“Passionately Curious”

As a former mathematics teacher, Pi Day always held some special significance. With all the wonders of mathematics that students are predisposed to – for no better reason than mandates issued by the USDE (United State Department of Education) – students all know for certain that pi is roughly equivalent to 3.14 and is nearly synonymous with March 14.

As a former mathematics teacher, I was never envious of the competing factions to Pi Day.

• National Potato Chip Day isn’t worth its a salt compared to Pi Day.
• Constitution Day captures just the Andorran audience of the 11th smallest country (by population) in the world.
• I own four dogs, and will protect them with all my might – but National Dog Theft Awareness Day isn’t in the fight.
• Unlike my dogs, I own no spiders – I do, however, refuse to stomp them out. I release them back to nature every day (at least every day a spider comes across my path) not just today on National Save a Spider Day.
• How about National Valerie Day, National Organize Your Home Office Day, and Dribble to Work Day?

There are some celebrations, other than Pi Day, that I can get behind though: Celebrate Scientists Day, International Mathematics Day, Science Education Day, and National Children’s Craft Day.

While these are fantastic reasons to have a slice of pie following a little ditty about 100 digits of Pi, the most impactful moniker for March 14 is Genius Day. A term bandied about recklessly at times, in the style of Webster a genius is a person who displays exceptional intellectual ability, creative productivity, universality in genres or originality, typically to a degree that is associated with the achievement of new advances in a domain of knowledge.

This day marked the beginning and the end of two significant figures in the history of the scientific world, geniuses by anyone’s measure.

Albert Einstein was born on March 14, 1879.

Stephen Hawking died on March 14, 2018.

Genius Day is all about trying new things, taking chances … and most likely failing at some point. These explorations cannot happen within our schools unless we deliberately design experiences for our students. This takes some creative confidence on the part of the building leader, the teachers, and the students. As the designers of the moments during which students learn the most (not necessarily quantity but lasting quality), we should approach the work from a human centered point of view rather than a standards-centered point of view. We need to sidestep the traditional approach to teaching in order to create a lasting moment – deep learning. Tom and David Kelley, in their book Creative Confidence talk about their process as educators and designers:

“Being human centered is at the core of our innovation process…An empathetic approach fuels our process by ensuring we never forget we’re designing for real people…[design thinking] is our process for creativity and innovation…Design thinking relies on the natural – and coachable – human ability to be intuitive, to recognize patterns, and to construct ideas that are emotionally meaningful as well as functional.”

School should be more than just a distribution facility unloading facts, assigning feeble practice and engaging in the occasional activity that peaks students’ interests, but doesn’t necessarily invoke creativity, invention or innovation in their learning. There is certainly a time and place for these traditional aspects, but true learning moments come from peak experiences that fully involve the students senses and emotions.

This shift to a focus on exploiting the genius in each of our students is not an easy one, but teachers need to develop their own creative confidence to make the attempt. Without trying new experiences, new knowledge cannot be gained. If we always rely on the traditional approach to learning, we will not be able to discover how far-reaching our boundaries may stretch; and therefore, how much we may be limiting our students depth and breadth of knowledge. Anders Ericcson and Robert Pool, authors of Peak, share that “in this [traditional] view, all that you are doing with practice – indeed, all that you can do – is to reach a fixed potential. With deliberate practice, however, the goal is not just to reach your potential but to build it, to make things possible that were not possible before.”

Think of a moment in which you truly learned something. What were you doing? How did you feel? What made the learning memorable? I would guess you weren’t finishing building your 20th lattice on a two-sided worksheet when you magically solved the ambiguous two-digit problem of what is the product of 29 and 17?.

Einstein didn’t always get the right answer. Actually, if I recall, Einstein wasn’t a great student by traditional measures. He didn’t want to “do school” the way school was (is) designed. Einstein’s genius was that he followed his passion and his quest for understanding the unknown. He was an explorer. Einstein, pictured at the top of this blog, was once a young child who attended school much the same way our children attend school today. He once claimed “I have no special talent. I am only passionately curious.” If we use Einstein as a model – fashion if you dare, but more importantly a model of genius as “creative productivity”, we can begin to develop an education system that optimizes deeper learning for our current and future students.

Educators should consider themselves “experience engineers”. What can we do differently in schools to expose students’ curiosity through an exercise of empathy in order to provide opportunities of learning moments that are authentic and meaningful? Take a look at the following produced by Jackie Gerstein, author of the blog User-Generated Education. If you’re not already trying some of these strategies, pick one and see what happens. Don’t worry if it’s not perfect, try again – don’t give up. Learn from the attempt and eventually you’ll discover ways to make moments of learning that will have a lasting impression on your students.

