Embed from Getty Images
Ofsted are the English schools inspectorate. Back in the noughties, they used to go around telling schools that their lessons needed to involve more personalised learning and have less teacher talk. But they are supposed to have stopped that now and no longer have a preferred teaching style.

Well, that’s the theory.

In a report written in June of this year, the inspection team ask, “What does the school need to do to improve further?” and then answer:

“Continue to improve outcomes by… providing regular opportunities for the most able pupils to deepen their understanding by applying their skills and knowledge in enquiry, investigation and problem-solving.”

They continue:

“Overall, there is too little opportunity for pupils to develop reasoning skills in a range of subjects. Pupils are not consistently challenged to enquire, investigate and solve problems. This is limiting the progress of some pupils, particularly the most able pupils and students on post-16 study programmes.”

Investigative work is not a *terrible* idea. Done well, a little investigative work can be effective, but only if students have already been taught the required content. Unfortunately, no such caveats are stated in the report. Many people interpret calls for inquiry to mean the use of inquiry *from the outset *of learning about a particular area and there is very little evidence that this is effective. It might even be damaging.

On what basis are the Ofsted inspectors making this recommendation? Do they have research to support it? Is it just a personal view?

The impact of having this written in Ofsted reports is that consultants and other schools will see this and think, “we need to do more problem-solving in order to please Ofsted.” This is damaging for schools who are trying to develop a coherent, long-term approach.

### Like this:

Like Loading...

*Related*

Problem solving is one of the three key strands of the new Maths curriculum. It is essential to develop mathematicians who can function beyond the limited demands of an exam. I’d be extremely concerned if a school was found to be not teaching problem solving, not just in maths but across the board.

I also disagree with you about most able pupils deepening their understanding. Surely that is how we challenge them, by ‘deepening’ their learning, asking those challenging, searching questions that probe their understanding and challenge them to justify their knowledge/skills/understanding.

Finally reasoning – my understanding of reasoning (and I am no expert) is the ability to explain why. Surely as educators we should be looking beyond a list of facts and skills and getting students to explain why? Or am I missing the point on this?

It is not really possible to teach problem solving in a general sense – you can only teach students how to solve specific problems. See this paper:

Click to access TricotSweller_revised.pdf

I am not surprised that the new maths curriculum is confused about this.

In the first section that you quoted, the words “applying their skills and knowledge ” imply to me that the intent is that inquiry, investigation and problem solving are to be used after the required content has been taught. Students are required to apply what they have learned through their participation in those types of tasks.

In the second segment, the point about students having little opportunity to develop reasoning skills in a subject area is a valid one if the type of tasks routinely given to students mostly ask them to pay attention to direct instruction, remember what they were told, recall it and apply it during practice tasks, and memorize it for test purposes.

You state that ” a little investigative work can be effective, but only if students have been taught the required content.” I am wondering what you mean by ‘effective’. Do you mean that investigative work can help students to deepen and extend the knowledge and skills they have already learned? Or, do you mean it can be effective because it engages students and helps them to feel positive about the subject.?

You express a negative view of teachers using inquiry from the outset of learning, yet there is much research that I have read that describes the value of carefully -designed and teacher guided inquiry to engage students in learning targeted concepts or relationships between concepts, for example, by using thinking skills to make predictions, observe, record, and analyze data, compare and contrast outcomes, identify patterns, make inferences, and then with a teacher’s help, generalize from specific instances to more broad and powerful constructs that are the content of a subject area. I would use prompts to guide students in engaging in the thinking. An example using a Math content expectation, could be that students are to know the relationship between increasing the dimensions of a rectangle by a given factor and the resulting change in area. I could choose to explicitly teach it to them by demonstrating examples on the overhead, calculating areas with them, working with them to summarize the results, and then writing a general rule that they copied into their workbooks and were expected to memorize. Or, I could have them investigate what happens when the dimensions are changed by different factors, analyze the data they gather, look for patterns in the factors and the increase in area, and give them time to talk together about why they think those patterns arose. Following that teacher-guided investigation, I would lead a discussion and make sure that I use the data they gathered to explicitly explain the relationships mathematically. To extend the learning, I might then have them predict what the pattern might be if we examined similar changes to dimensions and the effect on the volume of 3D shapes. I would have them investigate that , gather and analyze data, and share and discuss the results. Followed of course, by an explicit teaching session to make sure the core content understandings were clear.

