Author: mathwithjz

One of the rare times I learn when others did the work

2015-07-17 09.07.30

One of the “interview committees”.

All three cohorts convened today for 3 mock job interviews. Next to the GREAT15 Conference, this was the most helpful learning experience of 1.75 summers in MAET. Among the loads of observations, I found four overarching themes from watching 3 of my peers bravely model a job interview in front of 50 people. I admire their courage.

  1. Little things matters. Before the interviews began, I found it helpful to see that he reworded his assigned question to be more “user friendly”. Instead of asking the candidate about his framework for teaching, he asked “How are you going to decide what and how to teach?” I found this helpful because I had made up in my mind that interview committees are less like people and more like document scanners looking for keywords or phrases. Other things that matter: smile. Shake hands with everyone. Laugh. Be human. How I sit, how I talk, how I command the room (or not). Avoid self-depricating comments–there is no need to invite people to dislike me or my work. They have no reason to think I am not a perfect fit for their institution when I walk in the room, and I should believe that.
  2. Dr. Roseth summed it up beautifully: show don’t tell. I took a fiction writing class once from an author that has since won the National Magazine Award. His version of the same advice for a different context was “don’t tell your readers something you can show them”. We all connect to stories, and we all seem to glaze over when someone goes on and on about theoretical concepts. Stories that illustrate our answers to questions provide evidence that I have actually formed an understanding of the theory or concept and applied it in my day to day job. Showing offers points of connection between the interviewer and the candidate, and these connections are ultimately what is going to get me the job or not, assuming I meet the basic qualifications for the position. In fact, I walked away from today’s interviews convinced that discovering if those connections exist or can be made between the job seeker and the institution are really what the interview is really about.

    2015-07-17 09.07.48

    The audience. No pressure at all!

  3. My online presence matters, whether I care about it or not. Especially since I am in Educational Technology. So I’d better start caring about it. The message today was loud and clear to me: be aware of what is out there about me online. I was reminded of my rule for dressing for school: when in doubt, don’t. The same applies to posts and pictures online.

What Mike said about e-portfolios was profound. What I have not liked about my website so far is that it was created for MAET, which is exactly what he was talking about. One of my goals for this summer is to transform it from being primarily about MAET to being primarily about me. I also left today with permission to really be myself online and connect all the pieces of myself together in one location. Leigh said something the very first week like, “at the end of the day, you’re you”. Authenticity matters, otherwise I’m just another person out there with similar training to everybody else. As Stephen pointed out yesterday, it is possible and quite easy to just go through the motions of teaching, not really pursuing excellence. I don’t want that to be me.

  1. Do your homework on the institution. Chris’s insight on this was powerful. As did other people, he mentioned being specific about where you met people and what connections you have with them. In my experience, these connections are how I end up with interviews and opportunities. Once I get the interview, the first three takeaways really start to matter.

Reflections on a truly #GREAT15 day

Today, for the first time in my life, I presented something I created in a conference setting. It was at GREAT15, a conference the 2nd year cohort of MAET Overseas puts on each summer. The process was amazingly transformative. I cannot believe how much I have changed through this experience. The revelations that I am relishing here at the end of this amazing day are

  • Actually practicing the presentation over and over again eliminated that anxious pit-of-my-stomach panic feeling I have always had the day of presentations in the past. I had none of that feeling today.
  • Writing out the script verbatim of what I was to say and on which slide was miraculous. It forced me to deal with the nitty gritty details of my presentation–those details that are so easy to overlook. I ended up deviating from it a little bit, but I was so familiar with it that I was confident in what to say and where to interject.
  • I needed help. Okay, this in and of itself is not a revelation. I think the more amazing part to me was that I asked for help, I accepted it, and, for the most part, did so without resistance. In other words, I was willing to have help.
  • Accepting feedback was super uncomfortable at first. I felt exposed and vulnerable and I didn’t like it one bit. What I realized as I went along, though, is that feeling exposed and vulnerable is 1) part of the process; 2) eases with repeated practice; 3) a fear that my value as a person is on the line;  4) is a big part of what makes the people I admire really good at what they do.
  • I am not inherently incapable of presenting well. Or researching well. Or doing almost anything else well. But I grew to accept that I can be. It’s like in Outliers when Malcolm Gladwell points out all the work that people we consider to be smarter or inherently more talented than the rest of us have mostly just put in their 10000 hours to become expert at something. What I am saying here is that I, too, can learn to do this kind of stuff well, I just have to work through the struggles involved.
  • Struggle is part of the process, not an indicator that I am doing it incorrectly or that I am incapable.
  • Here’s the big one: self-doubt is one of my greatest enemies. I have known this for a long2015-07-16 15.59.00time because I’ve seen it eat away at other parts of my life. However, seeing it take hold of me in this process gave me tangible benchmarks to see how it was interfering with my growth and progress. Every time I doubted myself, I started over. This meant that as deadlines approached I was still trying to come up with a better plan because I had seen a flaw in my current idea and taken that as an indicator that I needed a new idea. I really got it that this cycle of self-doubt has no exit except stick-with-it-ness through the discomfort of believing my idea stunk.
  • MY buy-in to my work is way more important that anyone else’s. I felt intimidated after I heard the welcoming speaker because he was dynamic and funny and didn’t read from a script. I almost changed my presentation because I feared mine would be too stale and boring after that. But I caught myself and changed nothing. Rather than change my stuff to align to what my brain told me people would like better, I decided to believe in my own work, as is, and be proud of what I had accomplished. I reminded myself that this is my first presentation, that we all start somewhere, and that I have done honest, good work.
  • All of us are people first. I sort of thought before this that “academics” were a breed of non-emotional humanoid nerd-type people. Today I realized that we are all people with families and kids and pets who get hungry and have emotions and who love their jobs for some of the same reasons I do.
  • I CAN! When I was making the website, people would ask me if I could do ___. I immediately said no. Then I’d figure out how to do it, do it, then jump up and down.  That about sums it up!

