Inquiry or Discovery? Are You Confused?

A colleague of mine has been struggling recently to understand how to develop inquiry in her mathematics classroom. Despite having secure content knowledge and a vast experience of teaching she finds it challenging to devise teaching activities that truly manifests as inquiry. After observing her a few times, it became clear to me that she confused Inquiry with discovery.

David Perkins, Professor at Harvard Graduate School of Education, proposes the idea of “playing the whole game” in his book Making Learning Whole. The central thrust being that learning should be provided in a whole form, rather than in topics as is more normal. This is particularly intriguing for mathematics instruction. His metaphor of a baseball game being a different experience compared to learning different skills in a training setting is curiously poignant.

So what is the difference? I can almost hear teachers going “yeah, what is the difference?” Or even “what’s wrong with discovery?”

For many teachers, this “inquiry method” is just another name for discovery method. But is it? I beg to differ and I can only support my view with experience and the tsunami of research out there.
Discovery teaching relies heavily on two things in my opinion:

• The learner is unaware of the learning intention
• A logical activity that is well planned leading to a predetermined outcome

The ignorance of the learner is critical to the success of discovery methods since if the learner is familiar with the content, the long process of proving sometimes disengages.  How many times is the annoying learner encountered who chooses to blurt out the intended destination of the lesson?

Another pitfall of discovery teaching in Mathematics is the lack of transfer in weaker learners. They logically follow through the process, but struggle to connect it to the Mathematics on the board. We have all been there.

A popular topic is the sum of interior angles in a triangle. The logical process of drawing a triangle, cutting out the ends, joining them and voila a straight line relies almost totally on the teacher guiding – telling perhaps – the learners. Despite the process being well supported by logic and the outcome undisputed many learners still do not remember the simple fact. Transfer is lacking. Or at least independent transfer.

Inquiry teaching takes another route to learning, as it is largely inductive and demands questions from the learners for it to thrive. Questions are promoted with further questions, one answer by a learner is followed by another question probing understanding, questions are focused on concept formation and the learners are leading the learning by virtue of their own curiosity.

As a teacher in an International School, I have found inquiry to be the safest and most effective method to introduce learning in Mathematics. My main reasons were:

1. International students are normally second language English learners
2. International students have covered different aspects of the syllabus before
3. Variety of teaching experiences and methodologies seen by learners
4. Differentiation required since most are largely non-selective

Questions are the key and the versatility of the teacher to guide the learners, deeper into thinking, thus probing understanding and challenging certainties. I for one have been known to not provide answers, or as my students say, answer questions with questions. This is a great atmosphere to have in your classroom, it makes everyone equal and the pursuit of knowledge joins everyone together.

It means that the learning in your classroom becomes more deliberately focused on conceptual formation rather recognition of content validity. Proving that the angles of a triangle add up to 180, only adds another bit of content but it doesn’t explain why. Why does this happen? Why is there a limit to all triangles?

Understanding the triangle explains all polygons including the circle. Is the circle a polygon? Ask your class to think about this, but with colleagues probe this deep thinking? Is the reason because it fits on a straight line? Surely there is something more conceptually profound that commands it to be so.

Inquiry teaching will challenge your thinking and understanding but it fosters a positive learning atmosphere in any classroom. I must admit that many teachers find the adjustment challenging, but in the modern world where knowledge is free, analysis and synthesis are invaluable skills. Deliberately pushing every interaction with your learners into a questioning atmosphere will develop your own inquiring skills.

Inquiry implies involvement that leads to understanding. Furthermore, involvement in learning implies possessing skills and attitudes that permit you to seek resolutions to questions and issues while you construct new knowledge.

