It was such a privilege to simply be at the New Zealand Principals’ Federation Conference in Rotorua at the start of last week, in the presence of so many dedicated primary and intermediate principals from around the whole country, let alone be invited to speak. The atmosphere was positive, energetic and energising. It really is no wonder these outstanding people were all selected to become school leaders!
Somehow, despite trying to remain discreet during the pōwhiri, I ended up on stage, sitting next to the Associate Minister of Education, Jan Tinetti. I was truly humbled by her special mention of me in her speech.
There were some brilliant speakers at the conference, and not only did I get to shake Sir Ian Taylor’s hand, I had a one-on-one with him at Rotorua Airport before we both flew home.
As for my own session, here is a bespoke slide to tie in with the conference theme “Power, Passion, Pace”, signifying the need to renew, refresh and move ahead after a fragmented year in 2020.
I asked my audience to engage with the sobering data presented, and to be inspired by the students at a decile 1 school whose lives changed forever when their teacher showed them how to line up the columns. This is not just about getting better results in our local and international tests – this is about equity in our education system, and ultimately, equity in our society.
The feedback has been overwhelmingly positive, with many special messages like this one:
“Your talk was the highlight of the NZPF Conference for me, as far as what can be done to change practice in my team to improve outcomes for students. What you said made sense and the changes that need to be made are not major. Thank you for enlightening us. I hope the government take notice and promote your ideas!”
Special thanks must go to NZPF President Perry Rush, for leading the charge this year to do something about New Zealand’s maths education. The hundreds of principals who jumped onto this website as soon as he sent them a link are a testament to his tremendous leadership. Let’s see what these amazing school leaders can do on the ground. Wishing them all Power, Passion and Pace!
In my previous post, I provided an overview of the past 20 years of mathematics education and declining student achievement in mathematics. With the announcement of a refresh of the New Zealand Curriculum (NZC), this seems like a good time to discuss the first steps towards restoring confidence in mathematics education in Aotearoa New Zealand.
Explicitly value the culture of mathematics and mathematicians
Earlier this year, I attended a Ministry of Education (MoE)-facilitated hui for Mathematics and Statistics. It was explained that the Ministry desires a bicultural curriculum that explicitly values all cultures, and that we need to shift to a decolonised, anti-racist curriculum.
Immediately, we are faced with a paradox. The word bicultural suggests that we should explicitly value only two cultures, or at least value two cultures more highly than other cultures. Does that not sound a little bit racist?
I do not wish to discuss racism here. In the context of mathematics, I don’t have to. When writing a good maths curriculum, it is the culture of mathematics and mathematicians that needs to be explicitly valued. Studying the common language of mathematics is naturally inclusive and promotes equity in the system. The beauty of mathematics is revealed to people when they realise, not only can they apply mathematics within their own cultural context, it is the same mathematics that can be applied in other cultural contexts. Mathematics is a unifying approach that fosters understanding between communities.
The social landscape of Aoteroa New Zealand is changing rapidly. Of course, local schools and kura must respond to the cultural needs of its learners and whānau, but continually writing new maths problems is exhausting for teachers and hardly a sustainable approach. It’s not mathematical thinking, either. Teachers should contribute the rich materials they write to a central bank of resources, for the benefit of other teachers and their students. As the database grows, we will spot and appreciate patterns, the same mathematics being applied in different contexts and cultures. This must surely be the ultimate in cultural sustainability.
Celebrate column addition (and other column-based methods)
“Education in New Zealand is a student-centred pathway providing continuous progression and choice.” – Ministry of Education website
It’s hard to imagine any education system in the past that wasn’t centred around students. I cannot think of anything more student-centred than giving children the wisdom of our experience and empowering them with the best mathematical tools available, so that they can make continuous progress with their maths and have a full choice of subject options at secondary school and beyond.
