Mark Barnes
ABOUT THE AUTHOR

Mark Barnes

Mark Barnes is the Founder and CEO of Times 10 Publications, which produces the popular Hack Learning Series. Barnes presents internationally on assessment, connected education, and Hack Learning. Join more than 125,000 interested educators who follow @markbarnes19 on Twitter.

The Power of Unanswerable Questions

Let me begin with full disclosure: Before I learned about Unanswerable Questions in Hacking Mathematics, by Denis Sheeran, I thought just about everything math related was unanswerable. Admittedly, math has always been pretty elusive to me.

After reading about Unanswerable Questions, though, I’m looking at math and pedagogy differently.

Rather than talk around Denis Sheeran’s concept, I thought I’d just share it straight from the mathematician’s mouth–or at least from his book.

From Hacking Mathematics: 10 Problems That Need Solving, with permission from Times 10 Publications

THE PROBLEM: STATISTICS FILL DAILY

LIFE, BUT NOT MATH CLASSROOMS

You’ve just about finished a chapter in your textbook

or unit in your curriculum materials and then

you notice it, right there, staring you in the face. What

is it you see, menacingly staring back at you? The last

section of the chapter: the statistics section, sometimes

called “statistical connections” or “data around us” or

“modeling.” No matter what it’s called, it gets translated

by a lot of math teachers as “Skip me, you don’t have

time.” But don’t jump on the skipping bandwagon.

Find the mean. Find the median. Find the mode. Make

a bar graph or pie graph. What’s the probability of flipping

heads on a coin? Twice? These are the instructions

and questions that encompass the complete statistical

learning many of us received in middle school, mostly

with data sets of five to ten pieces of information. Some

of us who had more adventurous teachers may have even

made graphs of bivariate data and tried to come up with

our own lines of best fit using completely non-statistical

methods by employing our understanding of writing a

linear equation using two points.

 

 

 

 

We live in a different world now, where large data sets

are available instantly and calculation tools can organize

and calculate all we need to know in less time than it takes

to sharpen our pencils. It is no longer useful to spend our

time teaching arithmetic and calling it statistics. In today’s

classroom, the mathematics teacher has the opportunity

and responsibility to create statistical thinkers.

Unanswerable Questions will develop statistical thinkers

in your classroom.

Rather than dwell on the past, let’s look at the present

and the future for most of us. Our standards and materials

spell out the statistical concepts we are to teach. What has

changed for our students is that the standards no longer

ask for students to calculate and find statistical values,

but instead to recognize relationships, understand variability

and its effect, and make predictions based on

interpretation of data. In short, true statistical thinking

is missing. Statistics in today’s schools should be based on

Unanswerable Questions.

THE HACK: ASK UNANSWERABLE QUESTIONS

When we ask students to find the mean of the heights of

the twenty-three students in our class, we are asking them

to average numbers together, which is a very easy question

to answer and an even easier question to grade. Instead,

when we ask, “How tall is the seventh grade?” our students

must begin an investigation that takes them much deeper

into statistics. They will discuss how to obtain the necessary

information, devise a plan (one that likely won’t work

or is completely unrealistic), refine that plan, measure each

other, standardize their measurements, find means, graph

information, and maybe even come across the idea of a distribution

of data. That’s all before the teacher even needs to get involved.

Since up to this point in their mathematical education,

most questions have had numerical and final answers, the

desire to answer an unanswerable question will continue

to motivate the students to work and think and collaborate.

Finally, they will come to a point where they are

satisfied with their inexact solution to the problem, therein

revealing the heart of statistics: using what we know to

infer about what we don’t know until more information

comes along and either changes our minds or gives us a

reason to reopen the question. Unanswerable Questions

will develop statistical thinkers in your classroom.

WHAT YOU CAN DO TOMORROW

There’s a reason your textbook or curriculum source

has the stats section where they do. It’s very likely that

it ties into the unit you’re teaching in a deep, meaningful

way. Here’s how to start harnessing the meaning

and inspiring your students to think statistically.

Look at the statistics section first. See what

statistical concepts are connected to the lessons

you’re teaching in this unit, and work

backward. Find an Unanswerable Question

that you can share as you open the chapter,

and refer to the question throughout.

Find claims in the media to discuss. Every

single day, you can find stories in the media

with claims made about a company, a government

office, an auto manufacturer, or a

school. Present students with the opportunity

to debate those claims. It’s likely that in little

time, they’ll need a statistical process to back

up their claims.