Here are some pointers, to promote real inquiry in your MYP classrooms

1. Write down the conceptual questions you want to cover in your lesson. This will help to keep you on track if you tend to lose it a bit in the questioning phase. Having a written record means that you would have thought about the activity and expects to discuss this as priority.
2. Avoid answering learner questions. Develop a habit of not answering any question. Reward the questioner by saying good question and either follow up with another or pass it to someone else. This will promote good questioning and make the curiosity element in your class active. At first your learners will find this weird, but eventually will feel the benefits in their conceptual understanding.
3. Ask at least two questions to the same responder. Begin with a factual question and follow up with a conceptual one. As a rule I try to ask at least two questions to probe understanding. Why did you say that? How do you know?
4. Keep some question stems that promote deeper thinking. I like using “Can you think of another example?” “Is your answer always correct?” “Is there any value in knowing this?” You can see my point.
5. Promote lateral thinking and transfer. Allow your learners’ questions to veer off as long as it naturally follows the topic being explored. Having a prepared list of questions will help to guide the conversation back to the learning. Thinking is deeply rewarding if freedom reigns in your learning space.
6. Accept only written reflections. I always let my learners write their reflections down before sharing. As soon as the concept is covered, I ask them to write their reflections and then read them out loud. This forces deeper thinking and allows them to really reflect since writing is a more involved process. This works well if you ask them to “write three things they learnt today”. Do not ask for one! Three pushes them deeper.
7. Focus the learning on concept rather than content. Keep the concept formation as the guide to the questions, be alert for opportunities to delve deeper in ideas proffered by learners. Concept acquisition is far more valuable than content.
8. Video yourself and count the number of questions in your classroom. Check to see who ask the most questions. Try and improve the quality of your questions, watch for opportunities missed and learn to capitalize on them. An audio recording is equally useful if a video intimidates.

These are just some of the pointers I have garnered over the years. The list of suggestions, are by no means new and are not intended to solve every problem. However, the aim is to share some ideas as to how to convert your classroom into an inquiry one. As with most changes, it begins with you.

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The 4Cs are Transforming Schools Today: You Can Transform Your School

We couldn’t resist publishing this article by Dr Michael Anderson, Professor of Education at Sydney University and published in The Age newspaper this month. We recently emailed our schools database with the same sentiments … so please read on:

As the political battle over school funding rumbles on, we run the risk of neglecting a glaring question: how can we prepare kids for a coming world where almost half of jobs will be displaced by technology?

Imagine a school where the teachers are really developing skills in innovation.

Innovation in how learning generates creativity in their students. Innovation that re-imagines learning as evermore engaging and challenging.

Imagine a school where the students have the agency to know how to learn. Where students have the curiosity and confidence to engage with the world as active citizens in small and big ways.

This is what we call 4C schools, and these schools exist. The 4Cs are creativity, critical reflection, collaboration and communication. In their classrooms and staffrooms, 4C schools are transforming learning and teaching through this quartet. But in these schools it takes will, energy, inquiry, courage and determination.

The 4C evolution is only just beginning in certain schools but it is always characterised by a climate of re-invigoration, excitement, challenge, difficulty, uncertainty and possibility.

However, this is not always the climate across all schools.

The onward march of NAPLAN, testing a limited set of 'basics' with its teach-to-the-test oppressions, and league tables, have transformed education into a much-reduced experience for teachers and students alike. This is professionally disappointing for teachers and it is a profound threat to the students in schools.

While we chase ever-increasing 'accountability measures' we are relegating the aspects of schooling that will prepare students for the realities of work and life in the 21st Century.

The world our students now face is complex, contradictory and to a certain extent more chaotic than the world our schooling system was designed for. And yet our school systems have only changed incrementally.

Simultaneously, the world of work is changing so that many jobs in health, law and transport will not exist when a child starting Kindergarten today finishes high school.

A landmark Oxford University study found that 47 per cent of jobs would be affected or severely affected by the technological 'colonization' of human work. The authors of the study found that for workers to stay in the 'jobs race' they would need to develop 'creativity and social skills'.

No one is pretending changing schooling is easy.

There are, however, green shoots. In a number of 4C schools principals working collaboratively with their teachers and communities are seeing a change in their classrooms and their school organisations.

In these classrooms students are more engaged, they learn the skills of the 4Cs through experience: they are interdisciplinary rather than siloed in their learning and thinking. This change does not happen quickly. It is slow and sometimes difficult. Where it does work the whole school community commits resources and energy to the task of transformation.  They have made these hard decisions because they appreciate the gravity of school relevance and work hard to make the change. 

There are resources that schools have an abundance of: compassion, ingenuity and energy in their teachers, students and leaders. In fact, there are few other professions in my view that can make this change a reality. We, however, need more than green shoots. We need schools to be enabled to fundamentally change. And teachers need more than policy: they need support to make these capacities understandable and teachable for their students. More broadly, they need political, policy and resource support to make these hard changes possible through effective professional learning for their school communities. 

So, if we are to make these critical changes we need to connect with the capacities. These capacities are the reason many teachers entered the profession and they can make our schools exciting and relevant to the world their students are entering.

The time to do this is now because ignoring creativity, collaboration, critical reflection and communication and leaving it to chance may leave our schools and our kids unable to face the challenges of this brave new world.