Our decimal number system is a place-value system that was designed to be used in columns. The decision to actively discourage our youngest children from lining up the columns not only disrespects one of the earliest key breakthroughs in mathematics, it disadvantages the children who need it the most. I don’t have to explain the benefits of column addition to any parent or caregiver who has seen their child struggle with the cognitive load of a mental strategy.
If this idea still rankles anyone in the education sphere, please read this discussion and note England’s progress since they brought back column addition eight years ago. Or, more locally, look at the progress achieved in a Decile 1 class of Year 7/8 students who caught up on three years of knowledge in five months.
Respect the cognitive science of learning and support children to learn their times tables
Despite this being an achievement objective in the NZC, it does not seem to be happening.
I do not support rote learning times tables if rote means “mindless recall without understanding the concept of multiplication”. But the messaging is that children should be using “number properties” to work out multiplication facts before committing them to memory. This is a false prerequisite.
This topic was discussed years ago, but more recently, I have come across some alarming research, detailing observations of the concept of multiplication being introduced in New Zealand classrooms. It was mathematically unsound, and the poor children were so confused, they ended up regressing. We’ve got serious problems.
Cognitive neuroscience informs us that fluency with basic facts really does matter. See discussion here.
New Zealand’s own John Hattie has synthesised the results of tens of thousands of studies to measure the effectiveness of different teaching practices. The average effect size is 0.4, meaning that teachers should be aiming higher than that.
Direct instruction (0.60) and explicit teaching (0.57) are more effective than inquiry-based learning (0.4) and discovery-based teaching (0.21).
Scaffolding (0.82), deliberate practice (0.79) and linking new learning to prior knowledge (0.93) all have very high effect sizes.
Within-class ability grouping has a very low effect size (0.18). There has been plenty of discussion about “labelling” children, but there are far more pragmatic reasons for abandoning it. Preparing multiple lessons creates more work for the teacher and significantly reduces the contact time that any one student has with their teacher, resulting in low engagement levels and poor learning.
When done well, whole-class teaching means that students remain engaged for longer and everyone moves forward together, generating effective classroom discussion (0.82). This does not necessarily exclude group work, but the objectives of social, co-operative learning are quite different and should not replace whole-class teaching and individual practice for the core learning of mathematics.
The OECD’s PISA study in 2012 found that student-oriented learning was negatively related to mathematics performance in every education system – that evidence is very hard to ignore. If it doesn’t work for 15-year-olds, for whom it might be plausible because they should have the knowledge and maturity by then to be more self-directed in their learning, then it’s not going to work for younger children.
The same research found that teacher-directed instruction was positively related to mathematics performance, but high levels did become negatively related.
Thus, we have a strong case for mostly whole-class explicit teaching, with student-oriented approaches on the fringe. Perhaps the progressive educationists who support constructivism (the theory of learning in which children construct their own knowledge through their own experiences) forgot that the school day hasn’t gotten any longer. If students are to keep up with the rate of learning required to meet curriculum expectations, we simply cannot wait for them to discover maths by themselves, or risk them giving up when it starts to feels too hard.
There may be no silver bullet to fix New Zealand’s big maths problem, but bringing back column addition is probably as close as we will get. Let our young children line up the columns again and see their confidence restored, and likewise their teachers’ too. Then we can look forward to building a rich and flexible maths curriculum that will meet the needs of all learners.
NB: In 2019, TIMSS conducted their survey on paper in some countries (including New Zealand and Australia), and electronically in other countries (including England and Singapore). Relative placings and international averages are for the paper survey only. Combined relative placings on the questions above differ by no more than one place. Combined international averages on the questions above differ by no more than four percentage points.
In case you hadn’t noticed, that last question was multiple choice. New Zealand’s success rate is exactly the same as in 2015, and worse than what we would expect from random guessing (25%). An earlier cycle of TIMSS suggests a constructed response success rate would have been much lower.
