Saturday, October 21, 2017

Teaching kids real maths

I've been doing some research about teaching mathematics, and decided to start by reading and listening to the thoughts of the British technologist Conrad Wolfram, who for a number of years has been arguing that we need to rebuild a maths curriculum for the computer age and that students should be calculating "just like everyone does in the real world".  His argument is that school maths is very disconnected from the maths used to solve problems in the real world, and that it needs to be more practical, more conceptual and less mechanical.

I watched his TEDtalk where he states that maths is more important to the world than at any point in human history, yet at the same time there is falling interest in mathematics education, and a lot of this is because we are not teaching "real" maths in schools.  He argues that maths isn't something that is just done by mathematicians, it's done by geologists, engineers, biologists and so on, often using modelling and simulation, yet in education it is mostly being taught using "dumbed-down problems that involve lots of calculating, mostly by hand".

Conrad Wolfram talks about how mathematicss education should basically be done in 4 steps.
  • Posing the right question
  • Taking a real world problem and turning it into a maths problem
  • Computation
  • Taking the answer back to the real world and seeing if it answers the question
The real issue with the way maths is taught in schools today, argues Wolfram, is that most of the time is spent on step 3 - probably about 80% of the class time - and we are teaching students to do step 3 by hand despite the fact that this is the step that computers can do much better than any human.  He argues that we should be teaching students how to do steps 1, 2 and 4 which involves conceptualising problems and applying them, and teaching students how to use computers to do the computation.  He says
Math has been liberated from calculating. But that math liberation didn't get into education yet.
As Wolfram sees it, the problem is not that computers dumb down maths education, but that without them we can only pose dumbed-down problems to students right now.  We don't need to have students work through lots of examples in order to come to an understanding of mathematical concepts, what we really need to do is to teach students to understand how maths works, and the best way to do that is to teach programming, which makes maths both more conceptual and more practical.

Wolfram also argues that using computers in maths allows us to reorder the curriculum.  We currently teach according to how difficult something is to calculate - but he says we need to change this so that we reorder according to how difficult it is to understand the concepts - the calculating can be done by computer.  He talks about moving from the knowledge economy to the "computational knowledge economy" and this can only be done by a "completely renewed, changed maths curriculum built from the ground up" and based on using computers to perform the calculations.  Hearing this, as someone who really believes that technology can transform learning, I became very excited indeed!

Photo Credit: fdecomite Flickr via Compfight cc

Saturday, September 30, 2017

Future Forwards Volume 7: Exploring frontiers in education

Today ASB published the final volume of Future Forwards. The online edition is available at this link. Future Forwards is a collection of thoughts, hypotheses, discussions, and reflections on practices, research and ideas that are relevant to emerging new paradigms of teaching and learning. The focus of this volume is on prototyping.  This fits in nicely with my current reading on innovation, as in the introduction Shabbi and Scot write:
Prototyping results in new tangible innovations that educators, schools and school systems can see, try, evaluate and learn from as they focus on creating something new and better to meet the needs of their students in their schools.

In Volume 7 of Future Forwards you will read about a prototype in elementary school to address the gender achievement gap in maths, developing "glocal" mindsets based on the ISTE standard Global Collaborator, self motivated learning projects in a middle school, ASB's teacher training programme for local educational institutions (my joy - probably the most rewarding thing I've done over the past 6 years), closing the gender gap in STEM in the high school, and developing mobile apps in the middle school.

In his book The Innovator's Mindset, George Couros asks the question "Would I want to be a learner in my own classroom?" I think with our R&D task forces we asked ourselves "How can I be a learner in my own classroom?"  As George writes, "the innovator's mindset starts with empathy for our students ... but equally important is the desire to create something better."  What we have done on R&D is to ask "Is there a better way?"  George also points out that many teachers who want to change lack clear guidance and support to make the desired change.  Prototyping through our R&D teams has given us that guidance and support.  He also writes that "being in spaces where people actively share ideas makes us smarter" and that social media provides a place for ideas to spread.  He writes, "sometimes the most valuable thing you get from the network isn't an idea, but the inspiration or courage to try something new."  It is with great pleasure therefore that I share the links to prototypes we have been conducting at ASB since 2011.

