A Mathematical Conundrum

It’s Wednesday.  I’m sitting in my office with two students waiting for a third to arrive when one of them shares this epiphany.

“I couldn’t stop Dr. Podraza.  I worked on this problem the entire weekend.  I looked up articles.  I had my parents Google stuff.  I got everyone involved.”

“And I don’t think the math is actually right.  After all, it doesn’t make sense that my answer was in the billions.”He then went on to explain why he thought his answer was implausible citing relevant facts.  

There it was.  The thing educators all dream of.  A student who was so engaged in learning that he pursued it for the pure joy of it as opposed to turning it in for a good grade.  

So what caused all of this determination and excitement? 

Right before Winter Break, I was talking with these same students about how they hated the current way they had to learn math because they were given problems that were either out of context, completely fake, or that they were being forced to solve them in a way that was inefficient. 

“So what do you think we could do about it?  How would you like to learn math?”  

“We think math should be connected to the real world.  We should be able to solve problems about things that we can connect to, not some weird story about a monster at the bottom of a made-up lake or worse, Felicia’s cookies (this is an inside joke).  We get that we have to solve problems and learn the math behind it, but it’s frustrating when we are told we have to use a specific way of doing it.”

“Ok, so what might that look like?”

“Well, there’s stuff going on in the world.  Like global warming.  Stuff that’s actually a problem and math is probably related to it.  We want to solve problems like that.”

This was how the Top Secret “Tangerine” project began.  We decided at that meeting that the three of them would create their own YouTube Channel (real name forthcoming) based on real-world math problems.  It would be a weekly show where they presented a math conundrum to their viewers based on something happening in the news.  There would be opportunities for viewers to suggest problems or topics as well, but the work would always be done by the students.  They’ve even tossed around the idea of writing their own curriculum one day.  

I’ve seen this type of enthusiasm in students hundreds of times throughout my career and it’s always related to the same type of work.  Ryan & Deci would attribute it to something called, “Self-Determination Theory” which hypothesizes that any human needs competence, relatedness, and autonomy to be intrinsically motivated.  In non-theoretical terms, it’s really just offering students relevant and meaningful work that they can connect to.  Genius Hour, Passion Projects, Project-Based Learning, Inquiry-Based Learning, & Service Learning are all examples of how educators are currently harnessing the power of relevance in their classrooms.

So here’s what I’m currently grappling with.  Students would love to pursue this type of work all day every day if we let them.  The group of kids in the Tangerine project has requested to come to school as early as 7:00 a.m. to work on it and would stay until five or later if I had the time.  It’s easy to jump to the conclusion that school should be a place where everyone pursues projects all day long, but in reality, that may not be the case.  It’s made me wonder…

  • What would school look like if we gave kids longer periods of time to work on big projects instead of the way we currently teach?  What are the opportunity costs of this approach?
  • How do we balance teaching students’ skills with working on the projects themselves so that they can handle the cognitive load required?  What types of teaching structures might work best for this? 
  • Do we teach the skills in isolation first and then give students time to explore projects or do we have them work on projects first and teach the skills as they come up? (the chicken or the egg question)
  • What professional learning would educators need to successfully approach the classroom this way?  Are there any mindsets shifts that need to occur (within myself and others) related to this?

I wish I could tell you I had an even semi definitive answer to these questions, but unfortunately, I don’t.  I keep hearing that we live in a VUCA world (volatile, uncertain, complex, ambiguous), so it makes sense that we should give students experiences where the answer is not immediately obvious.  However, within this world of unpredictability, there are also constraints that we all must adhere to so it also seems relevant to provide students with structured learning experiences as well.   The only way to really know how much of each is to continually experiment in the classroom and see what works best with our students. 

 

 

 

Predictions for the Next Decade of Education

I recently read this article from the Atlantic titled, Elementary Education Has Gone Terribly Wrong.  It’s an interesting read for a variety of reasons, but what stood out to me was the plethora of evidence that confirms what many of us have known for decades: the standardized testing movement simply doesn’t work.  Despite our efforts to systematize learning and add more “rigor,” we continue to end up with the same results along with an ever-expanding achievement gap.