Gladwell, M. (2008). Outliers: The Story of Success.

Research to Practice Session @ GREAT15

I had the honor July 16 to present at the GREAT15 to a group of my peers and professionals in educational technology. Though it was part of the MAET program I am in, the research I did was valuable to me as a practitioner. The presentation was part of a larger project of building a lesson plan out of investigation of empirical research on our chosen topic and pedagogy.

I took the opportunity of being with 10 colleagues to gather their opinions and feedback on the possibilities of transferring a well-studied reading comprehension strategy called Reciprocal Teaching across disciplines to mathematics. I also asked participants to fill out a quick survey. Both of these materials are listed below.

<a href=”; target=”_blank”>Reciprocal Teaching in the Mathematics Classroom Presentation</a>

<a href=”; target=”_blank”>Presentation Feedback</a>

Reflections and Epiphanies on the Design Process

It is an understatement to say that the process of revision and lesson study has influenced my thinking about the design of the learning experience I’m creating for learners. It is informing it. Participating in this process has forced to the surface the weak spots that exist in how I design lesson plans and learning experiences in my professional life. If I am honest, the design process for my students thus far in my career has taken on the following form most of the time:

  1. Decide the topic to be taught
  2. Come up with some way to teach it, often this involves lots of Google searches.
  3. Implement.
  4. Reflect

And so this is the process that I implemented when I began working on my learning experience. The problems quickly became apparent. Step 1 took me a while but I didn’t worry too much. I figure this is all part of the process, it will come together eventually. As it turns out, Step 2 is much easier to do once Step 1 has been done. Thus my troubles began. I kept going round and round with ideas in my head but never really committing to one because none of them ever seemed like the perfect idea.

Traditionally this is the part of my “process” where I get stuck, be it in writing lesson plans, planning parties or writing blog posts. When it is time to get specific, I get lost.

The day we coded for TPACK was pivotal for me. It was difficult for me to do and I had much resistance to the entire process. It was tedious and I felt trapped and uncomfortable and an overwhelming urge to jump out of my skin. As I persevered, I began to realize what the root of the trouble was: I do not like making decisions. And coding is one small decision after another after another after another. We had to decide if and “idea unit” needed to be categorized and if so, into which of 6 categories it belonged. Again and again and again.

This is when I caught on to myself and realized that making decisions was at the the heart of my troubles in the design process.  I was afraid of making a mistake, being judged, criticized or looking bad. I was also afraid of picking a bad topic that I could not do anything with, resulting in wasted time and effort.

Even as I write this, however, I see the fixed mindset (Dweck, 2006) out of which that perspective is born. I am looking for a “perfect” design, lesson, experience, whatever, outside of myself. Always on the hunt for that one “magic” idea, I think I will never create a lesson that is good enough until or unless I find the perfect idea. This mindset feeds an unwillingness to let go of ideas I do up with for fear that I will not find any that are better.

What I see now is that designing is not so much inspiration that strikes a person all of the sudden (as I had previously thought) complete with a brilliant idea, implementation strategies and logistics all arranged nicely. I never saw the part of anyone else’s design process, so I did not see the iterations, feedback and struggle that went into their designing.

I now have an entirely different view of the design process and consequently of myself. I understand it now to be work and a process. I now understand that ideas can come from inside me. I do not have to stumble upon the “perfect” idea; I can start with a marginally good idea and refine it until it is a really good idea through the process of iteration, feedback and revision. Feedback becomes a valuable tool that can help in the refinement process rather than a threatening competition to see who “found” the better idea on their search for perfection.