Share the unlikely. Lottery winners, survivor

stories, and game show outcomes will foster a

statistical conversation in a hurry. When you

read about them or see statistics in the news,

make note of it and bring it to class to start

those conversations.

Find Unanswerable Questions in sports.

Don’t ask answerable questions, like what

a player’s batting average is now that he’s

struck out three times in a row. Dig deeper

for the Unanswerable Question, like asking if

batting average affects salary in baseball. Or

which baseball stat has the biggest impact on

player salary? Those are tough, if not impossible

to answer.

THE HACK IN ACTION

One of my favorite Unanswerable Questions comes from a

TV commercial that aired during my childhood. It involved

a cow, a fox, a turtle, an owl, and a boy. The Unanswerable

Question: How many licks does it take to get to the center

of a Tootsie Pop?

Show the old commercial to your class—it’s on YouTube.

Then, after fending off questions like, “Why does the

owl eat the lollipop?” and “Is this some kind of fable?”

and “Why isn’t the boy wearing any pants?” you can get

started.

The Answerable Questions:

What are the characteristics of a Tootsie Pop that we

need to take into consideration?

What is a “lick” for the purpose of the experiment?

What needs to be measured, and how?

In sixth grade, students need to be able to recognize that

a statistical question is one that anticipates variability in

the data. While the class is discussing and defining the

components of the Answerable Questions, they will see

that variability exists, even in their definitions, and as such,

will exist in their data. Even when they come to an agreement

on definitions and procedures, they will quickly find

that during the data gathering, different students are following

the procedures differently. This leads them directly

into the next question: What do we do with our data?

Students may have enough mathematical acumen at this

point to be able to make good, if not entirely correct, suggestions

as to what should be done with the data—so let

them. In my experience, by the third or fourth suggestion,

they come up with “Average it all together,” or “List it from

smallest to biggest,” and even “Graph it.” At this point, I

may break the class into teams to complete each of the different

valid suggestions and report back, or I may take one

of the suggestions and run with it, depending on the focus

of our previous and upcoming content instruction.

Click image to learn more

Sixth graders need to be able to describe the distribution

of the data using its overall shape, center, and spread,

and recognize that its center describes all the data at once,

while the spread (variation) describes how all the data is

different from each other. They also need to be able to

display the data on a number line (dotplot or histogram)

and describe the distribution in context.

I expect my sixth graders to be able to say: “After

licking both sides of our own Tootsie Pops until each student

reached the chocolate center, we counted the number

of licks per student on each side. The mean number of

licks was ##. This was more/less than I expected. When

we graphed the data, the distribution was almost symmetrical

except for one point which took many more licks

to get to the center. The median, or middle value, was

less than the mean, and I think that’s because of the large

number of licks it took on one Tootsie Pop. No one licked

more than ## times or less than ## times before reaching

the center.”

Remember, the goal with sixth grade is not to pass the

AP Stats test, but to introduce data-gathering methods,

require correct statistical language, and to develop the

ability to describe sets of data. To extend this to higher

grades, weigh the lollipops first and compare weight and

number of licks as a linear relationship. (There’s a surprise

ending to that one that I won’t divulge). Students

should also discuss whether or not the Tootsie Pops could

be called a “random sample,” and what randomness is

and why it is important.

— end excerpt

Learn more about Unanswerable Questions and other problems that need solving in Hacking Mathematics.

Available on Amazon

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More from the Hack Learning Podcast

Video produced by Tootsie Roll, 2012

kid hates school

My Kid Hates School But You Can Help

One social share can immediately impact change. “My kid hates school,” I shared on Twitter and Facebook, and suddenly I had support from people around the world.

Here’s what happened. I tweeted this then shared it on Facebook.

School must get all kids to comply. School must organize large quantities of children, manage them, sort them, quiet them and control them. For a lot of kids it may not be a big deal. For some, it’s like stealing their soul. — Anonymous

Some weighed in by raging against the machine:

One regular commenter in this Facebook group had this initial response:

No, you can’t. You can advocate, you can argue, and you can encourage him in a variety of ways. But you can’t change the school or the teachers–it’s not in your power. You can help him to find satisfaction in other ways/venues and maybe within the school or within certain classes. Teach him to hack his own way, eh?

After all of these incredible comments and suggestions, I kept coming back to the previous quote.

And I wonder, is this right? Is school change out of my control? Is it out of our control?

