Part Three: Alternatives To The Endless Exam Cycle
Options exist: Why not consider them for the UK?
I am more of a “ facilitator of learning rather than a teacher … I come up with the framework and the students are directing the path of the lesson.”
Sandy Fischl, Teacher of Mathematics, Ontario, Canada
The endless cycle of the pressure to obtain good mathematics exam results leaves little time for pupils in the UK to obtain the necessary problem solving skills required for the future. Other places in the world seem to produce good students without this method of assessment. It is time the UK started thinking of alternatives.
The assessment of mathematics in Ontario Canada
The province of Ontario in Canada had standardised final exams until they were abandoned in 1967 due to the fact that it was felt that the last year of school was spent teaching to the exam.
Fifty years later, the UK is still continuing the practice with the A Levels and also the GCSE exams at the end of year 11. While Ontario has continued to examine its mathematics curriculum and programme over the years and modernize the approach to the teaching and learning of mathematics, the UK has not really done anything radically new or different during that time.
The school system in Ontario is set up differently than in the UK. The last four years of schooling are referred to as high school or secondary school, which includes grades 9 through 12. This would be the same as years 10 through 13 in the UK. Students leave high school in Ontario with a diploma with a variety of credits in many subjects giving a better-rounded approach but at the expense of the level of specialisation that you see in the UK.
Students in Ontario are expected to take mathematics to at least grade 11 (year 12 in the UK) to obtain a graduation diploma, which means that every pupil needs at least 3 credits in maths for their diploma. To receive a credit a final grade of at least 50% must be obtained and this mark is given by the teacher with 70% of the grade based on evaluations throughout the year and 30% based on an “evaluation in the form of an examination, performance, essay, and/or other method of evaluation suitable to the course content and administered towards the end of the course.”
Ontario teachers are guided by an achievement chart that has categories of Knowledge and Understanding, Thinking, Communication, and Application, with an emphasis on the Mathematical Processes for effective mathematical learning – problem solving, reasoning and proving, reflecting, selecting tools and computational strategies, connecting, representing, and communicating.
The amount of content in each mathematics course is also much smaller than in the UK but with an emphasis on depth and understanding as opposed to volume.
Mathematical Processes
– Problem solving
– Reasoning and proving
– Reflecting
– Selecting tools and computational strategies
– Connecting
– Representing
– Communicating
EQAO – the only standardised math exam for senior students
The only standardised mathematics exam in Ontario at the secondary level is in grade 9. Called the EQAO (Education Quality and Accountability Office) test, Dr Timothy Sibbald of Nippissing University, Schulich School of Education, says, “it was brought in to make sure that the curriculum was being enacted the way it was supposed to be enacted. It was originally intended as a watchdog piece….it definitely flags places where the Ministry of Education may want to intervene because there are problems and they have done this” and goes on to add that it has it weaknesses because it ends up mostly testing knowledge and not the other aspects of the mathematics assessment. Only the marks are released and without detailed feedback, students and teachers do not get much out of it. Many schools use this EQAO test as their end of year 30% evaluation in grade 9.
Sandy Fischl, a recently retired Ontario maths teacher, believes that the EQAO test at the end of grade 9 creates stress and says that as a teacher you feel that you should prepare your students for what they are going to see. Fischl adds, “I would hope that we wouldn’t teach to the test but I don’t think you can get around it. I think that if there is this big test at the end…..you have to change the way you are teaching……I don’t think that they are going to be learning the mathematics the way that I would like them to learn it.”
Ontario teachers feel that the EQAO math test, a one time standardised test at the end of grade 9, affects the way they teach in that grade. It reflects the pressure that UK teachers feel all the time.
No standardised math exams, so how is math assessed in Ontario?
In order to teach within this framework, Fischl supposes that she is more of a “facilitator of learning rather than a teacher……..I come up with the framework and the students are directing the path of the lesson.” She feels that they have been practising the math concepts throughout the year and that the 30% internal final exam is just a formality.
Sibbald believes that teaching of maths in Ontario, frequently involves providing a new situation where pupils have to actually take what they have learned and apply it to a new situation. He gives an example where students are given a hands on task of measuring a flagpole using trigonometry but then when it comes time for the assessment you have them measure something much further away that has commonality but has something that makes it a bit different.
In order to teach within this framework, Fischl supposes that she is more of a “facilitator of learning rather than a teacher……..I come up with the framework and the students are directing the path of the lesson.” She feels that they have been practising the math concepts throughout the year and that the 30% internal final exam is just a formality.
Sibbald believes that teaching of maths in Ontario, frequently involves providing a new situation where pupils have to actually take what they have learned and apply it to a new situation. He gives an example where students are given a hands on task of measuring a flagpole using trigonometry but then when it comes time for the assessment you have them measure something much further away that has commonality but has something that makes it a bit different.
With time in the classroom spent on the items on the Ontario achievement chart, little time is spent teaching to the test, as the emphasis is on both formative and summative assessment without the high stakes exams that are the focus in the UK.