If you missed the earlier volumes, here are the links:

Future Forwards Volume 1
Future Forwards Volume 2
Future Forwards Volume 3
Future Forwards Volume 4
Future Forwards Volume 5

These eBooks are completely free - enjoy and please consider sharing them with others in your professional network.

Thursday, September 28, 2017

Learning from failure

Today at school we had a tech coach retreat.  As we are preparing for a robotics PlayDate next month, we spent some time exploring the possibilities of some of the new robots that we have purchased this year.  We have BeeBots for our youngest students in Pre-Kindergarten and Kindergarten, Dot and Dash for Grades 1 and 2, Roamers for Grade 3 (though they are still held up in Indian customs) and Spheros for Grades 4 and 5.  The idea of today's retreat was to play with each of these, try things out, learn by doing and failing, and think about the best ways to integrate robotics into our programme.

Tonight when I got home, I saw an article by MindShift about making mistakes.  There's a great graphic in this article which I am adding below (I'm very grateful that it has a creative commons licence so that I can share it).  In this article is a great quote from the educator Maria Montessori:
It is well to cultivate a friendly feeling towards error, to treat it as a companion inseparable from our lives, as something having a purpose which it truly has.

Alongside this quote and the graphic, I want to mention a couple of things from the next chapter of The Innovator's Mindset by George Couros.  George goes beyond the idea of failure and mistakes to something that I think is even more important - the idea of trying again after failure.  I was thinking about this as were were doing some block coding and driving of our robots today.  We weren't following any instructions but simply playing - sometimes the robots didn't do what we wanted them to do and we had to troubleshoot - in some cases making small adjustments to our programme and then trying again.  What George points out is that while failure can be important to innovation, what's even more important is resiliency and grit - learning from mistakes and trying again to do better.

Let's think about the 4 categories of mistakes mentioned in the graphic.  The best learning opportunities are going to come from what is called "stretch mistakes" which is where we are expanding our capabilities.  Whenever we try to do something that is beyond what we can already do, then we are bound to come up against some roadblocks and make some errors.  Maybe this is what Vygotsky called "the zone of proximal development" where things are really still a bit challenging for us but where with support we are learning some new skills.  At this point it's important to reflect on our learning - and then commit to application so that we change our approach and master whatever it is that we are finding challenging.  With this resiliency and grit, stretch mistakes can be extremely positive.

The second category of positive mistakes is that of the "aha moments".  This mistake is interesting because we actually do achieve what we have set out to do - but along the way we discover that what we tried to do was based on incorrect assumptions.  Once again, the way to move forward is to be reflective, and to think about how we can change things to get a better result the next time.

There are some mistakes that we don't learn much from, for example we make "sloppy mistakes" when we are not concentrating.  High-stakes mistakes are definitely ones we don't want to make and then learn from, because high-stakes mistakes are the ones that are risky and potentially quite dangerous.  They could also be bad mistakes to make if other people are relying on us.  

The basic argument of the article is that "mistakes are not all created equal" and adding onto this is the message from George Couros that if we don't have resilience and grit to come back after a defeat or an unsuccessful attempt, then mistakes are not experiences that we can learn from.

Tuesday, September 26, 2017

STEAM Maker Saturday

At ASB this is the year of courage and compassion.  How does this transfer itself into everything that we do?  Here's an example of STEAM Maker Saturday, which happens once a month, this one with a focus on courage.  Last Saturday about 100 students and their parents joined us to work together, meet challenges and solve problems while exploring science, technology, engineering, art, and math.  Enjoy!

