Knowledge before inquiry: when common sense makes no sense

The idea that students cannot inquire until they have acquired the knowledge with which to inquire seems common sense. After all, as one educational consultant says drolly, “You can’t go off-piste until there is a piste." Build strong foundations through explicit instruction, he counsels, and then children can explore, make choices, and be creative through open-ended tasks.

By labelling knowledge acquisition and inquiry as Mode A and Mode B respectively, he attempts to cloak his blend of teaching approaches in pseudo-scientific terms. He then proposes an 80:20 ratio for Mode A and Mode B based on nothing more than his own experience, although he claims to “often get quite strong agreement”.

Dots

Another educationalist who also argues for knowledge acquisition first claims that, “You can’t connect the dots if you don’t have any dots.”

The seeming truism gains weight from a link to an academic paper. The authors of the paper argue that a strong knowledge base is a prerequisite for creativity, and, in their turn, they quote Sternberg and Grigorenko: “Thinking always requires memory and the knowledge base that is accessed through the use of memory. ...One cannot apply what one knows in a practical manner if one does not know anything to apply.”

It seems clear then: explicit instruction loads up long-term memory with the facts (dots), then students retrieve them to think (use the dots), to make connections (join the dots), and to be creative (join them in new ways).

Mode A and Mode B again

The categorisation of teaching into Mode A and Mode B mirrors the dichotomy between memorisation and thinking.

While there is widespread agreement that Mode A must precede Mode B for effective teaching, there is less agreement over the 80:20 split. Indeed, the ratio appears increasingly radical for giving any time to inquiry-style learning.

In characterising students as ‘novices’ who learn effectively through Mode A explicit instruction, advocates of a ‘science of learning’ advise teachers to delay Mode B until students reach ‘expert’ status – a status that always seems beyond the horizon.

Thus, we end up with a prescription of Mode A before Mode B and, possibly (even probably), no Mode B at all.

What they really say

Now, if we return to the Sternberg and Grigorenko paper and read on a few lines, the authors make a completely different recommendation.

Students, they say, should be taught analytically, creatively, and practically (see the table below from p. 216 of the paper). Moreover, their research shows that, when assessed, students taught in these ways “outperform students instructed in conventional ways, even if the assessments are for straight factual memory.”

Sternberg and Grigorenko’s main point, which is lost on the academics who cherry pick quotes for their own ends, is that teaching for the memorisation of facts and teaching for thinking are not separate phases and to treat them as such promotes a false dichotomy.

As the authors say, “When students think to learn, they also learn to think.” Or, put another way, facts and thinking are connected in a reciprocal relationship. Moreover, it is possible to design a pedagogical approach to reflect that relationship.

Questions for the inquiry teacher

The separation of teaching into Mode A and Mode B raises two questions for inquiry teachers:

(1) Do students have to acquire knowledge before they can inquire?

No, it is possible to interweave instruction into an inquiry at a time when it is more relevant and meaningful than it could ever be as part of the teacher’s agenda. That is especially the case if students themselves request instruction through, for example, the regulatory cards or if the instruction comes from a knowledgeable peer instead of the teacher.

When the teacher sets the inquiry prompt at the correct level, students will come to the classroom with prior knowledge. The inquiry teacher draws out and assesses the level of knowledge (through students’ responses to the prompt in the Inquiry Maths model) and draws upon that knowledge to co-construct lines of inquiry. And those lines of inquiry can be developed through instruction in new concepts and procedures when they are required.

(2) Should we support the recommendation that Mode B teaching takes up 20% of classroom time?

In an educational climate in which policy-makers listen to teachers who denigrate inquiry, it is tempting to support any model that accords inquiry a place in the learning process. However, the 80:20 ratio does more harm than good because it accepts the dichotomy between knowledge acquisition and inquiry learning.

Inquiry is very much subordinate to explicit instruction both in terms of the time it is accorded and its place in the sequence of learning. Teachers can, therefore, view inquiry as inferior and supplementary to the ‘real’ learning.

When teachers are under pressure to meet curricula and assessment targets, it is easy to ignore inquiry entirely. This often occurs when students have not understood a new concept through explicit instruction. At such times, teachers feel they should use more Mode A teaching, rather than move on to Mode B.

Yet, it is conceivable that a Mode B approach would help develop an understanding of the concept (or increase the motivation to understand) when any amount of Mode A could not.

Furthermore, leaving out inquiry has implications for equity. If students do not understand first time, they are easily trapped in a cycle of instruction and practice. Meanwhile, those that show they have 'acquired' the knowledge move on to benefit from an experience of mathematical inquiry denied to their peers.

When common sense makes no sense

Rather than being common sense, the idea that students need to acquire knowledge through explicit instruction before being able to engage in inquiry makes no sense.

Not only can knowledge be acquired through inquiry, but students also gain more knowledge. They become aware at a metacognitive level of how and why they are acquiring that knowledge. They also become aware of disciplinary knowledge - that is, knowledge of how mathematicians develop the subject.

The idea that knowledge acquisition precedes the application of knowledge leads to the 'balanced' model of Mode A and Mode B in which inquiry plays a minor role at the end of the learning sequence. In such a position, it is easy for teachers to see inquiry as an add-on that can be jettisoned when Mode A is not working.

Andrew Blair, September 2025

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