Category Archives: Solution Fluency
For the past year, three other physics teachers and I have been investigating how explicitly teaching an expert-like approach in problem solving affects students in a modeling based physics classroom. We presented our findings Friday July 20th at Arizona State University and our report is, at last, complete!
We didn’t find anything groundbreaking. Unlike many larger/more popular educational innovations, our conclusions are conservative. Although we believe what we did has the potential to be beneficial to some students, we don’t claim it’s a silver bullet. In fact, we found that for students who didn’t build a strong conceptual understanding in physics, our explicit emphasis on problem solving was not beneficial.
Few people will likely be interested in reading our entire paper (it’s quite long!), but some may be interested in selected parts. I’ve posted our paper, Effects of Emphasizing Intentional Problems Solving here.
Here is our abstract:
Students begin their education in physics as novice problems solvers. Instead of carefully defining a problem, using qualitative models, and planning a method of solution, students often immediately attempt to find the answer to the problem. The result of this lack of methodical approach is that students are not only unable to solve problems, they are unsure of even the basic steps that lead toward solutions. Previous research has shown that intentionally teaching expert-like strategies increases students’ problem solving ability. Other studies have found that Modeling Instruction improves students’ expert-like problem solving ability. This study was initiated to evaluate the impact on students’ problem solving skills through teaching explicit problem solving strategies in addition to Modeling Instruction. There was no conclusive evidence that the gains from the two methods were additive; however, this approach was reported to be beneficial by study participants. There was substantial evidence that without a solid conceptual understanding, expert-like problem solving ability was limited.
I had a hard time coming up with an idea that incorporated global digital citizenship in a physics curriculum meaningfully. Ultimately I had my students work in small groups to plan and teach 20 minute lessons to small groups of lower school students. I had considered this idea initially, but was skeptical that it was practical. I owe a huge thanks to Roxanne Warner for putting all of the logistics together!
The planning stages of this project were very interesting. I wanted to ensure that my students were teaching meaningful physics vs. just playing with the elementary students. In that sprit, I let students know that a part of their grade would depend on the elementary students learning at least one thing from their lesson. They immediately bulked at this idea. What if their students didn’t pay attention or worse purposely sabotaged the lesson? As a teacher, it was great to see my students realize that teaching might not be as easy as they thought.
The lessons themselves were very successful – the elementary students loved them. It was fun to watch the elementary students experiment with and explain simple physics concepts. My students enjoyed the experience too. We used four class periods to complete the project (two planning, one peer editing, and then the actual lessons), but I feel like it was time well spent. From a physics standpoint, my students were learning as they taught. I was also pleased when I heard my students say things like:
This [teaching] is hard.
You do this for five periods?
Global Digital Citizenship still feels like an abstract hodgepodge of all the other fluencies wrapped in one to me. The 21st century learning site even states:
All the 21st Century fluencies are learned within the context of the Digital Citizen, using the guiding principles of leadership, ethics, accountability, fiscal responsibility, environmental awareness, global citizenship and personal responsibility.
As my students saw, teaching is almost the embodiment of this fluency. My novice-teachers solved problems, interpreted and manipulated information, thoughtfully used media, and worked collaboratively/creatively while planning and executing their lessons. Several of the guiding principles including leadership, ethics, global citizenship and personal responsibility were also key to our success. I especially like the fact that my students bought into the project as something “real.” I think it is very hard to encourage characteristics like personal responsibility or leadership in venues that seem artificial to students.
I was glad that this fluency was our last – I feel like it was great closure for our journey through 21st century fluencies this year!
“This is very stressful!” “We don’t have enough information!” “This is heartbreaking!” “This sucks; I wanna know so bad!”
These were the sounds that filled the classroom the day I introduced a lesson on solution fluency. The problem they were being asked to solve was to determine how I did a card trick. Before we began though, we brainstormed on the board examples of problems they had faced in the past and overcome(learning to tie my shoes, building a catapult in my backyard, passing my driving test, etc.) and what strategies they used to overcome said problem (got help from someone, kept trying and trying, studied and practiced). Armed with the successes of the past, I split them into pairs and gave each pair a deck of cards. They were given 20-25 minutes to solve the problem. While they worked (I informed them that I would not be giving them assistance), I walked around observing and recording. I noticed some roadblocks that prevented some students from preserving through problem solving:
1) Perceived predisposed weakness. When I told students that this card trick was taught to me by a Cambridge math professor, and that there was a math equation that showed how it worked, one girl said with dismay, “Oh, Math! I’m out!” She believed that because she wasn’t a “math person”, she wouldn’t be able to succeed. (yet interestingly enough, she was the first of all my students to solve the trick!).
