Unfold Learning

exploring the best innovations in learning and teaching


Playful Math

Ditch the worksheet

header image showing drawing created using Scratch coding blocks

What happens when you take one step, turn one degree, take one step, turn one degree, and continue the trend a total of 360 times? Of course, you will walk in a circle. Or, you walk along a 360-sided shape with each side measuring one step. The perimeter (or circumference, since it is technically a circle) is 360 steps. You can split this shape into 360 congruent triangles with angles measuring 1º, 89.5º and 89.5º degrees. 

This may not be new to you, and you may have an easy time understanding the above description and imaging the process and shapes I’m describing. However, if these ideas are new to you, you may have a difficult time creating a mental image of what’s being described. Asking learners to imagine things rather than showing them things can stress them if they are not familiar, or if they lack confidence. 

Luckily, nobody has to rely solely on imagination. We can replicate this process using Scratch — a simple, fun, powerful programming language developed by the MIT Media Lab. Using Scratch, we can carry out the process of ‘walking’ in a circle and explore what happens when we change things up. We can see the shapes generated and very quickly experiment with different numbers. Scratch’s block-based design (sort of like putting together LEGO blocks) makes it really easy to generate one shape after another

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Learning Online

Trichoderma strictipile

Image of Trichoderma strictipile

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Don’t Feed the Bird

Monster Collection

A group of monsters drawing using Keynote

I have written about the dangers of social media in education before, how trying to create “Twitter-worthy” lesson plans can lead teachers down a dangerous path of providing a veneer of learning designed primarily to look good in pictures. Back then, I focused on what happened in the classrooms around me, with students in attendance. Some teachers trying to impress administrators, or to get hired at a different district, often engaged in this kind of behavior at my former school division. It was annoying, and it encouraged the same kind of questionable praxis from teachers who might have otherwise stuck to their better teaching instincts. The worry of a bad evaluation if they were not visible enough loomed large in a district mired in merit pay experimentation.

After leaving my position in the district a year ago, I have made changes in my engagement with social media. I have grown the list of accounts I follow substantially, looking for people from whom I can learn, both in and out of the education field. Since one of my areas of interest has been the role of experimentation and play in learning, especially with technology, I’ve been following people who do creative work with easily accessible tools. Here I am referring to everyday tools that are free or low-cost rather than to accessibility features, although I appreciate accessibility features as well.

One of my favorite tools for creative onscreen play that fits this role perfectly is Keynote. If you have an Apple device, Keynote is part of the package. It was originally marketed as presentation software, and this is how the majority of people use it. But, it can be “hacked” to make super fun animations. Earlier in the summer I presented a session on using Keynote for creative pursuits, sharing examples of animated title sequences, custom clip transitions, green screen special effects, and even scientific illustration. My latest infatuation is making animated GIF monsters.

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image of fungus on a log


Learning Online

image of fungus on a log

Yesterday I took a picture of a carpenter bee with some gooey stuff stuck to its face. The bee did not look well. It was moving slowly and trying very hard to dislodge the stuff which seemed to be keeping it from feeding properly. I looked online for what might have been wrong with the bee, and then I reached out to the one person I knew about who worked at the intersection of insects and fungi.

It is important to say I don’t really know Dr. Matt Kasson. I know of his work, but we’ve never met. I ran across one of his tweets a while back and started following him out of curiosity regarding his research of a fungus that kills cicadas. I found his description of the dead cicadas as “spore salt shakers” darkly humorous. And while I reserve Twitter as a space to learn about education, technology, and social justice, I figured throwing in a few insect-related accounts would only improve the experience.

So today, I tagged Dr. Kasson in a tweet and hoped he’d get back to me sometime in the next week. Within the hour I was having a conversation with three different highly qualified experts who responded and helped me out. We discussed the ailing carpenter bee, and as a thank you, I shared a picture of one of my latest fungal discoveries made during an exploration of the woods behind my house, a fungus called Trichoderma strictipile (image above). This led us in a new direction as they discussed what my picture showed.

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Considering technology use with SAMR

Note: It seems this post is required reading for a group of students using Google Classroom. I’d love to know what the class is saying about SAMR. Feel free to leave a comment.

