“It was a very romantic, very nice sounding assumption about how students learn best,” she says.
When I first heard it myself, I was actually compelled, I thought, ‘oh, I’ve been learning maths all my life in the wrong way!’.
“‘It could have been more fun, it could have been more interesting and engaging instead of memorising times tables,’” she recalls thinking.
“I was sold. I actually went and tried to do that with my students, and it was a disaster.”
Evans lectures in mathematics, working with students undertaking mathematics majors, as well as masters level teachers, and those completing majors in maths-related fields.
For more than a decade now, she’s become increasingly concerned about the maths skills and knowledge of her students.
“Ten years ago we started to notice differences in the students that are coming into the university, they were less and less prepared year on year.
“And it’s gotten worse and worse and worse,” she says.
According to Evans, a dogged commitment to inquiry-based learning in schools and a vilification of teacher-led explicit instruction is largely to blame.
“It’s an interesting problem, I am digging down deep enough to be almost totally convinced that, by and large, it is a problem that was endorsed by the Ministry of Education about 20-something years ago,” Evans says.
“There’s this misguided assumption from constructivist philosophy, that is very romantic, that children learn best when they discover things for themselves, and the teacher should be a facilitator of learning, not a ‘sage on the stage’ but a ‘guide on the side’.”
Evans says this philosophy has been strongly embedded in initial teacher education for at least two decades, with graduate teachers being told to minimise their instructions and explanations.
“They’ve been convinced that the learners should be left to discover mathematics for themselves, that way they learn it in a better, more profound and deeper way.
“But there’s no evidence to support that,” she adds.
“The evidence we have from the sciences, cognitive science, cognitive psychology and educational psychology, goes against that premise. We have written a scoping review on this topic."
Evans wants to see a return to pedagogy which is grounded in cognitive science.
“The promotion of inquiry-based and problem-based learning needs to stop, and we need to go back to teacher-led explicit instruction,” she says.
“It’s more beneficial, more effective, and serves more learners with different prior knowledge.
“There is research to say that students who have low background knowledge actually benefit a lot more from teacher explanations.”
There’s a common misconception surrounding explicit teaching, Evans says, with many believing it requires the teacher to stand in front of the class and talk for the entirety of the lesson.
But she prefers to think of it in terms of ‘I do, we do, you do’.
“So ‘I do’, the teacher first explains the concepts fully, then the teacher explains all the procedures fully, modelling and showing examples of how to solve problems,” she explains.
“Only after that, the teacher says, ‘now you students try it and I will help you’, and there’s this scaffolded guidance, ‘we do’ it together.”
After students have worked on a number of similar problems with immediate feedback from the teacher, and large majority of the class are experiencing success, only then does the ‘you do’, stage begin.
“The teacher releases control and guidance, scaffolding is all down, and the students are prompted to work on challenging questions to solidify the knowledge, the understanding, be creative and look at open-ended problems, all of those things have a place,” Evans says.
“But the sequence is important, and the balance of how much time is spent on each of those ‘I do’, ‘we do’, ‘you do’, is also important.”
Critics of explicit instruction often argue it is less engaging, and that instead, we need to capture students’ interest from the get-go, by posing an interesting problem for them to solve.
Evans, believes this notion too, is misguided.
“There’s this assumption that we need to make maths interesting, and then students will be motivated, and the learning will happen,” she says.
“Well, guess what? There’s no evidence to unequivocally support that…that hypothesis doesn’t seem to hold up against the data from the TIMSS,” she says.
Tests are an important part of mathematics learning and their impact on memory and long term knowledge retention should not be downplayed, Dr Tanya Evans tells EducationHQ.
A comprehensive report in the book Motivational Profiles in TIMSS Mathematics shows the students who prioritised valuing and enjoying maths did worse than those students who emphasised competence, which turned out to be justified in their confidence. Those confident students did better.
Evans says these psychological symptoms are consequences of competence; since becoming more skilled creates warranted self-efficacy, which is one of the best predictors of achievement we have.
So, in mathematics, interest and enjoyment don’t necessarily translate to better performance, Evans says.
“The students who are competent, they’re taught well, the teacher explains well, the teacher shows them how to do the procedures, then the teacher prompts them to practise enough so it becomes automatic, they become masterful at those tasks,” Evans says.
“So if they feel they can do mathematics, then engagement is increased and they do it more and everything falls into place.”
‘But maths education is about more than just test results’ is a common argument Evans calls merely a “cover-up story”.
“The reason the inquiry-based advocates downplayed the role of the tests is because they were hoping that the inquiry-based learning would manifest into better outcomes, but then it didn’t,” she says.
“But tests are important. They play a multifaceted role in learning mathematics, serving as assessment tools, diagnostic instruments, memory aids, promoters of metacognition, and preparatory experiences for real world applications.”
The testing effect, shows that taking tests serves as a form of retrieval practice, which has been shown to enhance long-term retention of information.
“For my university students, they now have a quiz after every single lecture and that’s improved their grades across the board.
“Fewer people fail the course, and they’re getting a lot more A’s. I’ve published a paper about it,” Evans says.
Finally, Evans is calling for a more knowledge-rich curriculum, instead of the current bare bones document which, she says, devalues the role of knowledge stored in long-term memory.
“‘Who cares about knowledge? You can look it up on the web’, that was the approach,” she says.
“It’s completely wrong. If you’re looking at a computer, ChatGPT, Google or whatever, the information comes through your sensory memory.
“Some of this information will be selected (through attention) to be processed in working memory – the thinking process occurs primarily in the working memory system.”
But research shows most people can only juggle several elements of information at a time, depending on the size of their working memory.
Whereas, Evans explains, if you get the information coming from the long-term memory, it can be retrieved much quicker, essentially overcoming the limitations of working memory.
“So that’s the benefit of education. We need people to know things and this knowledge has to be in their long-term memory, well-organised for easy retrieval,” Evans says.
“For us to think effectively, critically, creatively, we need a knowledge-rich curriculum.”
For the past ten years or so, as mathematics performance started to slide, Evans hasn’t been sitting idly by.
“We had many meetings and we set up groups to lobby the Government on behalf of the mathematicians, to try to see what was causing it and to offer our help,” she says.
A lobbying group was set up by the New Zealand Mathematical Society in 2016.
“We tried and tried, and we had no traction whatsoever, trying to engage with the Government and the Ministry of Education.
“They would have a meeting with us, but nothing would come out of it,” she says.
It wasn’t until 2021 that the Ministry approached Royal Society Te Apārangi, requesting an independent report on mathematics education performance in New Zealand.
The review chaired by Kiwi mathematician, distinguished professor Gaven Martin, was damning, leading the academic to declare a generation of New Zealanders has been failed.
“After that, I dropped everything from my research agendas and started looking into the concrete factors to discern what is happening in our schools? what can we change?’ and I’m still continuing to work on this,” Evans says.
The educator says we must act quickly to decisively identify the correlational and causal factors contributing to the decline in the quality of mathematics education over the past two decades.
“It’s lamentable that we’ve managed to dismantle a once world-class educational system in such a short span,” she says.
“We must refrain from falling prey to educational fads fuelled by collective hype within educational circles, which often disregard scientific evidence published in journals focusing on cognitive science.
"This issue transcends New Zealand – it’s a well-documented phenomenon in the Anglosphere,” Evans says.