This is not exactly news. Looking at the TIMSS 2015 results for Year 5 students,
If you think it doesn’t matter that children can’t perform these basic numeracy tasks (e.g. “they don’t need to calculate any more because we have calculators” or “it’s more important to develop their reasoning and problem solving skills”), then think again. When examining the performance of all countries participating in TIMSS 2019, there is a strong positive correlation between performance in the Number content domain and performance in the other two content domains, Measurement and Geometry, and Data. Similarly, there is a strong positive correlation between performance in the Knowledge cognitive domain and performance in the other cognitive domains, Applying and Reasoning. In other words, strong numerical proficiency paves the way for success in all aspects of Mathematics and Statistics, and you can’t solve higher-order problems or perform complex reasoning unless you have a good bed of knowledge to begin with.
What on earth has gone wrong?
Twenty years ago, a radical new approach to teaching mathematics in New Zealand, known as the Numeracy Development Projects or just the Numeracy Project, was rolled out across the nation before there was any robust proof of its effectiveness. In fact, the decade-long roll-out was the research experiment.
The goal was to raise student achievement by strengthening the capability of teachers through professional development. The philosophy was to prioritise conceptual understanding over procedural knowledge and skills (frequently called “rules”, with a negative inference). Despite acknowledging the interdependence of “knowledge” and “strategy”, the teaching of knowledge was relegated to a mere “ten-minute whole class warm-up at the beginning of lessons“. Written methods such as column addition and subtraction, divisively labelled as “algorithms”, were not to be taught to students, if at all, until students had jumped through a series of hoops for five or six years, calculating in their heads using increasingly complex mental strategies. The easiest methods for adding and subtracting numbers literally became the last lessons on addition and subtraction.
The Numeracy Project researchers created their own stages of progression called the Number Framework, and so the research conveniently showed that students were, um, progressing.
Or were they? In 2005, the National Education Monitoring Project reported that students were “improving in tasks that require quantitative reasoning skills, but declining in basic mathematics facts and solving simple number problems.”
In 2009, “there was no meaningful change in number task performance between 2005 and 2009, for either year 4 or year 8 students. The most notable change in performance was a decline for year 8 students on multiplication problems, where changes in computation strategy were clearly evident.”
The long-term trend from 1997 to 2009 was “a small net improvement in mathematics performance at year 4 level (held back from a larger improvement by the decline between 2001 and 2005 in basic fact knowledge), and essentially no net change in mathematics performance at year 8 level.”
It was clear the researchers needed to do something to address the deficiencies shown up by NEMP. They did do something. They shut down NEMP.
And, presumably, knowing their jobs and their Numeracy Project facilitators’ jobs were on the line, they secured their future by having the Number Framework embedded into the revised New Zealand Curriculum and writing the Mathematics National Standards to align with their aspirations, just as the experiment was coming to an end.
In 2010, the awful truth could not be hidden any longer. The final, longitudinal Numeracy Project study concluded that “the absolute levels on the Framework attained by students were in many cases well short of the numeracy expectations for students at particular year levels stated in the New Zealand Curriculum and in the Mathematics [National] Standards.”
An estimated $100M (based on $70M spent in the first seven years) of taxpayers’ money had been spent on a revolutionary approach to teaching maths, and it didn’t work. The experiment had failed.
But it was too late and presumably too embarrassing for the Ministry of Education to pull the plug, and much easier to go along with the idea that it was a “temporary situation while teachers are continuing to upskill themselves”. Apparently, “many teachers stuck very closely to the printed NDP resources (the “pink” books)”, which “could reflect the low levels of confidence that many teachers still have [despite two years of professional development]…In retrospect, it may be that teachers needed to receive support by facilitators for considerably longer…”.
It’s remarkable how the teachers could be criticised for doing exactly as they were told. Did the Ministry ever wonder whether the pink books were the problem? And what does “considerably longer” than two years of professional development look like? It suggests that not even our student teachers would be adequately prepared to teach mathematics by the time they complete a three year Bachelor of Teaching degree.
