What Is Your Default Teaching Approach ...
And Are You Defending It?
If you want your mathematics teaching to improve - i.e. experience more passion, deliver more extraordinary lessons, and foster more agency and understanding in your students - then you'll need to explore the prairie!
We are dabblers!
We mathematics teachers, are good at dabbling. We come across a new strategy that may lead to deeper mathematical understanding and agency in students, and we respond, “Ooh, I’ll try that”.
And so we dabble.
However, when most of us encounter a new, potentially excellent strategy, we rarely consider it a potential game-changer. We rarely consider the possibility that the new strategy might provide a window into a more effective way to present mathematics on a daily basis.
What I mean is that we rarely, if ever, consider the new strategy as potentially changing our DEFAULT approach to teaching mathematics.
Nevertheless, we are happy to dabble with new strategies and add them to our repertoire - as long as our default remains intact.
And so we dabble.
However, when most of us encounter a new, potentially excellent strategy, we rarely consider it a potential game-changer. We rarely consider the possibility that the new strategy might provide a window into a more effective way to present mathematics on a daily basis.
What I mean is that we rarely, if ever, consider the new strategy as potentially changing our DEFAULT approach to teaching mathematics.
Nevertheless, we are happy to dabble with new strategies and add them to our repertoire - as long as our default remains intact.
What is your default approach to teaching mathematics?
Your default approach is the approach you use most often. It's the approach you fall back on after conducting a different type of lesson.
Here's how it works.
Once every few weeks, we might run an activity with students collaborating in groups or doing some inquiry learning or PBL. But then we return to our default approach, whatever our default is.
The thing about default approaches to mathematics teaching is that we tend to view them as sacred ... a thing that should never change.
It's not that we consciously think, "This is my default approach ... don't try to get me to change it". Instead, our defence tends to be more hidden. We tend not to consider that we have a default approach in the first place. Our default is simply something most of us don't think about. And yet, we defend it without knowing we have it.
Here's how it works.
Once every few weeks, we might run an activity with students collaborating in groups or doing some inquiry learning or PBL. But then we return to our default approach, whatever our default is.
The thing about default approaches to mathematics teaching is that we tend to view them as sacred ... a thing that should never change.
It's not that we consciously think, "This is my default approach ... don't try to get me to change it". Instead, our defence tends to be more hidden. We tend not to consider that we have a default approach in the first place. Our default is simply something most of us don't think about. And yet, we defend it without knowing we have it.
The most common default approach ...
The most common default approach is the one through which I - and most likely you - were taught through our school years and university. The most common default is step-by-step algorithmic teaching, with students passively replicating the teachers' examples.
And we believe this default is the only realistic option to enable us to finish the syllabus on time.
And we believe this default is the only realistic option to enable us to finish the syllabus on time.
What does this have to do with a prairie?
As dabblers, we are a bit like the horse sticking its head through the fence that backs onto the prairie ... we nibble on the greener prairie grass but remain within the safety of the paddock.
The paddock represents our default approach - the approach that tends to produce passive learners, whether we realise it or not.
On the other hand, the prairie is where new strategies lie, under a different framework (in our case, the Understanding-first, Procedures second framework) with the potential to bring about deep understanding to more students. And to foster inspiration in students who then take ownership of their learning ... students with agency.
The paddock represents our default approach - the approach that tends to produce passive learners, whether we realise it or not.
On the other hand, the prairie is where new strategies lie, under a different framework (in our case, the Understanding-first, Procedures second framework) with the potential to bring about deep understanding to more students. And to foster inspiration in students who then take ownership of their learning ... students with agency.
And here's arguably the essential message ...
Unless we jump the fence and hang out in the prairie (for several months), we will never know which option is the better - the paddock or the prairie, the default or the new.
A mathematics teacher tend to do the 'I'll-stick-my-head-through-the-fence' thing every time they dabble with a new,
potentially game-changing strategy while remaining with their familiar default.
potentially game-changing strategy while remaining with their familiar default.
What if our default approach is nowhere near as effective as we think it is?
What if our default approach - without knowing it - makes our students’ understanding of mathematics more difficult than it needs to be?
What if, by using our default approach, we inadvertently foster passive learners, learners who demand to be spoon-fed, learners who take little responsibility for their learning? Learners, who make teaching mathematics more difficult, less inspiring, and more draining than necessary?
That would mean our default approach is making OUR task of teaching mathematics more difficult than it needs to be. And less enjoyable and less meaningful for US and the students.
What if, by using our default approach, we inadvertently foster passive learners, learners who demand to be spoon-fed, learners who take little responsibility for their learning? Learners, who make teaching mathematics more difficult, less inspiring, and more draining than necessary?