Learning and innovation: 3 quotations

In Chapter 1 of The Innovator's Mindset by George Couros there is a section entitled New Opportunities which starts with the following quotation from William Pollard:
Learning and innovation go hand in hand.  The arrogance of success is to think what you did yesterday will be sufficient for tomorrow.
This struck a chord with me because I've been asking myself for some time now whether we are looking backwards or looking forwards.  It also reminded me of our Visioning Task Force, where several members of my group expressed some anxiety about changes that might be coming to education in the future.  It also reminded me about the need for constantly moving forward, not resting on our laurels and thinking "we're a good school" and so continuing to do what worked in the past.  Times are changing, and in a big city such as Mumbai, change also means competition from other schools that are opening huge campuses.  And while it's very flattering that some of these schools appear to be copying our approach to designing spaces, curriculum and so on, my question is do we now need a new approach that will take us towards the future?  When we talk about innovation, we need to be clear what this means - and it doesn't just mean doing things differently from others!  It also means building a culture when innovation is seen as being normal - what we would call at ASB "part of our DNA".  For many years teachers on our R&D core team have been innovative and trying out new things - but how far did this permeate across the whole school?  More and more I've come to see that anyone can be innovative given the right environment - one where it is not seen as a problem to try something that maybe ends up not working that well (because that is a learning experience).  We need to move away from compliance, the cookie cutter approach, where everyone is doing the same thing at the same time!

Just as Sir Ken Robinson defines creativity as "the process of having original ideas that have value" - and which includes both imagination and innovation, George Couros defines innovation as "a way of thinking that creates something new and better"  This can also include iteration, which means changing something that already exists.  However it goes further than just having a new idea: Sir Ken writes "innovation is putting new ideas into practice."  And let's be clear about this, as George points out, "it is a way of considering concepts, processes and potential outcomes; it is not a thing, task fo even technology".  And this brings me back to my previous post - should schools be employing tech directors, or has the time for this now passed - should they be employing directors of innovation?  Of course technology can have a role to play, but clearly innovation is not about the what, it's about the how - and the how is all about empowerment.

In the past I worked at a school where questioning was not seen as critical thinking but as criticism.  Since that time I've always argued that questioning what we are doing and why is essential for moving forward and growing.  Another quotation that jumped of the page at me was this one by John Maxwell:
Change is inevitable.  Growth is optional
But should it be optional?  If we know what the trends are for the future (and at my school we have spent a long time exploring these trends) then can we make a choice NOT to grow?  Certainly this does not seem a responsible choice to make when we consider our students' futures.   And I really disagree with my colleagues that change can be scary and unsettling - in my opinion NOT changing is even scarier.  Change should not be left to chance!

Here's the final quote from this post - again from Chapter 1 of The Innovator's Mindset - this one is by Seth Godin:
Change almost never fails because it is too early.  It almost always fails because it's too late. 
As an educator in a school that has always been seen as "cutting edge", I'm hoping that we are not already too late.

Photo Credit: Wiertz S├ębastien Flickr via Compfight cc

Sunday, September 24, 2017

Is the role of tech director dead?

This is a question I've been asking myself over the past 2 days.  Do schools need tech directors, or do they simply need someone to be responsible for tech support while the job of educational technology morphs into something more like a director of innovation and learning?  As I was pondering this thought, I started to recall one of the biggest shifts in my professional life - when I stopped thinking that all my PD had to come from within my school, but instead started to connect  with others via Twitter and by reading blogs of educators all around the world.  One of these was George Couros.  As I thought more about this question yesterday, I decided to get the Kindle version of George's latest book, which is focused on an innovator's mindset, change and moving forwards.  And wow - I'm glad I did!  So far today I've only managed to read through the introduction but here are some brief bullet points of the things that most struck me and helped me to consider my question again:

Dhobi Ghat, Mumbai - traditional open air laundry. Not much has changed here despite the city growing up around it

Change (or not?) in schools
  • Change is an opportunity to do something amazing, yet within the institution of education there is often a reluctance to embrace new opportunities.  Even in schools that have the latest technology, teachers and administrators use that advanced equipment to do the same things they did before.
  • If we don't really think about the way we teach, and, more importantly, how both educators and students learn, we will all miss out on the opportunities that lie in front of us - right now we have many 21st century schools with 20th century learning.
  • The world is changing and if you don't change with it, the world will decide that it doesn't need you anymore.
Fort area of Mumbai
Our role as educators 

