Elaborations for Creative Thinking in STEM

Feb 25, 2017 by

As I watch the proliferation of digital learning platforms, particularly in STEM education (where there are lots of objective-type problems), I am excited by the increased focus on learning and adaptivity but also a little uneasy. For the most part the motivations to “go digital” are pure – increase access to courses that students need, provide help that is more tailored to each student, give immediate feedback, provide more practice if the student wants it, and let students move at their own pace.

My worry is that math and science students aren’t getting anything but highly-structured problems. Every problem that a computer delivers is one where there is a carefully constructed set of constraints on the problem and a highly uniform (and thus gradable) answer.

But the problems of the real world aren’t carefully constrained and the problem solutions aren’t highly uniform. If we only teach students to solve the “lives in an orderly box” kind of problems, what are we preparing them for? Are we creating experiences that lead to curiosity in STEM subjects? Do students even see subjects like math as highly connected networks of concepts or just as discrete concepts to be learned one-at-a-time inside a digital system?

What is a Problem Elaboration?

This semester I’ve fallen back on a very old assessment technique I developed about 15 years ago that I call a “Problem Elaboration.” Students have to turn in a two problems per topic/section where they complete the problem (the old-fashioned way on paper) and then do some kind of mathematical elaboration on the problem. In other words, they have to do something that wasn’t asked for. They have to think in the space around the problem and consider:

  • What else could I find?
  • What other mathematical things could I do with this?
  • How does this connect to other things we’ve learned?
  • How could I check this to make sure it’s right?

It’s fascinating to watch the initial struggle of many of the students with the sudden freedom of elaborations. Students fall into three categories in the beginning of the term, but every student that makes an honest effort moves up this ladder to increasingly creative and complex elaborations over time.

Trepidatious: How am I supposed to find something that I’m not asked to find? I don’t even know how to begin! This is crazy! Your job is to support these students with examples, suggestions, and a “you can do it” attitude. These students will eventually try, and when they do, encourage them!

Compliant: If there is some way to check the problem, I’ll do that. If I wasn’t asked to graph the problem I’ll do that. These are the not the most creative elaborations. But it is an exploration that contributes to mathematical maturity. This tends to end up being what students do when they are short on time.

Elaboration 1: Notice the actual problem is highlighted in a lighter color. The elaboration is to check the answer. It’s not particularly glamorous, but the student knows how to check the answer, she knows it’s right, and that’s pretty awesome.


Elaboration 2: This also has the standard “check your answer” type of elaboration, but it goes one step further. This student shows me that she knows how to GRAPH both sides of the equation and verify that she has the right solution!

Curious:  What happens to this graph if I change this number or this sign? I did “X” and was expecting “Y”. Why didn’t that work? How does this connect to what we did yesterday? How would I find this thing I don’t know how to find?

Elaboration 3: Now we see an elaboration that really begins to explore the “what happens if” space. What happens if this is a 5th root instead of a square root? What happens if there is a number multiplied by the square root in the original equation?


Elaboration 4: This students starts by checking the answer, noting where they made a mistake the first time, and redoing the check. Then the student explores whether they can square individual terms in the equation instead of isolating the square root first and get the same answer. See the question the student is left with? “Not sure if that means something or not.” That’s the opener to a conversation in pen pal form about the right way that squaring both sides actually works.

As I grade these assignments, I find that what I’m really doing is opening up a conversation with the student. The elaborations aren’t always right, and often the students are asking questions in the elaborations. This is our chance to explore the math together in a back-and-forth letter to each other, assignment after assignment. Over the course of a semester, I watch many students develop mathematical maturity, mathematical confidence, and ownership of the math they have learned.


I assign 2 problems to turn in with elaboration per topic, using a particular grading rubric for these problems, based on 5 points:

  • 1 point for rephrasing or rewriting the problem (students end up solving a slightly miscopied problem, or don’t catch all the parts of the problem)
  • 2 points for showing all appropriate work to solve the problem
  • 1 point for actually finding the correct answer
  • 1 point for the elaboration

I also award a bonus point for really great and thoughtful elaborations (at discretion of instructor). Typically students earn between 0 and 5 bonus points per unit depending on their effort and thoughtfulness.

If a student makes an honest and thoughtful attempt at an elaboration, they will get the point even if their elaboration ends up being wrong or using incorrect terminology. The point is that the student explores and tries. My role is to correct improper terminology and to help when their reasoning wanders into an area where it no longer holds.

At the beginning of the semester, I do provide some idea of what an elaboration might be. A single elaboration might be any one of the following, but this is not an all inclusive list of what could be done.

