Tag: math

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Inquiry Into Being a Mathematician

This is the 3rd installment of learning identities provocations (completed: Inquiry into being a Writer, Reader).

Inquiring into what it means to be a mathematician is near and dear to my heart because I certainly never identified as such during my school years. So many of us are/were of this mindset: convinced that mathematicians are those people, with little to do with us.

But the truth is we can all start telling  ourselves a much more inclusive story. Being bad at recalling math facts does not exclude one from being a mathematician; nor does being a pro at reciting math facts automatically create a mathematician. Rather, we must all reframe our thinking, identifying our own very real, practicable, and even creative mathematical applications, that do, in fact, make us mathematicians.

Resource #1: Beauty of Mathematics by Parachutes

Resource #2: Tweet by Aviva Dunsinger

Resource #3: Which One Doesn’t Belong? collaborative website by Mary Bourassa

Resource #4: Infinity & Me by Kate Hosford & Gabi Swiatkowska & A Hundred Billion Trillion Stars by Seth Fishman & Isabel Greenberg

 

Provocation Questions:

  • What does it mean to be a mathematician?
  • How does doing math compare to being a mathematician?
  • What is the connection between creativity and being a mathematician?
  • How can we build our sense of ourselves as mathematicians?
  • What is our responsibility to be a mathematician?
  • What impact does mathematics have on our lives? On our communities?

featured image: DeathToTheStockPhoto

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Inquiry into LARGE Numbers

My hope is for this provocation’s use to not be limited solely to teaching place, but to help kids gain a greater perspective of this bewilderingly large universe. That though we may be finite, with limited comprehension of the vastness, we do, in fact, have a place in it all. Enjoy!

Resource #1: VIDEO (not embed-able) “Forest of Numbers” by Emmanuelle Moureaux

Resource #2: A Hundred Billion Trillion Stars by Seth Fishman and Isabel Greenberg

Resource #3: How Much is a Million by David M. Schwartz & Steven Kellogg

Resource #4: Infinity & Me by by Kate Hosford, Gabi Swiatkowska

Provocation Questions:

  • How do we measure large numbers?
  • What are characteristics of large numbers?
  • Why does it matter to be able to measure very large numbers, even when they seem beyond comprehension?
  •  What is the difference between large numbers and infinity?
  • What does infinity mean to you?
  • How do large numbers, and/or infinity, impact your life?
  • How do large numbers, and/or infinity, impact society?

featured image: DeathToTheStockPhoto

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Inquiry into Numbers

An educator in my PLN, Matthew Oldridge, recently shared a fabulous perspective on mathematics:

“Kids should see mathematics as a thinking tool to use to engage with the world.”

I have long since been an advocate of helping students see the power and wonder of their words; I’m afraid I cannot say the same for numbers. So this week’s provocation centers on helping our students inquire and wonder into numbers.

Resource #1: A Brief History of Banned Numbers, by TED-Ed

Resource #2: 1+1=5: And Other Unlikely Additions, by David LaRochelle

Resource #3: Beauty in Numbers: Pi, by Rebecka Taule

Provocation Questions:

  • How do numbers work?
  • How do numbers allow us to interact with the world around us?
  • What if we did not have numbers?
  • How are words and numbers related?

featured image: DeathToTheStockPhoto

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On Jumping In Too Fast #TeacherMom

My 3 year-old asked to play a round of “Go Fish.” Apart from his tendency to ask if I have any sharks every time — whether he has any sharks himself or not — he has gotten the general idea of the game by this point.

As we started to acquire matching sets, I deliberately modeled 1 to 1 correspondence as I counted out my sets (ie, “Onnnnnnnnne” [while laying out the first card], “Twwwwwwwooo” [while laying out the second], etc).

And with probably excessive satisfaction, I watched as he reciprocated 1-1 counting with his own sets.

While starting to count one of his subsequent sets, I noticed that he missed the correspondence of naming “One” while simultaneously laying out the first card. And of course, as 1 to 1 correspondence requires us to understand that we can only count one number per object, I was ready to jump in to supply correction.

But, in that brief moment, sensing he was still working things out, I decided to bite my tongue and hold back. And I observed his quiet thinking: “Oh…wait, no…Onnnne” [while firmly laying out that first card again].