Developed by Dr. Ruben Puentadura based on his observations and study of a statewide laptop initiative in the us state of Maine, the SAMR model has become a popular, though frequently misunderstood, benchmark for considering the incorporation of technologies in education. The chief point of misunderstanding comes from a mistaken belief that the levels constituting this taxonomy can be entirely distinguished by differences in the learning content or its delivery or that a particular technology or tool automatically places one at a particular level in the taxonomy. Of course, both of these elements may be part of the story, but as we have seen with the Cubic Learning model, considering only the content dimension (either when considering content delivery or the use of a particular tool) only tells part of the story – and oversimplifying the SAMR model to focus primarily on content delivery obscures this model’s broad applicability as a guide for educators. Continue reading


How Hard Is It?

Rigid Post Image

The definition of rigor, according to the dictionary, is “strictness, severity, or harshness, as in dealing with people.” Over the past decade, this word has crept into eduspeak more and more, often to argue that students are earning high grades for work that is too easy and does not lead to learning. Do we really mean to make classrooms inflexible places? Probably not.

Search for the words “rigor” and “education” together and you will mostly find a wide range of new “definitions” for this word. More than definitions, many of these are circumlocutions: rambling explanations about challenging students without really getting at how to challenge students and how to ascertain the aforementioned rigor. There are no tools or scales for measuring rigor and no advice on how to identify it.

The buzz about rigor is not new. A post at the Hechinger Report from 2010 states that students are leaving high school unprepared for college-level work or the workplace. The post mentions designing a curriculum that prepares students for college, but gives no specifics. The post also mentions an expert who tells us there is a difference between rigorous teaching, rigorous questioning, and rigorous assessment, but the differences are not actually expressed. I have some rigorous questions of my own about “rigor” to help me think through this word that seems to be more of a political construct with suspect motives.

What is the point of rigor in schools? If the goal is to ensure students are working hard, is the hard work a means to an end or an end in itself?

Challenge is necessary for learning. Doing what is already known is easy, but does not lead to further acquisitions of skills or knowledge. Learning happens at the edge of what has already been learned and what can be learned next. It happens at the edge of what is easy and what starts to pose a challenge. Vygotsky used this expansion metaphor to describe learning when he wrote about the “zone of proximal development” (ZPD). If rigor ensures students are challenged so they are constantly learning, there must be a way to figure out if students are challenged, and how much so. Too much of a challenge (a leap too far into the ZPD) leads to frustration. Not enough challenge leads to boredom and a lack of learning. However, hard or easy varies with each individual, and teachers and students judge the ease or difficulty of any situation very differently and they do so for different reasons.

The Glossary of Education Reform defines “rigor” as an element of “…lessons that encourage students to question their assumptions and think deeply, rather than […] lessons that merely demand memorization and information recall.” This is not very different from the goal of Deeper Learning, which is defined by the Alliance for Excellent Education and the Hewlett Foundation as academic activities that lead to students acquiring the following six competencies.

  1. Mastery of core content
  2. Critical thinking
  3. Problem solving
  4. Collaboration
  5. Communication
  6. Self-directed learning

If learning activities are designed to challenge students while promoting the development of these competencies, rigor does not need to be quantified and assessed as a separate element. So why is it?

We ask students to learn things that are definitely hard, but have little or no connection to what will be required of them after graduation, and we do it in the name of rigor. As the Glossary of Education Reform notes, “While some educators may equate rigor with difficultly, many educators would argue that academically rigorous learning experiences should be sufficiently and appropriately challenging for individual students or groups of students, not simply difficult” (emphasis added). Until there is a consensus on what rigor means and how it can be observed and measured for individual students, we should ask ourselves questions that help us ensure students are challenged for a clear purpose and that learning outcomes are genuinely productive. Continue reading


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When Tweeting Is for the Birds…

Twitter mirror[Here’s another important new post by Bea Leiderman. Bea is an instructional technology coach at Goochland County Public Schools in Goochland, Virginia. Bea has been a Twitter user since the very beginning, and she’s spent much time thinking about effective teaching and effective professional development. As always, I’m grateful that she contributed this article.]

About a year ago, I stumbled upon a weekly Twitter chat in progress. A local educator I had recently started to follow was extolling the importance of teacher-led professional development. He was claiming great success at his school but was not providing any examples. I was very curious, so I tagged a couple of tweets with the chat hashtag and very explicitly asked for an example.

