Creativity in Education: The Growing Publicity

Podcaster Dan Carlin recommends a reassessing the value of a K-12 education... he's not the only one.

Podcaster Dan Carlin recommends a reassessing the desired outcomes of a K-12 education… he’s not the only one.

I’ve discussed before the ideas on the increasing need for instructing our young people in a spirit of increasing creativity and flexibility in their learning. Sir Ken Robinson (@SirKenRobinson) is my favorite speaker on this need. He has some fantastic TED Talks that make the point strikingly clear. His book, Out of Our Minds, is a fantastic manifesto relating to this issue as well.

Until today however, the only people I was hearing making this point were educators. Until today. Today, I heard a podcast from Dan Carlin (@DCCommonSense), who is a political commentator formerly from the radio who has spent the last several years podcasting exclusively. His podcast, Common Sense with Dan Carlin, comes out every other week or so and usually stays to topics like the economy, foreign policy, and governmental corruption. He tweets to nearly 10k followers and his podcast is downloaded by probably five times that many people. I am a regular listener and he normally doesn’t discuss the education system.

Yesterday, he went there. He referenced Sir Ken Robinson and went on to echo much of what I find exactly correct about Robinson’s message. Says Carlin: “[The education system in the United States] was put into place 100 years ago to make good factory workers out of people, basically, to count change back at retail establishments, to be able to read the directions on the machines at the assembly line at auto assembly plant. Whatever is was, we were trying to create a level of middle class job-seekers that had the minimal skills required for their employer.”

He goes on to add, “The economic situation is such now that that is not the right kind of education for our students to have. [Our schools need to create] a different kind of person. You don’t need a person who is trained for a job. You need a person with a firm foundation that will enable them to be flexible and creative.”

And he doesn’t blame the teachers: “It isn’t that anybody in teaching doesn’t see the value in creativity. People who do are as stuck in the machine as any of the rest of us. If you are a teacher who is saying, ‘my goodness, the worst thing that is happening at my school is that the music programs are getting cut,’ what the heck can you do about it? Right? You’re trapped in an inflexible system just like we are when we talk about problems the government has.”

In his latest podcast, he expresses concern over whether or not the needed changes to the education system are going to be realized. Carlin’s skepticism is pointed at the structures that would likely put up roadblocks in the path of true progress in this regard: state and federal governments and the teacher’s unions. Whether or not he is correct in that regard is a matter of debate, but at the very least, innovation in education is lagging the innovation in most other areas of society.

So here we are. The days of industrial education should be coming to end. Many of us in the educational community are becoming aware of it and now those outside of the educational community are echoing the message. People from all over, in different fields, are recognizing the problem and are understanding the solution. At least Sir Ken Robinson and Dan Carlin seem to agree.

Our education system is designed for a world that doesn’t exist anymore.

The quotes are taken from Dan Carlin’s podcast entitled “Pie-in-the-Sky Cynicism” released 30 Jan 2013. It is currently available for free on iTunes.

Beyond Geometry (Help me please!)

A literary-minded student's contribution to my classroom decor

A literary-minded student’s contribution to my classroom decor

In my fifth year teaching high school geometry, an opportunity has come to me that seems interesting, challenging, and worthwhile. So, in addition to integrating the Common Core’s version of high school geometry into our school’s math program, the lot has fallen upon me to do the necessary research for (what could become) our school’s new AP Calculus class. Well, actually, I kind of requested the job because I need the hours for my masters program and I would be interested in teaching the class once it is planned.

Okay, so confession: I don’t have any idea what I’m looking at or looking for. I took calculus as a high school senior several (or more) years ago. I took Calc 1 at Lansing Community College and Calc 2 at Western Michigan University. I’d like to think that I could give the students a better experience than I had. In that mindset, I’ve spent the last two hours or so looking at different unit plans, textbooks, labs, and syllabi. I even put “the best calculus textbook in the English-speaking world” into a Bing search bar to see what came up. (Nothing useful, by the way.)

So, here’s where you can help.

I need advice. What are the best textbooks? What should I look for? What are my red flags?

I’m very inclined to project-based, or at least student-centered curricula. What resources are you familiar with that will support the students in an exploration of calculus instead of a year-long teacher presentation?

Can you provide links to awesome problems or labs?

All suggestions and recommendations is welcome. Even a word or two of advice would be welcome. Load up the comments. If it’s longer, is the way to get ahold of me.

Thanks for everything!

The Snickers Problem: The Aftermath

What math class looked like this week

What math class looked like early this week

There is nothing quite like watching the students get there hands dirty with the mathematics. This is especially true when the students are literally getting their hands dirty. In this case, it was with caramel, chocolate and nougat.

Here is some of the aftermath of the students exploring The Snickers Problem. (Check it out for a description.)

Snickers #2

To me, the value of this assignment lies in its ability to draw the students in. This problem featured 100% engagement. It featured the type of proportional reasoning that shows up in endless amounts in our unit on Similarity and Dilations. The students were analyzing the size comparison of a fun-sized Snickers and predicting the number of peanuts.