  • Our job as educators is to provide new and better opportunities for our students.
  • Students remember great teachers, not because of the test scores they received but because their lives were touched.
  • Kids walk into schools full of wonder and questions, yet we often ask them to hold their questions for later so we can "get through" the curriculum.  If students leave school less curious than when they started, we have failed them.
  • Compliance does not foster innovation.  In fact demanding conformity does quite the opposite. In a world where new challenges constantly arise, students must be taught to think critically about what they are facing.  They must learn to collaborate with others from around the world to develop solutions for problems.  Even more importantly, our students must learn how to ask the right questions - questions that will challenge old systems and inspire growth.
Worli fishing village - with the Sealink and new skyscrapers being built in the background.  Here the traditional way of life is under threat - can the people adapt to change?
Learning and growing
  • If we want innovative students we will need innovative educators.  Teachers want to be innovative but instead of connecting and learning from others around the world .... they spend their time in staff meetings that often seem irrelevant to the heart of teaching.  They are constantly told that if they want to be innovative they are going to have to find time to do it. As leaders, if we ask teachers to use their own time to do anything, what we're  really telling them is: it's not important.  We must make time for our teachers to learn and grow.
  • Leaders of the most innovative organisations in the world know there is no end to growth and learning.  Schools, more than any other organisation, need to embrace a commitment to continuous learning.
So as I was thinking about my original question and framing it in the light of the above main headings, I'm considering this:  as a tech director am I encouraging the use of technology to do new things in new ways, or simply letting teachers digitize what they are already doing?  Do we still have 20th century learning (sadly the conclusion that I came to was yes we do) and in that case should the role of a tech director be redundant?  Does our current focus on standards get in the way of inquiry and curiosity (again, yes it does seem to), and how can I encourage the use of technology to have students reach out more to experts in the global community?  How can we use technology to help students ask and find the answers to deeper questions than just those demanded by standards (most of which could be Googled)?  How do we find time for our teachers to "play" and so learn in the same way that we encourage our young students to do?  Does having the word "tech" in the job description limit me too much?

By the way the photos that I've included in this post are from my walk today around the Worli Fishing Village and South Mumbai where I was contemplating change.  A lot of the images show the traditional life in the foreground, and change that is threatening this life in the background.  

Saturday, September 23, 2017

Resolving problems: when to paraphrase and when to question

As I'm coaching teachers at school, I spend most of my time in planning and reflecting conversations, however sometimes it's clear than although I start with thinking that a teacher wants to plan or reflect on something, it can often be that during the conversation something happens that lets me know that the conversation is not really about planning or reflecting, but instead the coachee has an issue that he or she is stuck with and that planning and reflecting are not the best ways to address this.  That's the time that a Cognitive Coach will need to switch to a problem resolving conversation.

I remember at a previous school I had a number of conversations with a member of the administration where I also felt I was stuck in a problem - the biggest problem that I faced there was knowing that the school had not bought the required number of licences for the number of computers a particular piece of software was installed on.  This went totally against my principles and deeply affected my sense of integrity.  However whenever I would raise concerns about this or anything else, I was told that I was a "glass half empty" person and that I needed to focus instead on what was going well, not what was going badly. I remember feeling an enormous sense of frustration after these conversations, above all else the feeling that I was not being heard and that my concerns were not validated.  Usually I came away from them feeling worse than before.  Now that I've trained in Cognitive Coaching the reason is very clear to me: what I said was never acknowledge (which is what we call the existing state and is done using a paraphrase), what I felt was never acknowledged (instead I was told I should not feel it), and I could see no pathway forward (which could have been achieved by questioning me about what the desired state would be and what resources I might have to achieve this).

