Blog Posts

Examining the Water: Part 2 of Diving Into Inquiry

With the book Dive Into Inquiry in hand I was very excited to embark on the journey reading this book. As I shared in my previous post in this series linked here, I had already connected with the author on Twitter, had a conversation with a colleague about the book, and so I was very anxious to begin. Before I get into the content of the book there’s a couple things I want to share that immediately got me excited. First is the bi-line to the book: “Amplify Learning and Empower Student Voice”. I loved how this was so student centered. A lot of books I have read or have come across in education talk about “improving my teaching” or how to “better deliver content” etc… I immediately connected with the focus on the student experience and so I had a feeling that this book would deliver.

And the second thing that jumped out at me was the length. It is a short book. Most academic books or books about teaching tend to be at least 300 or so pages and on up to 600 pages at times. This book was clocking in at a cool 120 pages total. This made the topic feel approachable and broke down any walls I may have had about incorporating inquiry into my classroom.

So now to the visual layout of the book. The main thing that I want to focus on, that goes along with the short length of the book, is how approachable everything is. There are simple to digest phrases about inquiry that are set in a much larger and different font spread throughout the paragraphs. These are marked with the hashtag #DiveintoInquiry. These are little nuggets that can stand on their own as important pieces of learning to take into your classroom. Also there are easy to read bolded sections in each chapter along with a number of bulleted points that the author wanted to emphasize such as a series of prompts to use during student discussions. Finally there were a number of illustrations and QR codes to resources that are great summaries of important points and additional resources.

Now what about the content? All of those things I mentioned about length and layout are moot if the content isn’t good. Well this is where I think Trevor McKenzie really brings it all together. In a very sequential way he lays out the different types of student inquiry from structured to free inquiry with examples of what each would look like in a variety of high school subject areas. One thing that I was left wanting is some examples added in for the middle and primary levels.

After explaining the different types of inquiry, the author lays out the seven steps in the inquiry process: the four pillars of inquiry, creating an essential question, creating your free inquiry proposal, exploration and research collecting learning evidence, creating an authentic piece, and a public display of understanding. For those that may be very early in the process of getting to know what authentic inquiry will look like and how it can be designed, I think this is a very simple to follow road map to help in the first introduction into this type of learning. I included an illustration from the book so you can get a better idea.

What this all does is keep the reader grounded in some fundamental and easy to follow directions on how to get started. The language of the book is clear and simple, yet guided by forward looking educational pedagogy.

The first part of the inquiry process is the “Four Pillars of Inquiry”. These are the different ways that students can connect with the inquiry process either through exploring a passion, aiming for a goal, delving into curiosities, or taking on a new challenge. Each of these pillars are complimented with some helpful insights about how you could introduce these into your classroom with concrete learning tasks for students to complete during the process. These are definitely sections that have the potential to be built out in more detail as obviously the entire learning progression of all four pillars of inquiry cannot be communicated in a 120 page book, but there is enough there to at least get your creative teaching juices flowing to begin the design process of creating your own inquiry curriculum.

Moving into the second half of the book the author starts to dig into the meat of inquiry based learning, with particular emphasis on essential questions, the proposal, and the exploration and research phases. Again what I liked so much about how the book is written is that author provides very easy to follow and applicable tools to use immediately in the classroom. I have read a lot of things on generating essential questions, completed workshops on this, done collaborative work with colleagues, and I found the layout by Trevor McKenzie to be the best approach I have yet to come across. By categorizing different types of essential questions, along with question stems for students to use to begin drafting EQs was an effective way to structure this often challenging part of the inquiry process.

This all leads up to the concluding section of the book in which the author effectively bookends the knowledge he had shared with some helpful advice and suggestions. Now I will admit that in my excitement to start the process of incorporating inquiry into my classroom I missed a couple crucial elements in this section that I will layout in my next blog post. But most importantly I can read back on this and chuckle at the last piece of advice he leaves us with, “Find comfort in the mess of uncertainty”.

I do believe that there is a fine line in the commitment to being an agent of change in our classrooms and schools. We don’t want to just blow out the entire structure of what we do and run the risk of creating confusion for the students in which they are not clear about where they are going. But at the same time we don’t want to continue to keep regurgitating the same learning experiences year after year for our students when we know that they are yearning for so much more. So what do we do about this tension? Well as an educational intrapreneur I think the answer is to stay grounded in the fundamentals of design thinking. By constantly empathizing with our students with an honest desire to create engaging learning experiences for them, along with a humble commitment to iterate, revise, and improve, we can minimize the negative impacts of being an innovative risk taker. Top this all off with a focus on developing relationships with our students and we have the opportunity to be co-creators along with our students on this wonderful journey of learning.