In New Zealand, a distinction is made between mathematical (content) knowledge and pedagogical (content) knowledge (i.e. how to teach maths). The parallels with the Numeracy Project are uncanny: initial teacher education (ITE) focusses almost entirely on pedagogical knowledge, with little regard for mathematical knowledge. A 2012 survey of first-year student teachers showed that “students enter ITE with minimal levels of mathematical content knowledge…It is questionable whether their performance can be brought to an acceptable level. Currently students are not assessed before graduation to ensure they meet numeracy competency requirements.”
If publishing the results of this survey was intended to raise the flag on the universities’ inadequate preparation of their student teachers, it fell on deaf ears. To this day, still only one university in New Zealand bothers to assess the numeracy of all their student teachers before graduation.
What can be made of such a muted response by the universities? There is little incentive to improve the training of pre-service teachers if there is an opportunity to sell Ministry-funded professional development to in-service teachers. In the decade following the Numeracy Project, primary school teachers in New Zealand engaged in higher levels of mathematics professional development than the international average. Yet, the “temporary situation” of 2010 has not improved. Page 53 of this report provides insight into what some Ministry-funded professional development programmes look like.
If, on the other hand, publishing the results of this survey was intended to provide a reason for the failure of the Numeracy Project, the researchers had left it too late. They weren’t assessing students taught in the days of old; they were assessing the earliest victims of their own experiment. These kids were now feeding back into the system as teachers.
Enough is enough. The results speak for themselves. Our primary school teachers are not at fault for a flawed curriculum based on an academic theory of learning. Our children deserve a quality mathematics education; right now, some of them are not even getting a basic one.
What should happen next? That will be addressed in my next post.
Isn’t it crazy that, in 2018, we’re still “working out what works” in Education?
In fact, some of us do already have a pretty good idea of what works, but getting the right people to listen is a different problem altogether.
And so, a group of like-minded individuals (and maybe a couple of sceptics) gave up their Saturday on Queen’s Birthday weekend to attend New Zealand’s very first researchED conference in Auckland. researchED is a growing movement based in the UK but spreading internationally, “a grass-roots, teacher-led project that aims to make teachers research-literate and pseudo-science proof” (and by golly does this country need proofing). Founder Tom Bennett quickly realised that his own teacher training was based more on edu-myths and dogma (e.g. learning styles) than any scientific, evidence-based research. He’s not the only one. Daisy Christodoulou’s book, Seven Myths About Education, is the coffee that any waking 21st century learning fanatic should smell. Briar Lipson at the New Zealand Initiative hasn’t spent very long in this country, but has already sized up our education system very well and should be commended for bringing researchED to New Zealand.
Every talk raised serious questions about how we teach in New Zealand, and everyone was there in the belief that we can, and should, be doing better. Not surprisingly, the academics are calling for the Ministry of Education to change their ways and look for evidence before adopting fads as policies, while the pragmatic principals and teachers cannot afford to wait and are simply getting on with things.
The common factor of the day was subject knowledge and the importance of committing knowledge to long-term memory. The 21st century learning ethos suggests that we should leapfrog, or at least skim over, these foundational skills in a bid to produce generic critical thinkers and problem solvers, but surely common sense tells us we cannot reasonably expect students to think critically or solve problems unless they actually have some knowledge to work with.
I have no desire to repeat what has been said so well by others, so instead I will direct readers to a newly created blog by Derek Hopper, a music teacher at Tauraroa Area School who has read up on what works and is spreading the word. He and his colleagues are seeing significant improvements in student behaviour and achievement. Happy students, happy teachers. Having already spoken to a maths teacher at Tauraroa who is offering guidance to their primary teachers, I believe this school may well provide the model for other schools to follow.
Some other reflections of the day:
Tom Bennett, founder of researchED: Teachers might think that indulging in (catering for individual) learning styles is a harmless bit of fun, but there is no time to waste when teaching children from disadvantaged backgrounds. Every minute counts.
