This paper describes research on a classification of physics problems in the context of introductory physics courses. This classification, called the Taxonomy of Introductory Physics Problems (TIPP), relates physics problems to the cognitive processes required to solve them. TIPP was created in order to design educational objectives, to develop assessments that can evaluate individual component processes of the physics problem-solving process, and to guide curriculum design in introductory physics courses, specifically within the context of a ''thinking-skills'' curriculum. Moreover, TIPP enables future physics education researchers to investigate to what extent the cognitive processes presented in various taxonomies of educational objectives are exercised during physics problem solving and what relationship might exist between such processes. We describe the taxonomy, give examples of classifications of physics problems, and discuss the validity and reliability of this tool.
We describe three iterations of a Massive Open Online Course (MOOC) developed from online preparation materials for a reformed introductory physics classroom at the Massachusetts Institute of Technology, in which the teaching staff interact with small groups of students doing problems using an expert problem‐solving pedagogy. The MOOC contains an e‐text, simple checkpoint problems and homework. We show how certain course design aspects affect student behaviour: (a) frequent quizzes correlated with students reading a large fraction of the e‐text, and (b) When homework sets are arranged by increasing (instructor‐estimated) difficulty, we found strong correlations between difficulty and time to solution, but weak correlations with percent correct. Modifications to the second offering of the course resulted in higher retention. These modifications included targeting physics teachers and posting materials well in advance. We define retention as certificates earned relative to participants who make a significant effort on the second assignment. Retention measured this way varied between 44% and 72%, being highest in the course aimed at teachers. We show that there is significant learning among MOOC participants. Applying item response theory to common homework problems showed that the MOOC participants had significantly higher ability than students in a Massachusetts Institute of Technology course and that they maintained this advantage over the duration of the MOOC.
Abstract. We are building in LON-CAPA an integrated learning environment that will enable the development, dissemination and evaluation of PER-based material. This environment features a collection of multi-level researchbased homework sets organized by topic and cognitive complexity. These sets are associated with learning modules that contain very short exposition of the content supplemented by integrated open-access videos, worked examples, simulations, and tutorials (some from ANDES). To assess students' performance accurately with respect to a systemwide standard, we plan to implement Item Response Theory. Together with other PER assessments and purposeful solicitation of student feedback, this will allow us to measure and improve the efficacy of various research-based materials, while getting insights into teaching and learning.
Abstract. We investigate student-chosen, multi-level homework in our Integrated Learning Environment for Mechanics [1] built using the LON-CAPA [2] open-source learning system. Multi-level refers to problems categorized as easy, medium, and hard. Problem levels were determined a priori based on the knowledge needed to solve them [3]. We analyze these problems using three measures: time-per-problem, LON-CAPA difficulty, and item difficulty measured by item response theory. Our analysis of student behavior in this environment suggests that time-per-problem is strongly dependent on problem category, unlike either score-based measures. We also found trends in student choice of problems, overall effort, and efficiency across the student population. Allowing students choice in problem solving seems to improve their motivation; 70% of students worked additional problems for which no credit was given.
As part of an ongoing project to reform the introductory algebra-based physics courses at George Washington University, we are developing a taxonomy of introductory physics problems (TIPP) that establishes a connection between the physics problems, the type of physics knowledge they involve and the cognitive processes they develop in students. This taxonomy will provide, besides an algorithm for classifying physics problems, an organized and relatively easy-to-use database of physics problems that contains the majority of already created text-based and research-based types of problems. In addition, this taxonomy will reveal the kinds of physics problems that are still lacking and that are found to be necessary to enhance students' cognitive development. For this reason, we expect it to be a valuable teaching resource for physics instructors which will enable them to select the problems used in their curricular materials based on the specifics of their students' cognition and the learning objectives they want to achieve in their class. This organization scheme will also provide a framework for creating physics-related assessments with a cognitive component.
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