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

3 Reasons 1st Grade Isn’t Too Early to Teach Digital Citizenship #TeacherMom

For a kid whose internet use is still limited almost exclusively to Netflix, I’ve been surprised just how enthralled my first grader has been by White Ribbon Internet Safety Week. I’m sure that this has more than a little to do with all the prizes her school is raffling off for participation, but still.

She came home eager to chat about all the Internet safety “power boosts.” What surprised me even more than her enthusiasm was her ability to make important connections, even without the context of full internet use.

So today’s #TeacherMom post is a follow-up on my post entitled, “3 Reasons High School’s Too Late to Teach Digital Citizenship.”

#1: It helps them build intuition and confidence.

In the course of our conversation, my daughter and I watched a Youtube video about cyberbullying that featured some boys taking a picture of a classmate, adding unkind captions, and then circulating it through the school. When we finished, my daughter told me about how an older student asked to take a selfie with her at Halloween, and she wondered if that had been cyberbullying.

In that moment, the protective mama-bear side of me just wanted to blurt, “Never let anyone take your picture without permission [because cyberbullying]!” But instead, we discussed that moment in the video when the boys sneakily snapped that girl’s photo and walked away laughing. I asked her how that moment felt, and how it compared to how she felt when the student asked to take a picture with her in their Halloween costumes.

She concluded that the older student had not intended any harm in her situation, and was able to begin to learn about identifying and trusting her own gut feelings. And since I know I won’t be there in most of her future moments of uncertainty, I’m grateful that she is learning such discernment now.

(I also loved that she made a great connection here with a phrase from her teacher: “Hurtful or helpful?”)

#2: It helps them learn to be true to themselves.

Given that my daughter doesn’t yet have much of an online presence, it was a bit confusing for her when we discussed the “power boosts” that involved friends doing or saying silly things online. But we were able to start the discussion about how some people think that their internet lives are different than their “real” lives, and so they do and say things online that they would never say in-person. I loved that we are already building the foundation that we should “ALWAYS be the same in person as you are online” (LivBits, an inspiring young digital citizen I recently wrote about). As a result, she doesn’t even have time yet to develop the notion that her online self will differ from her in-person self.

#3: It gives the opportunity to model our own digital lives. 

Because the White Ribbon week focuses on safety for young kids, one of the power boosts says, “I will use tech to connect with my REAL-LIFE friends. People online are not always who they say they are.” In this context, we discussed how there are people who try to “make friends” online and get kids to meet with them to cause harm. However, I also got to tell my daughter about how now, as an adult, I get to connect with and learn from teachers all over the world that I haven’t met. But we also returned again to safety measures that I take now as well.

When my daughter wants to play outside with friends in our neighborhood, we talk both about the safety and the possibilities. I am grateful for the opportunity to lay the same foundation for her digital life.

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Inquiry into Collaboration

Whether you are beginning the PYP Exhibition or otherwise would like to recharge your students’ teamwork skills, this week’s provocation centers on collaboration.

One word of caution however: spend more time “coaching from the side” than you do lecturing from the start. Chances are, they’ve heard it all before, and they need hands-on, timely feedback more than anything! (I’ve definitely gotten this all backward in the past, giving far too much time and energy to the initial instruction and then expecting them to put it into practice effectively).

Resource #1: “They All Saw A Cat” by Brendan Wenzel

via Amazon
via Amazon
via Amazon
via Amazon

Both the advantage and disadvantage of collaboration lies in the fact that we all have different perspectives. Enter “They All Saw A Cat” to get kids thinking about what this means.

Resource #2: 21 Balançoires (21 Swings) by Daily tous les jours

Every time I watch this, I keep forgetting that the background music was not, in fact, a professional soundtrack, but was created by these people simply cooperating with one another on the swings. Sure to evoke serious thought from your students!

Provocation Questions:

  • Why does perspective matter when it comes to collaboration?
  • What makes collaboration work?
  • How has the need for collaboration changed over history?