Teaching is not magic

We are in a unique position to have a significant influence on the development of young people at a time in their life when conscious and unconscious growth is prevalent. This opportunity is brimming with responsibility. We are partners with parents, siblings, grandparents, coaches, and other influencers to help our students to grow. While educating our community’s children is not an easy task, an overwhelming concern we face is “what are we really trying to achieve?”. What are the goals we have for our students? What are the goals our students have for themselves? 

As educators we often think about the daily lessons and activities that our students will be expected to engage in. Curriculum units are often created around standards and understanding is measured by a test. Standards and tests are static, inanimate, unthinking, and unemotional. The craft of teaching brings life to learning, and needs to be deliberately designed to invoke learning. This craft is not witchcraft –  teaching is not magic. The simple act of ensuring your students know the learning intention for a lesson or activity and the success criteria associated with the experience may be enough to connect teaching with learning –  but not always.

Oftentimes we do need more to help direct our students from not knowing-to-knowing, or redirect them from misunderstanding-to-understanding. We have several tools we can employ when enhancing the learning experience for our students and the teaching experience for ourselves. As a point of clarification, enhancing the learning experience is grounded in design for deeper learning. We don’t want to just comply – cover the standards – get through the book – turn the page. 

These nine principles provide a framework for designing for deeper learning:

You are likely doing a lot of these things without realizing it or at least recognize some of these principles under a different set of vocabulary. How much of your planning deliberately includes each of these principles? How evident are these principles in your classroom? If you’re telling yourself you can probably do better in this work, consider us partners in elevating our collective attention and intention to grow our students in a deeper and more meaningful manner.

Over the next several posts, we’ll be digging into each of these principles and how they connect instruction to authentic performance tasks (and further) to the data that helps inform when and how we move forward in scaffolding the growth of our students..

If you can’t wait for our next post here are some resources to learn more about designing for deeper learning.

Deeper Learning Hub

New Pedagogies for Deep Learning

Design for Deeper Learning Kaleidoscope

What’s Deep about Deep Learning

Too many eggs in one basket

My daughter, Maddie, will be turning 22 on Sunday, April 10. She is the oldest of our four children. When she was just 9 years old we bought her a dog. Ruby, the dog (not my daughter … remember her name is Maddie), is blind in one eye (she thinks she’s look at the camera) and generally can’t hear, but she has three younger brothers (that’s true for both Maddie and Ruby) to keep her acting like a puppy (Ruby – not Maddie). My oldest son Christian has a dog, Jake. My two youngest sons, Sean and Finn, have twin dogs, Rider and Comet. Needless to say we are a dog family. So what happens when our children grow up and out of the house? How can we take four dogs and divide them among six people?

Most 3rd graders should be able to attempt this problem, but not solve it “correctly”. What about 4th graders? 5th graders? … High school?

Of course if we enact our skills of extracting critical information from the situation (does it matter what ailments Ruby has or how old my daughter was when she got her?), and then apply the algorithm of either “repeated” subtraction or the notion of fair-share, we realize each one of my family members (myself included) would be able to cuddle up with just 2/3 of a dog once properties of division are satisfied and we all agree fractions are numbers too. The math makes sense, but I really hope you see a problem with a fractional solution in this unrealistic situation. The real (non-mathematical) answer is that my wife and I keep all four dogs.

In 2001, the National Research Council published Adding it Up: Helping Children Learn Mathematics as a guide for educators to rethink how mathematics should be taught in grades pre-K through 8. The core of the text suggests there are five strands that are necessary for learning mathematical concepts.

Students spend a lot of time practicing procedural fluency, but under the auspices of standardized testing and time constraints we convince ourselves the other strands will either come naturally as students mature … or just aren’t as important as being able to do the math in order to get the right answer.

Graham Fletcher presented some of his learning progressions at the Montgomery County Intermediate Unit recently. This image of Graham shows a simplified form of the five strands where Application serves as a big bucket category for strategic competence, adaptive reasoning and productive disposition.

Graham Fletcher presenting at the MCIU on March 29, 2022.

Building authentic context around problems, and engaging students in modeling and conceptual understanding offers greater opportunity for students to participate in their learning. The introduction of design thinking, project based learning and interdisciplinary teaching and learning may be a bit of a stretch right now. Consider the dynamics of your classroom, and the balance of rational thinking versus algorithmic thinking that you expect from your students on a daily basis.

