number of houses, while ensuring that each house was connected to each other. Read on to find out how this is connected to entomology!

I only recently discovered the csunplugged.org site, which takes key concepts from computer science and maths, and suggests hands-on activities for children to learn about these concepts. There is an e-book with all the activities which you can download for free from the site, or you can search for a particular concept and just download the activities relating to that concept.

If you have a map with various points that you have to visit, a ‘spanning tree’ is a route that connects all of those points so you can visit each of them at least once. There are usually many spanning trees for the same map, but a minimum spanning tree is the shortest route that connects all of the points.

Note that in the specialised area of mathematics known as graph theory, the map, points and route described above are known as a graph, vertices and path.

Other similar problems that are well known in mathematical circles are the travelling salesman problem, the seven bridges of Königsberg and the Chinese postman problem.

Think of how many networks there are in our society – road transport, power grids, water supply. Computers use pathfinding algorithms to find the minimum spanning trees in these networks and therefore make them more efficient. Also, routers in communication networks often have spanning tree protocols to avoid looping.

How on earth is this connected with entomology? I have been interested in minimum spanning trees since reading about Dr Tanya Latty‘s work on swarm intelligence in slime moulds and ants. Dr Latty is currently at the University of Sydney and she works in collaboration with researchers from many different disciplines, including computer scientists.

Ants have very small brains, and slime moulds don’t even have a brain at all, yet their simple behaviour can solve complex problems in a similar way to that of a computational algorithm. Get colonies of Argentine ants to connect three nests together and their resultant path will have a central hub, making the shortest possible path which connects the three points. (This is known as a Steiner tree, which is rather similar to a minimum spanning tree, just with extra vertices allowed if it makes the solution shorter.)

You can learn more about Tanya Latty’s work on the tvs show Enquiring Minds, where she was filmed as their insect expert. There’s more information about using collective behaviour to make decisions here, explained by Prof David Sumpter.

Visit the csunplugged site to see many more activities related to minimum spanning trees and related mathematical or computational problems.

## What makes a good teacher, and can they ever be replaced?

Did you see the report about MIT BLOSSOMS: “Ed Tech that requires nothing but a TV and VCR?” (It’s from mid last year, so not exactly current, but it was recycled in the MindShift news feed recently.)  The BLOSSOMS approach offers videos on certain topics recorded by an ‘expert’ in the field. The key difference between this and something like Khan Academy is that the teacher pauses the video at certain points to conduct activities with her students – not computer based, but in real life – before she starts the video again.

I have quite a few mixed feelings about this report.

Firstly, what’s new? This approach seems to be quite similar to what I experienced at primary school and sometimes in secondary school. Every now and then a CRT television (the big old heavy ones) with a video player plugged in underneath, was rolled out on a trolley for the class to watch a video. It didn’t happen very often because there was probably one TV in the whole school and the teachers had to book their time to use it. In fact this BLOSSOMS approach was said to have arisen in “a rundown school in rural central China” which had a video and a VCR but not much else. Not so different to my primary school. The videos were used to illustrate certain points or introduce you to certain ideas, but not as the sole teaching method. I don’t think any teacher would have showed a video about long multiplication, for example, and said that they had covered that part of the syllabus with us, with no further work required.

Does it really challenge current orthodoxy? The author says the BLOSSOMS approach is “not student-centred”, “not BYOD” and “does not encourage each student to work at his or her own pace.” She suggests this is ” blasphemy in view of the hardening orthodoxy of the ed tech establishment.” I suspect there is not yet any orthodoxy in this area.

But with the current trend to use a computer program for every part of the syllabus, what does student-centred really mean when you are using a computer to do your teaching? Does it mean that the student chooses what activity to do, and what level to do it at, while still completing little tests online or watching the videos that someone else has written or created for them? That’s not really student-centred. Even if the program has some clever AI built in so that it increases the difficulty to keep the student challenged, it’s still not student-centred.

Also, there are key benefits to children working in a group, but working in a group does not have to exclude each child working at their own pace, and certainly doesn’t exclude student-centred learning. (Someone find me a good example of this. I’m sure there are many on the internet but I’m writing this late at night and I want to get a bit of sleep.)

Anyone who has been following news around education and learning in the past few years will know about MOOCS, blended learning, upside-down classrooms and the maker movement. But what I feel has been largely missing from the discussion is talking about what makes a good teacher, and the difference that a good teacher can make to the whole learning experience.

Yes, if all you are going to do is deliver a lecture to your students, then that might as well be done by getting them to watch a video, and if all they are going to do is watch a video, why do that at school or college, and why have the teacher there at all?

From the article: “Champions of educational technology often predict (with barely disguised glee) that computers will soon replace teachers, and some school districts are already looking to ed tech as a way to reduce teaching costs. The message to teachers from the advocates of technology is often heard as: Move aside, or get left behind.”

The thing is, that computers cannot replace teachers. Computers and/or videos can replace teachers as sources of information, but that’s absolutely not what I consider my function is when I am teaching. (Computers can also replace teachers in marking certain very narrowly constrained assessments, but then the problem is, what happens to the outcomes we cannot measure so easily, and are they devalued by being less quantifiable?)

Maybe my experience is skewed by having worked for the Open University, widely acknowledged as having been one of the first education providers to use the ‘flipped classroom‘ model. In the Open University, students receive the course material in some form (book, video, CD-Rom, online courses) and work through it in their own time. They don’t have to come to tutorials at all, but if they do, they will not be repeating the same material. They will not be listening to a lecture. They will be interacting with the teacher and the other students, working through activities in an attempt to gain a deep understanding of the material and how to apply it. Education is not just a way of passing information from one receptacle to another.

I suspect the essential key to the success of BLOSSOMS is to have a good teacher in the first place. What the lessons require, for them to work, is interaction between the teacher and the student. A good teacher, in my book, will know what to expect from each student in their class. They will be able to differentiate the work for the students who need stretching, just as they do for the ones who need more help and explanation of what is going on. This adjustment can happen ‘on the hoof’ during a lesson, and will lead to differences between each student’s experience of the lesson, even if everyone is working together towards the same ultimate goal.

The author of the piece suggests that the BLOSSOMS approach works because many teachers lack confidence in their own subject knowledge. If I had a teacher whose own understanding of science or maths was dodgy, I would prefer to be shown these videos and to be working on activities that someone better qualified has suggested, than to be working through a textbook, with nowhere to go when I had questions. But I think that’s not the main point of the program. I think that the main point is the interaction between students and each other, and between students and the teacher. And, to go back to the start, I don’t think that’s anything new.

After drafting this post, I saw that one of my favourite teacher bloggers, Pernille Ripp, was writing about personalized learning. That’s exactly what I’m getting at. I feel that if a teacher cannot provide true personalized learning, then our classes might as well be all computer based. Conversely, even with computer-based curriculum, a teacher who adds that personalized touch can make all the difference.

Was I extremely lucky with my primary teachers? Have I missed something in this current race to promote computer-based activities and downplay the value of human teachers? I’d love to hear your thoughts.