The transformation of my thinking from a fixed mindset to a growth mindset encompasses my view of myself as a technology integrator in the making, as well.

Previous to about four days ago, I have not thought of myself as a technology integrator, even since I began MAET. At the school in Boise where I teach, I am not in an official technology position, and even after completing the first year of MAET, I did not see myself as a “technology integrator”. My school is loaded with technological devices and people who know how to use them. Each class has a set of chromebooks, a document camera, loads of of calculators and software to run with them, and we have a brand new teacher who was trained on many interesting and engaging web tools.

I had decided that I could not possibly become a “Technology Integrator” because I am just not inherently put together that way. Upon deeper reflection, a Technology Integrator is a person that is skilled at effectively blending technology and best teaching practices. They understand how to maximize student learning utilizing whatever technology is available, be it paper and scissors, a website or creating a movie. This I can learn to do.

The iterations of my Theory to Practice project have taught me that I am not inherently any labelthat I can learn and work and struggle and revise and chisel myself into anything I want to be. The definition I was using is another demonstration of a fixed mindset (Dwek, 2006). I discovered through the iterative process first, that I can redefine what “Technology Integrator” is to me, and second that I can grow into whatever that definition turns out to be.


Dweck, C. S. (2006). Mindset: The new psychology of success. New York: Random House.

I have a confession…

20140718_225826#1The internet is not changing my deepest desires, but it is changing the way I think about those desires. This became super evident to me on my “vacation” to Killarney to run in the ½ marathon.

In spite of myself, I discovered I was gathering evidence to support the conclusions of some of the authors we read in class throughout the weekend. I decided to go with it.

I have been scrapbooking for about 15 years. Yes, I cut and paste and still print out real, tangible pictures that I cut up, decorate, embellish and use to create stories of my adventures in a scrapbook. When I go on trips I gather things: receipts, tickets, pictures, brochures, maps, little scraps of paper people on the street hand me, and whatever else I can find to document my travels.

Before the internet, specifically Facebook, my mind was always thinking

  • in camera shots. What pictures would look good together on a 12×12 page? What color cardstock could I use? What embellishments could I make to add to the page? Could any of the debris I have collected (like a ticket or a receipt) be put added to the page?
  • Caveat: before digital cameras, I was very judicious about my film. Much effort and care went into what I took pictures of–there was no delete button! One of the worst feelings in the world was picking up three rolls of 36 exposure film from the drugstore and finding that ⅓ of the pictures were blurry or of the ground!
  • in titles. What would I title this page? The title not only had to be catchy, but I had to be able to construct a visual representation of it as well. When I went to Las Vegas, the title was “Viva Las Vegas” with paper “lights” blinking all around it. (I would show you a picture, but it’s in a scrapbook at home, and I have never taken a picture of it, as it seemed to defeat the purpose of having a scrapbook).
  • about chunks of time. Big ones. When am I going to carve out the 3 or 4 days it would take me to do this? I am chronically behind on scrapbooking. For example, I didn’t get divorced in “scrapbook time” until 5 years after my real divorce. The reality is that I think about the process way more than I engage in it. It’s quite an extravaganza: I haul this big pile of debris out of my cabinet, organize it on my kitchen table (thereby decommissioning my table), work for 3 or 4 hours at a time over the course of a week or so, forget about it for about 2 more weeks, then, when I can’t stand it any longer, I put everything away. I don’t like to start this process unless I have time to create a good 10 pages or more, for obvious reasons.

With the internet and Facebook, my mind is now thinking

  • in camera shots. No longer am I thinking about what pictures will go together. My mind is constantly looking for a shot that will get “Liked”, so it has to either be funny or a really good picture.
  • Caveat: with digital technology, I have become careless about pictures. I will take pictures of things now that I wouldn’t have even considered pulling my camera out of my bag for before. The concept of “DELETE” has made me careless about my pictures, but has also given me the freedom to try a shot four or five times.
  • in captions. With scrapbooks, I use words and expressions. I just write out what I was doing and draw an arrow to the picture I’m talking about. With Facebook I find myself thinking in 140-ish character sentences, always looking for one that is really funny. I want to be “Liked”! I am always looking to match or top my favorite status post of all time (not mine): “Dear winter: suck it.”
  • about time. But not chunks of days and weeks anymore–just hours. Last summer I went to Eastern Europe. I knew I was going to have a party when I got home and I wanted something to show my friends from my trip. I knew i wasn’t going to have time to make a “proper” scrapbook, so I made a photobook on iPhoto during my flight from London to Canada.