Others preferred the more antiquated utensils...

Others preferred the more antiquated utensils…

This was a fantastic activator. Formal proportional reasoning is difficult for many students, but informal proportional reasoning is intuitive. Many of the students found that their predictions were pretty close. (Although, we did find some Snickers that had remarkably low numbers of peanuts.)

Knife and fork worked for some

Knife and fork worked for some

And the fantastic questions that come up when students are thinking mathematically.

Is this prediction close enough?

What do we do about half-peanuts and peanut pieces?

Their prediction was right, but ours was wrong… but we predicted the same thing! Our snickers had different number of peanuts!

These are all evidence of students having to have an experience with the mathematics. That’s something I’d like to see more of.

Mathematical Creativity: Multiple Solutions to the Pencil Sharpener Problem

I enjoy watching students exploring a problem that forces them to come up with their own structure for solving it. Today, a group got a chance to mess around with The Pencil Sharpener Problem, which is a problem I posted a month or so ago. (I’ll leave you to read it if you are curious what the problem is.)

From my perspective, what makes this problem interesting for the students is the ease with which it is communicated and the complexity with which is it solved. It seems quite easy. The answer is fairly predictable, but the students quickly found out that if they were going to solve this problem accurately, they were going to need two things:

1. A way to organize their thoughts and,

2. a way to verify their answer.

As long as the solution process included those two things, the students ended up fairly successful in the process of this problem.

I submit to you four examples of student solution structures. They all look different, but they all have one thing in common: The students could tell you with absolute certainty what was on the page and that they were right. (I withheld judgment from the correctness, but I will say that their final answers were all pretty much the same.)

This one includes a bit of a floor plan

This one includes a bit of a floor plan

In this first one, shown above, this pair of students decided to draw a floor plan with each of the pencil sharpeners (and the bucket they were tossing their leftover pencil nubs). The solution process progressed from there.

Guessing and Checking

Guessing and Checking

These two students are classic minimalists. They worked to guess-and-check, which requires a bit more skill than it might seem. They needed to decided what number they were going to guess (sounds like an independent variable) and how to check their answer (sounds like a function producing a dependent variable). They weren’t using the vocabulary. It didn’t seem to be a problem for them.

Guessing and Checking

Guessing and Checking

These two were a little more formal with their guess-and-check process, and they were using the terms independent and dependent variable. For the record, the time was independent and the number of pencils sharpened was the dependent variable.

A graph of multiple equations (where the solution does not include finding an intersection point)

A graph of multiple equations (where the solution does not include finding a single intersection point)

These two struggled a bit to convince themselves that they were on the right track as they completed this graph. They were discussing the need for the graph to be accurate (essential), how to interpret the three sets of points (one set to represent each pencil sharpener). Eventually, the were able to find the spot on the graph when the numbers added up properly. The number along the x-axis represented the final time. (Once again, they didn’t call time the independent variable, but it looks so nice along the x-axis, doesn’t it?)

Each of these students would have likely looked at the others with confusion, yet their answers largely agreed. What it required for them to solve it wasn’t me, as teacher, telling them how. On the contrary, it required me, as facilitator, designing a problem they would engage with and then giving them the resources to make sense of the problem with each other.

Why aren’t more people talking about this?

About a week ago, Common Dreams reported on growing boycott of standardized testing coming out of Seattle.

I heard about it through an e-mail from a former professor of mine. When I posted it to Facebook, it got 2 likes, 1 share and a single comment (that also got 2 likes). Not a lot of interest.

There is also a growing number of post-secondary institutions that are shying away from ACT and SAT results when making admissions decisions. You can read the list of schools here. It isn’t a short list.

So, why isn’t this story of more intrigue to people? Standardized testing has become the means through which we make most of the decisions across the country. Whether you support them or not, why isn’t a growing boycott a bigger story?

To me, this is a great opportunity. If more school’s get on board and some momentum can be  built, this a fantastic chance for conversation to begin. Not a conversation about which test to give, or what content to test, but instead whether or not standardized testing is an effective means of evaluation.

I’ve talked about this before. In The Growing Case Against Standardized Testing, I reveal my hand as a skeptic of testing as it is currently done. I would love the conversation to get going because I think that educational community needs to produce answers to some key questions:

1. Do we have an agreed upon definition or description of a “successful” school? Have we done any studies to demonstrate the standardized testing process is an accurate predictor of a school’s “success”?

2. Why do we have so much faith in the standardized test results? What have we done to ensure the fidelity of the results?

3. Why is important that students get tested so often?

4. Do we have an agreed upon definition of a “successful” student? Are we convinced that test results are a predictor of current or future success of an individual student?

All of these questions get at the heart of Standardized Testing. There is a growing body of evidence that is piling up against the standardized testing model as an effective means of evaluating anything… a school, a student, a teacher, a leadership team, or a community, but policy makers seems to be taking no notice.

So, I ask again: when a major public school system has schools that are boycotting the tests and major universities are ignoring the results, why aren’t more people talking about this?

