Half term report (or simply: breathe!)

As I alluded to previously, Christmas 2014 saw me change jobs after 4 and a half years. Having reached the end of 6 hectic weeks, I thought it might be a good time to document my experience, thoughts and fears, not least because hopefully putting my thoughts down in print will allow me to mentally declutter!

  • Change is difficult at any time, but especially part way through the year – I guess this is obvious, but even now I still don’t think I am fully ‘there’. I was so comfortable at my old school – too comfortable, in fact, which was one of my reasons for leaving – and the first week in particular was a huge shock to the system. In fact, it became a simple case of survival at times. But a rough plan of what I was doing, and supportive colleagues who helped me bed in quickly, got me through to the weekend, where I could regroup.
  • Schools which appear quite similar can be very different in practice – both my old and new schools serve predominantly white, working class intakes from ex-mining communities. But that is pretty much where the similarities end. The ethos of my new school, the behaviour management systems, and the aspirations are all very different (in a good way). I know this was a great move for me. I can’t wait for that day when I finally feel like I’ve arrived and am fully comfortable in the post.
  • Expectations on all levels need raising  – both in terms of behaviour and in work ethic, it’s clear standards for some of my students were a little low. My year 8 class admitted earlier in the week that the previous teacher was soft on them in terms of the BM system in place – which all staff are required to follow religiously. I feel like I’ve made some progress here, although there is still a way to go.
  • I have a large/scary amount of control over my class AND my environment – the freedom I have is something I have found difficult to cope with at times, and has led to me having crises of confidence on many occasions. We have no scheme of work at all, so I decide what to teach and for how long. This can be quite a daunting prospect, although I also recognise the huge opportunity it provides. Similarly, the fact I now have my own room is a great opportunity for me to impress my values and expectations on students – it had been my aim to get a display put up this week, but the replacement of windows and the associated removal of asbestos prevents this from happening.
  • I just need to focus on the process and not worry (too much) about the outcomes: like George Michael, I gotta have faith – in my running, I’m all about the process – running consistently, through all weathers and good and bad runs alike, will deliver the outcomes I want. Similarly, I need to be confident in my methods and strategies of teaching, and know that if I am producing the goods day in, day out, students will make the desired progress.

Although half term hasn’t really started yet, I’m looking forward greatly to the second half of the spring term. I feel in a much happier place, and feel this is the time to start kicking on and making big inroads on student progress. I look forward to catching up with old blogs to inspire me as ever!

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Day 1 reflections

New year, new term…..NEW JOB?!?!?

Finally, after much waiting, I took up my new post. I felt I’d had a decent break, I slept well and woke at the time I’d planned. I was in school early, eager to get cracking….until stuff got in the way. Like not being able to get in the building (note to self: if the school has a keypad entry, find out the code BEFORE the first day), not being able to connect to the school wifi, finding out my year 9 class have 6 lessons a week, not 5, and therefore one lesson a week with another member of staff, who teaches them on a Monday, and………

Yes, it was busy. No, I still don’t have a clue what I’m doing. But yes, it WILL get better. I am sure of it. Not least because I have my own room (although I haven’t really even begun to think about what I’m going to do with it), lots of TAs to help me, a very understanding HoD, and a corridor full of colleagues willing to listen, and help.

I’ll be fine. It’s just going to take a while to get up to speed.

I can’t wait for that day….!

And another one….

Triangles and rectangles

 

I saw this just as I was settling down in bed last night. 1 1/2 hours later, and after double, treble and quadruple checking, my solution is as follows*. Another fab puzzle, putting into practice a variety of skills. And I even managed to find two routes to the answer!

IMG_0400

 

*Upon further inspection last night, I had made a mistake and posted a slightly different solution on Twitter. Still a bit rusty!

Looped polygons (odd number sides)

So much of my Sunday was occupied with the looped pentagon problem. Having solved that, I was intrigued to see how the problem would play out for other polygons. I have spent most of my time since focusing on odd-sided polygons (because I think even-sided ones are relatively straightforward, although I need to check) and thought I might share what I had come up with so far.

Firstly, I have to say this has been a bit of an eye-opening experience for me. Not having a solution, or any real help, has added to the intrigue. I’ve extended the problem, I’ve made connections and generalisations, and I’ve refined my approach all the time until now, where I feel I have a method to share. It’s the kind of thing I’d love to spend time on with students….if only!

The general problem is like this: a polygon is marked, with circles of 1cm radius placed around its vertices. A piece of string in looped around each vertex and pulled tight so there is no sag. The challenge is to calculate the length of string needed. In the original pentagon problem, the distance from vertex a (at the top) to vertex c (bottom left) is given as 5cm. I will refer to it simply as l.

The main issue I have found so far, and which I may well go back and revisit at some point, is deciding the order in which the string is looped. Once you move to a heptagon there are options. In all cases I present below, I have opted to go for the furthest vertex from the top vertex, which I have called the bottom left. The string then loops back up to the vertex immediately to the right of the top vertex, and so on.

I had, you will recall, noticed that l was parallel to the string – it must be so, as extending the string would create a tangent to the centre of the circle. My approach therefore involved a lot of angle theory. Beginning with the equilateral triangle, I split the interior angle in half to give 30 degrees, as this allowed me, by deduction, to calculate the angle from due North to the string. This done, and the two added together to give 150 degrees, I subtracted the tangential right angle to leave an angle of 60 degrees from due North to the tangent. Drawing a right angled triangle showed me that the angle from the centre of the circle to the tangent was 30 degrees from East, meaning that on both sides of the circle, the string was wrapped around an extra 30 degrees before moving towards the next triangle.

