It seems obvious. First, we should consider what we want students to learn and then we should figure out how we might teach it.
It is a model that is hard-wired into many lesson plan templates that ask teachers to first declare their learning objectives. My school is teaching a new physics course next year and our first step was to sit down and look at a list of the objectives across the year. Do they make sense? Are they coherent? Do they progress in a logical way? Are key concepts revisited? If we were to put it in psychological terms then we might ask: Does this sequence of objectives promote optimum schema building?
The idea of starting with the objectives is one that draws support from across the otherwise polarised educational landscape. Traditional approaches have always emphasised a sequenced set of objectives and Grant Wiggins and Jay McTighe developed the idea as their philosophy of ‘backwards design‘.
Yet, in practice, we are bombarded with what I have described as ‘activity based learning’. Have you ever been in a meeting where a colleague says that there is this really cool activity, that he did it last year and that the kids loved it? Where is the learning objective here? Are we somehow meant to derive one after-the-fact?
I remember a training that I once attended where the presenter waxed lyrical about a particular task. The idea was to present students with a drawing of a field that contains chickens and pigs. You tell them how many animals there are, how many legs there are and the students have to work out the number of pigs and chickens. Then, as extension work, you could throw in a few crabs.
I couldn’t really follow the thinking. This was about simultaneous equations but they were never mentioned. And once the crabs arrive then you can’t even solve it. Instead, the activity was presented solely as a cool, fun thing to do with no word about when or how it might fit into a sequence of instruction.
It’s the same phenomenon that sees teachers trying to shoe-horn the latest craze into their teaching. How can I use Minecraft in my English teaching? How can we do something with Pokémon Go? How can I use iPads in science class?
I agree with the criticism that these ideas are gimmicks and that once a teacher starts using Pokémon Go it loses its cool. Teachers should not be try-hards. But this is not my main point. Potentially, Pokémon Go might be the perfect example to help students learn a particular concept. But we would need to start with the concept. First, we need to figure out what we want the students to learn.
An almost perfect example of activity based thinking can be found in Dan Meyer’s recent blog post. He knows that he wants to do something with bottle-flipping. Apparently, it is the latest craze and all the kids are doing it. He videos the bottle-flipping and it looks cool. He tries to link it to some maths but the maths of bottle-flipping is hard. He can’t think of anything in the end and wonders whether to give up.
Here’s a thought: why not start with the maths we want the students to learn?
Filling the pail 
Reblogged this on The Echo Chamber.
I had to self-edit out my comment about that bottle flipping post. Not so much Meyer, who at least had the wisdom to realise it wasn’t going anywhere, as the comments underneath. So many “cool” activities that would end up with the kids remembering the bottle flipping part and forgetting the minimal maths that was the supposed reason for the activity in the first place.
One of my prime drivers when writing questions is to make sure that the context is not more interesting than the Maths. I’ve seen too many lessons dragged off into discussions about the context when it is interesting, leaving the learning about Maths to diminish badly.
(In fact it is relatively easy to model a parametric equation of the movement of a specific part of the bottle — a circular motion around the parabola of the centre of mass isn’t that taxing. I could even do it with some of my cleverer Calculus kids as a bit of fun on the side. But it adds nothing to doing the standard ones, like cardiods or spirals, so I probably won’t.)
Greg:
Right. That’s what I did. I hold all of that math in my head. K-12 mathematics. Then when I see a context that interests me or students, I venture off and see if any of the math I want students to learn is more accessible, concrete, or interesting by way of that context. If it’s there, great. If it isn’t, I’m done, because the maths is primary. It wasn’t.
Chester:
I’d love to see how. The task of modeling the centre of mass stumped some of the engineers where I work. The problem is that it’s sloshing around a bit.
Hi Dan
You seem to have missed my point. I suggest starting with what you want to teach and then finding a good activity. If you start with an activity and try to map it to some K-12 maths concept then the problem that you have is that this activity might not actually be a very good way of teaching that maths concept. As Chester suggests, some contexts even distract from the maths. You might also end up with a distorted curriculum where activity-friendly concepts are emphasised at the expense of others.
Wiggins and McTighe are good on this issue.
Greg
Teacher #1 asks herself what’s the best way for students to apply the solution of equations to the world. She designs an activity that involves a school fundraiser.
Teacher #2 is thinking about a school fundraiser and realizes that it’s a vehicle for helping students apply the solution of equations to the world.
They both teach exactly the same lesson.
How is the genesis of that lesson important?
Teacher #1 rolls a dice to decide which car to buy. Teacher #2 selects a car based upon an analysis of cost, fuel economy, depreciation and so on. Both teachers pick the same car. How is the genesis of this decision important?
I can’t identify the logical fallacy here but I think there is one.
That metaphor is inapt.
Both teachers are thoughtful about their content objective. They’ve both prepared explanations. They’ve anticipated misconceptions. They’ve prepared hinge questions. They’re ready with an exit assessment.
These are observable characteristics of lessons it’s reasonable for us to expect and critique.
