Why student-centred approaches are problematic for high school teachers!
This article, the first of a 3-part series, proposes that a conceptual approach should also be student-centered. It explains that the byproduct of a student-centered approach is an increase in the spread of students throughout a unit of work. This increase in ‘student spread’ proves to be problematic for many high school teachers seeking to embrace a student-centered approach. The second article Student spread within mathematics education offers some strategies which go a long way to solving the problem posed by increased student spread. The third and final article Let’s encourage student spread in math units argues the case in favour of encouraging student spread within a mathematics unit of work.
What is a conceptual approach to teaching mathematics?
In the article Procedural knowledge vs conceptual knowledge in math education I offer the following to give some idea of what a conceptual approach to teaching and learning mathematics looks like.
An effective conceptual approach enables the following to occur:
Teaching by telling
The vast majority of math teaching leading up to today has been teacher-directed. In other words it has been the teacher who decides what students learn and when. It has been the teacher who sets the pace of learning. Traditionally, the teacher imparts mathematical instruction and demonstrates the proofs using a whole-class lecture format. Consequently, there has been little room for student collaboration and discovery. Teachers have traditionally not seen a need for collaboration between and discovery by students. The traditional approach has typically focused on the direct teaching of mathematical rules and procedures. It has been a top-down, ‘teaching by telling’ approach.
What is a student-centred approach?
A student-centered approach, in many ways, is the opposite of the above. In a student-centered approach the student is at the centre of his or her learning and is predicated on collaboration, inquiry, and discovery. A significant aspect in favour of a student-centered approach is the fact that it empowers students (i.e. students begin to take charge of their own learning). In contrast, a teacher-centered approach has the teacher in charge of the students’ learning.
“But a student-centered approach doesn’t work. Students need direct instruction!”
This is a common cry from opponents of student-centered learning. In my view this cry is not entirely wrong; in fact it is 50% correct. Students do require direct instruction. They need expert guidance. But they also absolutely need to take ownership of their learning. In my experience the only approach which has within it the ability to enable genuine student ownership of learning is one which contains a fair degree of student-centered-ness.
On the other hand, the cry ‘But a student-centered approach doesn’t work’ is very limited. Meaningless almost. Its about as meaningless as me saying ‘A teacher-centered approach doesn’t work.’ In this article (link-new, untitled) I state that the argument should really be about the skill of, and delivery by, the practitioner. An expert teacher will gain success (depending on how you define success) using either approach. In the article (link) I also argue, however, that a cleverly designed, well executed, student-centered approach offers teachers more avenues through which to engineer engagement of, and understanding by students than does a teacher-directed approach. The disclaimer is that a cleverly designed, well executed, student-centered approach MUST be well scaffolded. It MUST contain quality instruction and guidance from the teacher. It’s not about the teacher providing a bunch of materials and saying “OK students, go learn something.” (That last idea could prove valuable on occasions with a highly motivated class, but generally speaking, this is not what I’m advocating as a quality student-centered approach.)
A conceptual approach is ideally student-centred.
We began this article talking about a conceptually-based approach to teaching and learning mathematics, and then segued into student-centered learning. I argue the two are closely related. I propose that a conceptually-based unit ideally needs to be student-centered and that a well constructed, well delivered, student-centered unit, by default, is an ideal foundation from which to enable students to gain a conceptual understanding of the mathematics at hand.
Why conceptually-based, student-centered approaches typically attract criticism.
I suspect when most teachers think of the terms conceptual approach or student-centered learning they see students surrounded by loads of hands-on materials yet learning very little of mathematical worth. Or they see students being left to their own devices to learn from un-scaffolded information. They see a teacher not teaching, not guiding, yet a teacher who is happy because ‘Hey, I’m doing student-centered learning – I’m swimming with the tide.’ They see students having fun yet who are mathematically disengaged – or somewhat engaged but not learning much. And they see the resulting, lower test scores.
If the above is what conceptually-based, student-centered learning is about, then let’s retreat to the safety of a teacher-directed approach. I absolutely would recommend an excellently delivered, teacher-directed approach over an ineffective student-centered approach as outlined above. Yet what is described in the paragraph above are mostly misconceptions (link-Teaching math conceptually: Some common misconceptions) to the type of conceptually-based, student-centered learning proposed, implemented by myself and many others today.
A well scaffolded, well delivered, conceptually-based, student-centered approach is inherently engaging.
This is obvious to any teacher who has experienced delivering such an approach successfully. It is not, however, at all obvious to any teacher who hasn’t experienced delivering a successful, conceptually-based, student-centered approach. And it may take students a while to embrace the new regime. It will definitely take some students a while to become used to the resulting decrease in ‘spoon fed’ (link) information that they receive. Before long, however, the level of overall engagement within the classroom should significantly rise.