Common Core Geometry: An update one semester in

End of first semester provides a chance to reflect

Photo Credit: Flickr User “Neil T.” Used under Creative Commons.

This is our first go-’round with the Common Core Geometry. Without a usable textbook, our local geometry team has been responsible for most of the content. So, where are we?

We completed three units: Unit 1 was an introduction to rigid transformations. Unit 2 used rigid transformations to develop the idea of congruence, specifically congruence of triangles. Unit 3 began to formalize the notion of proof by using angles pairs and rigid transformations to discuss parallel lines cut by transversals, isosceles and equilateral triangles and parallelograms. (We should have finished one more unit, but that always seems to be the case…)

So, how did the first semester go? Well, the algebra-writing relationship is an interesting one. In previous years, our first unit was dedicated to writing and solving equations based on geometric situations. To see if the students thought that those two angles are congruent, we would put an algebraic expression in each angle and see what the students did with it. It turned largely into Algebra 1.5 with the mysterious “proof” added in for good measure. It didn’t seem to make much sense.

We have moved away from this for two reasons:

First, proofs are about expressing relationships in writing. It seemed silly that students would learn most of the geometry concepts through an algebraic lens and then we had to change gears to try to develop proof. We thought to start with the writing to smooth out the transition. Then, we could add the algebra back in later. The students have been through three straight algebra-based math courses leading up to geometry, so that will come back much more easily.

Second, we thought that another “same-ol’-math-class” might be what was sapping the enthusiasm and engagement. So, we have gone heavy on writing, creation, and visual transformations. The students have responded well. We’ll see what happens when the algebra makes a comeback in the second semester.

But, improvement is definitely needed. We weren’t prepared for the shift in the needs of our students in a non-algebra class. Our students aren’t learning with a great deal of depth. They are having a tough time writing with technical vocabulary. They are having a hard time making connections across topics. These are problems we are going to have to address moving forward. We were algebra teachers. I know dozens little tricks for solving all sorts of different equations. I don’t know a single one to help a student remember the different properties of a parallelogram.

I think we have done a nice job creating activities that will engage the students, but now we need to make sure the content depth is appropriate as well. It might be as easy as changing the questions that I ask. I can think right now of an activity regarding parallelograms as one that I didn’t draw out nearly enough depth from them. I didn’t facilitate the student thought and discussion. It slipped back into teacher-led note-taking. They struggle with the parallelogram proofs on that test. No surprise.

Please. If you have ideas, resources, processes, thoughts, lessons, handouts, anecdotes, or other helpful offerings, I will be accepting them starting now. Load the comment section up and be prepared for follow-up questions.


Oh, and if you are interested in reading a semester’s worth of my previous reflections on our new common core geometry course, here they are:

From Jan 7 – Vocabulary: The Common Core Geometry’s First Real Hiccup

From Dec 12 – Why you let students explore and discuss – an example

From Dec 7 – When measuring is okay…

From Nov 16 – Proof: The logical next step

From Nov 15 – When open-ended goes awesome…

From Nov 2 – Improvement under the common core…

Balancing Ruler Problem – A Surprising Solution, Part II

This is the last part of a multi-part series on balancing rulers. If you’d like, you can check out the original problem or the first part of the solution.

So, I mentioned last time that I was rather surprised at the result of the Balancing Ruler Problem. I expected the balancing point to be further away from the center. In case you are having a hard time reading the ruler, the balancing point of the one penny-two pennies ruler was at 5 7/16″ inches. This means that the prism was moved 9/16 of an inch toward the two pennies end from the center.

One Penny - Two Pennies

One Penny – Two Pennies

So, I decided that I would see how the position of the prism changes if the proportion of the masses stays constant, but the amount of mass changes. So, I recreated the balancing act with dimes instead of pennies.

One dime - two dimes

One dime – two dimes

The balancing point appeared to be at 5 9/16″. The prism was located a full eighth-inch back toward the center. In my mind, this demonstrated that the mass at the end is a variable as much as the proportion of the two masses. Also, it seemed to suggest that the prism will move away from the center if the masses are greater. So, I decided to test this hypothesis by combining the coins so that there was one penny and one dime on one end and two of each at the other.

One Dime, One Penny - Two Dimes, Two Pennies

One Dime, One Penny – Two Dimes, Two Pennies

The balancing point is located a 5 3/8″ meaning that combining the masses moved the balancing point another eighth-inch away from the center. This supported my hypothesis.

Well, what about quarters? Balancing point: 5 3/16″

one quarter - two quarter

one quarter – two quarter

And quarters and pennies together? Balancing point: 4 15/16″.

photo 4

One quarter, one penny – two quarters, two pennies

So, it seems like there is more support for my hypothesis.

Then, a student and I decided to grow the project a bit.

One calculator - two calculators

One calculator – two calculators

With the number of variables that have changed, this photo doesn’t really mean a whole lot, but we had fun trying to balance calculators on a yardsticks.

The balancing point of the calculators

The balancing point of the calculators

So, how can we explain this phenomena? What causes the balance point to move predictably even though the ratio of the masses at the end is a constant?