Just in the process of writing this article, I have come to appreciate the differences between recording my memories in each fashion. There has been a part of me the felt betrayed last summer when I made the photo book, and Fred Tomaselli (2010) hits the nail on the head when he says, “In this landscape of endless copies, a real thing, made by a person, with its repository of the creator’s time and it’s tactility, scale and surface quality is almost startling in its strangeness.”

Eastern Europe 2013

The cover of my photo book. In a scrapbook I would probably use textured paper and the text would be in my own handwriting.

The photobook was a huge success at my party, and people were amazed and impressed that I had “created” it. I, however, knew better. I had skipped the parts that made it meaningful to me, things that I knew intuitively but couldn’t name until I read Fischl’s article “Replacing Experience With Facsimile” (2010):  a sense of scale, a loss of differentiation between materials, and the process of making.

Facebook exists only on a screen. Once my witty status update is posted, it quickly fades into history, never to be seen again. I can count on one hand the number of times I have gone back in my Facebook history to recover a status update.

My photobook of Eastern Europe is tangible, and a good basic documentation of my travels, but it is missing the process of making it. I could write in text boxes, but I had a limited number of photobook templates to choose from, templates could not be combined, and I the space in the text box was restricted. I did go back when I got the book and draw arrows and write in more details, but it was still missing part of me.

My scrapbooks are just that: mine. They are for me, not anyone else.  It’s nice that other people are impressed with them, and I do pull them out to show people old pictures of me or my kitchen before the remodel, but it is the process that I love. That pile of debris from each trip? When I finally get to it, I organize it all chronologically and make a page for pile of stuff I have. I include pictures, baggage tags, menus, cards, fliers, tickets…whatever. I will make folders to hold things that won’t fit. I write all over the page in different colors. I use glue sticks and stickers and make a mess.

page 1

Page 1 of my photo book. This page has a cool background, but in a scrapbook I would have a map of the location of the hotel, more text with arrows and probably a room key attached.

The second best part (the best is the finished product!) is that the stuff I don’t use from the debris pile gets thrown away. The sense of completion from this disposal of unnecessary baggage is indescribably satisfying.

The readings from this month in MAET about how the internet has changed the way we think have enabled me to reframe the way I see scrapbooking. I used to be just a little bit embarrassed to admit to it. I used to wonder why I didn’t just make an online photo book for every trip and save time.

But now I will think of my scrapbooks as art, valuing the process, time, love and energy that goes into them.  I will not get sucked into the myth that just because with digital tools I can do things more quickly, I should.

I will continue to collect debris from my trips, pile it up in my cabinet, fret over when to decommission my kitchen table for three weeks, and rejoice in the process!


Fischl, E. (n.d.). Replacing Experience With Facsimile. Retrieved July 22, 2014, from

Tomaselli, F. (n.d.). Cut and Paste. Retrieved July 22, 2014, from

The Pro-Comfort and Anti-Reality Era

In his book The Anti-Education Era (2013), James Paul Gee lists a multitude (really 15, it just feels like more) of things humans do that keep us stupid in the first half of his book, then offers ways we can stop being stupid. He says that his book is about “what it means to be smart and to be a fully awake participant in our high-risk global world in the twenty-first century” (p. xi). Funny, as I was trying to sum up the book before writing this, I wanted to say it is about staying awake, but I hadn’t remembered this quote until later.

We do stupid things, in my opinion, because we don’t want to stay awake. Why don’t we want to be awake? Because we are uncomfortable and afraid.

To be awake means “to become conscious or aware of something” according to But to be aware of something has hazards, among them discomfort, fear that what we see will be good enough, fear that we will be hurt, and fear that we might have to change.

I believe that the fear of discomfort and that we as individuals might have to do something different to fix a problem is one of the primary underlying motivations behind our stupid behavior.

The chapter that I read, for example, “Flight from Complexity” (chapter 16), is about how we humans stupidly apply short-term solutions to long-term problems.

We don’t want to take a long-term view, cooperate or delay gratification because these things are uncomfortable. There is an inherent dis-easiness in looking at a problem that we do not know how to solve. We see it every day in individual lives. Women stay with men who beat them; mothers who really want to say “no” say “yes” when their child throws a fit; teachers extend assignment deadlines to please a student; we see our child suffering at school but we pretend that she’s fine because we don’t know what to say and it’s too hard to just talk to her.

We do these types of things because we do not want to endure the discomfort that would result if we did otherwise.

To change these behaviors requires a tremendous amount of energy, because of the discomfort one must endure when we change. We know this is true with our physical bodies. For example, I ran the Leavenworth Marathon marathon abouy 9 months ago, and when I went to run a few days later, my knee was in so much pain I couldn’t go. My physical therapist told me I needed to learn to run correctly, i.e. I had not been running correctly all tAfter the Leavenworth Octoberfest Marathonhese years. So, for the next 7 months I had to go through the process of re-learning how to walk. It was arduous! I had to learn how to cross train, to stand differently, to do about 6 exercises twice daily (every day), buy new shoes, slowly build up from no running to running for 1 minute, then two minutes, then 3 minutes, always stopping if ever there was pain. I won’t bore you with any more, but you get the idea.