Katharine Birbalsingh, keynote speaker and founder/Headmistress of the evidence-informed Michaela Community School in London: Her teachers do not play “Guess what’s in my head?”, i.e. they don’t question their students before the relevant knowledge has been taught, so that every student, regardless of their background, has an equal chance of answering the teachers’ questions correctly. A subtle but powerful way to address social inequity and level the playing field.
Dr. Michael Johnston, Victoria University: When new skills are learned and practised sufficiently, they become automatic and free up the working memory to concentrate on higher-order thinking. With particular reference to mathematics pedagogy, the current NCEA internal assessment system provides little incentive for students to practise skills and procedures to the point of automaticity, and if they haven’t reached that point, then they will struggle with the cognitive demands of solving the contextualised problems presented in assessment.
Prof. Elizabeth Rata, Auckland University: Already widely known for her views on the lack of academic knowledge in the curriculum. When she used the definition of the apostrophe as an example of understanding the epistemic structure of academic knowledge, I genuinely thought she was going to ask the audience if they had spotted the misplaced apostrophe in the previous slide. She didn’t. I suddenly felt alone.
Dr. Graham McPhail, Auckland University: There is little evidence that deep learning occurs through subject integration. Wineburg and Grossman (2000) warned that ‘often the choice to implement a new curriculum is based on symbolic factors, such as a desire to be seen as progressive and in the forefront of reform’.
Louise Zame, primary school teacher: When listening to a teacher speak so eloquently about the professional challenges of implementing Inquiry Learning…to a bunch of 5-7 year olds…you realise just how much the Ministry of Education has lost the plot. As part of her Master’s research, Louise asks the pertinent question: what content knowledge do young students (aged 5-7 years) gain through inquiry learning?
Dr. Shaun Hawthorne, Cognition Education Ltd: Prof. John Hattie has recently updated his list of influences on student achievement, and top of the list is now “collective teacher efficacy” with a whopping effect size of 1.57. For those who don’t know about Hattie’s effect size measure, almost everything on the list has a positive effect, so teachers and schools should not be too complacent. They should be looking to maximise their impact, and punching above the average effect size of 0.40.
To finish:
I was probably the only person excited to spend a bit of time in the Vaughan Jones Room during the lunch break.
Great care must be exercised when evaluating “evidence-based research”. There is a lot of rubbish out there. For example, the Numeracy Development Projects “research” showed that if you teach children strategies then children will learn strategies. Big deal.
The panel discussion at the end left me in no doubt of the monumental challenge we face trying to fix New Zealand’s education system. To quote John Morris, “Currently education policy is being determined by political imperatives. It should not be. All policy initiatives, and in education there are so many of them, should be evidence-based.”
Tom Haig from the NZPPTA was naturally highly sensitive to the political undertones of the day and felt the debate was too one-sided. Perhaps that’s because there is little to debate when we rely on evidence. If the focus on credible and reliable evidence can take the politics out of Education, then bring it on I say, for I can think of no group of stakeholders less politically-minded than our precious children.
It turns out Ed Sheeran’s number knowledge is not so bad, but subtraction is his weak spot.
Last month, I delivered a talk to members of the New Zealand Educational Institute (NZEI Te Riu Roa) in Christchurch. The talk was oversubscribed, limited by the size of the venue.
I explained why the current primary maths curriculum is failing our children and the cognitive science behind it. I demonstrated how to develop algebraic thinking (another big failure of the Numeracy Project) to support computational thinking (in the context of the new Digital Technologies curriculum).
I also responded to teachers’ feedback on the areas their students find particularly difficult. It wasn’t a great surprise to see that subtraction was a common problem.
Ed’s maths quiz and fondness of mathematical symbols inspired me to write a maths-themed version of his Platinum hit “Shape of You”, the deeper meaning of the lyrics revealed in my talk.
“Maths I Can Do” is for New Zealand teachers and their students to sing in their classrooms, but classrooms in other countries may enjoy it too. It is for non-profit educational purposes only. Please do not use it commercially.
