In this strand, we will focus on several aspects of teaching problem solving skills across STEM disciplines. Beginning with the choice of problems for students to engage with, we will discuss elements of problem solving that are common across STEM disciplines, as well as differences in the way that problems are framed and delivered. To equip students with improved problem solving skills, we will examine ways that thinking during problem solving can be effectively modeled, scaffolded, and coached for students and structural elements of classrooms, activities, and technological tools that assist in training for problem solving skills.
Bradley "Peanut" McCoy, Dept. of Physics at Azusa Pacific University, and Chris Rasmussen, Dept. of Mathematics at San Diego State University, have organized the various sessions related to problem solving in STEM education. Information about these leaders can be found on the Problem Solving Theme Organizers webpage.
Morning Workshop– Problem Structure and Analysis
David Quarfoot, Mathematics, UCLA
While there are numerous research lines related to problem solving in STEM disciplines, most of these occur "after the curtain has raised": that is, after a student encounters some task to work on. In this workshop, I focus on some "before the curtain" issues:
- Problem Structure: When we think of "good" problems, or problems that "facilitate problem solving", what features (e.g., novelty, cognitive sophistication, numerosity of steps, etc.) do they tend to have? What features do educators in specific fields hope to see in their problems (if the goal is to promote problem solving development) – and do these differ across fields? What major features have been identified in the literature, and how are they correlated in problems we currently use?
- Problem Analysis: How can we measure the amount of a feature present in some problem? For example, are educators able to judge the amount of creativity demanded by a problem? How about the number of solutions? Do students accurately report "difficulty" levels? Can a computer determine the novelty of a problem? Each of these settings (expert ratings, student self-reports, empirical calculations) offers its own challenges. In the case of expert ratings, we can use statistical techniques from the field of multi-rater inter-rater reliability to measure the level of agreement, and hence, of well-definition for problem features.
Contributed Paper Session
One of the biggest challenges in teaching is providing a learning experience that challenges every student at the same depth regardless of their background or experience. All too often, courses overly challenge those who are relatively less experienced, and underserve those who have an extensive background. In 2016, the speaker created a course whose primary goal was to resolve this disparity. Little did the speaker know how transformative the experience would be for the students.
For solving problems, especially ill-structured ones, a solver must employ metacognitive strategies to be successful. Unfortunately, most textbooks portray problem-solving as a process devoid of any metacognition. Rather than showing examples of how one can identify and correct errors within a solution, they show only correct and optimized solutions. To mitigate this poor representation of problem-solving and facilitate student development, class activities and course structures have been implemented to emphasize the metacognitive aspects of problem-solving. To avoid introducing students to unfamiliar jargon and to keep the emphasis on the examination process, rather than the subsequent adjustments, these strategies have been labeled as monitoring. Among the changes implemented in several STEM classes were modified test structures that rewarded monitoring, homework and in-class problems solved homework problems via a think-aloud protocol, and instruction that gave students prompts based on the categories of monitoring observed in successful solutions. It was observed that solvers who frequently monitor their thinking and work were generally more successful than those who did not.
Improved problem solving ability is an important outcome in physics classes, and may be more important than physics content knowledge, particularly for non-physics majors in introductory courses. Yet many physics students take inexpert approaches to problem solving, such as memorization or plug and chug strategies. Research on problem solving can help us understand and address these issues. This talk will explore physics problem solving from perspectives that emphasize individual cognition, the use of tools and representations, students' views about physic and learning physics, and the social and cultural contexts of learning. Integrating these multiple perspectives provides a more complete understanding of student difficulties with physics problem solving and leads to recommendations for instruction.
This session focuses on how to support students to develop problem-solving and metacognitive abilities in mathematics. I introduce Peer-Assisted-Reflection (PAR), a cycle of activities that requires students to: (1) work on meaningful problems, (2) reflect on their own work, (3) analyze a peer's work and exchange feedback, and finally (4) revise their work based on insights gained throughout this cycle. Participants will learn the theory behind PAR, how to support students to give productive feedback, and gain access to practical materials they can use in their own classrooms.
Research on problem solving can be traced back more than half a century. During that time, researchers have had many different perspectives on issues including what constitutes a problem, what are the cognitive processes critical to problem solving, characteristics of expert versus novice problem solving, and how problem-solving expertise can be measured. In this talk, I describe a perspective of physics problem-solving framework and how it has influenced our work on using computers to coach students to become better problem solvers, as well as how we assess whether students have indeed improved their problem-solving skills.
Real world experimentation and testing is riddled with challenges that need to be resolved. One might find themselves in the middle of nowhere without the required specialized power cord and the need to power a system for a demonstration to a group of Marine Corps Generals. One might also find themselves running a test in the middle of the desert in July with computers overheating and rebooting every 5 minutes making data collection impossible. The role of the scientist or engineer is to be a problem solver. The most valuable scientist or engineer is one who can think outside the box, inside the box, or with no box included. Creativity is key to solving the difficult problems that might arise. When teaching students how to solve problems, it is critical to create a learning environment that promotes multiple solutions and creative thinking. Ensuring that the problems being solved have relevance to the learner will increase the interest and relationship with the problem. Why does this problem need to be solved? What will be learned by creating solutions? How can one determine the best solution? Utilizing the vast experience of scientists and engineers can enhance the problem solving learning environment.
Afternoon Working Group
- Structures (Dan Reinholz PAR-Peer Assisted Reflection, Math Circles, Olympiad hierarchies)
- Tools (Physical, technological, pedagogical: Gamification, Virtual Reality, Discourse Moves)
- Equity (around implementation, around problem choice (e.g., sports and gun in physics), around the problem solving process, group dynamic re: equity and problem solving)
- Multidiscipline Research (how can research in PS in one field influence/inform another?)
Participants will self-organize into groups according to which question they are most interested in answering. The goal of the working group will be to solicit ideas and produce an outline of an answer or approach to answer the group question. Each group will be asked to continue work beyond the conference to prepare a submission for the conference proceedings.
Questions? Email BreakingBoundaries@lmu.edu