The Sweet Spot

numeracy leaders teachers Nov 23, 2023

This year I have spent hours and hours reading research to become better informed around the 'Science of Maths' and 'Science of Learning'.

At the heart of the 'Science of Maths/Learning' is a desire to provide the best conditions for our students to learn mathematics. Optimum maths instruction is something I am very passionate about. So I have been keen to learn more in this space.

Currently, only small amounts of the 'Science of Learning' content is covered in pre-service maths programs (unfortunately we only have a limited amount of time to teach maths, so most often it is the content we are trying to cover). This means that many teachers and school leaders may not be aware of this research and are left to find out about this content in their own time.

You all know how busy teaching is, so many teachers simply do not have time to take a deep dive into this area.

In my position as a university academic and maths consultant I feel it is my responsibility to be well read so I can share informed, balanced opinions when I write this blog and work with schools and teachers. 

I do not pretend to be an expert in this area- it is new to everyone- but I have read A LOT.

As we know...'when we know better we can do better'.

I have run several sessions this year with various groups and at conferences unpacking what the 'Science of Maths' is (and is not) for teachers and leaders (I am presenting on this at the MAV conference next week if you are attending!).

In these sessions I aim to clearly present the facts, encourage schools to always consider their own context and make small changes (don't throw the baby out with the bathwater, there is LOTS of great stuff going on in schools). To me the heart of school maths improvement is developing teacher PCK. 

When researching I always take a pragmatic approach. This means I try to see and consider 'both sides' of the 'coin'. As I have said many times, the answer is almost always somewhere 'in the middle'.

Unfortunately, the 'Science of Maths' debate is often made into an Inquiry vs Explicit 'teaching war'.

To me this is counterproductive and a misrepresentation of the research.

We all know explicit teaching is critical in maths, yet so is allowing students to develop problem solving and reasoning skills through Inquiry. There is definitely a 'sweet spot' we need to find. But as we all know...this is a huge challenge! 

Interestingly, this week I found a 2017 report called 'How to improve student educational outcomes: New insights from data analytics'. In this report the McKinsey company who conduct research in many fields including education, conducted an analysis on the 2015 Program for International Student Assessment (PISA) data.

PISA is an international assessment administered by the Organisation for Economic Co-operation and Development (OECD). It takes place every 3 years. In 2015, 540,000 randomly selected 15 years olds across 72 countries sat the PISA. It produces a BIG data set!

In 2015 the PISA focused on science, with reading, mathematics and collaborative problem solving as minor areas of assessment.

This means that the findings I am about to share relate to Science teaching. However, I think it is fair to say there are enough similarities between the two content areas, for this research to be worth considering.

The finding that most interested me was: 

Students who receive a blend of teacher-directed and inquiry-based instruction achieve the best outcomes, (Mourshed, Krawitz and Dorn, 2017, p.7)

Firstly, the paper defines teacher-directed instruction as 'the teacher explains and demonstrates ideas, considers questions and leads classroom discussions', and Inquiry-based teaching as 'students are given a more prominent role in their learning- for example by developing their own hypotheses and experiments' (and remember this data is looking at 15 year olds).

The report talks about a 'sweet spot' in the use of these teaching methods.

Importantly, it notes that students require a strong foundation of knowledge gained through teacher directed learning before they move onto inquiry based methods. This makes sense to me, and aligns with the reading I have been doing around the Instructional Hierarchy (Haring, Lovitt, Eaton, & Hansen, 1978) which talks about students moving through stages in their learning of concepts. Basically, you need knowledge before you can be expected to apply it. 

The second point the report makes is that inquiry-based teaching is 'inherently more challenging to deliver and teachers who attempt it without sufficient training and support will struggle' (p.9)

Amen to that!

Inquiry lessons are really challenging to teach!

There are so many variables and teachers need to have a really deep understanding of content and pedagogy to teach these sessions successfully.

This doesn't mean we don't do them- it just means we need to acknowledge the difficulty and keep working to support our teachers in this mode of teaching.

For me, the most important piece in this puzzle is helping teachers to have the pedagogical content knowledge to recognise (through quality assessment) when each teaching approach is suitable for their students and their context (year level, proficiency level of students, confidence of teacher, maths topic being taught, student's opinion of maths).

So this week I encourage you to think reframe your thinking about explicit and inquiry teaching. I think we need to see it not as an 'either/or' decision, but as a 'when, where and why' decision.

Have a great week!


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