Please share as widely as possible to raise awareness of New Zealand’s big maths problem.
At the end of 2014, a representative sample of 6,321 New Zealand Year 5 students with an average age of 10.0 years were surveyed. Out of 49 countries, New Zealand placed 34th, behind all other participating predominantly English-speaking countries. Radio New Zealand put it a little more bluntly.
To be fair, some of the questions were considered too advanced for a New Zealand Year 5 student. However, when restricted to the questions deemed appropriate against the New Zealand Year 5 National Standards, the average student answered fewer than half of those questions correctly.
And yet, the National Standards data for 2014 tells us that 73.2% of New Zealand Year 5 students were at or above the National Standard. If we match this up with the TIMSS international benchmarks, it suggests that some of these students who were at or above the National Standard would probably have been classified as Low achievers in TIMSS.
A student meeting the Low international benchmark “has some basic mathematical knowledge. They can add and subtract whole numbers, have some understanding of multiplication by one-digit numbers, and can solve simple word problems. They have some knowledge of simple fractions, geometric shapes, and measurement. Students can read and complete simple bar graphs and tables.”
This is well below the standard we should expect for a 10-year-old. Now, spare a thought for the students who were classified as Below Low…
16% of our 10-year-old TIMSS participants were Below Low. These students completed fewer than half of the Low benchmark tasks correctly. This is a significant proportion compared to other countries, e.g. England (4%), the United States (5%), Australia (9%). In the top performing countries, less than 1% of their 10-year-olds are Below Low.
More concerning are the statistically significant increases in the large proportions of Māori (26%) and Pasifika (31%) students who were Below Low. If we are going to address the inequality in this country, providing these students with a maths education leading to greater opportunities would be a very good place to start.
I analysed the performance of our TIMSS 10-year-olds, question by question. They were mostly on the wrong side of average, but the stand-out questions were the basic arithmetic questions:
To add to the humiliation of coming last, 27 x 43 was a multiple choice question with four options. New Zealand’s result is worse than what we would expect from random guessing (25%). The previous cycle of TIMSS suggests a constructed response success rate would have been lower.
Our current maths curriculum has made our children so bad at basic arithmetic that they’d be better off guessing. Is this a standard to be proud of?
One might claim that it doesn’t matter – maths is not about the numbers, after all. TIMSS dispels that myth. There was a very strong positive correlation between country performance in Number versus both Geometric Shapes and Measures, and Data Display. There was also a very strong positive correlation between country performance in Knowledge versus both Applying and Reasoning. Suffice to say, number knowledge is a very strong predictor of success in all areas of mathematics.
Taxpayers should consider how much money has been spent on primary maths education since 2000 and question a further $126m being spent over four years on more of the same, without addressing the obvious weak spot in the curriculum. I spoke to Radio NZ about it.
TIMSS informs us that New Zealand has higher proportions of teachers who participate in maths professional development compared to most other countries. Despite all this professional development, student performance has not improved since 2002, so why should we believe that further money spent on teacher training will make any difference?
To put these astonishing sums of money into perspective, the Government will spend just $40m on rolling out the brand new Digital Technologies curriculum, including $24m on teacher training. This is an area in which teachers will have very little experience, especially programming.
There is a much cheaper and effective form of professional development. Roll out my recent presentation to members of the New Zealand Educational Institute (NZEI Te Riu Roa) nationwide, and then see the maths that our kids can do.
The latest Trends in Mathematics and Science Study (TIMSS) data has been released. At first glance, it looks like New Zealand’s maths scores have improved since 2010, but unfortunately we cannot be certain of this. The scores are published with a statistical margin of error, which means that if we were to run the survey again with different samples of children, we might not see the same “improvement”. If we include the published margins of error, we see overlapping bands of achievement rather than increasing lines from 2010 to 2014. In fact, over 20 years, New Zealand’s performance has been disappointly consistent. We’re still below average.
