Inquiry, PYP

Math + Exhibition = Opportunity for Inquiry!


There is a great opportunity for students to showcase their learning in math through the Exhibition.  For some classes during this time, “math class” is often a welcome relief in all the busy scheduling of Exhibition.  Many school keep a constant math period and continue to work through their curriculum while also working on math related to the Exhibition.

Three sources of internet-found brilliance are definitely worth taking a look at if you are interested in seeing how an inquiry approach can be taken to the integration of math in the Exhibition.

Authentic Inquiry Maths is a blog by Bruce Ferrington. He is interested in making “the kids do the thinking”. A teacher in Australia, Bruce’s blog has a number of posts related to the Exhibition that show how students have integrated their mathematical knowledge with their inquiry topic.  He has some great examples of interactive graphs, using balance scales for participants to voice their opinion, and graphing data pictorially.  The posts related to Exhibition are great but his whole blog is worth taking a look at for some great ideas about math inquiries.

Rebekah Madrid is a teacher at Yokohama International School. She has written an excellent, detailed post supported by real-life examples of the work of her students on the topic of Infographics – making numbers sing.  In this post she details how she has her kids make infographics using found household objects to convey their data points. The post is well documented and supported by loads of additional resources should you wish to recreate her lessons with your own students.

Would You Rather? is a great math blog that asks students to choose their own path and justify it using math.  Written by John Stevens, WYR? poses questions such as:

Screen Shot 2015-02-23 at 19.28.07

This blog would be a great place to get inspiration for kids to write their own WYR questions based on the knowledge they acquire throughout the Exhibition process.

How do you showcase Math in the PYP Exhibition?


Concept-Question Cards

UPDATED: The cards have been updated here to include related concepts! 


concept cards 1

Last year, I wrote a post about Questioning Conceptually.  The basic premise of this post was a look at how teachers and students could use the PYP concepts to deepen their inquiries through the generation of a wider range of questions. The post goes on to help narrow the focus of the inquiry into an area of interest that one is really passionate about, that you care about, and that is worthwhile spending time on.

I followed this up with another post about the same topic: More Conceptual Questions.

Both of these posts make reference to a set of Concept-Question Cards.  These cards have one side with a PYP concept, guiding question, and explanation and another side with sample questions from different subject areas.

I have had sets of these cards in my ‘toolbox’ for some time now.  They are great.

Screen Shot 2014-02-19 at 2.39.35 PM Screen Shot 2014-02-19 at 2.40.08 PM Screen Shot 2014-02-19 at 2.40.31 PM Screen Shot 2014-02-19 at 2.40.48 PM

To download a PDF set of cards, click here.

Let me know what you use them for!

21st Century

The Playbook in Action

The Playbook

Over the last two days, I have introduced the Playbook to my class.  I started on Wednesday with a group of seven or so kids who were ready to move on.  They took to it like bees to honey! On Thursday, I had a couple of kids from that initial group share it with the rest of the class.

Like most things in my class, there was a large spectrum of engagement and interest.  Some saw it as a chore (“Do we have to do the whole thing?”), some were inspired (“Can I start now? Do I have to ask you to do the next play?), others wanted to share the love (“Can I take one home for my dad? I know he would want to do it with me!”).

My initial reaction:

  • they like that it is different and that their responses are going to be unique to them
  • kids do a way better job of inspiring kids than I can!
  • when left to their own devices, it is quite inspiring to see what they will create
  • this is what school should be like – a journey of self in which learning is intrinsically built in

The Playbook ‘plays’ are split into five categories.  As they progress through the book, your kids will be:

Five Categories of Action


The skills they will be ‘forced’ to use will stretch their thinking and challenge them intellectually, socially, creatively and emotionally.  They will make connections across different subject areas and in different parts of their lives inside and outside of school, humanly and digitally.

Here are some examples from the first play in the book:

What if....?


Manifesto 1


Manifesto 2


These manifestos are popping up all over the school.  One of my kids, without prompting, wrote his manifesto and posted it at the place he takes after-school vocal lessons. Inspired by him, I have challenged others to post an additional copy of their manifesto somewhere outside of the school in the spirit of “putting themselves out there”.

