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Jumping In: Part 3 of Diving Into Inquiry

This is the part of the journey in which I made the bold and adventurous step of directly incorporating the inquiry model into my classroom. Having read the book Diving Into Inquiry by Trevor McKenzie I had arrived at the point in which I could see with some level of clarity how this would look in my teaching.

Just to back up a little, I did have some experience with an inquiry model in a digital technology class that I had been teaching for a couple years without even knowing it. I may not have had the framework or lexicon to describe what I was doing as being pure inquiry, but looking back by taking a student centered approach in how I designed rubrics, gave students agency in choosing artifacts for their learning, and through the creation of an authentic audience for their products, I had already been espousing the main tenants of inquiry based learning in my classroom. The jump I was looking to make this school year, was to have it more transparently embedded into the learning the students would be doing. So in looking at step one of starting the inquiry process, “Think big and plan for the future classroom you want for your learners”, I had already made progress towards that goal.

What I did do this year in a class that I had rebranded as “Music Technology” was to combine the elements I had already been using with the language of inquiry, and to also embed the framework of a design thinking model developed by John Spencer and AJ Juliani called “The Launch Cycle” into the process. I could write a whole series of blogs on the launch cycle model and their accompanying website and book, but I am just going to point you to their resources on the web and let you explore them yourself. So go here to learn more about the Launch Cycle. Basically this is a design thinking framework. And one that I think when it is combined with the tenants of inquiry espoused by Trevor McKenzie can combine to be a powerful force for learning. I included a graphic from their website for reference.

So how did this look? Well first I started off with the process of getting students to explore and investigate music technology as a broad topic. I started with a video that showed a music producer demonstrating how he uses technology to create an entire song from scratch using only his phone and his computer. The video showed how we as people are music creators and how through the use of technology we can design and build original musical creations with minimal resources. I then provided students the space to just explore different ways that music and technology work together to create original products. I held discussions with students in which they were encouraged to share what interests them and what they are passionate about. A student who liked surfing shared about the types of songs on their favorite YouTube surfing video. A student into video games shared about how music is effectively used to convey emotion during certain idea game sequences. Anything to get them to connect the topic of music technology to their own lives. And that’s what the overall goal was in this first phase, to just get them to connect to the learning that we were doing.

The way Mckenzie describes this process in Dive Into Inquiry is through the four pillars of inquiry. We were primarily living in the “explore a passion” and “delve into your curiosities” pillars, but you can see in his book that there are other areas in which you can get students to begin the inquiry process. In terms of exploring a passion McKenzie does provide a series of prompts that you can use for students to reflect about their passions which was very helpful. In the Launch cycle this is what Spencer and Juliani call “Look, Listen, and Learn”. It is essentially an opportunity for students to just be free, explore, investigate and begin that process of connecting with a topic or idea that they are passionate about engaging with.

Once students has identified something that they are passionate about, the next stage of this process was to start asking questions and doing some research. Now here is where there is a little dissonance in approaches between the “launch cycle” and the inquiry model proposed by Mckenzie, but I think both are equally valid approaches. McKenzie proposes that students should create an essential question, make a proposal, then begin researching. The launch cycle suggests researching, developing ideas, then making a proposal (they call it the “ask tons of questions”, “understand the process or problem”, and “navigate ideas” sequence). I have tried both, specifically in my year long Capstone course that I teach, and I personally have found that having students conduct the research then making the proposal afterwards as proposed by Spencer and Juliani has some advantages. But I do not think that it is black and white and that there is a lot of validity in having students make a proposal then beginning the research afterwards.

Again, having tried both, I personally found that when students make the proposal first before having done extensive research, they end up making changes to their idea. Where as if we provide students the space to do the research first and then make a proposal, they have more information to draw from when pitching their idea. I will also add as a follow up that many of these steps are cyclical and if students make a proposal, then research, then make edits to their original proposal they are still arriving at the same point of incorporating their learning into their proposed product. So in this sense as long as you are providing students the space to dig more deeply in their topic during the process of pitching their idea students will be successful in having agency in how they are going to be representing their learning. Much like anything, try out different approaches, see what works best for you and your students, reflect, and as always be open to change. All in all if there is some form of research and a proposal after students have identified an idea or topic that they are passionate about you are supporting student inquiry.

There is one thing I do want to mention here before we move on, there were a series of protocols and presentations of the learning that took place during the research and proposal phases. For the research, each student did have to submit their notes to me that was assessed on a rubric that they created through a process of collaborative work. They also created a slide deck summarizing the key information that they learned about their topic that was presented to the class. That was also assessed on a rubric that they created as a class through a collabroative process of suggesting different grading criteria. Not only did these steps encourage ownership and agency in their learning, but it also gave them an opportunity to practice those crucial 21st century skills of collaboration, communication, and critical thinking. In proposing their project idea they worked in small groups and pairs “pitching” their project idea and using a protocol of clarifying and probing questions from their peers in which they collected feedback. They then used that feedback to edit their proposals and prepared them for final submission to me for approval. Spencer and Juliani have something they call the twenty minute feedback system that was helpful here.