The Ministry of Education has been honest and sober in its reporting, but nevertheless, the Minister of Education has said, in congratulatory tones, that average scores had increased! How can she claim there is an improvement when her own officials say that scores haven’t changed? Is she wilfully ignoring them, or does she needs a lesson on how to interpret statistical reports?
There was some encouraging growth in Year 5 students working at an “advanced” level, but at the other end of the spectrum, less than half of the student samples were working at the desired level of mathematics in the New Zealand Curriculum, and when looking at only the TIMSS questions which fit with New Zealand curriculum expectations, the average student answered just under half of these questions correctly. We have a high proportion of under-achieving students compared to other countries, and at the Year 9 level, this proportion has grown since 1995.
The Bring Back Column Addition Campaign was launched in response to New Zealand’s poor performance in TIMSS 2011(*). It would appear there is no reason to stop campaigning. We asked for some simple, pragmatic changes to the curriculum that would allow under-achieving students to progress. Without them, any improvements are likely to remain statistically insignificant.
Dr Audrey Tan, Mathmo Consulting
29 November 2016
(*) Internationally, TIMSS data is labelled by the odd-numbered years in which students in the northern hemisphere are assessed. New Zealand students are assessed at the end of the year prior, hence the even-numbered years referred to in the Ministry’s reports.
It’s time for New Zealand to look past the hysterical response to this year’s NCEA Level 1 MCAT exam and try to understand what’s really going on here.
Was the exam appropriate in level and difficulty?
In my previous post, I analysed the second of the two (supposedly) parallel papers and found that most of the questions were at a reasonable level for NCEA Level 1, and also reflective of the title “Apply algebraic procedures in solving problems”.
There was a section that was more investigative in nature and new for MCAT (but such questions have appeared in other Level 1 maths assessments in the past). This section was made difficult by its poor construction and confusing wording, and most Level 1 students would have struggled to understand the intention. But most exams have a Very Hard Question (VHQ), so I guess this is the VHQ for this exam.
Was it too different from previous years?
Apart from the investigative question, I don’t think so, but I might have said differently last year, when there was a noticeable step up. From the 2015 MCAT Exemplar:
“This year at least one of the three questions will not have any directed straight procedure-based parts and the other questions a maximum of one such part.…candidates will not be able to provide evidence by following a direction to solve factorised quadratics, factorise, expand, write or solve a linear equation, or simplify an expression involving the collection of like terms in response to being told to. One part in each question may direct the student to perform such procedures; but without further evidence at Achievement level, this will not be sufficient for the award of the standard. Utilising procedures such as factorising, simplifying a rational function, or writing an equation from a word problem will provide evidence of solving a problem. Candidates must know that given a word problem, they will be required to write equation(s) and demonstrate consistent use of these in solving a problem. Candidates will be expected to have a basic understanding of the relationship between a quadratic function and the associated graph.”
MCAT was last reviewed in 2013 and is up for review at the end of this year. Whether a change in style between reviews is appropriate should certainly be up for discussion.
So why did students find it so difficult?
The unfortunate reality is that students did struggle with this exam. The gap between what MCAT is expecting of students, and what students are actually capable of, is widening.
There are complaints that the lack of “gimme” questions at the start of the paper has left students “shell-shocked” and “killed” their confidence. Are we seriously saying that our students are capable of factorising a quadratic when explicitly told to do so, but they are unable to decode a basic word problem and factorise a supplied quadratic expression for themselves, even though they probably wouldn’t know of anything else to do with an expanded quadratic? What does this say about the resourcefulness or resilience of our students?
We cannot blame this year’s Level 1 maths teachers for what has happened, and they should rightly feel insulted. The problem started many years before this one.
What we’re really seeing here is the fruits of a flawed primary maths curriculum floating its way through the system. Even two and a half years at secondary school isn’t enough to turn things around. The damage is too great.