It’s only in it’s infancy, yet the Playbook is moving up the ranks to one of my favorite things.

Thanks FutureProject!

Creativity, Innovation

Spark an Idea, Follow an Interest, Cultivate a Passion

There was an article on Fast Co. recently that caught my eye. The title of the article? Do Like Steve Jobs Did: Don’t Follow Your Passion.

The article references Job’s now famous Stanford commencement speech and then goes on to detail how he lived and how his passion was not always technology. There was a lot of commentary following this article, including comments from the author of the book from which this article excerpt was taken, Cal Newport.

Newport puts his own twist on the “Passion Hypothesis” : The key to occupational happiness is to first figure out what you’re passionate about and then find a job that matches this passion. His take on this:

“Don’t follow your passion, let passion follow you in your quest to do something valuable.” -Cal Newport

One reader suggested the catchphrase “following an interest—finding a passion”. Cal suggested a slight semantic change to “following an interest—cultivating a passion”.

Passion is what drives me to teach, to share about what I learn though teaching, to find out more and better ways to do what I love to do. The more I pursue my interest in teaching, learning and education, the more passionate I become. There are things that could make one despondent with regard to education but for me, I am “intoxicated by the possibility” (thanks, Hugh!).


So how to we help our kids “follow an interest, cultivate a passion”?

One way might be to implement “Spark Files”. Coined by author, Stephen Johnson, the Spark File is a process/tool that he uses to collect “half baked ideas” with no regard to organization, hierarchy or taxonomy. For eight years, Johnson has collected ideas, notes, articles, thoughts and documented these in what he calls his “Spark File”.

Once a month, he goes through the file in its entirety. He looks for patterns, connections, revisits old ideas and looks to connect with newer ideas.

As I read this, I thought of my Instapaper account = the quick, simple, “read later” button that I hit on a regular basis whilst rolling through my Twitter feed or perusing the internet. I am always intrigued by what happens when I review this file. This post is a culmination of two “read later” posts. Some things get deleted, some get me thinking of past experiences, some get to feature in blog posts having gotten me thinking.

The same could work for our kids, using free Instapaper accounts or using the web-clipper tool in Evernote. As I look toward the end of the year, where my kids will be undertaking “The Passion Project” as their fifth grade PYP Exhibition unit, this could be another way for them to collect ideas to inspire them.

For more ideas, take a look at this less than five minute animation of Johnson’s TED talk on “Where Good Ideas Come From”

PYP, Teaching

Teaching Without A Plan….What??

Earlier this week, I read an article by Eric Barker: 6 Rules That Should Be Guiding Your Career. Barker shares “the rules” as developed by Daniel Pink.

The Rules:

  1. There is no plan
  2. Think strengths, not weaknesses
  3. It’s not about you
  4. Persistance trumps talent
  5. Make excellent mistakes
  6. Leave an imprint

I know it says rules for career development, but what about classroom development? The first ‘rule’ might have some teachers breaking out in a sweat.  No plan?  What about the Planner for each unit of inquiry?

Rule One: There is no plan

Pink shares the number one thing people regretted on their death bed:

I wish I’d had the courage to live a life true to myself, not the life others expected of me

It is true that as teachers we need to have a plan. But there is nothing in the PYP that says that plan has to be a rigid one or doesn’t have to take into account all those “x-factors” that come into play when you are dealing with the human dynamic of inquisitve little people each day. When I first began teaching in a PYP school I quickly became confused by the use of a Planner. How could it be child-centered inquiry if teachers were planning out every minute of the six week unit? We began to use Design Thinking to plan ‘backwards’ – starting with the end in the mind.  As a group, we would think about the unit’s central idea – the big idea that was globally transferable, timeless, interesting, challenging and engaging.  With this idea in mind, we would then think conceptually about the lines of inquiry which we would use to begin to open this idea up to our children.  We would pick three concepts and create lines of inquiry based on a different concept. We would then move on to create an assessment task that would help students showcase their understanding of the central idea.