  • Show a different way to solve the problem.
  • Show how to check the answer.
  • Solve for something extra in the problem.
  • Relate the concepts in this problem to something else we’ve studied.
  • Relate the concept in the problem to a graph (if there wasn’t a graph required in the problem).
  • Hypothesize on how a change to the problem might change the answer, and then try it.
  • If it relates to this problem, investigate something we did in class that you found difficult to understand or remember.

Why the unease?

Online learning and learning through digital platforms is highly structured and scripted. Students learn exactly what they are scripted to learn. They only “explore” in the sense that we sometimes allow them to choose the next highly-scripted chunk of learning they engage with.

How do we build digital learning spaces where something like elaborations and this personal conversation between myself and the student about the mathematics can also be encouraged as a part of learning?

And if we don’t encourage our most engaged and curious students to go deeper, to question more, and to make more connections, what’s going to happen to our STEM pipelines?

Possibly Related Posts:

read more

What should K-12 teachers be learning about technology?

Oct 17, 2015 by

A few months ago I answered some interview questions about technology and the education of K-12 teachers. The interview questions and answers were never published, but I thought I would share them here.

Photo from Brad Flickinger: https://www.flickr.com/photos/56155476@N08/5667861006/

Photo from Brad Flickinger: https://www.flickr.com/photos/56155476@N08/5667861006/


What should K-12 teachers be learning about educational technology?

Ed Tech is a fast-changing world right now, and it is not always easy for teachers to make choices about what technology to use with students. First and foremost, teachers need to learn how to choose tools that improve learning or create efficiencies to free up their time to work more closely with students that need more individual attention. Making the decision about whether a technology tool is effective is a hard-enough call to make, but teachers are faced with other constraints too: they must pay attention to the cost of the tool, the platforms it is delivered on, whether their students’ data will be protected, and if students will have reliable access to the technology from their homes. Necessarily, the choice of platform is often made at a school-wide or district-wide level. Sometimes, the best educational technology simply can’t be used because of one or more of these constraints. What teachers have to learn is that a lesser tool is not always worth it. We should never use educational technology just for the sake of introducing technology into the curriculum.

Because the educational technology (both platforms and individual apps and programs) is changing so rapidly, it is important not to focus on teaching specific tools to teachers. It is possible that a tool will be out of date before a student graduates. What we should teach is learning principles for classes of tools. For example, what benefits can learners get from giving a digital presentation? What are the best practices if you assign a presentation? How do you scaffold the experience so that students get the most out of it? How do you write a rubric to assess whether the student has been successful in the task? Simply teaching a future teacher how to use the latest cool presentation software will not be useful to them if they go to a school where they need to use a specific program they have not learned.

Teachers need to learn how to make the decision about whether the technology will enhance the learning and engagement of their students, and they need to learn how to learn a new technology.

One of the things we can’t lose sight of is that access to the world’s information is now provided through hardware connected to the Internet. We should separate the use of educational technology tool from the general need to incorporate the Internet into daily classroom life. These are two different issues. Students absolutely need to learn how to make sense of the information presented online every day, to discern the credible from the nonsense, and to develop habits that make them good citizens of the digital world. Using the Internet is necessary and valuable enhancement to teaching and should be part of every students’ learning experiences in K-12.

What is the state of ed tech?

Ed tech is a category we use to describe a large set of tools including, but not limited to: digital learning games, adaptive learning, testing programs, analytics tools, tutorial programs, video-based learning, and experiential learning with VR. Some of these tools, like learning programs built around video, are more mature (consider that YouTube and the MIT Open Courseware project are now more than a decade old). But we see new twists on some of these older tools. For example Khan Academy, which began as a video delivery platform, now has analytics tools and flexible learning paths built into the platform.

Maybe it is better to look at ed tech with respect to the number of teachers it now affects. Recent surveys show that teachers are somewhat likely to use technology to improve their own workflow, but are most are still not incorporating technology with students. However, teachers in the United States are under enormous pressure to make sure that students perform up to state and national standards. With their jobs on the line, there is little room for experimentation that may or may not result in improved learning outcomes. No doubt, we do have educational technology today that can help teachers to give more individualized learning experiences to their students, but there needs to be greater dissemination of the findings for what works (see the What Works Clearinghouse from the Institute of Educational Sciences) and administrators must find a safe way to allow teachers to try new approaches without fear of losing their jobs. The best research can tell us that a technology is likely to work, but the infrastructure of schools and the population of students served. For example, research conducted at a suburban school with good internet access and one-to-one computing initiatives may not be transferable when it is tried at a rural school where students don’t have internet access at home.

Again this brings me back to my first point. It is incredibly important that future teachers learn how to evaluate how a particular tool might affect learning and engagement within the constraints of their environment. We can do this with teachers who are still in school, but this leaves us with a large population of existing teachers who may not be getting the right training to feel comfortable making the decisions about what ed tech will actually help their students.