It was a big pain. I had to do a lot of work. But I want to qualify for the Boston Marathon before I’m 87 so I stuck with it.

What does this have to do with our stupidity?

Who wants to do all that work if the way things are is good enough? It may not be perfect, we tell ourselves, but considering the amount of work, anxiety, time and energy required to change ourselves or our situation, I’ll just keep things as they are, thank you very much.

Ruby Payne refers to this in her book A Framework for Understanding Poverty (2005). She says that students from poverty do not have the emotional resources to deal with the anxiety that results from changing their social class or status, and I believe that as a collective we have the same issue when dealing with complex issues.

I understand that this is a wicked problem, our educational dilemma. Just curing people of anxiety and denial is not going to suddenly make our schools work and create happy places where everyone learns and gets along.

But it’s going to help.


Gee, J. P. (2013). The anti-education era: creating smarter students through digital learning. Palgrave Macmillan.

Payne, R. K. (2003). A framework for understanding poverty. Highlands, Tex: Aha! Process.

Wicked, Wicked Problem

I had never heard the term “wicked problem” before last week, so the first thing I learned from this project is that a wicked problem is one that (I’m paraphrasing here) has only bad solutions. Every “solution” is like a band aid that mostly reveals a different problem that was heretofore hidden.

It’s not dissimilar to remodeling my house that was build in 1950. I would like to paint the outside, but then I might as well replace the windows first, but if I’m going to do that, I should have the front stairs rebuilt, but really I may as well do everything at once and remodel the kitchen… My solution? Do nothing and hope the front stoop doesn’t fall down while someone is knocking on my door.

My take away from the “Wicked Problem” assignment, my topic for which was how to redefine failure as success, is that doing something really is better than doing nothing. I have been an all-or-nothing person for all of my life, in pretty much every area, happy to pontificate on what other people should be doing differently.

That’s the other thing that really stuck with me: I can do something. However big or small, we all can do something, and all the “somethings” count, no matter what.

I will bring this idea into my classroom by trying things that I have been avoiding because of fear.  The discussion after our presentation has got me thinking about my grading system, as well. I would like to emphasize the process rather than the tests and quizes, but to weight things differently I need to change the work that is actually done in class from worksheets and notes to more meaningful projects and activities. 

Implementing these ideas into my teaching is, in itself, a wicked problem.

Me, a Scholar?


a person who has studied a subject for a long time and knows a lot about it : an intelligent and well-educated person who knows a particular subject very well


a fund of knowledge and learning


Just hearing the word scholarship makes me want to yawn. It brings to mind caps and gowns, solemn ceremonies and graduate degrees. It is not a word I have ever associated with myself. One of the reasons I have not pursued a graduate degree before now, actually, is because I did not think I could achieve the level of scholarship I thought was required.

Luckily, the desire to study overseas was bigger than my fear of scholarship. Since the beginning of MAET in Ireland, it was obvious that my colleagues are scholars. They know a lot, they seem to have tried a lot of things in their classrooms, and most have great study skills. I felt more like a nitty-gritty, education-by-the-streets type. Eileen Bender and Donald Gray (1999) in their article “The Scholarship of Teaching,” sum up whatever “scholarship” I arrived in Galway with precicely:

Conversations about teaching outside our classrooms characteristically pull up short of what we like to imagine and cherish as the mystery of our effectiveness. Instead, these talks bump along on the level of anecdote, disjointed news about good days and bad, tactics that worked and assignments that did not or, frequently, finer points our students somehow missed.

I carried a chip on my shoulder and believed that I knew the best teaching practices. I quickly moved to discount or affirm (whichever disagreed with my beliefs) any theory presented to me at professional developments using my own anectdotal evidence. I could feel the weakness of my case practically as I began talking, but I couldn’t stop myself. My own experience was all I had.

That, and the National Council of Teachers of Mathematics (NCTM) journal Mathematics Teacher. Isn’t that enough?

Articles and citations and theories were forums where “scholars” who didn’t spend time in an actual classroom pontificated about the way we teachers were supposed to be doing things. I planned to endure this part of the Masters of Arts in Educational Technology Program through Michigan State University.

After three weeks of MAET

After two days of MAET, I knew I was wrong.

It was Glogster day, and I had almost nothing on my Glog after 30 minutes. I was humbled. I began to see how much I don’t know. Surprisingly, I was delighted!