And that is really the main point I want to make here. Often we think of innovation and creative thinking as being this gambling risk taker and taking chances. But one thing I have learned is that quite the opposite is true. Being an agent of change within your organization actually involves carefully curating change. There is a lot of legwork in research, reading, considering, evaluating, talking, sharing, and analyzing before making a change. When working within an organizational structure I feel we need to be even more sensitive to this as we are often using other people’s resources, money, time, and experience to create the change we are looking to make. And that is what I like so much about Trevor McKenzie’s book. I think it is an easy to follow, clearly written, and well grounded book on inquiry. One that I would encourage any educator who is looking to add student voice and choice into their classroom to familiarize themselves with.

I hope you join in my next post in this series in which I dig into my experience with inquiry based learning in my music technology class.

Arriving at the Pool: Part 1 of Diving Into Inquiry

Towards the end of the school last year I posted on Twitter asking for any requests about good summer reads with a particular focus on project design, inquiry, or student agency. One suggestion in particular stood out to me, a book titled Dive Into Inquiry by Trevor McKenzie. I asked a colleague friend of mine who I often discuss new ideas with about the book and he said he hadn’t read it but he’s heard good things. He also suggested I follow Trevor on Twitter as he is a good follow and posts a lot of interesting things about education, inquiry, and teaching in general. So I asked my principle for the $20 for the book, got approved, and put in my order.

In the meantime I came across this graphic on Trevor’s twitter about inquiry:

I engaged with some different educators in a few conversations on Twitter about the different levels of inquiry, when they are best used, and the scaffolding that goes between the different levels. So with some early insights into the concepts I eagerly awaited my new book.

So there’s a couple things I want to focus on that I think are important in the context of intrapreneurial thinking before I get into the content of the book. First I got the idea for the book from a Twitter request. While a lot of people have a lot of preconceived ideas about what Twitter is and what goes on there. I do think it is important to point out that there is a rich community of educators on there who are very supportive. I have found that I can pose questions, make requests, or throw out an idea and get many insightful and well thought out responses. So one strategy to increasing your capacity within your organization is to get active on Twitter as a platform and engage with other educators.

Secondly, I shared with a colleague of mine about this new book I was looking to get. First it is important to develop relationships within your organization with people who have similar interests and are open to new ideas. This way you have someone to run things by, to get input from, and to engage in conversation with concerning different thing you are trying. There is a lot of value in avoiding trying new things in a vacuum. Don’t have anyone that you engage with on this level? Bring a book that you are reading with you to your next faculty meeting. Ask a couple people if they are familiar with it. Ask your principle or leadership person if you can announce in the meeting if anyone is familiar with this book or if anyone else would like to get a copy ordered and you can read it together. Anything to get the conversation started internally can be beneficial. You never know who those people are within your organization that have those similar interests until you put it out there.

And finally, after getting the book I reached out to the author on Twitter. I commented on some of their posts. I made my own posts mentioning that I ordered the book and I tagged them. I engaged in some conversations with others who had mentioned or tagged the author. Creators are very engaged on Twitter. They rely on their audience to build and maintain their presence so they are more than willing to engage with you many social platforms. Since reaching out on Twitter I have had many correspondences with Trevor either through direct messaging or via his posts and I have been able to build a relationship with him. He has kept me in the loop about professional development that he is leading in my area and has also connected me with other educators who are looking into similar topics.

So with all that said, before I had even gotten the book, I had already begun to engage with the topic, build my network, and start the process of creating new ideas and relationships that I can use to leverage my capacity as an educator and support student learning.

I look forward to sharing more in this multi part blog series on my journey with Dive Into Inquiry. I will cover the ideas and concepts in the book, how I prototyped using inquiry via my music technology class, some ideas about how I am looking to use inquiry in my math classroom, as well as how inquiry fits into some broader institutional initiates at my school.

Professional Development Versus Arrested Development

I participated in a Twitter chat the other night that focused on professional development in school. I have always found this idea of PD to be an interesting beast. When I first got into education I thought, wow this is great! My school is going to pay me to go learn something and then I will come back to school and share about it with all my colleagues and they will be amazed at all the new things I’ve learned and we can all advance our teaching hand and hand into a golden rainbow of the future.

What I soon realized though is that the true reality went something like this. My school would pay to fly me somewhere, I would sit in a large conference room where a keynote speaker would tell me how bad standardized testing is and how we all need to change education for the future, and then I’d meet up at the bar with some teachers I just met to talk trash about our respective schools. I’d then return home, tell my peers how great it was, look over a bunch of random notes I made on my iPad, not really remember all that I crammed in my head in three days, and go back to teaching life as normal.