I never got one.

I was determined to get to the bottom of this since I knew several teachers at the school. I found it interesting that in all our conversations, we had never run into the topic of teacher-led PD. Continue reading


Scrum Soup: A Metaphor for Classroom Projects

[I’m grateful to be able to include a new post by Bea Leiderman, who is an instructional technology coach at Goochland County Public Schools in Goochland, Virginia. Bea has been working with Scrum at her school and she and her colleagues are having incredible success with it!]

Alt Wiener Erdäpfelsuppe

Photo by Brücke-Osteuropa (Own work) [CC0], via Wikimedia Commons

Over the last year, our team has adapted the Scrum framework to help our students work through class projects. In the classrooms where Scrum is used regularly, students have a deep understanding of what it means to collaborate and be part of a learning community. Teachers can plan complex projects, confident that students will rise to the challenge and present outstanding products to their classmates at the end of a few weeks. To us, Scrum makes perfect sense. And it is not too hard to implement with some guidance and coaching. However, getting started on your own can be tough, especially because most of us have never tried anything like it.

When talking about Scrum, we bandy about lots of unusual words to refer to the roles, artifacts, and ceremonies involved. Even those three make Scrum sound like a strange cult. Instead of suggesting books and articles, It might be useful to walk through an everyday, non-educational project in Scrum to give interested teachers a frame of reference. It might also be a good way to introduce Scrum to students in classrooms.

Let’s make a vegetable soup following an everyday workflow (the procedure we use to accomplish things in Scrum). Everyone knows how to make soup, right? What are the steps?

  1. Gather all your ingredients
  2. Clean, peel, and chop all veggies and maybe some meat
  3. Cook all ingredients in a pot of water with salt and seasonings
  4. Serve and eat

Generally, that’s how soup works. Of course, the stuff I put in my vegetable soup might not be exactly the same that you put in yours. How long the process takes depends on how many different ingredients I have to prepare before adding them to the soup. If I had to plan this down to the smallest detail, I’d have to expand the above steps to include everything. Continue reading


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Rethinking the coding craze…

Today’s post is by guest author Bea Leiderman. Bea is a technology coach at Goochland County Public Schools in Goochland, Virginia, where she helps middle and high school teachers use technology to design effective learning opportunities and environments. Bea has won numerous accolades for her innovative teaching, and her work with colleagues incorporating Agile / SCRUM to transform learning projects was featured in the June 2016 issue of ISTE’s entrsekt magazine. Bea is the author of six books of insect macrophotography and a book about iBooks Author, all available on Apple’s iBooks Store. You can find more of her amazing insect photos on Flickr, and can follow her on Twitter, where she also has a channel for insect photography and information.

Final Cut Project

A complex Final Cut project

For as long as humans have been alive, we have been problem-solvers. The idea of designing solutions and executing them did not come about with the advent of the personal computer, although the personal computer and other related technologies do make the iteration of approaches and ideas so very convenient. This might be why Steve Jobs said in a 1990 interview that a computer is “the equivalent of a bicycle for our minds,” allowing our creative and problem-solving processes to go so much faster.

Coding in particular seems the most obvious method for teaching the design-and-iteration process that develops creative and critical thinking skills. Using coding is transparent, and it is easy to contrive ways of bringing coding into the traditional school schedule. It is also easy to dampen the joy that comes with ideating, designing, and executing an idea when coding is adopted as the only way to do so. As much as we might think we are helping students be creative, by making them all learn “coding,” whether they are interested or not, reduces coding to the same level as anything else we have ever forced upon children in schools.

I’m not against the idea of teaching coding, but I believe we are pushing too hard in the wrong direction. We don’t all need to know how to develop apps, as fun as it might seem to some, especially because each of us have our own particular idea of fun and our own plans for our future. Knowing how to code is not as important as knowing the ideas behind coding: designing a process and making it happen. If indeed all jobs will require coding in the coming century, everyone will have a better incentive than a grade on a report card (or *gasp* a standardized test) to pick up the skills. Continue reading


Thanks, EdCrunch!


I had a spectacular time at Moscow’s EdCrunch. Amazing speakers (including Wikipedia’s Jimmy Wales), great exhibits, and some spectacular conversations. It was a privilege to participate. If you’d like to see the video of my keynote, you can watch it here.