On the very first day of our PGCE Secondary Mathematics course, 21 enthusiastic, and probably relatively nervous trainees gathered together to start their teacher training experience.
We sat in a large circle and everyone had to ask one of the people sitting next to them to introduce themselves. We then had to introduce each other to the rest of the group, by providing our partner's name and a word describing them. As a memory exercise, the group had to repeat the newly introduced person's name and also the names of those who had already been introduced. This involved copious
repetition of some names, but the very last person's name was mentioned only once (for example, in a group of 3, we would have said 3 + 2 + 1 = 6 names overall. In a group of 4, we would have had 10 names, etc...). A challenge was to find out how many names we had mentioned in our group of 21 people.
Although we didn't know it at the time, we had inadvertently just used an NRICH activity in working out how many times each person's name had been said (it was an application of this nice problem: Handshakes). The activity also served to kick-start our love of triangle numbers! To see why, solve the problem...
On that first day, we also got involved in trying to find a reliable - and justified - way of finding the minimum number of moves needed to rearrange the lined-up order of two sets of coloured frogs from their initial starting positions (a lovely animated version of this problem can be found here: Frogs).
We demonstrated this task interactively, where many of the 21 trainees became frogs to be part of the experiment. In fact, the Frogs Investigation became part of every trainee's research during the year, where each trainee had to deliver a lesson or series of lessons on teaching Frogs to pupils at their placement schools. After having taught the lessons, we then had to provide our pupils with
formative feedback on how they had completed both class work and homework, and had to use the outcomes of the work as part of the data for our own research assignments.
Around October time, whilst the trainees were taking part in a serial placement of three days a week at university and two days a week in school, we were introduced to NRICH as a concept and as a website, and were shown some of the benefits of using NRICH activities in classes. We not only listened to a talk on NRICH, but throughout those first few weeks, we completed many NRICH tasks as a cohort
- some of us with far more speed than others! (see here for some of our favourite problems) .
We were charged with keeping a promise of teaching at least one lesson during our first school placement which used an NRICH activity before January. Needless to say, I think that many of us used NRICH far more than just once. As a hint for any budding trainee, or indeed teacher, I would strongly recommend that if anyone does want to use an NRICH activity in class, you should attempt to solve the
problems for yourselves first, before presenting it to your students. It will highlight the potential difficulties of the problem, and it will make it far easier for you to provide helpful explanations or hints when needed.
In January, we returned from our school placements to spend some time at the University Faculty, and we continued our group's use of NRICH as a team, notably looking at the problem of Tilted Squares in more detail.
We only had three weeks of respite at Faculty before we started our 15 week placement at our second and final school. At the schools, we had to rely on our own skill and the support of teachers and our mentor to find useful NRICH material, and implemented these in our teaching. The Curriculum Mapping Document for Secondary teaching (which can be accessed from this page) was a
rather useful way to start looking for suitable problems.
Just before the Easter holiday, the trainees met up again for two days at Faculty, and we took part in an NRICH Mathematical Roadshow, where we were able to play with some of the more visual problems for a few hours. Giving mathematics teachers a chance to play with their favourite problems is a far more exciting experience than one might think!
By the end of our 15 week placements, some of the cohort had used a tremendous amount of investigations or problems from NRICH. In fact, one trainee spent a whole week with his classes doing nothing but NRICH activities...
Going to Faculty for the final two weeks of our course in June provided our last few chances of using NRICH as a group of curious investigators. From now on, we will be the ones going forward into our teaching careers being the motivators of future pupils. I believe that all of us will be guiding our classes and individual pupils in the direction of using NRICH for a really positive and enriching
experience of mathematics at its best.