Or, is it possible that we have all the power, and we only have to choose to exercise it?

At the very least, one expert, New York Times bestselling author Jessica Lahey, believes that we need to keep showing the evidence of what’s best for kids to educators. Here’s what the author of Gift of Failure tweeted:

What You Can Do Tomorrow

  • Talk about best practices: Create discussions on social channels and at your school about best practices. Ask, “How can we eliminate old school methods and replace them with progressive pedagogy that inspires student engagement?”
  • Share stories like this one: Share podcasts, blog posts, and Facebook statuses, in which parents and educators discuss their experiences about kids who hate school and what they’re doing about it.
  • Encourage participation: If a kid hates school, encourage her to join a club, go out for a sport, or try out for the play. The more kids participate in things related to school, the more likely they are to start enjoying it.
  • Be present: Talk to teachers, school leaders, and parents in your own school district–especially where you kids attend school–about making learning fun. Don’t let them tell you it’s not about the fun; that’s a load of crap and simply not true.

So, what’s my final take on all of this? I’ll continue to advocate for my son, and I’ll continue pushing his teachers–and all educators–to be the absolute best they can be.

With your help, I believe we can make a difference.

More hacky stuff

Find the Facebook discussion here.

Share your thoughts on Twitter at the #HackLearning feed here.

Subscribe to the podcast here.

Your Mission: Teach Kids to Debate, Rather than to Diss People on Social Media

Love him or hate him, it’s hard to argue that the president sets a great example of social media use for kids.

In her breakout book, Hacking Digital Learning Strategies: 10 Ways to Launch EdTech Missions in Your Classroom, internationally-renowned presenter and education technology consultant Shelly Sanchez Terrell demonstrates precisely how to teach students to debate issues appropriately, rather than disrespect people on social media.

Here’s most of Shelly’s Teach Kids to Debate EdTech Mission from her new book, reprinted here with permission from Times 10 Publications.

THE PROBLEM: ONLINE ARGUMENTS RESULT IN PERSONAL ATTACKS

Lately, the news has featured the long-standing Twitter feud between President Donald Trump and the media. The public has criticized both sides for their behavior. At one point, the argument escalated and the President tweeted a GIF of himself symbolically body-slamming CNN.

The news media took offense, claiming the GIF encouraged violence toward reporters; the Office of the President and Twitter disagreed. Tensions continue to rise.

This incident exemplifies the nature of many online arguments.

Children to adults share their opinions openly on social networks but are offended when others disagree with them. They react with aggression or resort to personal attacks. All involved seem to overlook the true issues, and all parties leave the conversation upset, learning nothing new about the topic and missing a powerful opportunity for debate to open our minds and elevate our thinking.

We need to transform the digital debating mindset and help students see debate as a vehicle to strengthen their intellect and character.

The way schools teach debate doesn’t align with how our learners conduct arguments in real life. Traditionally, we teach students to debate by writing argumentative or persuasive essays.

While this is important, our digital learners need to engage in online debates.

They need the opportunity to draft shorter arguments to share with the public, as well as practice in responding intelligently to those with opposing views. Our students may regularly debate or argue on social media, yet schools rarely afford them the opportunity to acquire respectful debate skills as part of the curriculum.

 

THE MISSION: ENGAGE IN A THOUGHT PROVOKING ONLINE DEBATE

In Missions 2 and 3, your students gained confidence in defining their digital identities and became aware of how their posts and shares impacted their digital reputations.

Those first steps laid the groundwork for this mission to participate in a respectful and thought-provoking virtual debate. Rich debate keeps the conversation going, celebrates differences of opinions and perspectives, and values well-constructed arguments.

All involved realize how a strong opponent opens their minds, challenges their beliefs, and improves their critical thinking skills. Additionally, healthy debate fosters peace, promotes democracy, and builds community relationships.

First, our digital citizens will learn how to craft clear, persuasive, and compelling arguments for an online forum. Their argument will state their positions, help their peers understand the reasons and logic behind their positions, and back up their views with support and evidence.

Then, classmates post respectful and logical counter-arguments, which further the dialogue. Students read these counter-arguments with an open mind and revise their initial arguments with new insights.

They develop strategies for dealing with abusive and hurtful comments, and learn how to passionately argue while keeping their emotions in check so they don’t personally attack peers, but instead argue points of contention.