That would mean our default approach is making OUR task of teaching mathematics more difficult than it needs to be. And less enjoyable and less meaningful for US and the students.
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And if it turns out that our default approach is a bit of a dud, how would we know? We couldn’t possibly know. Our default has that Do Not Disturb sign on it, remember? |
We always defend the default paradigm before adopting the new one ...
The earth was the centre of the universe until Copernicus and Galileo showed us otherwise. Rumour has it their new idea didn’t go down well at the time. This is human nature - we defend, to the hilt, our default paradigm until we become sufficiently familiar with the new one.
Here's the question is for YOU (because you have got this far in the article) ...
Here's the question: Will I remain in the paddock (but stick my head through the fence and nibble on the new strategies) ... or will I jump the fence, run headlong into the prairie and hang out there for a few months? Will I give myself the best chance of experiencing the many benefits of this Understanding-first framework?
What does 'hanging out in the prairie for a few months entail?
If it is not already obvious, hanging out in the prairie for an extended time means implementing strategies multiple times across all classes and with all types of students.
You might wonder why I'm making a big deal about this prairie-multiple-implementations thing.
Well, because I want you to avoid dabbling. I want you to avoid implementing (only) one or two strategies a couple of times each. I want to push you past your inner, unconscious drive to protect your default.
I'm making a big deal to maximise the chance that you will make strategy implementations a major priority.
We want you to gain experiences that have you exclaiming, "Ahhh ... so THIS is what it means to have students with agency ... so THIS is what it's like to have students with deep understanding ... so THIS is what it is like to have students who feel connected with the work and have a sense of control over their learning."
And the ONLY way to have you experience the fruits of the Understanding-first approach is to implement multiple strategies across multiple classes. Granted, the ideas and strategies need to make sense to you. The role of the PD is to have the ideas and strategies make sense to you. And once they make sense, spend a few months in the prairie, and implement the ideas repeatedly.
You might wonder why I'm making a big deal about this prairie-multiple-implementations thing.
Well, because I want you to avoid dabbling. I want you to avoid implementing (only) one or two strategies a couple of times each. I want to push you past your inner, unconscious drive to protect your default.
I'm making a big deal to maximise the chance that you will make strategy implementations a major priority.
We want you to gain experiences that have you exclaiming, "Ahhh ... so THIS is what it means to have students with agency ... so THIS is what it's like to have students with deep understanding ... so THIS is what it is like to have students who feel connected with the work and have a sense of control over their learning."
And the ONLY way to have you experience the fruits of the Understanding-first approach is to implement multiple strategies across multiple classes. Granted, the ideas and strategies need to make sense to you. The role of the PD is to have the ideas and strategies make sense to you. And once they make sense, spend a few months in the prairie, and implement the ideas repeatedly.
For example ...
When you see how to use Mini-Lessons to handle a wider spread of students, use Mini-Lessons across all/most of your classes. Consolidate that idea for a few weeks. Then you might want to focus on Diagnostic Interactions. Explore these in conjunction with Mini Lessons.
Then when you encounter the extraordinarily brilliant Assessment for Learning (Card Matching) activity, run it several times. Work as a team in a couple of department meetings and produce multiple sets of cards for multiple topics. Then use those card sets for your implementations. You'll feel like a pro when you've run the Assessment for Learning activity several times!
And so on ...
Then when you encounter the extraordinarily brilliant Assessment for Learning (Card Matching) activity, run it several times. Work as a team in a couple of department meetings and produce multiple sets of cards for multiple topics. Then use those card sets for your implementations. You'll feel like a pro when you've run the Assessment for Learning activity several times!
And so on ...
In summary:
- Become aware of your default approach.
- Specifically, become aware of any practices you use that inadvertently foster passive learners.
- Be aware of any resistance you have to changing your default.
- Commit to discovering time-efficient ways to present mathematics that better foster agency and deep understanding in students.
- If any of the ideas and strategies within the PD don't make sense to you - don't make you keen to implement them - let us know.
- Then implement those strategies multiple times across multiple classes.
- And hang out in the prairie for several months.
Your turn ...
This is a confronting article. At least, it should be!
And remember, most maths teachers have a default, it leans towards fostering passive learners, and yes, teachers are defensive of it!
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- What is your default classroom practice?
- Does it mostly foster passive or active learners?
- And are you protective of your default?
And remember, most maths teachers have a default, it leans towards fostering passive learners, and yes, teachers are defensive of it!
NOTE: Create a Hyvor Talk account before commenting (click LOGIN) -that way you'll be notified of replies and you won't be anonymous.
If you don't create an account, please state your name at the start of your comment. Thanks.