If you look at what the Numeracy Project was trying to achieve at primary school level, our secondary school students should, by all accounts, be highly numerate problem solvers, but in fact they are worryingly innumerate and apparently not very good problem solvers either. It’s ironic that one of the big selling points of this “new approach” to teaching maths was the development of early “Algebraic Thinking”. I think we can safely call that a Not Achieved.
A systemic failure in mathematics education is playing out before our very eyes. NZQA is trying to inch up the standard, year by year, when the reality is that students are actually getting worse at algebra, year by year. When students are struggling to master the basics, it’s hard to see how teachers can lift their students to the higher levels of problem solving now expected.
Given that next year’s Year 11 students will be the same generation of 9-year-olds who performed so abysmally in TIMSS 2011, alarm bells should be ringing loudly. It would not be surprising if fewer students were entered for next year’s MCAT.
Spring forward, fall back
NZQA could make the MCAT easier again, but that would be disappointing. I believe this year’s MCAT is the standard we should be aspiring to. If the examination team could tighten up on the construction of certain questions, the MCAT would be an examination to be proud of on the world stage. (The assessment side of things, however, needs a lot more work.)
And whilst I accept that normalisation is sometimes necessary, I do not think that assessment schedules should be adjusted to meet pre-defined targets as a standard practice. The universities have already discovered that NCEA grades are an unreliable measure of preparedness for tertiary study.
The best thing NZQA can do is go back to examining algebra at the end of the year.
September is a really bad time of year for students to face their first high-stakes external examination. Some students barely appreciate its significance when it is tangled up with mock exams for other topics and different subjects, and the ones that do appreciate its significance prioritise the MCAT at the expense of preparing for their mock exams.
The sensible thing to do, surely, is to fold it in with “Tables, Equations and Graphs”. We’re already seeing questions about graphs in the MCAT anyway, and why shouldn’t we? Algebra and Graphs are not separate topics, they are inextricably tied. As we now see, NCEA’s compartmentalising of topics as separate assessments is hurting students’ ability to make connections and become effective problem solvers.
The decision to deliver the assessment earlier in the year and have it administered by the schools has a distinct whiff of cost-cutting about it, but it has been a disaster for maths education and is costing the country dearly. If we want students to pursue STEM subjects at university, we need to give them every chance of succeeding in algebra at Level 1, as this effectively marks the fork in the road between calculus and statistics at Level 2. If we want to increase the “dollar value” of Kiwis contributing to New Zealand’s economy, fixing our maths education system is a very good place to start.
Dr Audrey Tan, Mathmo Consulting
22 September 2016
Such patronising recommendations from so-called “specialists” highlight the lack of understanding in New Zealand of what success in maths looks like. It is scandalous that the Ministry of Education continues to cling on to flawed ideals created by people who have no mathematical qualifications or experience, despite every indication our children are failing, year after year. They claim that implementing effective maths teaching and learning in classrooms is “challenging and complex”. It gives the impression they’d rather see students continue to fail at maths than acknowledge the compelling evidence of a quick and effective solution.
The Bring Back Column Addition campaign was never supposed to be a long-term crusade. I thought common sense would prevail; how wrong I was, and how much I have learned about attitudes within the education sector. This campaign will continue until the Minister of Education and her officials acknowledge that the acquisition of basic maths skills is not negotiable. Every child should leave primary school knowing their single digit addition and multiplication facts as well as they know their alphabet. They should be able to add, subtract, multiply and divide numbers fluently. They should be able to work confidently with fractions, decimals and percentages. As clients of the system, every parent should demand this.
Education professor John O’Neill says it would take 20 years to pull this country out of its downward spiral. It may well take that long, but while there are still some practising teachers who can remember life before the dreadful Numeracy Project was dispersed over the country like a gas bomb, let’s harness that experience and give our current children a fighting chance. Teachers, please let your students line up the columns and get them doing maths again. It’s the least you can do for our kids and our country.
Mathmo Consulting 