The down side of this or less is more
Time is needed to produce a programme like the one used in mathematics in Ontario. The UK prides itself on a very large maths curriculum but at what cost? In the book Teaching, Learning, and Assessment, John Blanchard quotes a teacher as saying, “Curriculum may well need to be trimmed to allow for better quality learning, consolidation, and follow-up work” and Newton proposes in Teaching for Understanding that “Quantity of knowledge is not synonymous with its quality.”
Tim Sibbard, says that in Ontario some people argue that that the curriculum may have swung too far the other way in cutting back content for understanding. A lot of time is spent leading up to a concept, for example, the idea of a derivative, but what is covered concerning derivatives is much less than it used to be before the major curriculum changes. He added that Ontario inherited their original system from the British Empire, but at some point Egerton Ryerson (1803-1882, chief superintendent of education) studied other systems in Europe and the U.S. and in 1846 introduced more progressive ideas to the education system. Sibbard sums up with, “we genuinely seem to have something that is a little bit different going on.”
Maybe ‘Less is More’
Robert Browning was not thinking of UK mathematics assessment when he used this in a poem, but doing less will allow teachers and students to gain more depth of knowledge and understanding. Newton points out that “overloaded syllabuses and teaching schemes allow little time to support understanding……understanding can be seen as a luxury.” The Ontario system has decided that it is not a luxury and has agreed that ‘Less is More’.
The systems compared – Ontario v UK
Comparing the two systems can be difficult but taking a look at the most recent results (2012) from PISA (Programme for International Assessment) conducted by OECD (Organisation for Economic Cooperation and Development), shows that Canada is ahead of the UK on maths scores. Canada performed 13th out of 65 countries on the maths assessment with a ranking of 8th on the problem solving section. Sibbard comments that Canada actually went down on the PISA test this time but went up in problem solving and added, “ they cannot raise problem solving without something else going on. You don’t just teach problem solving in a vacuum.” With the UK ranking 26 out of the 65 countries, this may be an indication of lack of certain skills in the UK.
A comparison of the two countries cannot be just based on another test, but the big difference between the two systems is the 100% standardised exam in the UK versus a 30% final internal evaluation in Ontario with 70% term conducted throughout the school year. The Ontario system seems to work.
Canadian universities have a good reputation abroad and many appear on the lists for the top universities in the world. The University of Waterloo in Ontario is one of the world’s leading mathematics universities with it’s own Faculty of Mathematics with currently 7000 students, 240 full time professors, and 500 courses in mathematics, statistics, and computer science. Professor Stephen Watt, Dean of the Faculty of Mathematics at the University of Waterloo is one of the creators of the Maple Algebra System. Dr Watt and other members of his team are the world’s leading experts on cyber security and an application of the mathematics behind Maple has lead to the development of tools used in Quantum Key Distribution (QKD), which is used to make encryption better.
UK universities accept Canadian students into their programmes with over 6000 Canadians studying at UK universities in 2012/13. Since UK universities feel that the Ontario system is viable, then it is not the UK universities insisting on the current method of evaluation.
The Trust Factor
The Ontario mathematics teachers interviewed were surprised that a 100% standardised exam was still used in the UK and some did not even know that it had ever existed in Ontario at one time, as it was abandoned 50 years ago. To most, this is just the way education is.
UK teachers were astonished at the differences in the two systems. Anne Haworth, ATM, responded with, “ I think it sounds wonderful, but it requires what we don’t have in this country – trust, presumably of teachers.” Rachel Henshall commented, “ I think it would be quite liberating….I don’t think teachers are trusted here.”
A report by OCED, on school leadership in the UK, also indicated the lack of trust as they found a history of accountability that is based on standardised exams and performance tables, with parents encouraged to investigate the tables and reports when selecting a school, and continued saying that it has “ contributed to a climate of mistrust limiting teacher professionalism….and encouraging teachers to ‘teach to the test’,” with an over emphasis on external accountability leading to a “lack of pedagogic innovation.”
A report by OCED, on school leadership in the UK, also indicated the lack of trust as they found a history of accountability that is based on standardised exams and performance tables, with parents encouraged to investigate the tables and reports when selecting a school, and continued saying that it has “ contributed to a climate of mistrust limiting teacher professionalism….and encouraging teachers to ‘teach to the test’,” with an over emphasis on external accountability leading to a “lack of pedagogic innovation.”
Is the UK ready for a radical change?
Teachers are trusted in Ontario
Ontario teachers are regulated by the Ontario College of Teachers (OCT)
Should the UK consider something similar?
Click to see more details
Being good at answering exam questions will not benefit our children or our society in the UK. The future requires thinkers and problem solvers that can adapt to change. The current method of evaluating mathematics to 15-19 year olds is not moving UK society forward.
Some attempts are being made to change the thinking in primary school but the fear and lack of trust that doing something different with older students confronts, along with an accountability obsession, keeps perpetuating the system.
SOMETHING COMPLETELY DIFFERENT – an entirely new outlook from Conrad Wolfram
Conrad Wolfram talks about why we need a math education revolution
ALSO See his TED Talk
Time to cut out some of the content in the mathematics programme, encourage problem solving, evaluate for the future, and break away from tradition. It is time to break the cycle of exams.