This gives a total contact with the circle of 180 + 30 + 30 = 240 degrees, or 2/3 of the circle’s circumference. The LENGTH of string needed can be calculated by 2/3 x 2 x pi for one circle, and then multiplied by 3 for all 3 circles. This gives a total of 4 pi for the circles, plus 3l for the straight bits, for a total of 3l + 4 pi. Knowing that the pentagon gave a solution of 5l + 6 pi for the length of string, I began to conjecture that for any s sided polygon, the length of string needed was sl + (s +1) pi.

I next tried a nonagon, being a shape with the number of sides being a factor of 360. And this was where I got stuck for a while. I guessed the answer was 9l + 10 pi, but this was based on me guessing the angle from due North to the bottom left circle. I eventually realised that the answer may lie inside the polygon – in the centre, in fact. By taking a line segment from the centre of the polygon to each vertex, I had the angles there, ready to go. So for the nonagon, each vertex was a movement of 40 degrees (360/9). Using angles on parallel lines, I could see that the angle created by drawing an isosceles triangle from the points due North, in the centre of the polygon and the bottom left vertex, gave me the angle I needed to subtract from 180 degrees. In this case that angle is 10 degrees, meaning the tangent/due North angle was 170. This, to cut things a little short, means that 10 degrees was the angle beyond 180 where the string was touching the circle on each side. Here, this resulted in 180 + (2 x 10) = 200 degrees, a total of 5/9 of the circle’s circumference. Again, the total curved contact can be found by calculating 5/9 x 2 x pi x 9, which equals 10 pi. So the total length is 9l + 10 pi.

Having found a shortcut, I then tried the heptagon. This was particularly brave given my lack of a scientific calculator, but I got there in the end. The large angle in the isosceles triangle I needed was 3/7 x 360, so the small angle worked out at 12 6/7 degrees. This was the angle beyond 180…..etc etc….and I eventually arrived at a length of 7l + 8 pi.

I had spotted another pattern here, and stopped to investigate. The proportion of the circle which was touching the string was 2/3, 3/5, 4/7, and 5/9, and can be expressed as (s-1)/s for a s-sided polygon. What I also found fascinating was angle from due North vertex to bottom left vertex as a proportion of 360: 1/3, 2/5, 3/7, 4/9…clearly this will gradually get closer to 1/2 without ever reaching it, and can be expressed as 1/2(s – 1) / s for an s sided shape. And if you add this angle to the sector touched by the string, you get 1 every time. Pretty neat, huh?

I realised now that this allows me to quickly work out the information I need without having to worry too about the angles – so for a 15-sided shape, we take 7/15 (168 degrees) as the largest angle in the isosceles triangle, meaning the angle beyond 180 degrees will be 4/15 (6 degrees) on each side, or 8/15 (12 degrees) in total. This will give total string contact of 15l + 16 pi.

With odd sided polygons, I think the next step is to investigate whether a different (but still repetitive) looping arrangement changes the total  amount of string needed. I’m not sure at the moment, but I do know I have some strategies which will hopefully allow me to find the answer pretty quickly!

I can’t get no sleep…. (or what I’ve been up to these past months…)

“But there’s no release, no peace
I toss and turn without cease
Like a curse, open my eyes and rise like yeast”

Insomnia, Faithless, 1995

This is one of the all time classic dance tracks (indeed, it is my favourite dance track of the 1990s) and it has been quite prevalent in my mind recently. Because for the past five or six weeks, I have been suffering regular sleep loss. This blog is hopefully part of the process of dealing with the issues that have caused my depleted sleep.

I was always adamant that I would never change jobs in the middle of a school year. In 2010, however, I moved at May half term, and spent the last 6/7 weeks of the year at my new school, settling in with no real teaching timetable (in reality, I DID teach a few lessons, to a greater degree as the half term went on, but it wasn’t really full-time teaching). It was pretty easy for me.

After missing out on a couple of TLRs, I had decided this would be my last school year at my current school. However, a chance browsing of the TES jobs site one day caught my eye. A job was advertised at one of the fastest improving schools in Leeds. They held an open day which I attended with my wife (just as she had done 5 years earlier before I got my current job). We heard the executive headteacher speak. He was deeply impressive in his vision and his convictions. He spoke of mindset and a rigid positive discipline system. To put it into context, he was so impressive even my wife said she wouldn’t mind working in one of his schools – and she can’t stand children!

So I applied, I heard back, I went for interview. The school was fantastic – not a new building, but one full of impressive displays, full of incredibly polite and attentive students. I could even have my own room! My lesson went pretty well, and I felt I nailed the interview. Hours later, the call came. I had been successful!

This was the Wednesday before half term. Since then, my head has been racing in my quieter times, including, clearly, last thing at night. I am racked with excitement, nervousness, and self doubt. I went for my day at my new school on Thursday and, although I know my timetable, I am still waiting for confirmation of topics to teach. And so my insomnia persists.

Let me make it clear: this is not a criticism of my new employers. I know what is expected of me in terms of end of the year grades. When I do receive the confirmation I am after, I shall be ready. Ready to begin intensively planning for this new and exciting chapter in my career. I chapter I WANTED to embark upon.

It’s just…..there seems so much to think about now:

  • what posters do I display?
  • what messages do I want to convey in my first week?
  • how can I help the students in making the transition from one member of staff to me as seamless as possible?
  • what happens if I go in too harshly?
  • and finally….what if I fail?

So now I have shared my worries, a) I hope I shall begin to sleep better, but b) I need your help. Those of you who have moved jobs mid-year – how did you cope? What advice would you share? Can you confirm that I will indeed be absolutely fine?

Please???