2) Lack of creativity. Since the first part of the trick involves flipping cards over face up, when I saw one student flipping cards over face down, I intervened and reminded him that the trick won’t work if he flips the cards over that way. He stopped and stared at me incredulously, arguing, “But how else can I flip them? There’s no other way!” The inability to see something in a new light prevented him from moving forward. This reminded me of how linked all the fluencies are (creativity fluency, where are you? We need you now!) Strategies attempted were very limited and mostly involved guessing the card at random over and over again and puzzling over why it wasn’t working. On the flip side though, I did hear a few choruses of “Let’s try it again and see”, while students tried one different strategy after another such as “thinking about the trick backward” “look on YouTube”or “find a pattern”.
3) Other people’s success. Often when one pair/student was successful at solving the problem, it led to a general decline in other students’ willingness to keep trying. Many pairs just quit completely at that point. One student wrote on the follow up survey to this experience that the most frustrating part of the whole thing was “not getting the answer when other people were”. Rather then seeing their peers’ success as an invigorating indicator that the task was indeed achievable, students tended to view it with a “game over” mentality, as in a video game where one player wins and ends the game for everyone else.
Overall, this experience reaffirmed what I already knew: students need more practice solving problems in an environment where it is okay to fail and try again. An environment where the teacher doesn’t rush in to “help” all the time but patiently let’s them squirm till they find their way out of an uncomfortable yet productive place of uncertainty and into a solution they found, rather than one we delivered to them.
My first venture into project based learning has been very interesting. I asked my film criticism students to create a movie trailer using iMovie. I felt that it allowed creativity within a framework that could be managed by 7th and 8th graders. I tried to give only a few restrictions, and I provided them with the tools that they needed to be successful. I told them that the trailer had to be for an existing movie, and only one group could use a genre so we didn’t have the same format and music over and over. We have seven groups with three people in a group. I tried to mix grades and genders to create a group that could work efficiently. I provided them with their notebook of terms to check and match with the iMovie requirements, access to a computer, and a great technical support person, my mentor Ami, to help answer questions. The initial reaction to the assignment- stunned silence and blank looks. After a few questions, and one eager student, I finally got a reaction to the project, and it was not what I expected. My “digital natives” did not have a clue how to approach the assignment, and several students expressed reluctance because although several of them had experience with iMovie, they didn’t think they could handle this specific program.
I then realized that it was not the technology, or the project itself- they didn’t know how to get started or organize their tasks. So we took a big step back and practiced some basic techniques of problem solving. It was fascinating to see how differently each group began their preparations. One group storyboarded their entire trailer by drawing it out frame by frame “just like Hitchcock did with his movies”- I was so proud because they obviously paid attention during that unit. Other groups made lists, divided responsibilities, tried to do every aspect together, and even had a few creative differences. The filming process challenged them artistically, and we learned how to use a green screen, and be patient enough to do several takes. We are watching the finished product on Monday. I suspect that the real lesson learned has more to do with the process than the product. If that is the case, I will consider this first project a success.
“Why won’t you help me? You’re the teacher.”
“This project is going to take FOR…EVER. Ugh.”
“You mean I actually have to think on this assignment?!?”
Ever heard one these grumblings from one of your students? Believe it or not, it’s a good thing. It means your learning environment is transitioning. Our students are programmed to succeed in the traditional educational system. They want to continue to use BASIC while the world now requires them to know Objective C.
FACT: The recent shift to 21st century learning – promotion of skills like creativity, collaboration, problem-solving, curation, and innovation – is just as difficult for students to embrace as it is for teachers. Shocked?
Our kids are accustomed to the age-old game of content acquisition (passive learning) and testing (regurgitation). And many have gotten downright amazing at it. You know them. They’re typically your honor students. The ones who breeze through the homework and ace all your tests. They average a 98% or better in your class. And they’ve found a nice, warm, cozy niche in your educational environment. The problem is that information, once scarce, is now abundant and instantly available in today’s world.
So now, you’re challenging them to move. You’re asking them to take knowledge and do something with it (other than just spew it back to you). You’re asking them to design. Create. Innovate. Share. Debate. Present. Choose. Imply. Ask questions. Manipulate the content – and do so in a team with others.
