Yesterday, the new Minister of Education, Hon. Erica Stanford, announced the formation of a Ministerial Advisory Group to review the primary school English and Mathematics & Statistics curricula. It is an honour to be named as a member of this Group alongside so many highly respected individuals, including the Group chair, Dr Michael Johnston from the New Zealand Initiative, and Distinguished Professor Gaven Martin, one of the earliest public supporters of my campaign to Bring Back Column Addition to New Zealand’s early primary maths curriculum.
I would like to take this opportunity to express my gratitude to everyone who has supported my endeavours over the past 10 years. That includes the teachers and students who have joined me on this journey to restore confidence in mathematics education in New Zealand.
You may not hear from me for a while, but rest assured that I will be working and thinking hard about important things next year.
Season’s Greetings and a Happy New Year to you all.
It was a welcome surprise to hear Brian Conrad talk to Kerre Woodham last week. Brian Conrad is a Professor of Mathematics and Director of Undergraduate Studies in Mathematics at Stanford University in California, USA.
Woodham had come across Conrad’s recent op-ed in The Atlantic, in which he discussed the findings of his examination of a 1000-page draft of the controversial California Mathematics Framework (CMF). The CMF is similar to New Zealand’s draft Common Practice Model (CPM) in that it proposes how teachers should teach and the rationale behind it, with a strong focus on equity.
I shan’t attempt to explain what is already very well articulated by Conrad himself. Believe me when I say this guy is thorough. You can go to the website he created to publicise his critique of the CMF, including a whole document about citation misrepresentations. It is, unfortunately, no surprise to me that Conrad discovered so many false or misleading claims in the CMF. One of the CMF authors has been called out in the past for making claims but citing research that says almost the exact opposite.
Conrad also shines a light on the CMF’s false promise of greater equity by meddling with traditional pathways (algebra and calculus) in a bid to level the playing field. Again, evidence of success in San Francisco over a span of 10 years was exposed as a misrepresentation of the facts. Removing an “inequitable” option led to a reasonably predictable outcome: the socioeconomically advantaged students found other ways to access that option, while the socioeconomically disadvantaged students were left even further behind, thus widening the achievement gap. In much the same way that New Zealand’s Ministry of Education sat on their hands for 10 years after the Numeracy Project turned out to be a failed experiment, California’s State Board of Education has decided to press on with the CMF’s flawed ideology, turning a blind eye to the truth and quietly removing references to the San Francisco experiment from the final document.
But algebra and calculus is so last century, right? Instead, the CMF wants high schools to focus on offering alternative pathways (data literacy masquerading as the more rigorous data science) that Conrad describes as “off-ramps”. That too has already happened here in New Zealand. Once upon a time, there was a fork in the high school road at the end of Form 6 (Year 12), when students could choose to study calculus or statistics in Form 7 (Year 13). That fork has moved forward to the end of Year 11 (Form 5), and in reality, for many students, their choice has been pre-determined. The modular nature of NCEA means that schools can offer different courses with more or less algebra in Year 11. Students with less algebra in their course are effectively limited to a statistics pathway, while students with more algebra in their course have the full choice of studying calculus or statistics in Year 12. Many students discover too late that their study and future career options are limited by a lack of algebra (and hence calculus) in their maths education. The struggle to get back onto the calculus track without the pre-requisite algebraic skills is enormous. Meanwhile, students on the statistics pathway are also short-changed because, over time, the mathematical content has been eroded and replaced with statistical literacy – the ability to interpret statistical graphs and critique statistical claims. Don’t get me wrong, these are very valuable skills to have in the age of information and disinformation, but as Conrad points out, statistical/data literacy on its own will not lead to exciting careers in data science, as promised by the CMF.
It is important to note that high schools are not to blame; they have a responsibility to navigate the system and find achievable pathways for all students, including those who struggle with algebra. Any high school maths teacher will tell you that students tend to struggle with algebra not because of the mysterious variables x and y, but because they lack fluency with basic arithmetic, especially division and fractions. In other words, the problems start at primary school.
While there are many similarities between what’s happening on both sides of the Pacific Ocean, there is one major difference. California’s CMF underwent two rounds of public consultation before being adopted in July this year, whereas no public feedback was sought when New Zealand’s Ministry of Education released Phase 1 of the CPM. In my previous post, I drew attention to the flimsy evidence offered to support one of the CPM’s theoretical teaching approaches. Schools would be right to be wary of claims that such approaches are “evidence-based”, particularly when some of the CPM authors are also teacher educators who have a commercial interest in promoting their research.
We are less than a week away from finding out whether the CPM will be made compulsory for all state school teachers in New Zealand. Whether or not you believe in the sociocultural ideals of the CPM, the sleight of hand in attempting to push this model through without public consultation is troubling enough.
Dr Audrey M. Tan 9 October 2023
Further listening/reading about the California Mathematics Framework:
The findings of the 2022 National Monitoring Study of Student Achievement (NMSSA) in mathematics and statistics have been released, and it’s the same old same old. Only 42% of Year 8 students are meeting curriculum expectations, down from 45% in 2018, with statistically significant drops in achievement among girls, and Māori and Pacific students.