He’s already recognizing 1-1 correspondence for himself, thank you very much!

And I realized that I almost missed the whole thing with premature intervention — and more importantly, that he almost missed the opportunity to let his thinking catch up with his hands.

Sometimes, we just need time. I am reminded of this by the many teachers in my PLN who are choosing to slow down as they start the school year, allowing their students to settle into all the new routines, absorb all the new concepts, and build all the new relationships.

It seems to me that when we are too hasty with our learners, we’re often making it less about their learning and more about our fears (falling behind, failing to preempt problems, etc).

Most importantly, making a shift from hurried problem-solving toward reflective observing/questioning, we leave much room for inquiry, curiosity, and quiet thinking.

featured image: DeathToTheStockPhoto

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How Ownership Can Get Rid of “I Suck at…”

Think having students self-grade and reflect is fluff?

Think again.

Over the course of a 15 year study, John Hattie analyzed over 800 meta-studies to identify effects that have the strongest impact on learning (and he is constantly updating this list through continued studies). Self reported grades is almost at the top of the list of over 150 effects.

It beat out motivation. It beat out home environment. It even beat out “decreasing disruptive behavior.”

The truth is, students know a lot more about their own learning process than we so often give them credit for.

Which brings me to the issue at hand: When a student claims he/she “sucks at ___.”

When I hear that claim, I hear a student that has become convinced that their personal rate of learning is inferior to classmates. That because their progress has not looked identical to their peers, it must mean they are defective. That their learning is fixed, hopeless, and beyond theirs or anyone else’s reach.

Now, discouragement is normal for all learners from time to time. But when said discouragement is also rooted in learning that feels irrelevant or imposed, we’ve got problems.

Enter student ownership.

Any time we empower students with tools to take their learning in their own hands, we are giving them ownership.

Self-assessments are one such powerful tool.

Michael BondClegg recently wrote about giving students the opportunity to write their own report card comments, encouraging teachers to help students identify “ways in which learners can identify their strengths and areas for growth” and “plans for improving.”

This may seem trivial, but really, it turns the whole “I suck at” model on its head.

When a teacher fills out the comments, it perpetuates the whole “this is out of my hands” notion.

When a student is encouraged to fill out those comments in this way, it places the learning back in the students’ hands.

A student in diagnostics mode is student on her way toward a stronger growth mindset.

 

featured image: DeathToTheStockPhoto

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Provocation Into Visual Mathematics

Many of us have spent just as much time in math courses as we have spent wondering the point of those math courses.

However, today, what makes mathematics most fascinating — that is, visual representations — are more widely shared and distributed largely thanks to social media. And perhaps this is how math teachers everywhere will at last be able to help their students understand “the point.”

Resource #1: Fibonacci’s Spiral

Resource #2: Charts that visually debunk falsehoods.

Resource #3: Power of Infographics

Provocation Questions: 

  • How can visual mathematics help societies?
  • How can visual mathematics help individuals?
  • What are patterns in visual mathematics that are relevant to your life?

featured image: DeathToTheStockPhoto

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Inquiry into Scale & Perspective

Being more spatially-challenged in general, I always had trouble as a child comprehending concepts like mirror images, rotations, and geometry nets.

Fortunately, as a grew older, I learned that these are all just facets of broader concepts of scale and perspective. I’ve also benefited by recognizing their applications beyond mathematics–from art to city planning to interpersonal relationships.

So this week consists of a provocation to help our young learners begin with the big picture of scale and perspective, hopefully encouraging them to draw their own connections and conclusions.

The first is a fascinating video that lays out the entire history of the earth on a football field.

The second is a photo series by artist Matthew Albanese. He creates stunningly realistic landscapes using forced perspective, using materials from nutmeg to steel wool to fake fog. Head over to his site to view the collection of images, along with the incredible behind-the-scenes images and information on his process. 

Provocation Questions:

  • How do people use scale and perspective to help us see “the big picture?”
  • How does technology allow us new possibilities to show scale and perspective?
  • How do scale and perspective change the way we see the world?
  • What is our responsibility to use perspective in our lives?
  • How are scale and perspective connected?
  • How does perspective help us understand other people?
  • How does scale help us understand the world?

featured image: DeathToTheStockPhoto