If we miss this opportunity we will be the generation that let our schooling fade into irrelevance because we lacked the imagination to create change.

Are You Teaching Thinking Skills to All Your Students?

A recent article on Ideas.ted.com http://ideas.ted.com/the-rise-of-the-useless-class/

predicts the creation of a new ‘unworking’ class. 

It gave a bleak view of the future for students in school today.

This made me think about how we must prepare our students for the future. But we’re not doing this … do you think we are?

The key element of preparation is to develop the thinking skills of every student. Now. Today. That’s a major responsibility of Teachers.

We mean integrating thinking as a discipline into your daily routine.

Most of what students currently learn at school will probably be irrelevant by the time they are 40.

Traditionally, life has been divided into two main parts: a period of learning, followed by a period of working. Very soon this traditional model will become utterly obsolete.

The only way for your students to stay in the game will be to keep learning throughout their lives. They will have to reinvent themselves repeatedly. Many, if not most of the students you are teaching today may be unable to do so.

When you read this Blog, make a decision to expand thinking skills of each of your students. This is the main reason why MathsRepublic was created.

Problem-solving, both individually and by collaboration, is designed to develop thinking skills particularly strategic thinking.

You can start here by registering for a Free Trial on this website.

2017 Must be the Year You Transform to a Mentor

Enormous changes are happening with the Teaching & Learning of maths. It’s the same throughout education globally.

But when you’re in it: you often can’t see it; or feel it. 

Each year seems to be the same … only the faces of this year’s classes have changed from last year's.

A few years ago, I discussed collaborative problem-solving in mathematics with Professor Tom Seidenberg from Philips Exeter Academy in New Hampshire, US. Every subject is taught there collaboratively by a teacher/mentor around a Harkness oval table.

The Harkness method has been the Exeter pedagogy for 87 years. It’s also been a model for many other very progressive schools.

The maths faculty has written hundreds of problems which you can access on the Exeter website (www.exeter.edu). These problems are the basis for the collaborative lessons.

I was inspired by Professor Seidenberg and Harkness. So much so that I started MathsRepublic for teachers to connect with their students through collaborative problem-solving.

You can support the vision by trialling MathsRepublic FREE and then being invited to subscribe. That’s the easy part.

The hard part is breaking through that resistance to change … a characteristic shared by all humans when change is happening all around them.

But this is the time when Real Teachers emerge. These are teachers who recognise that T&L is an evolution but now accelerated by technology or EduTech to reach warp speed.

Real teachers know that it’s the students that matter. They acknowledge that students today were all born into the Web World…that they interact from an early age with the web and social connections.

There surely must be a new model of teacher/student connectivity for learning.

We believe that putting Harkness in the Cloud through MathsRepublic will introduce all Teachers to collaborative problem-solving.

And to then engage in Real Teaching with your amazing students.

We're Inviting You to be a Guest Blogger

You Must Have Something You'd Like to Say!

We have (finally) added a Blog to the navigation bar at the top of the home-page of MathsRepublic. I will be busy each week writing about whatever comes to mind ... mainly about teaching & learning.

I would like to invite you (teachers as well as students) to send me your Guest Blog to mail@MathsRepublic.com.au

Of course I will have to review it before posting ... but I won't be some kind of censor in that your views on education have to align with mine. No way.

Let's get some healthy discussions going.

I look forward to reading your guest blogs.

Alan Power, MathsRepublic

How Do Students Learn Best?

When I reflect on schools, teaching & learning in my maturing years, I am always amazed by the conservative attitudes of the majority of teachers to that vital dynamic of learning.

I lay the blame on the reactionary Education systems. Australia is a good example. The system nutures and mirrors the same attitudes within teachers. And they, in turn, reflect these in their reluctance to explore the many advances in learning available in our digital age.

Who's strung out to dry ... well, the students of course. Did we forget that teaching is only about the students?

Let me give you a personal example ... when I started teaching I also taught science. Now I thought that the standard methodology then was a nonsense ie use of a graph book (lined on the LH side and graph page on the RH side).

The rigid process of an experiment was to follow a write-up template of Aim, Apparatus, Method and Conclusion. Diagrams were drawn on the graph page. Any of you remember this?

So I changed this process to ruling the pages vertically into halves and documenting each step with a short description on the LH box and a relevant diagram in the RH box. So the science experiment report became a series of small steps each with a brief description and a visual.

Because that was the way I thought students would learn better.