If you want some good news for a change, the schools that I work with defy these depressing statistics. Read all about it here. It shows you what progress and achievement looks like when you understand the mathematical and cognitive principles of teaching approaches that really work, and simply get on with teaching the kids.
The Minister of Education is probably right to be grateful that the results weren’t even worse after three years of disruption to learning during the Covid-19 pandemic. But can we honestly expect to raise student achievement when the Ministry continues to allow experimentation in the classroom, promoting “theoretical frameworks or approaches to teaching, informed by evidence of how ākonga learn”? It was dismaying to hear the Minister defend some of the highly dubious content in Phase 1 of the Common Practice Model (CPM), published earlier this year. Not to be confused with the refreshed mathematics and statistics learning area, where feedback was sought on the first two drafts before being finalised, there is no evidence the CPM was ever released to the public in draft form.
In this document, we are told that “a critical maths pedagogical approach uses maths to develop critical awareness about wider social, environmental, political, ideological, and economic issues. Critical maths recognises the importance of understanding, interpreting, and addressing issues of power, social justice and equity in the community and the wider world.”
Of the references offered to support this approach:
two were not publicly accessible;
one was 25 years old, an indulgent academic introspection suggesting that teachers play “mind games” to increase their awareness of the “values” (definitely not the numerical type) they signal to students when they teach maths;
one was a respected university professor’s plea for undergraduate teaching to move away from textbook problem-solving and towards the use of more open problems. Written 13 years ago, this opinion piece is not even close to being educational research, let alone applicable to either critical maths or teaching school-aged children;
this one was actually an interesting read, but the authors rather undermined themselves by citing an example of moving beyond teaching about and for social justice to teaching with social justice. They admitted the problem wasn’t real-world, let alone related to injustice – it was just inclusive teaching. Indeed, the authors acknowledged that mathematical proof is democratic in nature, so this was a fine example of how, if you respect the culture of mathematics, there is no injustice. Simple.
Which brings me back to one sentence in the CPM that ought to set alarm bells ringing:
“Ākonga are encouraged to interrogate dominant discourses and assumptions, including that maths is benign, neutral, and culture-free.”
Is the Ministry seriously proposing that teachers should encourage their students to challenge the neutrality of mathematics, to mistrust the very tool that would empower them to rise above dominant discourses and assumptions and reach their own conclusions through objective thinking, critical analysis and logical deduction??
My mathematical training compels me to keep an open mind, so I decided to ask an entity that could reasonably be expected to be benign and neutral (but not culture-free since it was created by humans. Well, two out of three ain’t bad.) Here is what ChatGPT had to say about the matter:
Q: Is mathematics benign, neutral and culture-free?
A: Mathematics itself is a branch of knowledge that deals with logical reasoning and quantitative analysis. As a subject, mathematics is generally considered to be neutral and culture-free because mathematical concepts and principles are universal and can be applied across different cultures and contexts.
However, the way mathematics is taught, used, and applied in different cultures and contexts can reflect the values, beliefs, and biases of those cultures. For example, the way that mathematical concepts are taught and presented may differ based on cultural norms and traditions. Additionally, the use of mathematics in various fields such as finance, engineering, and social sciences can reflect cultural biases and power structures.
Overall, while mathematics as a subject is generally considered to be neutral and culture-free, its application and use can be influenced by cultural factors. It is important to be aware of these potential biases and to approach mathematics with a critical and culturally-sensitive perspective.
ChatGPT 3.5
So even an artifical intelligence engine is able to recognise the difference between mathematics being benign, neutral and culture-free, as opposed to its application or the way it is taught. That the Ministry of Education failed to make that distinction is disturbing.
By all means, let students use maths to examine social injustice…in their social science lessons.
Believe it or not, I do actually have some good news to share.
Our decimal number system is a place value system. It was designed to be used in columns, and finally, the Ministry of Education agrees. The nzmaths.co.nz website has published new resources for teachers to support early learners with addition and subtraction of two-digit numbers, recording the calculations vertically! Column addition is officially making a comeback!!
Although these resources are intended to support students “not on track to meet the expected level”, absolutely no student should miss out on this foundational learning. If you are a parent whose child has been told by their school that they are not allowed to line up the columns, you can now politely refer to these resources and reassure your child’s school that it is officially okay. If you have a learner who is struggling with the “renaming/regrouping” method of column subtraction, you can show them the “borrow-and-pay-back” method, which is much easier to apply.
How far the nzmaths.co.nz website has come, proffering answers such as “Teachers should debate whether they will introduce the written form at all” and “Early teaching of the written form often locks students into low-level thinking from which they never emerge” until I called them out in 2013.
Please share this news widely, especially among teacher groups. Teachers already celebrating the column-based methods are seeing the benefits: their students’ understanding and problem solving are noticeably improved. In other words, they have been unlocked from low-level thinking and are now emerging! This is not a surprise if you understand the cognitive science of learning.
After two decades, the return of early column addition doesn’t feel so much like a victory, just a huge relief. Now, we can really start to fix New Zealand’s big maths problem.
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.
Mathmo Consulting 
