The programme for researchED was outstanding – interesting sessions, excellent speakers and a well structured day. Unfortunately I had to leave at 2pm to go to a wedding so I was only able to attend four sessions. I’ve provided summaries of those sessions here.

Thankfully I had the opportunity to briefly catch up with a number of Twitter friends throughout the day. This event marked the start of a busy conference season for me – over the next two months I’ll be speaking at four events – first up is LIME Oldham on 20th June where I’ll be speaking about quadratic methods.

**Comparing exam questions**

The first session I attended was run by representatives of Ofqual. They spoke about their work in comparing the difficulty of exam questions, and the sources of bias in judgements made.

Remember when the new GCSE sample assessment materials were first released by the exam boards? Many maths teachers said that the Edexcel papers were notably harder than the AQA papers. After Ofqual had accredited the papers, concerns raised by teachers prompted them to do a study of exam question difficulty. They asked 43 maths PhD students to do a comparative judgement of 2,150 questions. Their task was to judge ‘Which question is the more mathematically difficult to answer fully?’. In each case the PhD students were given two questions side by side on a screen and had to indicate the more difficult of the two. Later these questions were attempted by 4,000 pupils (presumably these pupils had actually been taught all the topics they were being tested on – it would be pointless to give pupils a question on a quadratic inequality if they hadn’t yet been taught that topic).

The questions shown below are those that pupils found harder than the PhD students expected. Here we have a multiple choice decimal/percentages question and an order of operations question. People generally, and often incorrectly, perceive multiple choice to be easy.

The circle theorem question shown below is one that pupils found ‘easier’ than the PhD students expected. Of course, this doesn’t mean this is an ‘easy’ question – it could well mean that teachers have anticipated the challenges and taught this topic well. At the end of the session someone suggested that this indicates that teachers are doing something right, a comment which was laughed off but is actually rather important.

I was frustrated by the decision to use PhD students instead of experienced teachers in this study – surely teachers have a far better idea of what pupils will find hard. Ofqual realised this too, and revised the process accordingly. Prior to accreditation of the new science GCSE, they asked science teachers to undertake a comparative judgement. Interestingly it turned out that the science teachers’ judgements weren’t as ‘accurate’ as we might expect. Ofqual identified a number of sources of bias that might explain the discrepancy. For example questions with a large word count were often judged to be more difficult than pupils actually found them.

I do wonder whether it is helpful to judge a question by simply glancing at it – surely one needs to complete a maths question to properly assess how hard it is. Twenty seconds a question doesn’t sound like enough.

**Engelmann**

Kris Boulton is an excellent speaker and I very much enjoyed his session on Engelmann’s ideas. Engelmann’s work provides detailed guidance on how to teach – scripts in some cases. I’m rather opposed to the scripting of lessons but his ‘my turn, your turn’ stuff is intriguing.

We rarely question whether our instructional methods are effective. I want to learn more about different techniques for explaining mathematical concepts. I think it’s really important.

Kris talked us through how he has used minimally and maximally different visual examples to help students understand concepts – he showed us slides including triangles and surds and it occurred to me that teachers would benefit from sharing a large bank of these slides. I have dabbled in this kind of explanation recently but I’m not an expert in creating a logically faultless sequence of examples.

**Times tables**

I like Times Table Rockstars very much. I think that every primary school should use it. It works well at Key Stage 3 too. Bruno talked us through his ongoing research from his vast data set – 1.5 million questions answered in a day! There’s lots to explore.

On the slide shown above we can see which questions are commonly answered incorrectly (shown in red). Interestingly children get 9 x 3 right more often than 3 x 9. When the bigger number comes first they are more likely to answer correctly.

Bruno has recently surveyed students who use Times Table Rockstars, using a selection of questions taken from the recent PISA study. The results suggest that as students get older, their intrinsic motivation drops (eg measured by responses to questions such as ‘I do maths because I enjoy it’) as does their self-concept (ie whether they think they are good at maths). Maths anxiety is relatively low.

The highlight of Bruno’s session was the delightful group of students who were there to demonstrate how Times Table Rockstars works and talk about their experiences. These highly competitive students are amongst the country’s fastest times-tablers. Their demonstration was jaw-droppingly awesome. I can not believe how fast they were able to answer the questions. It was amazing.

The students were very articulate, and rightly proud of their achievements. They all spoke about enjoying the competitive nature of the programme and how their desire to be faster than their friends motivated them to practise a lot. I suppose the big question is whether this fluency in times tables gives significant advantages later on. Will these students all go on to be amazing mathematicians?

I sat next to Nisha de Alwis who pointed out to me that all the students in attendance were boys, which raised the question of whether this indicates that boys are ‘better’ at times tables. Or perhaps this particular programme (ie the gamification and competitive nature) appeals to boys. Bruno shared some interesting data from the survey he conducted and will continue to explore the gender question.

**Lunch!**

**Primary Maths**

In my post ‘Knowledge Gaps‘ I wrote about my desire to learn more about how maths is taught at primary school. There seems to be a disjointedness in the way things currently work between primary and secondary. Jack Marwood is a primary school teacher with a maths degree and I attended his session ’10 things you should know about primary maths’. The slide below shows the potential confusion arising from the use of ‘remainders’ in division in primary school.

Jack recommended the work of Hung-Hsi Wu at Berkeley, particularly The Mathematics K-12 Teachers Need to Know.

Jack’s slides from his reasearchED presentation are available here.

I look forward to reading other bloggers’ write-ups of the sessions they attended. It was very much one of those ‘I want to be in three places at once’ sort of days. Thanks to Tom Bennett and Oxford University Press for an excellent event.

Finally, I must mention the venue! The University of Oxford Mathematical Institute is wonderful – look at the beautiful Penrose Tiles outside. The building is named after Andrew Wiles, the mathematician who proved Fermat’s Last Theorem. I had only been there once before, representing the Bank of England at a careers fair, and I actually bumped into Stephen Hawking that day! Amazing. Maths is awesome, isn’t it?