It all worked beautifully as the students observed, thought and recorded everything in small steps using both words and graphics.

It's not unlike the teaching of maths is it?

The point of this little story is to never give up searching for the Holy Grail of learning ... there is a better way and it's probably not the way you are teaching today. Or told to teach!

Think about your personal schooling, your teachers, your teacher training, your head teacher, your colleagues etc ... then relate all this to your kids. Don't you think there's a huge gap between the way your brain developed compared with those of your kids and their mates in today's world?

Now go into your classroom and keep exploring for the Holy Grail of learning. You'll find it.

Love your comments and views on this ... mail@MathsRepublic.com.au

Make a Difference from within Your Own Classroom

Go into your staffroom and yell Transform Now! Then go into your classroom and start Disruptive Collaboration. Read on …

Teaching & learning in the maths classrooms needs reform. Evolution. Transformation. YOU can make it happen this year.

Yes, just one teacher in one classroom is all it needs … let’s start with YOU.

Some background first: Australia’s maths results in 2015 indicate that the serious decline in performance is continuing. Sure there’s some hotspots but they should not obscure the fact that the transformation must happen.

Couple of facts you may not know … Australian maths students are three years behind those in Shanghai? Or that Australian 15-year olds have similar problem-solving abilities to 12-year old Korean students.

But read all the alarming facts and figures yourself in the Australian education research study published last year by three academics: http://theconversation.com/six-ways-australias-education-system-is-failing-our-kids-32958

While I too was shocked with the data and performance comparisons in the Study (as an ex-maths teacher), my view as to the steps we can take now differ from the report’s authors.

First, it’s curious that in seeking this transformation, we turn to the product of the system rather than the systems themselves. We criticise the egg instead of understanding the chicken. Of course, the bits and pieces of that chicken are complex to the point of obscurity (just like our education bureaucracies and the working of governments). 

This makes self-correction through iteration–the current model for education reform–a challenge.

The education departments in each state, with all their associated experts and consultants, plus the Pollies at both Federal and State levels, get behind the existing machine and PUSH.

We seek approval from the same power holders and institutions that nod their heads Yes or shake their heads No, forgetting it is their way of thinking that got us into this mess. We want transformational change not just from within, but from above.

Teaching is about the three Ps … Preparation, Presentation and Personality. The most important of these is Personality (yes, this is definitely lacking in many maths teachers but you can get around that). I wrote a Blog about this recently. And the quality and teacher-education is already there too.

So we have to stop battling the bureaucracy and start the transformation in your own classroom … right now. If you don’t then we slip further down the world’s comparative maths achievement ladder. If you don’t care about this then maybe you shouldn’t be teaching.

You need to be disruptive even if it’s simply for the sake of disrupting. Make noise. Draw attention. Walk into your staffroom and yell Transform Today because this whole thing isn’t getting anywhere very quickly.

Disruption in general is about unsettling, and is often thought of in terms of chaos. Disruptive collaboration is working together to force change. It’s the artful unsettling of that which has become inartistic. Reconfiguring systems that can no longer see themselves, or replacing them altogether. It’s about shifting the locus of control.

We could talk right now about helping our students collaborate disruptively – and we should – because they are being let-down big time. But most immediately, this is about teaching and learning. 

Now here’s the pitch … You should seek collaboration with your students that torpedoes those industrial-age ideas. Reject the ideas of the education bureaucracies that have shut off their innovation trying to please the Pollies above them.

You should want the product of your collaboration with colleagues and students to be disruptive, too. Existing systems have their own momentum and can’t be changed. They don’t need our hashtags or likes or affection. They’ve yielded the context that necessitates our collaboration to begin with.

If you want to go fast, go alone; if you want to go far, go together. So let’s build something that offers viable alternatives for everyone–especially those marginalized by the system that exists.

Let’s stop demanding rigor and accountability, and instead create something ourselves that is scalable beyond the walls of your school, or the reach of the concept of “academia” that continues to haunt learning everywhere. 

Something that thinks not in a pattern of school->curriculum–>content–>proficiency, but instead person–>learning–>knowledge–>lots of people–>lots of learning–>social capacity–>wisdom.

Let’s connect and build something that doesn’t serve you or the past or what’s already here but others plus the here and now and the future. Let’s build something we’ve never had –and do so by empowering everyone that’s a part of this.

Something that isn’t built to make your school or classroom spin faster. But rather is built for the real work of understanding something as beautiful as mathematics.