The author, Natalie Wexler poses the questions, “

“What if the medicine we have been prescribing is only making matters worse, particularly for poor children? What if the best way to boost reading comprehension is not to drill kids on discrete skills but to teach them, as early as possible, the very things we’ve marginalized—including history, science, and other content that could build the knowledge and vocabulary they need to understand both written texts and the world around them?”

She pokes holes in many common literacy practices in the U.S. as well as presents examples of teachers who are finding success in trying out different approaches.  The article got me thinking about education overall, how we have tried so many new things, abandoned many ideas, gone back to the same ideas, but education has, for the most part, looked the exact same way for generations.

The start of a new decade feels like a fresh start for everything, education included.  There is no guarantee of what the next 10 years will bring, but I am optimistic that this decade will bring what the past hundreds of years have not, an education system that is valuable for all.  There are a plethora of amazing educators who are leading the charge and sharing their stories on social media and beyond giving me hope that we can and will create powerful educational experiences to help ALL kids succeed.    

Predictions for 2020-2030

The ideas I present in this post are a result of two decades of personal experience working with students, a lot of reading, watching & learning, and most of all, connecting with amazing educators across the globe.  (Thank you PLN!)  You will notice that no idea is brand new.  I believe that we already have the answers which we seek, it is the way that we use them with students that has the power to shift education for the better. 

Less About the Right Answer & More about Great Questions

One of the chapters that stood out to me in The Innovators Mindset was the chapter where George Couros discusses the importance of students being “problem-finders.”  This was sparked from the work of Ewan McIntosh. The premise is that we spend a lot of time working with students to come up with solutions to problems, but what we really need in a dynamic world is students who can find problems and innovative ways to solve these problems.

Besides the fact that solving problems with predetermined answers can be monotonous and insanely boring, (geometry proofs anyone?), if we spend all of our time giving students problems to solve with a finite answer we are giving students the impression that the purpose in life is to simply get the right answer.   Students leave school thinking there is a simple methodology to life and if they follow the success formula given to them they will be successful when really the opposite is true.  We need creative thinkers, students who can look at the world with a new lens and make it better. 

A great way to develop this skill is by teaching students to ask great questions and giving them opportunities to explore ideas that are meaningful to them.  Genius Hour or Passion Projects, QFT, TQE Method, and Socratic Seminar are just some ways that educators around the globe are working to develop the questioning ability in students.  Each of these methodologies helps students to not only create questions of their own, but they encourage rich discussion among students as well which can lead to new ideas from students.  It is exciting to think about what kind of learning will take place when we spend more time empowering students to question, explore & discover as opposed to encouraging them to simply find the right answer.  

Experiential Learning 

In the next ten years, whether virtual or in-person, learning will extend more and more beyond the four walls of the classroom.  Mentioned in the Wexler article, research confirms students learn best when they have experiences and background knowledge to be able to comprehend the texts they are reading.  Creativity is the number one quality that employers are currently looking for.  Reeves & Reeves suggest in their book on creativity, The Myth of the Muse that one of the ways to enhance creativity is through inspiration from experiences.  The Next Generation Science Standards (NGSS) recommend starting science lessons with a phenomenon so that students have a shared experience to ask questions and develop theories from.  Although I still think the best experience is one in real life, Augmented and Virtual Reality makes this a daily possibility for students.  

One school that is doing an amazing job at teaching from this approach is the GEMS World Academy in Chicago, Illinois.  In this school, the teachers plan out larger units that explore a broad question related to an essential idea.  Included in each of these are field trips to a place in the city where students can explore.  From the shared experience students then create questions they have and spend the unit exploring answers to the questions they create.  Each subject area is tied into this big idea including specials.  The result is that students see learning as interconnected as opposed to limited to one subject area which enhances their creative ability to connect ideas and create new ones.

A More Personalized Approach to Education

If you would have asked me if this was possible ten years ago my answer would have emphatically been no.  It takes too much time.  It’s not necessary or realistic.  It is amazing what a decade of experience can do.  I now believe it is more necessary than ever.  As you will hear me mention throughout this post, in the dynamic world we live in we no longer need students who can just get the right answer, we need students who are curious, think creatively and can find new problems to solve.  We want students to leave school with a positive view of themselves, recognizing not only what their talents are, but how they can use them to make a positive impact on the world.   