The big Ideas I’ve learned at MAET thus far:

  • The Quickfires taught me to let go. At some point I just have to stop working and call it done. I think scholars do this–they must stop somewhere, so that they can move on. According to How People Learn: Brain, Mind, Experience and School, “the ability to recognize the limits of one’s current knowledge, then take steps to remedy the situation, is extremely important for learners of all ages” (p. 47).  Quickfires were the main way I discovered the limits of my current knowledge.
  • We are required to publish our work to the world, which scholars do. I understand an instructor reading my work, but to share it on a community spreadsheet so that anyone in my class can see my work, is unsettling. I felt vulnerable. It may be the sleep deprivation, but I got over it. I started to look at other people’s work and it was helpful! I found examples and ideas and guidance that I didn’t get before I was willing to share my own work.
  • I have been recorded, on video and voice. Ugh, what a “cringe” moment. But, I lived through the discomfort of hearing my own voice recorded. Seeing and listening to myself turned out to be a super useful tool. I have seen habits I do while I’m teaching that I wasn’t aware of and that I mumble–things that I can work to improve.
  • Affirmation. I received compliments of ideas I’ve had and products I’ve made. I have some good ideas–I wasn’t so sure before.
  • As I read the articles, I found statistics and ideas in these “scholarly” texts that were helpful and did directly apply to my teaching. Reading about the differences between novices and experts in the first three chapters of How People Learn: Brain, Mind, Experience, and School: Expanded Edition (2000), for example, was like reading about my classroom from May!

I now agree with the definition given by Bender & Gray of scholarship: “Nor is it simply teaching well. It is thinking hard and consecutively about the frameworks we have constructed and how we move within them.” Given this definition, I have been a participant a type of scholar all along!



Bender, E., & Gray, D. (1999, April 1). The Scholarship of Teaching. The Scholarship of Teaching. Retrieved July 22, 2014, from

How People Learn: Brain, Mind, Experience, and School: Expanded Edition. (2000). The National Academies Press. Retrieved July 22, 2014, from

Flipping Classrooms and Perspectives

So far in my three-year teaching career, I have used video only as a third party user, something to show my students to illustrate curriculum in a passive manner.  For example, whenever I teach exponents, I show a parody video of Super Base by Nicki Minaj made by Westerville South High School in Westerville, Ohio. Sometimes my students ask me to play a YouTube video for them at the end of class.

Thus ends my use of video in the classroom.

Then there is flipped learning, wherein teachers record a lesson for students to watch at home before the work for that lesson is given. I have not implemented it because, I told myself, my school is a “no homework” school. What could flip?  My students don’t have internet access at home. I always dismissed the idea of making videos for students because of the “no homework” policy, but then I heard that a teacher I admire in the district was flipping her AP Calculus classes, and I reconsidered.

Then I read “Flipping the Script in K12” by Ed Finkel on District (2012), and I had to realize that flipping is possible for me. He tells the story of Aaron Sams, a teacher at an at-risk school just like mine, and they just work around obstacles. They put videos on DVD’s, for example, for students who do not have internet access at home.

This got me thinking about how I structure and spend my class time now. It’s true, I spend it, as The Horizon Report says, “dispensing information” (p. 7), then I give students individual work to do. How can I flip this without assigning homework?

Some of the benefits I see in my own classroom are:

  • Everyone will be happier that I am not standing in front of the room teaching every single day.
  • Students who learn quickly can zip through the video, get his or her work done, and get on with other things.
  • Students who struggle can hit pause or rewatch the video over and over again.  According to Ed Finkel in “Flipping the Script”, this is a big deal in Special Ed circles.
  • The 2014 Horizon Report points out, however, that work during class time “could take the form of collaborating with their peers in online communities, curating online content, watching video lectures, listening to podcasts, and more” (p. 7).
  • A greater opportunity for scaffolding, as students can truly learn at their own pace.
  • Responsibility is placed on the student for learning rather than the teacher because it is not up to the student to ensure he or she understands the lesson before class begins. Finkel quotes science teacher Brian Bennett from South Bend, IN: “I’m not flipping the time when things happen; I’m flipping the responsibility and the leadership” (“Flipping the Script in K12).

My First Flip

I am going to “flip” my classroom within a class period. We have four 80 minute block classes a day, which is plenty of time for students to watch a short video at the beginning of class, then spend the greater part of the class period working on projects, asking for help or helping others.

I made my first video on zero and negative exponent rules. It was iteration #1. I spent way too much time on it, trying to make it fancy and fun. I quickly got frustrated and abandoned the idea. See for yourself how far my attempt went. Please keep in mind that I abandonded editing after about 2 minutes in because I realized the err of my ways.