Next came the part in which they began creating their product. In this phase it is really important to make sure that they had a plan for how they were going to get this product made. If a student was going to make a video of them dancing with original music that they created and added to the edited video, they had to present a detailed calendar of the tasks that they would complete to bring this idea to fruition by a set a deadline. This was initiated in the proposal phase, meaning when proposing their product they had to provide a rough outline of 4 or 5 major tasks they would need to do in order to bring their product to life. In McKenzie’s book he has a section titled “the plan and the pitch”. He also provides a nice checklist of items titled “Free Inquiry Proposal” that outlines the questions a student needs to have addressed before they move into the creation phase. What I am saying is that this rough outline needs to be brought out of the proposal and treated separately as its own step.

My suggestion here is to not underestimate the importance of this step. It needs to be made clear to students that this all needs to be worked out before you can give a go ahead for them to begin creating their product. I have also found that this is also the part the students struggled with the most. In my case I found that a student might have a good idea, for example make a video of themselves dancing with music, but haven’t been able to think through the steps required to get to the final product. And this is where I realized I had aimed a little too high in that not all the students had come into my class with experience in this type of learning. Also being in a mixed grade arts elective I had students of different grade levels with a variety of capacities to independently design their learning.

Regardless, through careful work with each student, and intentional feedback and guidance I was able to develop a plan for each student to create a sequence of tasks and a proposal that had a framework that they could follow to ensure an opportunity at success. I did have the advantage of a smaller class and at a smaller school in which I had established relationships with many of the students. So the ability to effectively connect with them and draw out their ideas was made easier than if I had a large class with students that I had not had any previous relationship with. So I would suggest that maybe you be very intentional about the level of expectation you have for students in being able to design an entire project with the experience that they have.

Once the plan and proposal was made and approved, I was now able to simply give students the space, time, and resources to bring their idea to life. I created a system in which we made a large white board with each student, their project plan, the major taks with due dates, and their essential question. Each day they had to write a brief summary at the end of class sharing about how they had progressed on the task that they were currently working on and what they were going to do next. At the end of each week they did a broader summary of the work that they did that week and how they were progressing in the their overall plan. I found that this kept them accountable to themselves and to their plan and gave them the space to reflect on how they were progressing towards completion of their product. This is somewhat along the lines of what McKenzie called “learning evidence check-ins”. I would say though that rather being a check in on the evidence of the learning, these are check ins on evidence of their product development. Essentially the purpose of the class is for students to learn how to use technology to create products using music, so in that sense I’m checking for evidence of their learning. I feel that the sentiment is the same, but above all it is important that I am regularly engaging with each student to keep tabs on what they are doing.

So a lot of my time was spent moving from student to student, making sure they were engaging with their product creation, and helping guide them towards resources that would help them answer any questions that they had. I did find this last step very important. Rather than be the one with all the answers I forced them to go and find answers to any questions that they had. Sometimes this was really hard because there may be asking me how to do something on Gargeband that I knew how to do, but I really wanted to make the creation authentic and get them to be more comfortable finding answers on their own rather than always turning to me. After a little while of this they became very used to this process and stopped always turning to me when they have a quesiton.

The other reason that this is nice is that sometimes we really don’t know how to answer their questions For example I had one student building a MIDI controller using an Arduino. This was something that I had zero experience with and I honestly couldn’t have helped him even if I tried! Where I was able to be of help was in connecting him with resources or mentors that might be helpful. For example I contacted a teacher at a local school who taught a music recording class for high schoolers and put them in touch via email. Through this communication the student was able to get some information about their question that ultimately allowed them to create their MIDI controller.

Moving forward as the students progressed through their product creation phase about 3/4 of the way through I created a check in phase where students shared their progress in small groups and asked for feedback on how to overcome a particular challenge. This would align with the “highlight and fix” phase from the launch cycle of Spencer and Juliani. I didn’t quite see this specifically built into McKenzie’s process in Dive Into Inquiry, but I will say that there are a number of mentions of peer feedback, and looking at other’s work. So while he may not explicitly outline a process for doing this in his model, the process fo eliciting feedback, sharing with peers, and revising your work based on that feedback is covered. Again, do not underestimate this phase as well. Students are very honest with each other and also I have found that since they are the ones in the process of creating their product, they can often see things or suggest things that we may not notice. And again, there is that built in power of students taking ownership of their and each others’ learning and having agency in the process. Rather than turning to me for validation or confirmation of their work, they are using input from their peers on how to make improvements. Of course it is important here that you have clear protocols and expectations in place for how this process will unfold in order to ensure respectful communication and collaboration. The last thing you want to see is a student getting discouraged or giving up because another student was inappropriately critical of their work. But I have found that students are very respectful of each other and are more than capable of providing effective feedback to each other.

