MAURICE O'Driscoll has long been a secret hero of mine. Unlike all my other heroes, he actually exists and I even occasionally get to bump into him at gatherings of maths teachers.
Maurice, under the pseudonym of OD Morris, is both author and publisher of The Text & Tests series of maths books which, as a maths teacher, I have been using in the classroom for more than 20 years. His books are like the man himself, models of clarity and understated precision, and have made my job a thousand times easier. Maurice has raised the process of setting self-educating, intelligent problems to an art form.
One of my students who had missed a significant number of classes on differential calculus recently was able to catch up simply by working from an old edition of one of his books. His textbooks have that rare power that, if you're willing to put in the time, you can learn everything you need to know from them.
He acquiesced, with visible reluctance, to being photographed with his latest book. We were hard-pressed to make a photograph of two aging maths teachers interesting and so I suggested the book. Text, after all, sells.
I wanted to get Maurice's thoughts on the new Project Maths exam, which all Leaving Certificate students are facing this June. How exactly has he managed to produce his new series of textbooks in spite of efforts from Project Maths to minimise, if not actually eradicate, the role of textbooks in the class room? With difficulty, it seems.
Being a true mathematician, he can see the textbook issue from both sides: "They wanted to change the pedagogical approach with teachers developing their own material and using on-line material. In doing so, they completely underestimated the time involved in constantly trying to come up with original problems. On-line resources are helpful for revision but not necessarily for introducing new concepts".
The seemingly scorched-earth policy of the Project Maths team towards text-books was referred to by American maths educationalist, Sarah Lubienski, in her fine paper, An Outsider's View of Project Maths. An anonymous 'Project Maths Leader' was quoted as saying:
"The teacher needs to be autonomous and say 'Oh, I realise it's all active learning' -- they need to be able to develop this [curriculum materials] themselves".
Lubienski explains that a similarly massive overhaul of maths education was attempted in America during the early Nineties. At the time, the American National Science Foundation chose to invest millions of dollars in the development of textbooks aligned with the new course. Teams of authors including scholars with expertise in the relevant mathematical areas were assembled and partnered with mathematicians and school teachers as they developed, piloted, assessed and revised their text for publication. The process took four to five years.
Lubienski concludes: "The NSF made this major investment because of past lessons learned about the critical importance of textbooks in maths instruction and reform."
No such thorough consultation occurred before Project Maths was launched amidst a flurry of photocopied work sheets in the 24 pilot schools in September 2008 with what many see as being "obscene haste".
Obviously the National Council for Curriculum and Assessment (NCCA) was concerned that government funding for a new maths course was in imminent danger of drying up but it doesn't excuse the lack of consultation that took place a mere two years before the pilot schools sat their Leaving Cert exam in 2010. The one body who knows most intimately about the daily pressures of delivering maths in the classroom, the Irish Maths Teachers Association, was under-represented on the committees where all the key decisions were made. This is the same group of people who are now left with the unenviable task of conveying an ill-defined course to a group of fearful Leaving Certificate students.
Lubienski's call for well-researched school textbooks is echoed by another balanced assessment of Project Maths from the maths department of UCC. In its interim report on Project Maths, it states: "There is an immediate need for a supply of textbooks to cover the [new] material. We recommend that the NCCA, as a matter of urgency, encourage the production of such textbooks, both in print and in electronic form, and that they are complete and definitive." Neither Lubienski's nor UCC's reports have received the attention they deserve.
The guardedness that shrouds the world of Project Maths has made writing a textbook like building an edifice on "shifting sands", according to Maurice.
He says: "I welcome Project Maths' aspiration to promote a deeper understanding of mathematics and its desire to help students in becoming better problem-solvers. Having said that, the level of difficulty posed by many of the 'reality-based' problems that have turned up on both the actual and sample papers is unrealistically high for most students."
We both agree that with our collective 70 years of maths teaching behind us, that the maximum percentage of "natural problem-solvers" that we had ever taught was less than 5 per cent of any given class. And yet half of the second paper in Leaving Certificate Project Maths this year will be devoted to problem-solving, some of it promising to be extremely tricky and simply undoable by most in the time given.
The UCC report is very clear on this point: "The syllabus contains no specification of methods to be used by students to formulate and solve context-based problems. However, half the marks in the Leaving Certificate examinations are being awarded for context-based material ... It does not appear to be recognised that students [and teachers] must be instructed in the methods of application of mathematics, even in the simplest of contexts and it should not be left to them to discover these for themselves."
For students trying to prepare for the June exam, Maurice has this advice: "Keep practising the basic skills and key procedures in all the main topics. Put in the time doing this and you will be able to apply all of these techniques to new situations."
Sarah Lubienski: An Outsider's View of Project Maths. www.maths.tcd.ie/pub/ims/bull67/
UCC Interim Report on Project Maths
All information regarding the Text & Tests series is at www.celticpress.ie