But what happened in between beginning the unit and the assessment?

In 2003, I was teaching in Bonn, Germany. We had an Inquiry Workshop at our school. During that time we examined loads of inquiry cycles and ways of ‘doing’ inquiry.  We then created our own.  The cycle I made has since been modified to include reference to ACTION – a part of the PYP that sometimes gets a little left out. I use this cycle with my class as a group, to show them collectively where we are in the life of the unit.  I have also used it individually and allowed students to guide themselves back and forth through the cycle over the course of the unit.

Inquiry Cycle (PDF= Click to download)

This is different to teaching without a plan, but it is a way to free the children up to inquire where they are drawn to.  It also frees the teacher up to observe, to help when needed, to question in order to move the inquiry forward. Tasha Cowdy, kindergarten teacher at Yokohama International School has a way of doing just this with her students.  Whilst some (myself) would consider her an expert, she would most likely disagree.  Her recent post on the shared inquiry blog, Inquire Within, paints a detailed story on what it can look like to create a classroom where student-led inquiry really does reign supreme and the challenges associated with balancing open, guided, or structured inquiry.

A more simple plan might be to tell students that based on the central idea, you are interested in learning more from each of them about:

  • What do you Know?
  • What do you Understand?
  • What can you Do?
  • What will you Say?

And then supporting them on their journey of learning.  The more we expose children to this line of thinking, rather than pushing them through the cookie cutter shapes of lessons we have planned for them, the more they will be able to really feel that school is a place for inquiry, not compliance.

How can you be more relaxed in your approach to following your plans?

How can you move your role as teacher from ‘sage on the stage’ to ‘guide on the side’?

Innovation, Inspiration, Internet

To Tweet or Not To Tweet – It is Now A Conscious Decision


Gone are the days when it was “cool” to not know what Twitter was.  Or any form of Web 2.0 technology that enables you to connect to the bigger picture.  I took a while to become a fan of Twitter and now, I can’t imagine my life as an Educator without it.

But first, came the change in my mindset or my world view and then came for the need for a tool to support that change and that tool happened to be Twitter.

That is worth me repeating.  Seriously.

First came the change, then came the need for a tool. 

I really don’t mind if you use Twitter or not.  What I do think is important, is that you challenge yourself to maintain a connection with other people wanting make the same kind of ruckus you are making – or wanting to make.  Over the last six months or so, I have become more active on Twitter and would site this tool as being in the top ranking of the Professional Development that I have gotten as a teacher.

Why? Because I am connecting with other Educators and we are not bound by geography.  We are able to quickly share in 140 characters or less, what is going on in our classrooms and to connect.

Just today, in the last half hour or so, I have:

  • Been inspired by the amazing work happening at my former school, Yokohama International, in a post titled Tech Pilots Taking Off.  It really is inspiring to not only read about a phenomenal program, but I am both blown away and grateful for the thorough documentation of the implementation and goals for this program.  The example set here of initiative, forward-thinking, collaboration and leadership is truly outstanding.  What’s more, it is not being hidden but put out there for others to use, copy, emulate, remix and build upon.  Did I mention I am inspired?
  • Been taken through a very thorough analysis of what it means for a project to be authentic.  “What Does It Take For A Project To Be Authentic?” gives great understanding about the use of the word authentic as it applies to Project Based Learning (PBL) or just learning in general.  It cleared up a few wonderings I had and has given me a new lens through which I can take a look at the assessment of and for learning that occurs in my classroom.
  • Spoken often of the amazing work in inquiry-based learning that I experienced first-hand in the classroom of Tasha Cowdy.  I was so excited to see Tasha post about the Morning Meeting routine she establishes with her kindergarten class.  It is phenomenal and so empowering and a must-see for anyone interested in inquiry teaching and learning.
  • Been reminded of a tool I was introduced to a a couple of weeks ago called Thinglink but have not explored fully.  Turns out I can now benefit from other’s explorations via the post 26+ Ways to Use ThingLink in the Classroom.
  • Been introduced to a new app called Kids Journal which I have not downloaded (yet!) but could be a fun tool for easily documenting summer activities such as the Summer Bucket List challenge we just set our fifth graders as a ‘prewriting’, information gathering exercise for their first sixth grade writing assignment in the new school year.