Then an instructor suggested not putting a lot of time and effort into flipping videos because the software changes so quickly that videos can become obsolete virtually overnight. I found this relieving and motivating.  I tried again.

My Second Flip

Here is my first every flipping video that I will actually use!  negative_exponents

I will use it in a peer teaching activity that I do about once a week. I ask for 4 volunteers to teach the class that day. During the warm up I teach those 4 the lesson for the day and give them problems to work on for the remainder of the warm up. Their problems are the ones they will be teaching to the class. After warm up, they break into four groups and spend about 8 minutes with each “teacher”. All four teachers have problems that are variations on the main topic for the day.

This video will replace me teaching during the warm up, freeing me to help students who are struggling, managing behavior and attending to the beginning of class housecleaning things.

A few of the things I learned while making these two videos which might be handy for others wanting to begin using video in their classroom:

  • Do not get attached to the video. Mistakes have got to be okay, or else hours could be spent recording and re-recording.
  • Keep it simple. One basic idea at a time is a good place to start.
  • Keep it simple. My first attempt had lots of editing and pictures and text and I burned out working on it after about 30 minutes. In order for anything new to work in the classroom, it has to be easy to implement.


Finkel, E. (2012). Flipping the script in K-12. District Administration. Retrieved from

Johnson, L., Adams Becker, S., Estrada, V., and Freeman, A. (2014). NMC Horizon Report: 2014 K-12 Edition.

Paper Circuits Shed Light On Exponents!

The Challenge

What is the difference between 3x and x3? Many of my students in Algebra 1 (and Geometry and Algebra 2, if I’m being honest) struggle with the distinction, especially when it comes to adding three x’s together to get 3x versus multiplying three x’s together to get x3.

The final products. 4x is represented by 4 candles (two sets of “Love Candles”), and x4 is one candle with four lights.

In her article “Rethinking Technology & Creativity in the 21st Century: Crayons are the Future”, Punya Mishra (2012) cites Lako and Nunez (2000)as having “suggested that abstract mathematical concepts are grounded (through thinking in metaphor) to sensory-motor experiences based on perception and action in the physical environment.” It was in this spirit that I decided to try combining paper circuits and exponents. Could students come up with a way to represent monomials with a paper circuit? To do so would demonstrated a deeper understanding of the meaning of a term such as 4x than just doing problems over and over again.

In this activity, students will create two paper circuits: one representing a monomials such as x2, the other representing the same variable with the exponent now a coefficient, in this case, 2x. They can do this in any way that makes sense to them, provided that their mathematical reasoning is accurate and they can justify their representation. When projects are completed, students will explain their circuits to the class, then write a blog post about their representations for the class website, including pictures of their work. This is intended to be a tool for other students struggling with exponents.


Students often confuse or struggle with what to do with the exponents of monomials in multiplicative and additive situations. The purpose of this activity is primarily to clarify when the exponent of a variable expression changes (multiplication) and when it stays the same (addition). Secondarily, students will make the connection that raising numbers to a power increases their value very quickly, especially compared to multiplying by a coefficient.

3+3 = 6    but   33 = 27

Thirdly, students will learn to create a basic series and parallel circuit.


Algebra 1 students or any student learning exponent rules, or any student struggling with the product rule v. combining like terms. This activity was designed with at-risk, poor students who have low confidence in their abilities and a history of struggling with mathematical concepts.


Commonly students “learn” these rules by taking notes, making flashcards and sheer repetition of doing problems. Even with these methods, however, many students still do not recall what to do when presented with a problem like x4 + x4. Some will think x8 (incorrect), some 2x4 (correct), others x16 (incorrect) and some will just give up. This lesson attempts to hit the “dynamic equilibrium” refered to by Mishra & Koehler (2009) in their TPACK model.  It combines content (exponent rules), technology (paper circuits) and pedagogy (we have to understand the exponent rules to represent them with the technology) to provide students with a new experience of material that has historically been difficult.

Dale Dougherty, founder of Makezine, says “Making creates evidence of learning” (2012) in the article “Learning by Making” at By allowing students to demonstrated their understanding of exponent rules in any circuit they can imagine, students will be forced to fully understand the rule, but allow for expression of deeper understanding. Those that just grasp the “rule” can make a circuit as valid as the students who understand the power of exponential growth and are able to incorporate that knowledge into their creation.

Students will start, persevere, perhaps struggle with, and finish a product over the course of three days. Gee and Fulton in “Digital Media and Learning: A Prospective Retrospective” claim that humans learn through well-designed experiences and that after lots of time, effort, and practice in different experiences, the mind finds patterns and associations (2013, p.1). In other words, to learn, we must struggle, persist and be patient.  This task requires students to stick with one task over the course of three days–something this cohort is not used to doing. It requires most of them to learn something totally new (circuitry), and use that as a language to express what is hopefully by now a less-new concept (exponent rules).