It’s not going to be an easy adjustment for some of them. And, as teachers, we must understand the challenge involved in figuring out the rules of this new game – 21CL. So, what can we do to help our students then?
Have you encountered student resistance to 21CL activities in your classroom? How have you handled it? Found anything that works? Share your experiences with the E21 blog community. Comment on this post.
We have to “deprogram” our students by increasing the 21CL opportunities. We have to talk with them about the fact that the game is changing. Discuss the new “rules” when you implement a PBL unit. Explain that it may seem at times like you’re not teaching them, but that’s because you want them to learn. The active process is now theirs, not yours. It’s because you want them to take ownership of their own learning. Assure them that you are not abandoning them – and they can call on you for help and guidance as they explore. Expect mistakes along the way…and encourage your students to learn from failure. You are their 21st Century Tour Guide.
Failure is okay. Some of the world’s most successful people failed miserably while learning to succeed. Remind your students that they fail time and time again playing video games.
And yet, in the end, they always save the world.
Application: Lab Practica
In order to compliment our written tests, I’ve been experimenting with a lab test or lab practica. In many ways, the lab practica is an opposite to the written test. Where the written test is solitary, the practica depends on a team effort (students earn team grades). Where the written test rewards theoretical knowledge, the lab practica is as much an engineering challenge as a theoretical one. In the practica, strong laboratory skills, construction aptitude, common sense and interpersonal skills are critical to success. Surprisingly, the students who do the best on the written tests often have the most trouble with the practicas.
One simple example of a lab practica I have used pits students against two different battery powered cars. Students must predict where the cars will collide starting from arbitrary starting positions. Each group is able to use an array of tools to come up with any of many ways to predict where the cars collide. However they can’t manipulate both cars at once. When they are ready to test, they roll a dice to determine where each car will start and then have three minuets to use their solution method to predict the collision point and run the test.
Lab practicas are always intense class periods. With a significant portion of the lab practica grade relying solely on the accuracy of the predicted result for the single test, everyone usually gathers around the group who is about to test. Many groups will accurately predict results within 3% or less. Others are wildly off. Many times the smallest detail is responsible for huge errors – not unlike the NASA rocket that blew up because engineers forgot to convert English units to SI units.
Although students sometimes stress over practicas (uncertainty is inherent), I think they are very powerful. I rarely see students more focused then during a practica. All those soft skills suddenly become important – and students know it. Working together on something that matters to everyone is a huge team builder for physics groups.
The Big Picture
Although the lab practica format is specific to science, the larger idea of creating a real world performance based group test is applicable anywhere. I think there is hesitation about grading based on performance (outside of established performance-based subjects like the arts, speech, & foreign language) Additionally, having students earn grades as a group instead of individuals presents some obstacles. With care, I think both of these concerns can be managed to a reasonable level. And ultimately, adults are almost exclusively evaluated on performance instead of knowledge. Additionally, and especially in the future, team performance is often just as important as individual performance. It’s not perfectly fair, but then no one said it would be.
I am a little behind where I thought I’d be so we have not actually started the energy challenge yet – I will post a recap (& pictures!) once it happens (right after spring break). Anyway, the basic idea of the energy challenge is to build a completely autonomous Rube Goldberg Machine that is capable of popping 3 balloons in a specific order. Students also earn credit for involving multiple energy transformations (i.e. a falling mass releases energy stored in a spring). To accomplish the task students are given a wide variety of household materials including masses, springs, popsicle sticks, cardboard, string, magnets, wheels/axils, pulleys, mouse traps, pvc pipe, thumbtacks, pins, plastic track, textbooks, supersized rubber bands, clothes pins to name a few.
Last year, when the first energy challenge occurred, I was floored by the diversity of ideas. I’m not exaggerating when I say no two designs were even remotely alike. Some groups of students designed machines so complex they would have impressed Goldberg himself. Others designed elegantly simple machines. Either way, you could see how excited students were to match their creativity against such an open ended challenge.
Another thing I think was neat about this activity was that it could have fit under solution fluency or collaborative fluency just as easily.
The Big Picture
Obviously this activity is best suited for physics. However, I think this project demonstrates some of the components that Ken Robinson wrote of in Learning to be Creative. First, creative projects require that many possible routes exist to a solution. Second, most creative activates require resources. Third, to inspire creativity, students need to buy in to the activity. Finally, since creativity is applied imagination – there must be a clear way to evaluate student’s creativity.