And this is just the surface!  I use Instapaper as my ‘read later’ service.  When on Twitter or browsing the internet, one click of ‘Read Later’ and all these goodies get stored on my Instapaper account – kind of like my own awesome newspaper of awesomeness.

I keep my Twitter account mostly for following educators but also writers, artists, musicians, curators, innovators, movers and shakers.  I want to know what is new and exciting in education but also around education – we are not in isolation.

If tweeting is not for you, fine.  But I encourage you to find some way of connecting yourself to big ideas in a way that works.  You will thank yourself and your parents and students will thank you even more.

Creativity, Inspiration, PYP

School…with a helping of learning on the side


Learning “by accident”. Sounds weird but that is what we have seen going on at school for the last five weeks as we have been headfirst, up to our knees in Exhibition – the culminating event for students in the IB PYP program.

Every day it seems, we are seeing learning EVERYWHERE. And it’s not just us (the two fifth grade teachers who are biased toward the genius our kids possess). It’s the kids’ mentors, other members of faculty who are working with our kids, people from our school community, Boise locals and people scattered all over the world who are constantly saying things like, “You are really only a fifth grader?“, “I can’t believe you are only in fifth grade!” and “You are amazing!”

In terms of ‘things we never planned but learning has happened anyway’ here is a short list of things we have observed that our kids are doing:

  • organizing themselves digitally
  • writing sophisticated letters/emails requesting help
  • following up requests for help with equally sophisticated thank you emails/letters
  • organzing meetings and interviews
  • setting up job shadow days
  • organizing their own field trips
  • taking their own photographs to visually represent their learning
  • taking the initiative
  • making and keeping appointments
  • supporting each other with their inquiries
  • planning a live TED-style presentation to showcase their utter brilliance
  • making, creating and doing their ‘art’, their passion

They are passionate, engaged, independent, committed, inquiring learners – and did I mention they are fifth graders?

But the learning doesn’t stop with them. My teaching partner and I are exhausted. And we couldn’t be having a better time! The school day – the school week! – fly by in a flurry of activity. We meet in the morning, fueled by coffee and a collective, unspoken commitment to facilitating this process in order to best support our kids. We ask each other:

  • what do they need?
  • what else can we ‘put out there’?
  • who could support them?
  • is there any coffee? (this one VERY important)

And then we get to work.

Our 28 kids and us on this journey that none of us have been on before, to a place none of us really have ever seen and none of are sure what it looks like. But we have each others backs and we want everyone to succeed.

I have been thinking a lot about the type of planning that is needed for a true inquiry based program to flourish. In a recent Twitter based #pypchat (that is on, my time, at 4am so not sure how engaged I would be!) the topic of discussion turned to how much we plan ahead and how much unfolds naturally along the way. There is an excellent article summarizing the thoughts on this topic. The chat participants were varied in their approaches but seemed united in their belief that inquiry is best supported by teachers who are prepared to forgo their plans in order to be ready to support and facilitate their students inquisitive natures and passionate wonderings.

I know, first hand, that this is hard work!

It is also so inspiring, so rewarding and so much fun. And what I signed up for when I decided to become a teacher.  In addition,  as I reviewed this post, it made me reflect back on my reading of Tony Wagner’s new book “Creating Innovators: The Making of Young People Who Will Change the World”. Instead of hoping kids will develop the type of skills listed above as an ‘aside’ to their school career, Tony believes we need to explicitly look for ways to equip students with skills needed for what he describes as “an increasingly flat world”.  He calls these the Seven Survival Skills:

  1. Critical thinking and problem solving
  2. Collaboration across networks and leading by influence
  3. Agility and adaptability
  4. Initiative and entrepreneurship
  5. Accessing and analyzing information
  6. Effective oral and written communication
  7. Curiosity and imagination