For our Cognitive Coaching bookclub, this week we are focusing on the problem resolving map.  The problem resolving map is really powerful as it can actually trigger physical and emotional changes in the brain that open you up to optimism, resourcefulness and creative energy, even when you are stuck and uncertain of what to do and feel trapped in a situation without alternatives.  The problem resolving conversation is made up of 2 parts:  pacing and leading.  A coach will pace to honour the existing state and to create awareness of a possible desired state.  Pacing simply lets the coachee know that there is no judgement on whatever he or she is experiencing.  In the previous conversations that I just mentioned, I always felt that my feelings were being denied or judged, and this led to me feeling even more stuck than I was before.  As it says in the Cognitive Coaching book, "by denying the speaker's feelings, it is more likely that the feelings stay unchanged".  Pacing reflects what is, and then makes visible what is possible.  Leading starts when the coachee has signed off on the desired state.  While pacing is all paraphrasing, during the lead the coach will mostly be asking questions.

One of the most important sentences I read in this chapter was as follows:
[We need to] set aside our desire to be consultants rather than coaches, not to be experts and fixers.  Instead the coach enters the world of the coachee with humility, empathy and compassion.
The pace and the lead belong together.  Art Costa and Bob Garmston write that leading without pacing is ineffective because most people can describe what they don't like, but often cannot describe what they want - the coach coming up with a possible goal statement helps the person being coached to see the problem differently.   The other thing that is really important about the pace is that it is not about coming up with a goal that involves doing something, but instead is about being, having or feeling.  As Art and Bob write, a goal is always about a destination, not a journey or what you have to do to get there.  And for many of us the destination can be summed up in 3 main ways:  it's about identify, connectedness or potency.    In the earlier example I gave, what it really amounted to was identity - being asked to do something that I was uncomfortable with was a threat to my sense of integrity.  Looking back now, the reason that the conversations I had at the time were unproductive was largely down to the fact that there was no pace.  The pace works directly on the emotions and (I love this phrase) "restores or refreshes the chemistry of hopefulness" so that the emotions of the coachee are validated without increasing the chemistry of defeat or frustration.

So once the pace and the goal statement are signed off, the coach proceeds to the lead.  Here the coach needs to think which state of mind needs to be awakened to deal with the wicked problem.  If questions around that state of mind don't appear to be productive then the coach can simply try asking questions around another state of mind.  It's also during the lead that you can deal with 3rd party problems.  These are ones where the problem does not belong to the coachee but to someone else. When this happens the coach needs to refocus on the coachee as you can see in the following set of questions:
  • What behaviours do you want from the person/group?  (focus completely on others)
  • What knowledge, skills or attitudes will they need to perform those behaviours?
  • What might you do to help them develop these resources?
  • What internal resources do you need in order to do that?  (focus back on the coachee)
The aim of a problem resolving conversation is not to solve someone else's problems, so there may be no real conclusive ending to the conversation.  Often a coach may pose a question for the coachee to think about at the end of the conversation.  In this way it's clear to see the distinction between coaching and consulting.  With consulting, the goal is to solve problems and the conversation ends when the coach has come up with an action plan.  With coaching, the goal is to support the internal resources and to restore states of mind of the coachee - so the conversation does not have to come to a conclusion in order to be of value.  For a coach this may be difficult as he or she needs to give up the need for closure or to know the end of the story.  

However there is a benefit to the coach as well as to the coachee.  In recognizing the 5 states of mind in others, the coach also comes to recognize these states in him/herself.  For example, I have come to see through coaching others that my lowest resource is the state of mind flexibility.  Now I'm much more aware of this and consciously push myself to see things from another's point of view.  So maybe I am a glass half empty person, or maybe with the right coaching I can be a glass half full person, or maybe the glass is intended not to be full for some reason or other.  What I am sure of, however, is that digging deep into coaching not only helps others, it also helps me to think more kindly about others (as flexibility increases) and so it helps me to become a better person too.  What an amazing win-win!

Photo Credit: Let Ideas Compete Flickr via Compfight cc