Architecture and tessellation

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I was reminded recently of an innovative house building design called a Hivehaus. I first came across this building on the Channel 4 programme “George Clarke’s Amazing Small Spaces” presented by George Clarke. The first time I saw the programme I remember thinking it was a brilliant design and how versatile yet simple it was. However, having now taught a couple of inputs on the Discovering Mathematics module it has occurred to me that not only is the Hivehaus design mathematically pleasing – well to me anyway, it is all based in the fundamental properties of mathematics as a result of its use of tessellation of shapes.

The pictures below are of the Hivehaus prototype and also the 3D plan view from the website planning tool, which you can use to design your own Hivehaus!Hivehaus prototype picture

Hivehaus 3D plan view

It is immediately obvious from picture above that the house is built by connecting (or tessellating) hexagonal units. What is not obvious from this particular picture is that you can add rhomboid or trapezoidal shaped rooms. These rooms are generally studies or bathrooms and fit into the gaps between the larger hexagonal rooms. I suspect that the gentleman who developed this innovative approach to house building used his vast experience of physically building things to ensure rooms of different shapes fit together well although it could be argued that without a fundamental understanding of shape and how shapes fit together, he would not have been able to make this work.

I will have to remember to use this example next time I teach on the Discovering Mathematics module.

 

Enthusiasm, knowledge or experience

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I had a really interesting experience this week that has made me think about perception, my practice and whether experience and enthusiasm for one’s subject is enough.

I had the opportunity to work with the MA2 students this week, not in my capacity as a lecturer in education but as someone talking about their experience as a headteacher.

My perception of this input was that the students were more engaged in what I had to say, they interacted more willingly and there seemed to be an atmosphere in room of genuine interest in the subject matter. One group even intimated that they felt that they should have given me a round of applause. I suspect this has not ever crossed their minds at the end of a mathematics lecture!

This flagged up several questions for me about what was different between this input and my others:

  1. Was it the subject matter?
  2. Was it the fact I was speaking about my experience as someone the students respect, i.e. a headteacher?
  3. Was it the fact the students were sitting in TDT groups rather than their usual friendship groups?
  4. Was I imagining things and was it more to do with how I was feeling rather than the students’ responses?

Subject matter – well…this is a whole other post I suspect. Mmmm…learning about maths as opposed to thinking about aspects of multi-agency working? I always try to think of ways to make what I’m saying and what the students are doing in my mathematics lectures/workshops interesting and engaging but perhaps that’s what I think I’m doing and is not the reality of the situation. However, perhaps the students have a different mind-set going into mathematics lectures than they do for other subjects and even if I was to do exactly the same in mathematics as I did for the multi-agency input they still would react differently. There were more opportunities to discuss things in the multi-agency input but that was the nature of input and during mathematics inputs there are different pressures and things to get through. Saying this I had a workshop with the MA2s later the same day which was completely practical in nature with very little direct teaching but lots of opportunities for talking, discussing, asking questions and engaging in mathematical activities. Whilst the vast majority of the students seemed to enjoy and participate enthusiastically in the activities, I perceived the engagement not to be as widespread as in the morning’s multi-agency input. This makes me wonder whether my third question above has a part to play in this as the students get to choose who they sit with, interact with and work with in my workshops – perhaps I should mix things up a little?

Did the fact I was speaking from experience as a headteacher make a difference to the students’ willingness to participate? This is a really interesting question as I would contend that I have far more experience and knowledge about mathematics learning and teaching to share with the students than I do about my time as a headteacher. Is it that they get me regularly in my role as their maths lecturer and familiarity breeds contempt?

Unfortunately, through all of this I seem to have more questions than answers and questions that will probably never be answered.

My next steps? Well…I can only do what I can do and I cannot make people be enthusiastic about my subject or love it the way I do. I can show my enthusiasm, which I think I already do, and prepare learning which motivates and encourages students to see the value in our time together; however, as face-to-face contact is so precious and limited sometimes there has to be ‘telling’ and not as much ‘experimenting’.

I wholeheartedly believe that mathematics is a subject where children should learn through activities that stimulate thinking and discussion about strategies and which young people can see has relevance to their day-to-day lives whilst also being:

“…beautiful, intriguing, elegant, logical, amazing and mind-blowing; a language and a set of systems and structures used to make sense of and describe the physical and natural world” (Ollerton, 2003, p.8).

This being said, it is my job as a university lecturer to teach our student teachers how to teach mathematics, how to plan activities and learning which will engage their learners not necessarily for the students to engage in the same activities; I can only ultimately provide the kindling and matches for the fire and it is up to them to decide to light it or not!

References
Ollerton, M. (2003) Getting the buggers to add up.  Chippenham: Antony Rowe.

Student roles and mathematical competence

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Just been reading an article from the Mathematics Education Research Journal about student roles and mathematical competence. I’m not quite sure what to make of it and what the article was ultimately trying to conclude. It describes how mathematics is taught in two different ways in a first grade and second grade class in an American school. The children who were part of the study had been taught one way in the first grade class and were now experiencing a different way of being taught in the second grade class. I suppose I was expecting to read that the more discursive, investigative way of teaching in first grade was going to come out as a better way of teaching and that the children would not enjoy being taught in a more traditional manner in second grade. It doesn’t seem to be that way. However, it has made me wonder if the children had been taught in the traditional way in first grade and then in a more problem solving based way in second grade if this would have made a difference to their feelings of security and success.

I think the one message that does, however, come clearly through is that the attitude of the teacher towards the children and their answers is similar in that both teachers treat incorrect solutions as learning opportunities and don’t discount the children’s answers, right or wrong.

 

Inspiring use of blogs by new MA1 UoD students

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I’ve just been reading through some of the blogs created by the new MA1 students here at UoD and have been blown away by their insightful, honest entries. If this is the face of professional learning together and sharing our highs and lows, then bring it on. Absolutely inspirational stuff; these young people are going to be our teachers of the future – brilliant!