He published this list of skills in his previous book, The Global Achievement Gap but has since conversed with people across different fields and discovered that there are other skills that needed to be added to this list of ‘essentials’.  These include:
  • perseverance
  • a willingness to experiment
  • taking calculated risks
  • tolerating failure
  • a capacity for “design thinking”
The last skill, ‘design thinking’, is a concept employed at IDEO . (If you don’t know a lot about this company, take a look here or go straight to this great Fast Company Design piece on what schools can learn from IDEO, Google and Pixar – brilliant!).  Wagner shares IDEO’s design thinking concept as an example of a way of viewing the world that is fundamental to any process of innovation. (Wagner, pp13).  The CEO of IDEO, Tim Brown, goes on to describe five characteristics of ‘design thinkers’:
  • empathetic – looking at the world from multiple perspectives and putting others first
  • integrative thinkers – being able to see all aspects of a problem and possible breakthrough solutions
  • optimistic – believing that no matter how challenging a problem, a solution can be found
  • experimental – being willing to use trial and error to explore possible solutions in creative ways
  • collaborative – this above all!

Wagner goes on to list further studies, more conversations and addition research that provide similar lists of requirements and criteria for innovative thinkers, ultimately summarizing them as follows:

    • curiosity – being in the habit of asking good questions with a desire to understand more deeply
    • collaboration – listening to and learning from others who have perspectives and expertise different to your own
    • associative or integrative thinking
    • a bias toward action and experimentation
What he then wrote should have us all leaping for joy:

As an educator and a parent, what I find most significant in this list is that they represent a set of skills and habits of mind that can be nurtured, taught and mentored!

What I have seen first-hand over the last five weeks is proof-positive of that. And it is a beautiful thing.
Design, Innovation, Math

The Best Way To Teach Math

I read an article that expressed extreme dislike (understatement) for the Everyday Math curriculum.  This is the same curriculum we currently use in school and was the same I used in my last school, as well as another of the schools I have taught in.

Do I love it?  No. Do I loathe it?  No.  I actually find it to be quite adequate as a basis for developing math skills within a class of students IF you make a few adjustments and additions to support student learning.  Having taught in one school where your progress through the math book was monitored on a day by day basis with repercussions for not being in line with ‘state expectations’, I know that words like adjustments and additions are challenging if not impossible to entertain.  If you are fortunate enough to work in a school that allows you the freedom to teach and facilitate learning amongst your students AND uses the Everyday Math curriculum, here are some points I have picked up along the way…

  • If you teach in an IB school, you are going to be asked to look for ways to authentically integrate data handling, measurement and geometry into your units of inquiry.  This is difficult but not impossible to do if the basis of your math program is EDM.  I haven’t done it yet, but I would love to sit down and look for the connections between these areas of math and our units and pull them into their own ‘math unit’.
  • Again, for IB school teachers, you are not expected to integrate number, pattern and function into your units of inquiry.  Think of these components of math as the ‘alphabet’ – addition, subtraction, multiplication, division, fractions, decimals, percentages…these all should be taught in their own right and EDM provides multiple ways of sharing the ‘why’ behind these processes.
  • Use your discretion!  As a teacher, you can decide how you present the content to your students.  I find the EDM methods for some things quite confusing.  I also find some of them really help me explain the ‘why’ to kids who then really get it.  If I have kids who are already solid in a method that works for them, great!  Just like we make kids eat a balanced diet, I ask my kids to at least follow along but the freedom is theirs to use whichever method works for them -mostly it is the one they are comfortable with but sometimes they will change it up and go with something new that makes even more sense to them.
  • Play the games – or at least some of them.  They are great for engaging discussion and when disagreements arise, perfect grounds for ‘forcing’ kids to demonstrate and explain their understanding of a concept.
  • Don’t start at the very beginning of each lesson.  It is just a guide, a plan.  It doesn’t say that if you don’t follow it precisely, the world will end!  There is actually a lot of good problem solving and analytical thought required in much of the enrichment and study link pages.  Flip things around and have students work collaboratively on these in class when they are supported by yourself and other students and can engage in discussion.
  • Use the Khan Academy!  It is brilliant.  I can’t figure out why more people don’t use it.  I have had a few parents say they don’t like it.  That they don’t want their child sitting in front of a computer and “can’t they just have a worksheet for once?”.  Seriously?  Who doesn’t want quality online support by way of the videos, hints that show the ‘how’ of solving a problem, instant feedback on their work and some really fun badges!  If you assign Khan videos/exercises for homework, your students are prepared for the more analytical problem solving challenges at school that ask them to apply their understanding.    We are fortunate, here in Boise, to have Sal Khan coming to town to share his thoughts on the changing face of education.  Educators were asked to share their experiences with the Khan Academy – here is an excerpt from my letter:

I never liked math as a kid.  As a teacher, I love it.  I love the mystery of it, the methods and the madness!  I am really grateful to Sal and his Academy for helping me develop a greater love for math.  I love that my kids get the chance to challenge themselves and review their work on a regular basis.  I love that the videos really explain the concepts in a clear way.  I love that I have more time for doing and less need for telling.  I love that I can see my kids whiz off into the math matrix with a huge interest and passion for developing their math skills.  It is “cool” to love math in my classroom and I have had kids log on each week, on average, for about 2 and half to 3 hours between Monday and Thursday nights.  The “requirement” is 15 minutes a night.

I think my own classroom math program could do with some work.  I would like to be a little more dedicated to integrating with our units in a more meaningful way and relying less on the unit tests at the end of each unit of work in the EDM book.  I would love there to be a few more hours in the day so we could play more of the games together.  Perhaps these could also become homework tasks?  What I would also like to do is to focus more time and importance on remembering to talk math with kids.  This article reminded me that more important than which book or website your ideas come from, make sure you are engaging kids in math related discussions – even (or especially) when it is not ‘math’ time.  A great way to do this with kids is to tap into the booming market of infographics.  They are everywhere and are a perfect way to bring math into the discussion.  Take a look at these as examples:

I see two uses for these – discussion and inspiration for creation.  I can already hear a few cries of ‘but we don’t have the technology to do that!”.  Who says you need technology to make an infographic? Ultimately, it is a graphic that shares information (we used to call those ‘charts’ or ‘diagrams’ or even ‘graphs’ when I was at school).  There are people in the wings, ready to launch infographic capabilities to the masses: here are ten sites you could use, a great resource called, or five kinds of infographics and free tools to make them.  (I can see another post coming soon after I try some of these out!).

Until then, take a leaf out of the book of this Portugese design firm, who created the following ‘low tech’ infographics that are awesome and totally do-able in any classroom and would again, encourage and stimulate mathematical conversations both in their construction and sharing:

What works for you in your math classroom?  Or as a parent, what works for you at home?

I know people may have extreme feelings towards Everyday Math, and if I were given no leeway in how to implement in my classroom, if I were not allowed to supplement where necessary (in my professional opinion) and to skip parts that seem somewhat pointless, then I might have some of those feelings too. Words like accountability and consistency are just the words that got Everyday Math its stronghold in many schools.  In order to have a prescribed set of units of work, complete with tests that even a muppet could pick up and spew forth over the the classroom, schools needed to subscribe to ‘something’ – and Everyday Math has become that ‘something’ for many schools.   What is missing – and can’t even be found by substituting the Khan Academy (gasp!) – is good math teaching.  I am not sure which comes first but if teachers were more confident in teaching math, pulling from a variety of resources to create a balanced math diet, student performance in math would rise, parents anxiety about their child’s level of achievement would dissipate  and administrators would breathe, have confidence in their faculty and let them do their job.

Am I going to throw my hands up in the air and rage against the Everyday Math machine?  At this stage no.  Am I going to blindly plod through each page in the text (do I even have to answer that one?). Ultimately, I trust that educators and administrators and parents can work together for the greater good – the kids.