Finally, I hope to empower my students. I want them to believe they can create anything they want to.  Creating a product from scratch provides learners with a sense of empowerment and ownership, according to Melanie Kahl.  In her blog post “Recasting Students and Teachers as Designers”, she says of students who create: “their sense of self efficacy and power was through the roof. They develop a new swagger, but also a tenacity that they didn’t have” (2012).

 The Lesson

I have allotted three 80-minutes blocks for this, as I have never done an activity like this before and want to make sure students do not have to rush. I also expect akwardness and resistance the first day.  A minimum of two 45 minute class periods is required just to make the circuits. It is useful to note in the timing that my classes are generally no more than 20 students. The basic lesson template is:

Day 1

  • Warm up- review exponent rules, 6 problems (10 min)
  • Introduce paper circuits- make a fun one for practice (45 min)
  • Share circuits (10 min)
  • Clean up (10 min)

Day 2

  • Bell ringer – 4 problems on exponent rules (10 min)
  • Introduce the task of representing 2 monomials with paper circuits & partner up (10 min)
  • Each pair makes 2 circuits (45 min)
  • Clean up (5 min)
  • Formative assessment: give warm up from Day 1 again to see any improvement (10 min)

Day 3

  • Finish up time, if needed (15 min)
  • Present circuits to the class (20 min)
  • Write explanation of both circuits to be published on class web page (40 min)


How to Make a Paper Circuit that Represents 2x and x 2

Materials Needed:

  • scissors IMG_4554
  • copper tape
  • 3V batteries
  • tape
  • LED lights
  • construction paper
  • hole punch
  • pencil



To Create the Circuits

Click on the top left picture below to go through the steps to create a series and a parallel circuit.

Next Steps – Share

  • Once the circuits are made, students will present their creations to the class, explaining how their circuits represent the monomials they were given.
  • They will then be asked to use Padlet tell how this experience was for them.  Do they feel like they learned more doing a project like this?  What were some things they didn’t like?
  • This is an opportunity for the teacher and students to help guide future learning in the classroom together.
  • Finally, students will post a written or audio explanation of their circuits on the class website, to be used as a tool for current or future students struggling with exponents.


  • Assign partners for the students. This saves time, hurt feelings, and you can build in a scaffolding structure by either placing kids at the same level together or a stronger with a weaker mathematician, depending on your situation.
  • Each student could be given just one monomial to make, then they have to find their “partner,”  i.e. the person that makes 4x has to find x4.
  • Students who get done early can document what is going on, taking pictures of the process of other students, or can assist those still working who may need help.
  • Give out strips of copper a little at a time to force them to use what they have before they get more.
  • Implement a “no throwing anything away” rule. This will drive home the point that everything can be repurposed.  I found this out myself after a few mistakes with the copper tape.  I just pulled it up, flipped it over and taped it down. The LED still worked beautifully!

IMG_4580 IMG_4579


My prototype went through several iterations, as did my “final” product. At every step of the way I find myself changing and tweaking and modifying, as I am sure will happen when I implement this in class.

From prototype to finished product, though either set could be a finished product.

From prototype to finished product, though either set could be a finished product.

I really struggled with finding a maker activity that could demonstrate knowledge of the content my students are expected to know. I discovered in the process, however, that it is possible to do, and that much of my resistance to the idea has to do with my own fear of letting go of control.  What if the students don’t buy in? What if they don’t stick with it? What if they still don’t know exponents when we’re done? What if I have to start sleeping at school because it takes so much time to plan these things (I’m not saying I have rational fears)?

What I complete this project knowing is that I have nothing to loose, but my students have everything to gain. I owe it to them to try something new, knowing the old way doesn’t work.

I’ll be back with a full report…



Dougherty, D. (n.d.). Want To Improve Science Education? Let Kids Build Rockets and Robots Instead of Taking Standardized Tests.. Slate Magazine. Retrieved July 20, 2014, from

Kahl, M. (2012, October 1). Recasting Teachers and Students as Designers. MindShift. Retrieved July 20, 2014, from

Mishra, P., & Koehler, M. J. (2009). ERIC – Too Cool for School? No Way! Using the TPACK Framework: You Can Have Your Hot Tools and Teach with Them, Too, Learning & Leading with Technology, 2009-May. ERIC – Too Cool for School? No Way! Using the TPACK Framework: You Can Have Your Hot Tools and Teach with Them, Too, Learning & Leading with Technology, 2009-May. Retrieved July 20, 2014, from

Mishra, P., & The Deep-Play Research Group (2012). Rethinking Technology & Creativity in the 21st Century: Crayons are the Future. TechTrends, 56(5), 13-16.