It’s unreasonable for us to proscribe the unobservable characteristic of the origin of the lesson. You’re telling teachers who happen across a promising activity not to subject it to principled lesson design. “Don’t bother. You didn’t come up with the idea in the right order.”
You’re making the job harder, and no better.
I didn’t proscribe anything. I am advising teachers to start with the end in mind and then select tasks and activities to meet that end. I am not alone in doing this. In fact, some have described this as common sense.
I thought you were suggesting that the means were irrelevant and only the ends mattered but now you are suggesting that the activity based teachers have been thoughtful about their content objectives. I’m not sure you can have it all ways. My point is that starting with what you want students to learn is more likely to lead to an effective teaching sequence. Starting with cool activities could lead to the activities not being the best ones to support the learning. Or they could even distract from it. I would observe that there is a lot of this around. The idea of trying to find a maths concept to fit to bottle-flipping is a case in point.
My reaction to this:
If you’re a content teacher teaching a specific course with a pre-designed curriculum, looking at the kids flipping bottles and thinking, “Hey, how can I turn this extremely annoying fad into a way to spend an hour in class?”, I’m on Greg’s side. That’s not the proper way to do things.
If you’re a consultant devising projects that will be put in a bucket for a teacher to choose from when, next summer, they’re developing course content, then I’m on Dan’s side. It’s a fine project for exploring data collection, statistics, variables, and such.
According to my understanding, Greg is more of a content teacher and Dan is more of a consultant these days, so perhaps the issue here is that you’re looking at this from different lenses.
Perhaps this is the case. But I also suspect that many teachers will go out on Monday and try the latest activity. I’ve seen that happen. There is an attitude among some teachers that it’s all okay as long as the kids are doing maths. Their primary goal is to engage kids in maths, whatever the maths is, because they want to build a love of maths. I don’t think you can build the love outside of a well-structured course because a well-structured course will lead to more learning which is more likely to lead to long-term motivation. So I think there is a genuine issue here.
I agree. And if teachers don’t do it voluntarily, administrators or curriculum coaches slap this sort of thing down on a teacher’s desk. “Why aren’t the kids moving more? This will get them moving!”
Uh, yeah, my lesson plans said this was the day for the Distance Formula. But okay, boss, whatever you say.
Is this a problem of over generalizing? The means to an end may or may not be important. Trying to say argue that it always is would be as difficult as arguing that it never is.
It is also fair to say an expert may pick the best means to an end without much conscious effort. That is almost a definition of being an expert.
The problem would be trying to teach novices to behave like experts by avoiding conscious effort is not always going to end well.
Just to be clearer here. I was responding to Greg’s quest for the logical fallacy. There is not one- you can prove something is always true with one example and you can’t prove it is never true with one counter example.
It should be fine to stumble upon a new way to do something and only then examine whether it works. But clearly this won’t be a good way to work all the time.
should be can’t in both cases there.
I like this.
When planning any sequence of lessons, I still use the principle I was taught on my PGCE:
What is the maths?
I completely agree. This is the subject of my current series of posts on education purpose. I have three points to make here.
1. It is not for teachers to decide on their educational purposes – that is for the curriculum, which should be influenced by a wider array of educational consumers, including governments, stakeholder and expert groups such as employers and subject academics, and direct beneficiaries i.e. students & parents. The teacher is the supplier in this, and suppliers do not determine the purpose of the service that they provide.
2. The problem with the doctrine that it is not for teachers to determine the objectives of education* (other than that most teachers do not accept it) is that the meaning of curriculum has been changed (or subverted). It used to refer to an aggregation of learning objectives; now it is generally used to mean an aggregation of planned experiences. So the very words we use encourage teachers to start from the teaching and then extract objectives as a sort of an afterthought.
3. This has been the fundamental problem with edtech – the geewhiz, start from the tech attitude – tech meaning Minecraft etc. But the OED definition of technology is “the application of science to practical purposes”. The technological approach to education is therefore predicated on the prior definition of purpose and then, exactly as you say, Greg, the effectiveness of particular activities becomes empirically testable.
Best, Crispin.
* Although teachers do, of course, decide on the intermediate objectives – the objective for this lesson, as opposed to the objective for this term. But such intermediate objectives are in fact another type of means to a superior end, and can therefore be evaluated in terms of effectiveness.
Crispin I think your first point is fundamentally flawed. As teachers we need to reclaim the ability to determine the students needs and respond to the,with effective teaching and learning. We don’t say to doctors, let a committee decide what is wrong with your patient that includes companies that are selling the products you use then treat the average answer with all the political correctness included. This is any Curriculum model given by the governments of the last twenty years (look at the increase of standardised testing written by companies that also sell textbooks and calculators) that are near incomprehensible by most and are dependent on one factor, age.
As teachers we need to determine the objectives a student needs to develop. This will allow these objectives to be relevant (something I think Greg is missing in his comments) then determine the best way to enable the student to meet these objectives. As teacher experience grows and they know the progress of understanding through a unit they often see a new device as a way to fill the needs of their students (what Dan offers in his many posts), that makes the content more engaging and/or easier to understand. We should never assume that our first idea is the best or that chalk n’talk is effective for all students.