Can you infuse experiences that allow students to develop critical thinking (effect size = 0.49) and exercise creativity (effect size = 0.58)? Have you tried 3-Act math activities? They are built into the enVision program already, and if you’re looking for more check out Graham Fletcher, Andrew Stadel, Robert Kaplinsky (Open Middle is another activity worth exploring) and of course Dan Meyer. If 3-Act math is old news, let’s now consider design challenges and project based or problem based experiences. As unique as each of our individual students can be, the experiences we design for them can be just as unique. Let’s start scrambling the content, strategies, and experiences into authentic and holistic learning moments to get out of the eggs-in-one-basket approach to education.

Postscript: if you’re looking for resources on design thinking and project based learning for your classroom, I’ll be posting additional content to help (sorry to leave you hanging at the moment) … but we can always use your help in creating new experiences. If you’re interested in helping, please reach out.

“3 and a bit”

How is pizza related to pi? (image source: Veritasium youtube channel)

We all know about pi and its common numerical equivalent for practical purposes (3.14). But where did pi come from, and why? The development of pi over the centuries is an example of mathematical innovation. As you know, today is Pi Day. If you’re interested in links to help students engage in pi for Pi Day, skip to the bottom. If you want to know a bit more about pi … keep reading.

First, pi is the ratio of a circle’s perimeter to its diameter.

The short history is pi was first approximated by the area of polygons with n=6 sides (a hexagon) that is inscribed (inside a unit circle with diameter = 1) and circumscribed (around the same circle). Pi was approximated to be between 3 and 4. Over a long stretch of time the polygon was bisected and bisected and bisected … and you get the point. The last time this method was used to approximate pi is in 1630 using a polygon with n=10⁴⁰. At this time, pi had 38 digits to the right of the decimal, but it took over 25 years to make this approximation.

That’s a long time to simply calculate a very precise numerical representation of pi. Here is where the innovation happens. In 1666 Sir Isaac Newton, while recovering from Bubonic plague (what discoveries may come from the conditions Covid-19 placed on society?) decides there has to be a better way. Through widespread understanding of Pascal’s triangle and the development of the binomial theorem, Newton “breaks” the rules of algebra, and applies calculus to the geometric theories of circles, and discovers the irrational nature of pi allowing anyone with a computer to calculate pi to whatever level of precision they desire. I’m sure everyone can find pi on a calculator.

This isn’t about how many digits of pi we can calculate, but rather to recognize that something as mundane as pi has a rich history of innovation that allows anyone to use it in its most simplistic form (3.14) in the discovery, creation and invention of both simple and complex ideas. Newton provides an example of how the following three aspects of mathematical innovation come together for a discovery that is now used by every student across the globe.

Arte Scienza – development of balance between science and art, logic and imagination. [Pascal’s triangle and the binomial theorem]

Conneccione – everything is connected to everything else. [pi is an amalgamation of algebra, geometry and calculus]

Curiosita – the curiosity to find the connections. [Newton was curious about how to calculate pi without the arduous task of bisecting polygons]

This line of thinking allows mathematical and scientific innovation to propagate into other disciplines. Here is a brief timeline of pi and it’s uses in other innovations.

Archimedes uses the geometry of a circle to introduce the concept of pi …

Keplar’s laws of planetary motion …

Galileo’s pendulum …

Euler’s use of algebra, trigonometry and geometry to develop Euler’s constant and what some consider the most beautiful formula in mathematics using 5 important constants:

(more on this in a future post)

Gauss’ normal distribution …

Einstein’s theory of relativity!

To hear more about the history of pi and it’s discovery check out the Veritasium youtube channel.

For resources to connect innovations in mathematics with your students check out MoMath .

If you’re looking for activities for Pi Day, What We Do All Day offers some great projects, and Jo Boaler just updated her youcubed website with this Finding Pi activity.

The Green (Hat) Apple

In September 2017, I defended my dissertation on the perceived value of procedural fluency vs. conceptual understanding among secondary mathematics teachers. I know – BOOOORING (my oldest son actually fell asleep during my presentation).

Non-mathematicians (and I’m sure some mathematicians) will likely find it difficult to see the connection between mathematics and creativity. At some point, we’ve all sat in a math classroom and witnessed a teacher demonstrate basic algorithms like addition and subtraction. What most of us missed was the opportunity to explore the creativity associated with discovering how and why the algorithms worked … we just trusted that they did, and there was sufficient evidence to back the teacher’s claims.