MISSION PREP

As we know, online debates escalate quickly and bring out the worst in people. Young people may question the value of spending their time listening to beliefs and opinions different from their own, and they may attack the individual instead of logically rebutting specific points.

The activities below prepare learners to approach varying opinions with an open mind and focus their arguments on the issues.

Confront fears, myths, and intolerance: Anonymously poll students on their attitudes toward participating in respectful debates. Find a list of possible questions for the poll in the Mission Toolkit (Find the Toolkit in the Appendix section of Hacking Digital Learning Strategies). Present the poll results and host a discussion about tolerance, open-mindedness, and how differences help us grow and progress.

Grab Mission Toolkit 5 in Hacking Digital Learning Strategies

Play the agree/disagree warm-up: Students must take a stand on issues to be skilled debaters. Use masking tape to create a line on your classroom floor. Line students up on the left side of the tape, facing you. State a claim, such as, “Dogs are better pets than cats.” Instruct students to remain standing on the left side of the line if they agree and to move to the right side if they disagree. Students then face their peers. Starting on the left, each student gives one reason to support the claim. Then students on the right give reasons that dispel the claim. Continue this activity with safe topics and coach students to handle increasingly intense topics.

At various intervals, share rules and guidelines for building a safe environment to share opinions: Record these guidelines and tips to review later. For example, before students share their reasons why dogs are better pets than cats, state the rule that all must respect the listener. Elicit examples of how we show respect to foster understanding of the rule. After the first sharing of reasons, guide a group discussion to identify the components of strong reasoning.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

  • Identify the guidelines for fostering a good online debate: As a class, evaluate how online debates differ from face-to-face debates. Present the class with the guidelines they came up with for respecting each other during the warm-up. Determine which guidelines work for fostering a good online debate, and add additional guidelines to complete the list.

Improve online arguments: Show the class an example of an online argument that went awry. The initial opinion should be strong and exemplify good writing techniques, before the conversation descends into an argument within the string of comments. Reddit’s Change My View forum has great examples of strong arguments followed by good and bad counter-arguments. The arguments and comments must meet strict criteria, and the moderator pulls any comments that violate the rules. Have the class analyze the strengths and weaknesses of the arguments and come up with guidelines for their own arguments. Then have the class analyze the counter-arguments and identify the most compelling ones. They should identify what makes the counter-arguments strong and come up with guidelines for their own.

MISSION LAUNCH

Step 1: Focus arguments with a specific claim.

Instruct students to jot down ten strong, evidence-supported belief statements or viewpoints. The warm-up may inspire ideas. Have them cross out any ideas that they are tied to emotionally, that they don’t care enough about, or that promote violence, hate, or discrimination.

Students choose one of the remaining statements as their topic for the online debate. Help them transform their statements into specific claims that focus their arguments.

Step 2: Outline six valid reasons.

Review the qualities of strong support delineated by the class in the warm-up. Students outline a minimum of six reasons to support their claims based on these qualities and conduct a quick search of each reason to ensure its validity. They show a few peers their reasons and ask them to choose the three most persuasive and interesting before deciding on the three reasons they will include in their arguments.

Step 3: Survey people to gather insight and evidence.

Students create a survey with at least five questions to gather insight and evidence to support their claims and reasons. Help students draft clear, short, specific, and simple questions that will elicit meaningful feedback. Ask them to opt for multiple choice, open-ended, or ranking questions – and to avoid only yes/no questions.

I recommend Google Forms as a tool for students to create surveys. You can learn more about teaching with Google Forms in Hacking Google for Education.

Hacking Google for Education

Look Inside

Step 4: Post arguments and create counter-arguments.

Students post their arguments in a designated online platform. Note that the idea isn’t to post a five-page argumentative essay with scholarly resources. Think of this as a precursor to these types of essays.

These online arguments should consist of three paragraphs or less in simple language, with logic, reasoning, and evidence. The idea is to spark debate, which means the arguments must appeal to their peers and be easy to digest. Your young debaters should begin to prepare their counter-arguments.

Step 5: Counter-argue and refute the counter-arguments.

Once students post their arguments, other students post counterarguments. The counter-arguments should challenge one or two ideas made by the author and provide reasoning and support for their contentions.

Writers should check the forum and refute all counter-arguments. These counter-arguments must be respectful and address the contentions with well-thought-out reasoning.

Encourage students to concede on certain areas of agreement. The idea isn’t to win the argument, but to refine belief systems and values. Additionally, conceding on specific areas moves the conversation forward to debate other areas of the issue, which leads to a broader understanding of the topic.