What should teachers look for in technology schools? What will be effective?

Teachers should look for technology that individualizes the learning experience, and I want to be very careful here to emphasize that the learning process should be clearly separated from the end-of unit or end-of term assessment. A good individualized learning tool will be adaptive, quickly moving the student through topics they show mastery of, and slowing down to give more help to the student if they are struggling with a topic. The tool should provide instant feedback to the student, but not necessarily the right answer if the student is incorrect. It is vitally important that learners be given a chance to reflect for themselves on what is wrong with their approach to a problem. At the point of impasse (where the student is frustrated or stuck on learning a concept), the technology should provide a good set of learning resources that will give scaffolding to the learning experience. On the teacher side, the educational technology needs to provide very good analytics on the competencies mastered by each student and a warning if any student seems to be struggling or stuck on a particular competency. It is good analytics that will help the teacher to feel comfortable that students are adequately prepared for state and national exams.

What educational technology are you most excited about?

For the near future (next 1-2 years) I think that true adaptive learning tools, ones that are modeled around the research about what makes human tutoring effective, have an incredible potential to help teachers. Especially in K-6, learning games can be a fun and effective way for students to learn (provided the games are decent).

For the farther future (3-5 years), I am pretty excited about the potential of new learning exploration spaces using VR tools built off of existing smartphone technology. This technology is in its infancy, but the barrier to entry is a smartphone and a pair of cardboard goggles (under $20) to wrap the phone. The focus on testing has reduced the time spent on creative exploration, and I hope that VR will let us create worlds of wonder for students to explore and learn in. We’ve been promised this before (e.g. Second Life) but I think that this time the technology is easy to use and will be readily available.

Possibly Related Posts:

read more

The Road Back to Higher Education

Aug 2, 2015 by

In 2012, I left Higher Education to work in the software world. It was bittersweet, because I had finished a Ph.D. on Higher Education Leadership only one year before I left. My decision to leave was a hard one, but I couldn’t see an effective solution path to change learning within traditional higher education. I studied effort after effort to make changes within departments, institutions, and systems, only to see that potential innovations to higher education rarely moved the needle very far from the traditional steady-state.

Maria at PhD Graduation

A proud graduate, but disheartened by the decreasing funding for higher education.

The semester that I finished my Ph.D. was the same one that huge cuts to higher education were announced in several states, most notably in Pennsylvania, where the higher education funding by the state was reduced by 50%.  By 2013, per-student higher education spending was lower than pre-recession levels in 48 states.

From the software world, I have watched as MOOCs, Coding Camps, and Microdegrees have been hyped as the next great thing to disrupt higher education. There’s no doubt that higher ed has been disrupted, though I would say it is more because increased regulation, lower funding, and decreased student enrollments put significant pressure on colleges and universities to increase efficiencies. While innovation like MOOCs show us that there is a tremendous market for learning outside of degree programs, these innovations are not focused at producing more teachers, nurses, or doctors – we still need higher education and traditional degree programs. We just need more affordable ways to get that first degree as well as flexible systems to update post-degree training, and allow quick pivots into other careers as the pool of available jobs shifts.

Finishing up my Ph.D., I knew that our institutions of higher education needed to move faster. Rather than taking years to develop new courses and programs, we needed to find ways to do it in months and without affecting students already in-program. In many degree programs, the curriculum needs to be adapted to the changing world every semester, not every 5-10 years. When I left higher education, I had a plan to learn everything I could about how the software industry uses agile techniques to iterate on solutions and pivot fast. I hoped that one day, I’d find an educational institution that would see the value in this unique learning experience, and take me back so that I could put what I had learned into practice (both from software and leadership). It was a gamble, but I knew that I couldn’t mentally survive at an institution where the pace of change was measured in decades instead of months.

The software industry was an interesting place to learn. It forced me to start thinking about what an agile institution of higher education would look like. What would you “bug” in a college or university? What processes could you refine through iteration? How would you explain the benefits of agile methodology to the stakeholders (faculty, administrators, and students)? Where should an institution be agile and where should it be traditional? This thought experiment has been occupying a processor in my mind, quietly chugging away, producing ideas and working through the implications.

2015-07-20 06.17.58

After a stunning sunrise, I saw this rainbow on my first day of work at WGU. Perhaps it was a sign.

Now I’m excited to announce that I’ve rejoined Higher Education as the Director of Learning Design for Western Governor’s University.  If you’re not familiar with WGU, it is an incredible institution (non-profit and accredited). The degrees are competency based (no grades), the classes are all online, students can begin a program of study any month, learning materials are provided to students at no additional cost, and the tuition is affordable. WGU separates learning, coaching, and assessment into distinct branches of the institution, providing a very unique and flexible structure.

