Learning, Math, Motivation, Uncategorized

Exploration in Mathematics- Allowing Explorers to Flourish

Exploration by it’s very nature is a step into the unknown.  Armed with no map, no set of steps, no set path, the explorer embraces the excitement of discovery with a willingness to get lost in the adventure.  Imagine for a moment exploration that was planned, with every destination known, every step predetermined…it would not be as much fun, it would not belong to the explorer, and it would not be exploration.

Mathematics is a place where exploration is not only possible…it is necessary.  Through exploration and play we can breath life into the learning of mathematics, as we open up opportunities for imagination, creativity  curiosity and wonderment.   These qualities can carry the mathematics beyond the textbook, the worksheet, the drill and practice.  They can make mathematics come alive.  This exploration needs to belong to the explorer and the explorer in every learner needs to be given opportunities to discover and create in mathematics.  There may be  times when we would want to give students the map with the route laid out and support them on reaching the destination but there should also be times where students face a problem or situation and need to reason your way to the other side, without the road map.   In those times it becomes about finding their own way, embracing the different but equally valid paths/solutions of others, and truly discovering not only the science of mathematics but it’s artistry and creativity as well.  This exploration does not need to happen in isolation.  Explorers can join resources and thinking power to help navigate the journey and share in the excitement of discovery.

In this video Dan Meyer‘s describes the problems facing mathematics education when we take all of the exploration out of the subject.

1. Lack of initiative- Translation- I don’t want to do it!

2. Lack of Perseverance- Translation- It’s too hard!  I give up!

3. Lack of Retention- Translation- I don’t know.  Blank look.

4. Aversion to word problems- Translation- Can I just have a sheet of numbers.

5. Eagerness for a formula- Translation- Can you just show me how to do it?

By purposely and deliberately creating an environment where mathematics exploration and discovery flourish we can harness the inner mathematics explorer in our students.


Exploration is really the essence of the human spirit.  Frank Borman

ETAD, Learning, Motivation, Professional Development

Learners or Students???

Is there a difference between students and learners?  This question has been rattling around in my brain for a while now. In fact it started almost 2 years ago when I read this amazing post about learners and students by David Warlick.  I began noticing that many people seemed to use the two words interchangeably as if they meant the same thing…but do they really?  In looking through dictionary definitions I failed to find any clarity.  Students are defined most frequently as people who learn in school.  Most dictionaries do not define learner.  Instead they direct you to the word learn and by so doing make the connection that learners are ones who learn.  All of the definitions gave me the impression that learners and students were the same thing and that the words could be used interchangeably.  

For me this just doesn’t feel right.  These definitions seem to fall short of capturing the true essence of what students and learners were.  So I’m back to my original question.  With the realization that the definition needs to come from me and be rooted in my experiences.

What is a student?  In my mind a student is a person who is learning, typically in a formal environment or institution.  Students are placed into grade alike classrooms, assessed and evaluated and moved on through the system one grade after another.  When I think of students I think of books, backpacks, desks, rows, and order.  Order in the classroom, order in the school, order in the system that is providing the education.  

Digging into my past experiences as a student in school I have many happy memories.   I was a great student.  I knew the “stuff” I was told I needed to know.  I knew how to be successful because I could easily figure out what teachers wanted from me.  I knew the game of school, what the rules were, how to follow them and could easily jump through all of the hoops.  I could memorize facts, poems, information, formulas and then recall them for my teachers when asked to do so.  I loved tests and exams because they allowed me to show how smart I was and almost always provided me with a chance to shine. 

When I became a teacher I realized that I had a problem…my learning as a student was not always helpful.  Knowing “stuff” didn’t matter, knowing “stuff” didn’t help the children in my class learn it, knowing “stuff” didn’t help me become a better teacher. What I needed to learn was not the “stuff” but how to use it, adapt it, make it my own and more importantly, make it work for my students.  From that day forward I needed to become a learner.

What was different?  As a learner I wanted feedback not grades.  I sought out opportunities for collaboration not competition.  I was in control of my learning and pursued not only areas of personal passion but also areas where I needed to grow to better support the learners in my classroom.  This learning was not always orderly in fact it was often very messy but it empowered me in ways that my learning as a student never did.  As a learner my learning was not confined by a building, a time or a preset curriculum it was set by me.  This learning was relevant, authentic, engaging and extremely satisfying

My inquiry is not over on this topic but I do believe that there IS a difference between being a learner and being a student.  This difference appears to lie largely in who is in control of the learning and in the creation of understanding that transcends any one place and time.