‘We can lead horses to water but we can’t make them drink” is a commonly quoted term in life but not typically applied to the classroom where, clearly, this principle is most apt. I say let’s find a way to have our ‘horses drink at the trough of math’. Applied to the realm of learning, engagement is everything. Try teaching me something I’m not engaged in (not interested in, don’t see the need for) and I’ll show you two unhappy people. You won’t succeed because I won’t learn what it is you are trying to teach me. Period. Granted, I’m well beyond the classroom, however, the principle still applies. Engagement is key. Many factors contribute to engagement. Some of the important ones are student ownership over learning, choice, inquiry, freedom to progress at one’s own pace and collaboration with fellow students to ‘work stuff out’. There are others, but the factors I’ve listed above are critical and each are the domain of an effective, conceptually-based, student-centered approach to teaching and learning.
A student-centred approach = ‘very big problem’.
The main reason a teacher-directed approach is popular, apart from the ‘it’s the way we’ve always taught’ reasoning, is that a teacher-directed approach is neat and tidy. We herd students together so that they progress through a unit as uniformly as possible. We deliver the teaching segments to the whole class. We avoid, as much as possible, repeating ourselves. We resist students falling behind and we resist students getting too far ahead. On the surface, a teacher-directed approach appears sound and logical.
The problem with a teacher-directed approach, as described above, is that any given room-full of students never learn uniformly, not even when the students are closely streamed. They each learn differently. They each learn at their own pace. Herding students does not have any real effect on the rate students genuinely learn.
However, if we are to embrace student-centered-ness we have a very big problem on our hands. The very big problem is the increased student spread created by a student-centered approach. As soon as we release the let’s-keep-them-all-together brakes, and students are free to progress at their own pace, the spread of students within a unit becomes significant. Many teachers find this threatening. (I need to state that the group of math teachers I’m referring to here are mainly high school math teachers – many of their primary-teacher counterparts are experts at dealing with student spread!)
You can’t blame high school teachers for feeling threatened by student spread. Think about it – put your feet in their shoes:
“In all my years of teaching I’ve tried to herd students through math units as best I can. I’ve developed a quality style of delivering quality information to my students using whole-class lectures. I make these as entertaining as I can. And then, suddenly, some PD guru has convinced me to embrace a student-centered approach. It all sounded pretty shiny at first. But now I have students spread out several lessons apart throughout the unit. How on Earth am I meant to deal with this? My expert, whole-class lectures have been rendered useless due to the spread of students. I have no strategies for this level of student spread because I’ve never been required to deal with it – until now. I have always successfully avoided student spread. This is chaos which I never signed up for! Help!”
A paradigm shift.
It is a challenge to write articles like this and not have it read as rhetorical ‘waffle’. The fact is the only way I know how to successfully guide teachers into implementing a conceptual, student-centered approach is through the 16 week, 15 hour online learning experience (link). It is impossible to have teachers magically transform simply through reading a few blog articles – although reading some articles can certainly help to inspire! The change from traditional teaching to the successful implementation of a conceptually-based, student-centered approach is a paradigm shift. To make a paradigm shift requires time, self reflection, quality guidance and practice.
I don’t know about you but in my early years of teaching I was petrified (only a slight exaggeration) by student spread. I literally could not cope when students got ahead or fell behind. Those poor students! I could write a short book featuring my “Ten best ways to turn off your best math students”. Fortunately, due to the resulting frustrations I faced during those early years, I found another way. I had no choice but to eventually embrace student spread.
Three major challenges of increased student spread.
Three of the major challenges posed by increased student spread, from my experience, are:
Not all high school teachers are bothered by student spread, but a high percentage of those I have worked with are. I know this because they tell me via the course (link). I strongly suspect the fact that many teachers are threatened by student spread is, today, one of the reasons student-centered learning is not as widely accepted as it could be.
When presented with ideas around student-centered learning teachers often respond “This all sounds fine but HOW do I manage the increased spread of students?” This is an anticipated and logical response because, from the outset, a solution is not obvious.
The next article in this 3-part series Student spread within mathematics education deals with problem #1, instruction – how to implement an effective approach to solve the issue of increased student spread.
If you are interested in a course to comprehensively guide you through the transition to adopting a more student centered, conceptual approach then this 16 week online course is for you. The course proves time and time again to be an exceptional change agent allowing teachers to feel more empowered in the classroom as the understanding and engagement of their students increases.
Richard Andrew likes to write about stuff that matters in education. That boils down to 'anything that helps teachers to better-engage their students'. His view? "Not much else really matters - engaged students learn. Disengaged students do not."
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