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There is Room for Us All. There is Room for Us All. There is Room for…

What alarmed me most, however, was what I saw in student eyes from up on that stage.  Those who wanted the event to take place made eye contact with me.  Those intent on disrupting it steadfastly refused to do so. It was clear to me that they had effectively dehumanized me. They couldn’t look me in the eye, because if they had, they would have seen another human being. There is a lot to be angry about in America today, but nothing good ever comes from demonizing our brothers and sisters. ~Allison Stanger

These are the words of a professor who participated in an attempted campus event for Charles Murray to speak (attempted because chanting, chair/window-banging, fire alarm-pulling, etc. ultimately prevented his voice from being heard).

Most, if not all, teachers I know advocate for the principle that we teach our students how to think, not what to think. They invite debate, research, critical thinking, and civil discourse.

So, what is happening here? What is getting so broken when assumptions and hatred win over open-mindedness and compassion?

I believe it comes down to dehumanizing those that seem on “the other side,” even as we work to dispel intolerance. And while I want to make it clear that I don’t believe teachers are to blame for this occurrence, I believe there are some important questions we can ask ourselves to ensure we are, at the very least, not contributing to the problem:

  • Do our students get the sense that there’s a “right answer” when discussing social justice issues?
  • Do we make more room for social issues that align with our personal ideology than with a wider scope (ie, issues facing only one group, a specific political agenda, etc)?
  • When there are misconceptions, do we work to familiarize our students with the individuals around whom those misconceptions center? (see a great example of Pernille Ripp’s class Skyping with a refugee).
  • When we direct our students to research material, do we ensure it is as neutral as possible, or at the very least, balanced?
  • When we disagree with our students’ (and usually their parents’) opinions, how do we respond? What measures do we take to ensure a safe exchange of ideas to promote learning for all (see lessons I learned when parents of one of my 5th grader started pulling their student early each day to miss our read-aloud that involved race)?
  • And perhaps most important of all: When we encounter opinions that sharply clash with our own, do we ourselves start to define that student/parent/colleague more by that opinion than by their humanity? In other words, do we fixate more on how we differ than how much we share in common?

As I have continued to ponder this matter, I realize that I keep seeing this message again and again — that there is genuine power in focusing on what makes each of us human. Here are a few examples from recent resources:

#1: From “Why do Labels Matter?” by SoulPancake

“If we get curious about each other and don’t stick in our bubble, I think that actually can save the world…Because that is where you get to the unifying things…You realize, oh, someone who has been criticized their whole life for what they look like — all of a sudden I remember the places where I’ve been criticized and I go, We have common ground there. So in a sense, we are all the same, but it’s through the differences that you get there.”

#2: “Drawing a Line in the Sand” from Seth Godin’s blog

Problems aren’t linear, people don’t fit into boxes. Lines are not nuanced, flexible or particularly well-informed. A line is a shortcut, a lazy way to deal with a problem you don’t care enough about to truly understand.

#3: “The Tough Work of Improving School Culture” by Brendan Keenan

via Edutopia by Brendan Keenan

#4: Trailer for Accidental Courtesy by Daryl Davis

“For the past few decades the black musician, actor and author has made it his mission to befriend people in hate groups like the Klu Klux Klan by calmly confronting them with the question:

“How can you hate me if you don’t even know me?””

Even when we vehemently disagree, there is room for us all. Because of our humanity. And this is a message our students deserve to have both protected and modeled in every classroom.

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Recovering from Perfectionism for Our Students, for Ourselves

Can you picture the first time you tried to write bubble letters? I don’t know about you, but for me, it did NOT go well. The letters bunched at the end of the page. Some parts of each letter were too fat. Others were too skinny. I knew my attempt looked nothing like my older sisters’ bubble letters, and even less like the cool typography I saw on posters.

I didn’t want anyone to see the ridiculous letters I had drawn. I wanted to hurry and throw the paper away and quickly revert to normal writing — quick! — before anyone could see that I had tried to deviate.

And that is pretty much how I felt about failure throughout my childhood.

AJ Juliani recently wrote about the difference between fail-ing and fail-ure, emphasizing the fact that when we focus on failing, we focus on the process and on how we pick ourselves back up. On the other hand, failure doesn’t have anything to do with getting back up, or with that resilience and determination.

And this is key for that wily perfectionism.

