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

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

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

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

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

 

Mirage of Success: Learning the Math Trick

If you, like me, have ever waffled on the debate of whether we “just teach them the trick” for math before, take a careful look at this side-by-side comparison of students showing their math thinking.

Example A:

Example B:

My question is this: even if teaching the trick gets students to pass the test and ace the class and get into the college–have we, as educators, truly done our jobs?

If we’ve never heard their creative approaches to making sense of math because we’re too busy telling them the right way to “borrow,” have we joined them in their learning journey, or are we scripting it?

If we just keep focusing our energy in helping them memorize, are our students ever going to see themselves as competent mathematicians? 

featured image: Shubhojit Ghose

Marveling Over Math

Many of us have a love/hate relationship with math. And depending on your students’ ages, they may have thoroughly convinced themselves that they hate it or are no good at it. If that’s the case, we have all the more responsibility to help our students see the bigger picture and the true beauty behind the numbers, starting with our own attitude.

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via Network Osaka

This is easily the most phenomenal mathematics video I’ve ever watched. Share it with your students to provoke inquiry and appreciation for math–and at only 1:41 minutes, don’t be afraid to play it again and again as the conversation deepens and understanding sinks in.

Provocation Questions:

  • What if we didn’t have a number system? (thanks Graeme Anshaw for sharing this excellent provocation)
  • Why do people decide they “don’t like math?”
  • What are the origins of math in human history?
  • What difference does it make in a person’s life to see him/herself as a mathematician?

featured image: DeathToTheStockPhoto.com

Come back next Monday for another “Inspiring Inquiry” post. Read here for the rest of my weekly blogging topic schedule/background.