At the conclusion of my defense, my professor, Dr. Fredricka Reisman, walked me to her office – exclaimed that I was her last doctoral student before retiring – and handed me the green glass apple picture above, something she has done for all of her graduates. Throughout my program, which focused on educational leadership and creativity, Dr. Reisman often referred to Dr. Edward de Bono’s Six Thinking Hats framework. The Green Hat (or apple in this story) is “the creative hat, used to generate new ideas and possibilities and to explore alternate courses of action.” [taken from Reisman and Tanner’s “Creativity as a Bridge Between Education and Industry: Fostering New Innovations” – the second book from top in the photo].

Reflect for a moment …

How often do you exercise creativity in your teaching?

How often do you ask your students to be creative?

How close is creativity associated with successful teaching and learning?

The challenge is:

How can we make learning in the classroom more fun?

One of the best ways to get inspired is to look outside your context. When working on new design challenges, IDEO designers often use analogous inspiration to gain fresh perspective. For example, emergency room doctors can get insights about organizing their medical supplies by spending time with a Nascar pit crew and an airline employee might get ideas about check-in by observing a hotel front desk.

IDEO U Blog

IDEO is a design firm that has their fingerprints on every industry, including education. We have used their work as inspiration in bringing the concept of design thinking (remember “Launch” and “Empower” by AJ Juliani and John Spencer) to some of our classrooms. Using the suggestion above, we stepped outside the context of education to examine this challenge of making learning more fun and engaging while also invoking curiosity and celebrating creativity.

David Kelley (not the creator of Doogie Howser), founder of IDEO and the d.school at Stanford University, writes in his book Creative Confidence, “[a] creative mindset can be a powerful force for looking beyond the status quo. People who use the creative techniques we outline are better able to apply their imagination to painting a picture of the future (p.18)”.

When is the last time you thought about this question from George Couros’ The Innovator’s Mindset (p.39), “would I want to be a learner in my own classroom?”

David Kelley and IDEO have a lot of resources to help us think through the challenge of (re)designing a classroom that brings joy and confidence to both the teachers and the students.

We’re building a team!

Do you own a Green Hat?

If yes (your answers to the questions throughout this post were in the affirmative), then GREAT we’d like you to join us.

If you don’t own a Green Hat, would you like to? We’d like you to join us also!

Kevin (Murphy) and myself will be visiting your school soon to talk about a collaboration with the MCIU and FluxSpace (a makerspace “sandbox”). We’re hoping to include some interested teachers in exploring the creation of lessons embing computer science, makerspace, design thinking and/or project based learning experiences in core content teaching and learning. Our work will begin with grades K-4, but we will be expanding once we get things off the ground.

This is the first in a series of blog posts related to innovative teaching and learning , so stay tuned.

Tech In Ten

The following link contains ‘Tech In 10’ lessons featuring CSD approved technology apps and websites. You will probably recognize many of the applications, but still take a minute to check them out as many have changed over time. There may also be some new ‘finds’ that you can incorporate into your classroom teaching.

Resources and 10 minute trainings to support instruction and learning 2021/22.

Tech In Ten Wakelet

Relaunching the CSD Innovation Blog

Science does not know its debt to imagination. — Ralph Waldo Emerson

As we continue to squeak out of the grips of the Covid-19 pandemic, a sort of rebirth defines the landscapes that we engage with both personally and professionally. In the Office of Education, the Department of Innovation is making changes to the lines of communication in an effort to streamline content, add greater diversity, and increase targeted and usable content in the classroom. One step in this change process is the relaunching of our blog with the option to subscribe and receive weekly messages in your email. Please follow us by entering your email on the right. The blog will also be linked on our website. (Apologies for the advertisements … we’ll have them removed soon.)

We have returned to in-person learning with fervor, and the challenges faced and the challenges we are faced with now linger in the domain of unfinished learning for our students. While the curation of data can provide some insight into where we should begin (again), the methods, manner and messaging of instruction to our students remains flexible to maintain personalization in the context of content, emotional well being, safety and security.

Now, more than ever, we need to rely on our passion as educators to provide captivating lessons to insight curiosity for learning among our scholars. Curriculum and textbooks serve as guides for the sequence and strategy that fill our classrooms with content, but imagination and understanding connect the content to the students of Cheltenham. The inimitable debate between teaching as science versus teaching as art should not undermine the value of the imagination of the teacher. Collectively we all work to help develop all of our scholars into successful contributors to society. We all have our own unique skill sets and innate gifts to transform content into learning experiences that will lead our scholars to a state of curiosity for more learning.

Take hold of your imagination, apply your training in the science of teaching, and present the passion and art of learning to your students as we continue to grow as the Cheltenham School District.