Like many beginning mathematics teachers, I had identified NRICH as an incredibly valuable resource with which to engage pupils in rich mathematical thinking from a relatively early stage in my training year. Perhaps like other mathematics trainees, I was a little too slow to implement NRICH tasks within the classroom, lacking the confidence to do so until I was sure in my mind I had the teaching
skills to facilitate more open-ended activities with pupils. However, one aspect of NRICH which had bothered me during my placement was I had only ever observed or taught such activities with pupils perceived to be at the higher end in terms of ability. In turn, this prompted me to ponder how an NRICH task could be used with pupils who demonstrate less aptitude for mathematics. During the final
week of my school placement, the opportunity to experiment with adapting NRICH activities came about, as classes had either finished the structured Scheme of Work, or required a 'mopping up' of remaining topics. This allowed me to have a free rein over the choice of topics with some lessons. I then identified as 'experimental' groups for these lessons a mixed-ability Year 7 class and a bottom set
Year 8 class. In the piece to follow, I hope to impart some of the successes (and failures!) I came across during this 'experiment' and the lessons learned because of it.
A Year 7 story:
The main consideration for choosing an NRICH task to adapt was to find one which would captivate the class' interest to enhance the chances of engaging the pupils in mathematical thinking. I remembered probability and dice games being a lesson which the Year 7 pupils found fun before, so set about scouring NRICH for an activity within this remit. An activity which caught my eye was Connect Three. This game appealed as it was multi-faceted, involving the integration of knowledge of negative numbers and probability. Furthermore, for a mixed set, the task lent itself to differentiated work, as those less familiar with the mathematical concepts could investigate different outcomes, and those more proficient could investigate the probabilities of certain numbers
coming up. A mathematical argument could also be formed on different levels to address the problem.
However, I was also acutely aware of the pupils' preference for whole class competition, which playing three in a row rendered difficult through its natural disposition towards paired work. Therefore, I decided to switch the focus towards bingo, providing all pupils with the same sheet as they would have ordinarily for three in a row, but instead needing to tick all the numbers off the sheet that
they could make from rolling the dice. A practice run beforehand appeared to indicate this would stretch the thinking of the class, and make them consider their tactics with regards to the numbers they could make. However, the game itself fell victim to the vagaries of probability as, try as we might, the dice on the interactive whiteboard would not comply to make an eleven or twelve! As a result
any notion of tactical thinking had been made redundant. The plan instead switched to why we had found it so difficult to make an eleven or twelve from two dice.
However, even though I had clearly adapted an NRICH resource and made it poorer, a poor resource does not necessarily have to lead to poor teaching! Whilst I pondered where to direct the lesson from its disastrous origins, a pupil exclaimed he knew why the game was “useless”. He could not work out how if all pupils had the same bingo sheets, how a pupil could outright win the game. Deviating from
the lesson plan completely, we then decided how we could improve Sir's 'useless' game, by choosing five or six numbers instead of all integers from minus five to twelve, investigating what the most likely numbers were to choose, and the least likely. We then played again with pupils' self-designed sheets, and finally could see the merits of mathematics aiding tactical thinking!
A Year 8 story:
Following the Year 7 lesson, I set about what appeared an even greater challenge with a bottom set Year 8 group, of whom a similar characteristic amongst all the pupils were very low levels of resilience to solve problems. As NRICH activities share the common traits of encouraging systematic approaches to solve problems, an impasse would seem to have been reached before the lesson had even begun.
However, I was determined to see how successfully I could fulfil my training objective for the week.
Again, when selecting activities the initial remit was to find a problem which would enthuse the pupils. Perhaps bizarrely to an outside observer, the initial criterion set when looking for an activity was for it to involve colouring in! Without fail the class always attempted tasks involving colouring with relish, so this seemed a good 'buy-in' to introduce an unfamiliar method of learning. I
then found the Shapely Lines task amongst the NRICH primary resources; an activity which would allow the pupils to explore different types of shapes, and improve their shape recognition. The big issue however would be allowing the pupils to draw their own lines onto paper, as it would run the risk of slowing the activity, and detracting the emphasis of the lesson from shape
finding. However, I had managed to take a ready-made pattern from a teacher at another school, which would do the same job, and provide arguably more interesting patterns. Incentives (in the form of Smarties) were provided for pupils to find as many shapes as they could, which I have found never fail to please as of yet!
When it came to delivering the activity, I split the pupils into groups and enlarged the pattern onto A3 paper to enhance clarity and to allow the pupils to engage in mathematical discussion. As expected, the pupils leapt at the chance to employ colour, and soon began to find the typical shapes as anticipated, such as different types of triangles, squares and rectangles. A few moved on to other
quadrilaterals, like trapeziums and rhombuses, as well as pentagons and hexagons, despite needing help for the technical vocabulary. However, soon after something less expected happened, as these pupils who were so adverse to investigative work started to look for shapes with as many sides as they could. Even better, from this lesson pitched to pupils who struggled with basic mathematical
concepts, I too was learning new facts. For example, did you know a twenty-four sided shape is called an icosikaitetragon? Well, you do now.
What can be learned from these experiences?
From these two stories, it is clear there were two very different lessons, taught to two very different classes who left with very different outcomes using two activities of very different quality! However, when all considered, both activities were adapted NRICH tasks, which promoted in their own unique manner a form of open-ended mathematical learning. The aim of NRICH is to “enrich the
mathematical experiences of all learners”, which by adapting a resource I could say with relative confidence occurred within these two activities. This experience certainly taught me it is possible to stray away from the conditions set in a resource, but it is imperative not to close off the task to remove the independent mathematical thinking. The key success of adapting an NRICH task still lies
in the original task itself, as after all, these activities are tried and tested already! In conclusion, I would certainly recommend having the confidence to adapt an NRICH task if you believe you can suit your class better, as you never know what your pupils will produce to impress you with their mathematics!