# The NQT year is almost over…

It has been an interesting first year in teaching to say the least. Aside from development in school I have particularly enjoyed engaging with the Twitter community in the sharing of ideas and resources, as well as getting involved with chats and attending CPD events. I have also had the privilege to be involved with the mathematics magazine, Chalkdust.  In this post I hope to document some of the things I have made use of or got involved with during this year.

One of the first Twitter chats I was able to get involved with was #mathsjournalclub which is hosted by Tom Bennison. A new chat which also started last year, the discussions have a mathematics education research paper as the focus, though discussions have also developed around ideas and suggestions which are raised during the chat. Past discussions can be found on Tom’s Storify page. The sixth chat is up for voting until the 9th June here and will take place on Monday 11th July at 8pm. If you don’t already take part, the discussions have all been very interesting and it would be great if you got involved!

I have also tried to get involved with the weekly #mathscpdchat and #mathschat discussions and have had the pleasure of hosting two #mathscpdchat discussions this year (Wild Maths and Marking at A-level). These discussions always have an interesting topic of focus with lots of fruitful discussions. Following a break for half term both of the discussions should be very exciting next week with a special #mathschat webinar and #mathscpdchat focusing on working collaboratively on teaching, learning and assessing mathematics.

I have attended ChristMaths and MathsMeet Glyn (organised by Jo Morgan), MathsConf6 (La Salle Education) and Maths in the Sticks (organised by Stuart Price). All of these event provided excellent presentations and provided me with lots of things to take away and think about. My next planned event is Tom Bennison‘s East Midlands KS5 Mathematics Conference which already has an excellent line up! I would highly recommend getting along to any good CPD event, especially when they are free!

I now frequent many maths teaching resource websites. For A level I tend to find myself looking for something on Integral Maths. For homework, Jo Morgan and Kathryn Forster’s Pret Homework website provides quality and worthwhile worksheets designed by teachers. In addition Jo Morgan’s Resourceaholic website provides access to some outstanding resources which can be used from KS3 to KS5.

I have without a doubt used an extensive list of other resources, however these have been of particular help when struggling to find something good to incorporate into a lesson.

I will be returning to my second PGCE placement school for my second year of teaching and I am looking forward to a change in dynamic and continuing to make use of the outstanding resources that have been made available by fellow mathematics teachers.

# Parametric equations card sort

Recently I taught an observed lesson on the introduction of parametric equations (Core 4). One of the tasks which I used towards the end of the lesson was a self-designed card sort activity. This task requires students to match a set of parametric equations with their corresponding Cartesian relation and graph. Within one set of cards there are five groupings, with some of the Cartesian relation and graph cards remaining blank.

A key idea that one grouping in the card sort helps to address is how restrictions upon the parameterised equations may not result in the full Cartesian graph.

The parametric equations used in the task are $x=\sin^2{t}, y=\cos^2{t}$, which for all values of $t$ only gives $x$ and $y$ values between $-1$ and $1$. This results in the Cartesian graph of $x+y=1$, but only a small segment of it (see graph on the left).

When I implemented the task students got engaged with it quickly, some making matches and others getting stuck with manipulating equations to eliminate the parameter. There were certainly a number of challenges encountered, though I thought that the task itself really helped to test their understanding of what they had learnt during the lesson, and provided me with a better idea of who needed more support.

Parametric and Cartesian equations cards

Graph cards

Solution sheet

Please feel free to provide me with any feedback on this task, I would be particularly interested in general thoughts or any suggestions on further developments that could be made to improve the task.

Please also let me know if you make use of this activity and if it is successful!

# ‘Evaluating probability statements’ Standards Unit task (S2) with year 8

Having moved on to the topic of probability with my year 8 classes this term I was reminded of my final university tutor observation of a year 8 probability lesson last year, which happened to be one of my better lessons during my PGCE. I had decided to ‘be daring’ and conducted the ‘Evaluating probability statements’ Standards Unit task (link courtesy of @mrbartonmaths) with the class. The feedback was good and I was able to get really fruitful discussions from the class.

The structure I re-used with my two year 8 classes last week, with some tweaks, which resulted in both classes being more engaged with mathematics and ‘real’ mathematical discussion than before!

The task encouraged students to, in pairs, discuss the validity of a number of probability statements. They were asked to ensure that following their discussions they wrote down their thinking in order to refer to it in a later whole class discussion. Some students found some statements difficult to interpret and these were left until the end where pairs were able to join together into a small group to discuss the leftover statements.

After the discussions I wanted to have some class feedback. Using iDoceo’s random student picker I was able to select a student to chose a statement and explain their reasoning as to why they had decided that it was true or false. This then allowed the opportunity to open up a discussion with the class as in many cases there was conflicting opinions or reasons behind pupil answers. It really helped to meet the task’s criteria of clarifying the misconceptions in the statements, and for almost every statement I was able to take a ‘back seat’ listening to my students argue their points and eventually reach an agreed conclusion through their discussion.

The Standards Unit tasks are probably some of the best classroom activities I have come across. They are challenging, promote mathematical thinking and engage all learners in the task. In addition to this they all contain a preamble with a suggested approach to the task which has been helpful on many occasions. If you haven’t used them yet, you should consider it!

You can find all of the Standards Unit tasks on mrbartonmaths.com.