As Director of Learning Design, I am responsible for the design of the student learning experience (from course design to software ease of use). It is an opportunity to help an already innovative institution incorporate agile processes throughout the learning and course design process. I think I’ve landed in the right place and I can’t wait to see what our design team is going to accomplish in the next few years!

Possibly Related Posts:

read more

10 Books to Push Your Thinking about Learning Design

Jul 7, 2015 by

Today I was thinking about what books I would recommend to someone in order to have some experience of the learning journey I’ve been on for the last 8 years.

If you’re looking for some summer reading that will help you grow your mind, here’s my list:

1. Theory of Fun for Game Design: This will help you to understand the principles that make games addictive learning activities and help you create more desire to learn for any audience. Really, I’m not kidding.

2. Bringing Words to Life, Second Edition: Robust Vocabulary Instruction: While this is written for teaching vocabulary to the K-6 age group, the research and activities described in the book are fascinating. The research principles and guidance on how to teach for various categories of words are sound for transfer to any age.

3. Design For How People Learn (Voices That Matter) I think this is a must read for understanding visual design principles related to learning. To be fair, I have also had the benefit of many long and interesting conversations about learning and design with Julie, so on this one, I might be biased.

4. Flow: The Psychology of Optimal Experience (Harper Perennial Modern Classics) During flow, people typically experience deep enjoyment, creativity, and a total involvement with life. We should seek to get learners into a state of flow, and then do as little as possible that disrupts them.

5. Don’t Make Me Think, Revisited: A Common Sense Approach to Web Usability (3rd Edition) (Voices That Matter) You don’t really understand usability until you’ve carefully considered how users interact with the digital interfaces they encounter. Everyone should read at least one book on usability if they are designing a digital product.

6. Cognitive Development and Learning in Instructional Contexts (3rd Edition) An amazing book about learning! James Byrnes is a top-notch explainer. It looks like it might be a textbook, but it is a fascinating and thought-provoking read. My copy has notes and highlights everywhere.

7. Understanding Learning and Teaching (Society for Research Into Higher Education S)The research group associated with Trigwell and Prosser has done some absolutely fascinating work related to motivation to learn, perceptions of the learning environment, perceptions of the discipline, and how students perceive themselves as learners. Most of the research is seated in STEM education, but anyone in education can appreciate the elegantly-designed experiments and their outcomes/implications for learning design.

8. Where Good Ideas Come From There are some great gems in this book (like the adjacent possible concept) that will help you to develop your own practice of innovation and understand that ideas are not as rare as you might think.

9. By Clay Shirky: Cognitive Surplus: Creativity and Generosity in a Connected Age which can only be read in conjunction with it’s complete opposite, The Shallows: What the Internet Is Doing to Our Brains

10. e-Learning and the Science of Instruction: Proven Guidelines for Consumers and Designers of Multimedia Learning  This is a newish version of an old standard, but I love it because every “prescription” is backed by research and conflicting studies are carefully dissected into their nuanced differences. It’s an easy read and a good “go to” book for when you need research to have your back.

Possibly Related Posts:

read more

University of Copenhagen Keynote

Jan 31, 2015 by

Just thought I would share the recording of “Surviving (and Thriving) in the Age of Digital Enhanced Teaching”, recorded at The University of Copenhagen. It includes some research I’ve been diving into about why student engagement, particularly interactions, are so important for learning. Enjoy!

Possibly Related Posts:

read more

NPS and Gamification

Jun 3, 2013 by

Last weekend I visited Bryce Canyon National Park and Cedar Breaks National Monument for a 3-day digital detox. [Yes, believe it or not, I can put away the Interwebs for 3 whole days.]

While hiking in Bryce Canyon, I stumbled across a bit of gamification of the hiking trails called Hike the Hoodoos Challenge.

With all the hype about digital badges and gamification lately, I can’t help but wonder why the NPS doesn’t take this a step further and develop a digital mobile game where you can earn activity badges in all the National Parks and Monuments by hiking the trails. It seems that you could just as easily use QR codes on the signage to “check in” to various trailheads via a mobile app. Better yet, let state parks get in on the action.

Maybe you’d rather just see the pictures though … here’s Bryce Canyon and our hike to the Queen’s Garden.

And here’s Cedar Breaks National Monument (we took the 2-mile hike to Spectra Point/Ramparts Overlook Trail)

Of course, if the NPS did create a mobile app game for hiking (Hiking the National Parks with Zombies?), then I suppose I would have to carry my phone with me, huh? Here I am, sans Internet-enabled digital devices.

Possibly Related Posts:

read more