It didn’t really click for me until a few years into my teaching when I went to a Visible Learning conference in which I was introduced to the idea of “collective teacher efficacy” that I realized what the problem here was. And the irony was that I was attending this conference all by myself with over 1200 of my closest new friends. Now I don’t want this to be some pessimistic jaded rant about the failures of large scale “edu-corporate” PD, because these gatherings can be very useful and I have gained a lot of insight in attending some of these.

What I do want to propose is that there are cheaper, more readily accessible, and less time-consuming ways to have a positive impact on the learning our students experience in our classrooms. And its something I’d like to call the “dream and do” approach (we can also call this the D-n-D approach too if you’d like). In fact, it’s the bi-line I chose to put at the top of my blog I believe in it so much. What this entails is dreaming up big ideas and putting them into action in your classroom. I’d suggest using a design-thinking framework when doing this to help you towards successful implementation. To get started I’d really suggest the Design Thinking for Educators toolkit that you can download for free here put together by IDEO.

As part of this process, I think it would be helpful to have open and candid discussions with your peer teachers that you trust about some of your ideas and be open to their feedback and input on what you are looking to implement. I’d carefully reflect on what you are doing and share out to teachers you trust or even ask one of them to come in and observe you in their free time if it lines up. Document everything you do, be attentive to student feedback and how they react. Pay close attention to how you are impacting student learning and be open to pivoting if you see that something isn’t working. Be honest with the students that you are trying something new with the sole goal of making their learning experience better.

Consider jump-starting an account on Twitter and begin engaging and interacting with other educators (follow me at I’d be happy to chat!). I think you’d be amazed at the level of development that you can have in your teaching profession with this approach. And the amazing thing is it doesn’t even cost a dime! Before meetings share with other teachers what you are doing, or start a conversation with a teacher that you don’t often talk to and ask them if they are trying anything new. What this does is it helps you start to be part of a community of learners, just like we ask our students to be.

And then, now here’s the kicker, when professional development opportunities do come up during the course of the year, gather the people that you’ve been engaging with and bring your proposal to your leadership member/s. Tell them that you feel a team of three or four teachers should attend this conference because it would support insert teaching skill here. Now you can start moving towards authentic teacher efficacy. You can start to build a tribe of teachers looking to create shared learning networks around a common skill or need. From there the learning can spread and create a culture of learning and development unlike the individualized isolationist “development” of the past.

Is this a perfect model? No. Is this going to work for every teacher at every school? Of course not. But if you feel like you have been just going through the motions with your professional development proposals and starting to look at which conference is closest to your cousin’s town so you can go to a wine and food festival afterward, you might want to try this approach and begin to engage more deeply with your work and with your teaching tribe.

Mathematical Storytelling

I participated in a webinar this afternoon led by mathematics educator Sunil Singh titled “Using Math History and Storytelling to Invite Equity Into Our Classrooms”. Since I started in mathematics education some seven years ago I’ve thought a lot about how I could incorporate this idea into my teaching, but I have struggled to find a comfortable entry point. Yes, I’ve tried a few different things. For example, a couple years ago I took an old world map that our geography teacher was going to throw out and pasted on a bunch of pictures of historical figures from mathematics like Brahmagupta, Al-Khwarizmi, and Euclid with little notes below about their contributions to mathematical thinking. I hung this up outside my classroom along with some pictures of other important mathematicians around my classroom. Those have been good conversation starters for some curious students who happen to notice, and an opportunity for some storytelling around the human part of mathematics.

But what I have been looking for though was a way to connect this to the content that we are covering in the Algebra classroom. Mr. Singh shared the following progression on the impact of history and storytelling: storytelling -> humanization -> belonging -> curiosity. As a teacher who values curiosity, wonder, critical and creative thinking, this was an intriguing invitation to dig deeply into this ideas of storytelling. He also shared that in order to create vibrant classrooms we need to find an intersection of us (teacher), them (students) and math.

So after this webinar I set out to examine some resources he shared to see what I could uncover to bring into my classroom. One person Mr. Singh mentioned is Jonathan J. Crabtree who does lots of work around incorporating ancient Indian mathematics into the current times. In researching his materials I came across some interesting things that I am looking forward to implementing. Here is one resource I would like to point to: It’s a pretty long slide deck, but he walks you through some pretty basic yet revealing ideas behind operations and the integers. And what I am able to glean from this is that there is potentially a comfortable entry point for an element of storytelling when covering content.