Step 6: Introduce a troll.

After a few days of healthy debate, announce to the class that a troll has snuck into their forum in an effort to thwart their missions. Trolls are individuals who target an online group and post inflammatory or off-topic messages to provoke a reaction or start quarrels. The troll doesn’t want your students to gain the skills to promote healthy debate, because he wants them to join him in spreading chaos on the internet.

Shelly Sanchez Terrell

EdTech Missions Creator Shelly Sanchez Terrell

The troll joins the group for a day or two, and only after your students have engaged in healthy debate. Set up an account with the username Troll, and wreak havoc in all threads so no one feels singled out. Your class troll will not name call, use inappropriate language, bully, or do anything that would hurt your relationship with your students.

Instead, the troll might make outrageous claims about the argument, post the same message multiple times, ask silly questions, or spam the thread with nonsense.

Step 7: Come up with strategies to end the troll’s havoc.

Students must come up with strategies to effectively handle the troll and limit his destruction. Allow students to search the web for tips using the query, “deal with trolls” and test these strategies.

Often, trolls suffer from mental illness and the best way to deal with them is to limit engagement. Other tips include reporting them, blocking, and muting. Eventually, the troll gets bored and moves on to the next victim.

Step 8: Reconstruct arguments with new perspectives.

Students use the Final Post Template–available in Kit 11 of the Mission Toolkit–to complete their final posts, and highlight three or more peer statements that made them think deeply about their topics. (Find the Mission Toolkit in the Appendix section of Hacking Digital Learning Strategies.)

They should identify statements that incited them, challenged their thinking, pointed out ideas they didn’t address, directed them to interesting research, or introduced them to a new experience. The students quote each peer’s statement and describe what they learned from it. Finally, they conclude their post by revisiting their initial stance and describing what has changed….

Read more

Don’t miss the Mission Obstacles and how to overcome them and the Mission in Action for this chapter, along with Shelly Terrell’s powerful Mission Toolkit.

Click here, order Hacking Digital Learning Strategies at our bookstore and get 25% off with promo code: podcast

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Forget Politics and Teach Tolerance

What happened in Charlottesville, Virginia should not be politicized. Many of us, including me, have made this despicable event about the president and what he said in the aftermath of violent protests of the removal of a statue.

Do I have opinions about these statements? Absolutely, but this isn’t the place to share them. Teachers, parents, and school leaders are better served with a discussion about how the events in Charlottesville can lead to lessons about tolerance.

But is teaching tolerance really a teacher’s job? You bet it is.

The attitude that we should stick to the curriculum is as archaic as the one-room schoolhouse. Educators can’t assume their students will learn tolerance at home; white supremacists had parents, and they obviously didn’t learn it.

We can’t be effective educators if we are ineffective at teaching humanity, and we can’t be humane if we are intolerant.

The Problem: humans hating other humans because they are different

This seems so obvious that I flinched at typing it. Still, if teachers ignore it, intolerance and hatred will fester.

Most educators are quick to condemn the actions of protesters in Virginia, but condemnation often ends with a flurry of barbs at the president and/or the perpetrators. Then we get to school, and race to our daily lessons.

The Hack: Teach tolerance

Sure, discussing racism and bigotry with kids can be delicate and risky, but when handled efficiently, it can unify your students and create an environment that is conducive to longterm learning.

Every book in one place

The key to success is to leave politics out of it. Discuss the actions of protesters and the impact of their actions. Reflect on history and similar events. Create plans to avoid hate and violence. When you focus on the dangers of hate and intolerance, much can be learned.

What you Can Do Tomorrow: Act now, while the topic is front and center

  • Tell students you want a productive discussion about hate and intolerance: Share facts only about what happened in Charlottesville, Virginia on August 12, 2017.
  • Be clear that statements by the president are not part of the discussion: Remind kids that they are welcome to their political opinions, but you want to discuss the impact of hate in our country and how to avoid it in the future.
  • Be emphatic that hating others because they are different is intolerable in your class, at your school, in your community, and in our society. There’s no acceptable pushback on this one. We must teach kids that hate is unacceptable.
  • Start planning: Invite students to create a plan of tolerance for your class and your school. This is the kind of grassroots effort that can make a difference on a grand scale later.

Pushback: There will be plenty of hurdles with a lesson on tolerance. Feel free to share your in comments and on our Facebook page, where this post is currently pinned.

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