I think the ineffective or damaging results to allude to regarding the use of investigation from the outset, is related more to instances in which students are expects to learn such concepts through a project that they are expected to complete on their own, often at home as homework with little opportunity for teacher input along the way. I agree that such approaches seldom work to achieve the desired content learning, and are especially difficult for and possibly damaging to struggling students.

In our Ontario (Canada) Math and Science curricula, reasoning skills are explicitly described as being essential parts of the content learning expectations for both subjects. In order to learn those aspects of the curricula content, students have to be engaged in using the skills, and taught how to use them while in the process of acquiring other content goals such as concepts, relationships, etc.

An example using a Math content expectation, could be that students are to know the relationship between increasing the dimensions of a rectangle by a given factor and the resulting change in area. I could choose to explicitly teach it to them by demonstrating examples on the overhead, calculating areas with them, working with them to summarize the results, and then writing a general rule that they copied into their workbooks and were expected to memorize.What? That’s a mockery of Explicit Instruction.

I would teach this by explaining that area is not increased at the same rate as lengths, showing a couple of examples to prove my point. For the more intuitive, I would explain that area increases as the square of the length increases.

Then over the next few lessons I would reinforce that by questions designed to remind them of the pattern. I generally mix this up with questions where the rectangles have mixed units (say a 2 m by 50 cm rectangle) because that is actually a much more likely situation than the abstract change by a “given factor”.

There would be no “general rule” copied into workbooks, and certainly not one they were required to memorise. All I would expect them to do would be remember that increasing length did not increase area at the same rate.

I don’t use your suggested method because 1) it takes far too long. Several lessons to explain a situation that the better kids get in two minutes, and the less good ones get by example better than explanation anyway. And 2) many of my students when asked to “discuss among themselves” will discuss almost anything but Maths — although they will be careful to look like they are if I am around to hear them, because they aren’t stupid.

A few questions

– Do you have a reference for what reasoning skills are explicitly describe as? That is not what they are parts of but what they are distinctly from the rest of rest of the expectations?

– If the approach you suggest is so effective – investigation first then explicit teaching why is the explicit teaching required? It is because for some students the time spent on investigation doesn’t work well? How do you know it wouldn’t be better to just give the explicit teaching part and cover more material?

Hi Stan. Re: your thoughtful question ” if investigation first then explicit teaching is so effective, why is explicit teaching required? ”

In my opinion, explicit teaching is always required to help students process and understand information they are expected to learn, no matter how students obtain that information. Investigation is simply one way to engage students’ minds by capitalizing on the fact that people’s attention can be aroused by curiosity and challenges that interest them, and they often enjoy exploring and working with manipulative materials while investigating and looking for answers to questions or ways to solve problems.

When I follow an investigation phase with a direct teaching lesson, I am hoping that the students will benefit from having had a chance to think about their results, look for and identify patterns, and try to explain what they found, before I present my input. Also, that they will be motivated and engaged by using their own data evidence as a basis for the thinking that I will lead them through during the discussions and explanations in the follow up lesson.

If I decide not to use investigation first, then I would present the information to them myself directly using spoken words and accompanying graphics. While they looked and listened, I would ask them questions, guide them in identifying patterns, and help them to understand why those patterns occur. They would be using and thinking about data I generated, not data they collected.

The investigation process followed by the explicit teaching phase, may involve the students more actively and may engage their minds more than only asking them to sit, watch, listen, and think as we present data and explain things to them.

As I said, I would use the nature of different curricular expectations to select when I would use one approach over another.

Also, when using inquiry as a way to engage students ingathering, recording, and processing information, I more often than not have students working on their own, not in groups. I want every student to be actively doing and thinking, and that does not happen readily when students work in groups, especially groups of mixed abilities.

If I use group work, I structure and monitor it it very carefully.

There is never a situation in which I would not follow an investigation exploration phase with a direct teaching lesson, but there are times when I would forego an investigation and begin with direct teaching instead.

That is a brief explanation of my understanding of how investigation and explicit teaching are complementary aspects of effective teaching in math and science.

From what I understand about how the human brain learns, we are aroused by things that grab our interest, or that pose a challenge, such as a problem to solve or a question to find answers for. As well, I understand that our brains are constantly processing data from our environment, and analyzing it to make sense of that data, during which time pattern recognition is a powerful tool. Sometimes, if we are interested in a topic, we can learn effectively from someone telling us and showing us things without us doing anything ahead of time on our own. Other times, we learn better if we first have a chance to try things out and explore for ourselves, then receive direct instruction from a more knowledgeable person to help us make sense of what we found.

Pingback: Is there really no best way to teach? | Filling the pail