As Brene Brown wrote in The Gifts of Imperfection,

“Perfectionism is not the same thing has striving to be your best. Perfectionism is the belief that if we live perfect, look perfect, and act perfect, we can minimize or avoid the pain of blame, judgement, and shame. It’s a shield. It’s a twenty-ton shield that we lug around thinking it will protect us when, in fact, it’s the thing that’s really preventing us from flight.”

For our students, who are particularly susceptible to making efforts based on peers’ perceptions, we owe it to them to model what shaking off perfectionism looks like. To show the fails and, more importantly, the subsequent attempts.

These days, I try to be honest about what my “getting back up” looks like on a regular basis (When DIYpd Goes Terribly Wrong…Or Does It; That Time I Failed At Inquiry; What Driving Stick Shift Taught Me About Teaching). Where our students are concerned, I think that’s the least we can do if we expect them to take risks and to be courageous as they stretch, fail, and grow each day. And let’s be honest — it’s the least we can do for ourselves.

Here are a couple of videos (by New Age CreatorsDiana Laufenberg) that have inspired me in my continued journey to let go of perfectionism, and to truly learn from failure. May they do they same for you!

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Citizenship: A Sharing the Planet Provocation

This is part of a series of of IB PYP units of inquiry provocations. For more, click here.

The notion of what it means to be a citizen has a longstanding role in schools everywhere. For this reason, we must recognize it in all its modern variations. In addition to traditional community/national citizenship, digital and global citizenship have also taken on crucial significance in the 21st century.  

In all its forms, citizenship comes down to helping everyone find a sense of belonging and contribution to the world. If we are to truly share the planet, we must do all we can to help our rising generation see themselves as local, national, global, and yes, even digital citizens.

Resource #1: “Lead India, The Tree” by Times of India

Resource #2: “I am Malala – UN Speech – Video Animation” by Juley Anthony

Resource #3: “The Power of One Young Digital Citizen

Provocation Questions:

  • What does it mean to be a citizen?
  • What are our rights as citizens?
  • What are our responsibilities as citizens?
  • How are education and citizenship connected?
  • Why are there different perspectives on what it means to be a citizen?
  • How is the concept of citizenship changing?

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The Issue of Focus: Working for Student Ownership

Glazed-over eyes. Wandering minds. Fidgeting bodies.

There are endless reasons our students might be disengaged, and almost an equal number of ways to address it. There’s the good:

  • Evaluating & reworking our practices (Too many worksheets? Not enough movement?)

The bad:

  • Ignore it and press forward with a ghostly Professsor Binns doggedness.

And the ugly:

  • Blame it exclusively on the kids and technology (vocalizing with key phrases like “newfangled,” “millennials,” and “lazy.”)

In the midst of a long winter while teaching 5th grade (February can be particularly tough around here), one approach came to me in the form of this quote:

“People think focus means saying yes to the thing you’ve got to focus on. But that’s not what it means at all. It means saying no to the hundred other good ideas that there are. You have to pick carefully. I’m actually as proud of the things we haven’t done as the things I have done. Innovation is saying no to 1,000 things.” ~Steve Jobs

The lightbulb flicked on, and I immediately turned the quote into a poster above my door.

As a class, we analyzed the quote together and came to several conclusions, the most important of which was to validate those “other good ideas” on our students’ minds. The discussion went something like this:

“So, is it bad to want to play with toys? Of course not! Is it bad to think about planning your get-together with friends? Absolutely not. Those are good and important things, too. It’s just that we have to say no to those other good things when you have other important things to turn  your attention to.”

This was pivotal for many of my students. The demand to “focus” had long been a struggle of good vs. bad — the things adults wanted vs. the things they wanted. This reframing helped them see that we all have to regularly choose focus by saying no to the other good things in our lives.

It became clear that this kind of validation strengthened my relationship with my students, building mutual trust. It helped them see that I am human, too, and that I, too, need to learn to prioritize my time.

One important note, however: if we view this or any other similar approach as a simple strategy to placate our students, we miss the broader picture. Rather, we should view this as one step toward greater student ownership over their learning. Only then will we move from disengagement to engagement, and then finally to empowerment.

featured image: DeathToTheStockPhoto