Hi Iain,
First, no one *needs* an education. It is an enhancement. Nothing in the nature of the uneducated student can tell you what sort of education is required.
Second, no one goes to the doctor to learn the objective of their medical treatment. The objective is health and everyone knows that because health is singular and normal, while disease is abnormal and varied.
In education, it is the other way round. What is normal and singular is ignorance, what is abnormal and varied is expertise.
What is the same is that neither the doctor nor the teacher determines the objective. In the case of the doctor, it is because everybody knows it already. In the case of the teacher, because that is not their expertise (actually, the same could be said of the doctor). Who knows best what sort of Maths is required for a university Maths course: a university Maths lecturer or a secondary school teacher? Who knows what skills are required for success in business, the successful businessman or the teacher, who has never worked in business in their life?
The expertise of both teacher and doctor is to help their charges attain certain objectives, which they themselves need to understand but do not determine.
You assert a lot, and you express a lot of frustrations with the current assessment regime, many of which are undoubtedly justified, but I don’t think you have really thought through the nature of your job. You are a service provider, not a priest.
Hi Crispin
We clearly have a very different approach and philosophy to teaching. I don’t believe the nature state of any person is ignorance. Expertise is achieved in so many things we don’t teach (I have never taught in a school that teaches skateboarding, yet many of my students could be considered experts) in fact often teaching is about developing expertise in things that otherwise wouldn’t be attempted. A lot of Greg’s debate is about whether we should engage in these areas and whether they can be effectively assessed. My point on this is that to many of the stakeholders in this discussion do not understand learning or the needs of students.
These stakeholders are often the maths professor (who thinks more people need to do maths degrees to protect his job) or the businessman (who wants the next group of middle managers with no questions of ethics or morality but only care for profit margins) or the textbook companies (who sell the exams based on the books and don’t properly proof their tasks and processes) or the politicians (who want history but only the bits they like or need us to improve standardised tests so they can tell the voters they are strong on education) or the morality police that want evolution vs creation or more aboriginal studies (the nice bits again we don’t want to upset anyone) or the parents (who want to be friends with their kids and not discuss anything uncomfortable like sex-ed). Yah I have faith in these stakeholders to decide what average my students should achieve that doesn’t reflect the learning difficulties or subject fascination my students have.
And yes I believe I’ve needed to be a priest to my students. Sometimes a parent, sometimes an elder, sometimes full of wisdom, sometimes with a story, sometimes proud of their success and sometimes harsh so they will improve. I’ve had to help my students be the best mathematician they can be and the best scientist. But I’ve also tried to make them the best person they can be with my limited understanding of the world and our place in it. In doing this I’ve earns their trust and the trust of their parents, sadly it seems the trust of the community is a little lacking and so someone else decides the what, but I don’t have to accept it as the only reality.
Iain,
You seem to have come by an incredibly nasty view of everyone else while maintaining an almost saint-like view of yourself and it seems by your confidence in them your fellow teachers. Just a suggestion, if you haven’t met any well meaning people outside your profession that might say more about you than anything else.
As a logical argument your generalizing straw man bad motives to everyone else only serves to show why someone such as yourself should not be free to teach children whatever you feel like. It poor logic and it’s nasty.
Take the math profs. Forget that these people are more likely great role models for people who put the love of learning ahead of personal financial gain. (Investigate how long they spend on higher degrees and low paying post-doc positions). The poor math skills of high school students lead to more demand for make up courses and staff to teach them. The prof’s demands for better math in high school can easily reduce the demand for their services.
Hi Stan
I can see your point here. A lot of people involved in curriculum development are doing it for the right reasons but we can’t ignore the others. My problem is how can they write a meaningful curriculum for every student?
I have meet curriculum developers on many occasions and they do want the best but also believe their model is the best. Tend to agree with Greg that without hard evidence a lot of these plans are flawed as they often work at the ends of the spectrums of students (super motivated, very weak, gifted, lots of money, etc) and this isn’t true of most classrooms. It is incredibly hard to write a relevant curriculum for approx 3 million students (a guess on the Australian student population) when the big condition is age.
I’m no saint and know I mess it up as often as I get it right. But I ask again, who has more knowledge about my students needs? Could the community ask for the best teachers that want the best for their students and see what happens?
Hi Iain,
Who are the best teachers and how can we tell them from the best at selling their ideas?
Now I don’t think the current curriculum authors have any obvious qualifications. Here in Ontario we have horrible government curriculum documents supported by pseudo research papers. At the same time a charity (JumpMath) has produced an entire set of material for grades 1 to 8 with detailed workbooks and supporting material at fraction of the cost the ministry spends. JumpMath has detailed prescriptions for those needing extra help and for those needing an extra challenge. They attempted to get as impartial research to validate their approach and tune it to be what works best.
I am absolutely ready to believe the best teachers can do a better job. I think at JumpMath they have. But check out the comments on Greg’s posting on that topic. Perhaps I am mistaken and their detractors are right but we will only know when we have more objective data on the outcomes.