When I say a more personalized approach to education, I am not saying that every student would be doing something different in every moment of the day.  Students need foundational knowledge in order to be creative, ask questions and generate new ideas.  However, I think it’s a different approach to looking at the school day.  Design39 Campus in California has been exploring this idea for the past five years.  You can check out this link for more information, but their day is split up into Integrated Learning Time, Deep Dives & Explorations.   During Integrated Learning Time is when they explore content across curriculums for purposeful application of skills.  Deep Dives is time for students to explore their passions in an academic setting.  Explorations give students time to explore new things they are interested in trying.  I love the way they organize their day because it gives students foundational understanding as well as time to explore passions and build new ones.  For more information on how the idea began and the success they are having with students, check out this podcast from Modern Learners.

Going Gradeless/Meaningful Feedback

At some point, we have to recognize that grades are just meaningless little letters that students look at and then toss.  Even when we add in comments to the grade or SBR number students associate more meaning with the grade and typically ignore the feedback.   Both John Hattie and Susan Brookhart have written books on the topic and the research shows that feedback is a much more effective learning tool for students over grades.  

Many educators are already moving towards a feedback-heavy or gradeless classroom.  (check out the #gradeless on Twitter) Instead of using grades or fear of punishment to motivate students to complete their work, they have shifted their instructional practices to have students set goals that are meaningful to them.  The teacher and/or peers give them feedback on progress towards their goal to move their learning forward.  Learning then becomes a continuum as opposed to an endpoint.  I’ve linked a few useful resources below if you are considering making this shift.

6 Tips for Going Gradeless by Starr Sackstein

More Teachers are Going Gradeless.  I Asked Them Why.  EL Magazine July 2019

Teachers Going Gradeless (TG² Podcast)

Collaboration Over Competition

One of the best videos I have seen this year that has had a huge impact on the way I think about the classroom is Why School Should Be about Us Instead of Me from Trevor Muir.  Besides the fact that it has a totally Hamilton-esque vibe, the premise that school sets up a culture of competition as opposed to what our world needs, a culture of collaboration, rings completely true.  I’ve watched it probably 20 times.

I was definitely one of the students who groaned every time I heard it was time to work on a group project.  There was always the people who did everything, a few people who did nothing, and then somehow a project evolved.  It never felt to me like there was any purpose in working together.  As a teacher, I tried to circumvent this issue by assigning roles to each student, but even this had uneven results with students continuing to work in silos as opposed to creating something together.

After reading a wonderful post by John Spencer about collaboration, what I realized was missing was students seeing the value in one another’s strengths and using those strengths to build something greater than what could be done alone.  Instead of starting group projects by assigning roles, have students share their strengths, set goals for the project together and give them opportunities to give one another feedback along the way.  This creates greater meaning for the work and also mirrors the type of work they will be doing outside of school.  In the working world students will be collaborating daily, we have to increase the amount of collaboration they do throughout the day, but it also has to be done in a way that is meaningful so that it doesn’t just become another one of the dreaded group projects.

If you’re looking for ways to create this type of classroom, Trevor Muir’s new book, The Collaborative Classroom, filled with practical ideas and examples, is a great place to start.

The End of Labels 

This last one I am most excited about, although I think it might take a little bit more time.  I predict that gradually the labels we use in education, “gifted, special education, EL” will disappear.  As we start to shift the focus of school from everyone ending up in the same exact spot to encouraging students to be curious learners who explore their passions and develop their talents, the need for labels will go away because we will see students for their greatness of whom they already are, not some arbitrary standard we want them to become.   



“Logic will take you from A to B.  Imagination will take you everywhere.” – Albert Einstein

We have spent the past hundred years approaching education from a logical standpoint.  Students need to learn ______________ so we will teach them ___________________.  We will set standards that everyone needs to reach and if they don’t reach those standards we will fix them with _____________________.   This is a very logical approach if we are working with products, but hasn’t always served us well with students.  We need more creativity and flexibility if we are going to reach all students.  

I am optimistic about the shifts I continue to see happening in our schools.  I believe that through these shifts we will have students leaving school with more creativity, empathy, equity, and curiosity than we ever have in the past.  It is inspiring to think about the wonderful world that these students will create.