Inventing a myth
In an analysis paper from The Centre for Independent Studies, three academics purport to have uncovered seven Myths that Undermine Maths Teaching. In an attempt to discredit inquiry, the third myth reads "Inquiry-based learning is the best approach to introduce and teach mathematics."
A myth is a widely-held but false belief. The authors need to show that, firstly, inquiry is widely considered the best approach to introduce and teach mathematics; and, secondly, inquiry is not the best approach. They do neither.
Below, on the left, we reproduce the analysis paper and, on the right, we address its contentions step-by-step.
Andrew Blair, June 2023
The authors provide neither evidence for the existence of a myth, nor an explanation of from where and when it 'remains'.
To back their claim, they cite just one meta-review about the experiences of disabled students. The review is not even about inquiry as such, but rather the dehumanising aspects of rote learning in mathematics education. The review calls for increased inclusion of pan-disabled students in research focused on inquiry and meaning making - a call that is both reasoned and timely, but in no way proof of the existence of a myth.
As the academics cannot present any evidence, we do not know who assumes that 'inquiry-based instruction' - a confusing term in itself - should be the standard method.
This is an example of a logical fallacy. Both statements are true, but they do not justify the conclusion.
In fact, we would argue that the opposite might be true. Remote lessons during lockdown necessarily focussed on discrete procedures and provided less opportunity for discussion and reasoning. Our emphasis back in the classroom should be on inquiry processes.
Teachers who use inquiry know from experience that it leads to an increase in all three. We have research to show that to be the case. Perhaps we do not have enough to convince the academics because research funding is currently controlled by politically-appointed guardians of cognitive science.
The danger of misalignment is greater with forms of direct and explicit instruction. In the inquiry classroom, students' questions and conjectures help the teacher assess their learning needs and adapt the course of the inquiry accordingly. All students benefit from such tailored provision.
Just because support, guidance, monitoring progress and access to relevant information 'align' with explicit instruction does not mean that they cannot be elements of inquiry as well. Indeed, they would be features of most pedagogical models.
The paper by De Jong and Van Joolingham refers to computer simulations that aid discovery learning in science. In conflating computer simulations with classroom activity, science with mathematics, and discovery with inquiry, the academics reveal their confusion.
The implication here is that inquiry teachers do not plan. Instead, we are both proactive and reactive, preparing support and guidance before the lesson and adapting during the lesson. (See Planning and unplanning mathematical inquiry).
The authors of the analysis paper, however, have misunderstood the point. Lazonder and Harmsen do not say that classroom scaffolds in inquiry classrooms are ad hoc; rather, their point is that studies of inquiry learning classify types of guidance ad hoc (p. 684). If researchers had an a priori classification based on a theoretical framework, Lazonder and Harmsen argue, we might have more fruitful findings about the types of guidance that are most effective.
Overall, Lazonder and Harmsen say that their meta-analysis provides "convincing evidence that inquiry-based methods can be more effective than other, more expository methods of instruction." That the authors of the analysis paper omit this conclusion and falsify another part of the meta-analysis suggests they are reading research from a particular ideological perspective.
The argument that 'novices' require explicit instruction is now used to consign students to a meagre diet of transmission and practice.
Students new to inquiry require more support and guidance, but that does not mean they should be denied the opportunity to be part of classroom inquiry. All students have the right to experience the disciplinary processes unique to mathematics.
The metaphor is ill-conceived. Teaching is a far more complex process than building a birdhouse. Even within its own parameters, however, the metaphor reveals the limitations of explicit instruction. The builder might have the materials and the tools, but not the self-awareness and abilities to regulate and monitor the building process. It is precisely through inquiry that students learn to become effective self-regulating learners.
'Evidence-based' has become code for practices backed by cognitive science. The reliable and robust research behind inquiry is accorded no recognition.
However, it seems from the confusing last sentence that inquiry is appropriate to apply skills to new concepts once explicit teaching has occurred. The authors are treading dangerously close to the myth they set out to refute. Inquiry might, after all, be the best approach for part of the learning process.
It turns out that structured and guided inquiry are permissible, as long as they incorporate explicit instruction to avoid misconceptions. What is not permissible, apparently, is inquiry as discovery learning.
It might have helped their case if the authors had mentioned discovery in the myth they invented.
They do not present evidence that the myth exists and, then, in a surprising twist, accept that their own myth might be true in certain circumstances.