The example that came to mind is when solving one- and two-step equations. Let’s take 2x-7=11 for example. When having to “undo” subtraction I find many students will try to “add a negative”, ie do “+ -7” to both sides and come up with 2x=4 and then x=2. Obviously, there is some carryover from their earlier math classes in which the idea of applying the rules of operations using negative numbers is getting jumbled up. I am thinking that this would be a great place to do a short lesson on Brahmagupta’s concept of negative and positive integers (see slides 71 and 72 from the above link from Crabtree). My instincts tell me that attaching a human storytelling element to the concept would have more impact than trying to repeat the abstract explanation that obviously didn’t work for that student before when the concept was first introduced at age 11 or 12.

In my Algebra class, we have just finished the first part of the text that covers linear equations so I may have to workshop this idea in more detail for next year. But what it has done is opened up my eyes to the potential power of storytelling and historical origins when teaching mathematical concepts. Looking forward to our unit on solving quadratic equations I will be building out a lesson I have done on completing the square in which I share how this was first developed by the Babylonians when calculating land divisions.

In this case, rather than just mention in passing that the idea of completing the square was first used many centuries ago, I would like to place that human experience at the center of the learning. My goal is to emphasize that the entire reason that we have this concept of completing the square was that humans found themselves up against a very real human problem that required a very real human solution. I’ll make a note to return to this with a blog post in the future when I arrive at that lesson.

I am very grateful for Sunil Singh to have started this discussion and offered his webinar. I am hopeful that more teachers of mathematics take his ideas to heart and are looking at their own ways of bringing this approach to teaching into their classroom.

It took me back to my own days when I was younger when my dad shared with me how the Greeks calculated the circumference of the earth. It was those ideas that got me so interested in mathematics in the first place. Why? I think because it tapped into my curiosity. My dad used storytelling to describe the human problem at hand and how there was a very real human element to solving this problem. This humanized the idea of pi, and the circumference of a circle. This made me feel a belonging to not only this mathematical concept, but history as well. And from there it tapped into my curiosity. How did they know the value of pi? How did we get a more accurate calculation of the circumference of the earth? How did we calculate the circumference of the moon? And I want to bring that joy into my classroom for my students to experience as well.

What is educational intrapreneurship?

I look at our job as teachers as being one of designing learning experiences for our students. And I have often thought of this process of designing these learning experiences as involving heavy amounts of risk taking and innovation. So one day as I was reading something or the other about entrepreneurial thinking I came across the term “intrapreneurship”. I came to learn that this was a term that was created by Gifford Pinchot III. He defined it the following way: “Those who take hands-on responsibility for creating innovation of any kind, within a business”.

This was a game-changing sentiment to me at the time. Since we as teachers are in the business of education, I made the connection that this is an apt description of what we do when we are at our best. We are taking initiative to create unique new ways in which to create learning experiences for our students. So in creating this blog, I thought this is the perfect manner in which to describe what I want to write about.

So what does educational intrapreneurship look like? I feel that it can take many forms, but at its core it is any learning that you design and implement at your school. Since we are all working “within” some school or institution, we are all working within the broader vision of that institution. While entrepreneurs create things from the ground up, we as teachers are most often working within an organization and so are having to build things from within. And I personally think that there is a lot of value in this type of innovation, and one that is often overlooked and undervalued.

For example, let’s say I am tasked with teaching how to solve quadratic equations in my mathematics classroom. I have two options, I can take the activities from the teacher text book, follow the pre-designed lesson plan and sequence, issue the pre-made assessments on the recommended date, and correction the test with the given answer key. And I could do all of this with doing very little if any deep thinking, and any other teacher could replicate that process and create a very similar experience for their students somewhere else in the world.

Or instead I can use a little intrapreneurial thinking and I could examine the provided activities, pick them apart, pull out the elements that I think will support student learning. Make adjustments to the scope and sequence of the learning, work with students to write our own success criteria and learning targets. Utilize student input to create formative assessments and create self-assessment opportunities based on the pace of the learning. Collaboratively design the unit assessment and allow for student agency in deciding how they can showcase their learning.

That is educational intrapreneurship!

In what I described I am working within the school organization to create innovation. It’s powerful stuff. It makes me as the teacher an active change agent working in collaboration with the students that are participating in the learning. It is an iterative process that asks the participants to be calculated risk takers. It requires us to independently research, to collaborate with our peers and be self-reflective in the process. As educators we are more than just facilitators of learning, we are designers, implementers, and co-creators!

To me this is a much more exciting type of education to be a part of. I hope to find more like minded teachers, learners, and designers who share this mindset and are looking to engage with others who feel the same way. It’s cool to be different. It’s exciting to initiate change. It’s important that we are reflective agents for change in the education space.