So this brings us to the final and most exciting phase. McKenzie called it a “public display of understanding”, Spencer and Juliani call it the “Launch”. Either way it is important that you provide students a platform to show off what they created. So I did this in a few different ways. First internally students presented their creations to their classmates via a prepared presentation in which they summarized their essential question, their process, and their final creation. Again they were assessed on a rubric that they collaboratively created as a class. I then created an opportunity during a lunch recess for all students to come into the digital media lab to see and interact with the products. And then finally I solicited a few projects to be shared at our school assembly. I also can add that the timing of the project completion conveniently feel right after our parent’s weekend event so while parents were visiting students were able to share with parents and families when their projects were right at about 95% complete. In the future I think I would create some sort of authentic showcase for all parents to interact with the student projects, possibly during a block of time after school.

Now I am not going to say that everything went peachy and happy. Some students were behind deadlines, some had to drastically reduce the scope of their project to create something tangible. Some wanted to shift their idea completely in the middle of the project creation and were sadly dissaponted when I guided them towards seeing their idea through. Some students struggled with learning the necessary skills to execute their project idea. But all in all, I asked students to be reflective on their process and identify where did things go wrong. I shared my own experiences of projects in my own life that had gone awry an how I had to pivot to get it completed. I constantly emphasized that this is a process and that in the long run it is most important that they learn how to think independently and to problem solve, rather than be able to create some masterpiece.

It was a big mental hurdle for students to revel in the process rather than the product. Students struggled to have to create something to represent their learning rather than just take a test. In fact about half way through one student said out loud, “why can’t we just take a test on this instead of having to do all this stuff?”. Fortunately one of the students shot back, “yeah but then we wouldn’t have anything that we created at the end, we’d just have some piece of paper with a number on it”. I quietly looked at up and thought to myself, “thank you, maybe we got a shot here”.

I can’t say how right McKenzie was when he said, “find comfort in the uncertainty”. I had no idea how this process was going to go. I feel fortunate to work at a school that trusts me and gives me the freedom to teach a class like music technology where my leadership can say, that sounds awesome, go for it! I know I am privileged to work at a school that can provide me the resources to purchases the items necessary to create music technology products. But as I will share in the next post in this blog series, this way of teaching and learning can work in a variety of classrooms with a limited budget. Because after this experience in music technology I was so inspired that I felt ready to take this into my grade 8 Algebra 1 class. I saw so much potential in these models developed by Mckenzie and the team of Spencer and Juliani that I knew I had to go deeper, I had to dive even further into his thing called inquiry.

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 year in June, I posted on Twitter asking for suggestions on a good summer read with a particular focus on project design, inquiry, or student agency. One suggestion that stood out to me in particular was a book titled Dive Into Inquiry by Trevor McKenzie. I asked a colleague I trusted 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 also engaged with various educators on Twitter about the different levels of inquiry, when they are best used, and the scaffolding that goes between the different levels. With these early insights into inquiry, I eagerly awaited my new book.

Before I get into the content of the book I want to share a little about my approach to intrapreneurial thinking that led me to this book. It started by posting to Twitter for ideas. There is a rich community of educators on Twitter who are very supportive. By posing questions, making requests, or throwing out an idea, I often receive 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.

Next, I shared with a colleague about the book. It is important to develop relationships within your organization with people who have similar interests and are open to new ideas. This opens up opportunities for conversation about different things you are trying. Don’t try new things all alone.

If you do not have anyone that you engage with, bring a book that you are reading to your next faculty meeting. Ask a couple people if they have read it before. Discuss with your principal if you can make an announcement if anyone would like to read the book along with you. Anything to get the conversation started internally can be beneficial. You never know who within your organization might have those similar interests as you.

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 conversations with others who had mentioned the author.

Quality creators tend to be very engaged on Twitter. They rely on their audience to build and maintain their presence. Since reaching out on Twitter I have had many correspondences with the author in both direct messages or via his posts. I have been able to build a relationship with him. Through these communications, I have learned about professional development that he is leading in my area. He has also connected me with other educators who are looking into similar topics.

So 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.

The rest of this multi-part blog series will cover my journey on Dive Into Inquiry. I will discuss 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 initiatives 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.