# Physics Union Mathematics

# ISLE Curriculum Summary

#### ISLE achieves the goals by developing science and mathematic abilities

ISLE (Investigative Science Learning Environment) is a comprehensive learning system originally developed for introductory college-level physics (funded by NSF DUE-0241078 and DUE-0088906). It incorporates the processes through which scientists acquire knowledge into students’ learning. It also purposefully utilizes a large array of multiple representations helping students move from concrete representations to abstract mathematical representations. The logic of ISLE is based on the elements of scientific reasoning (inductive, analogical and hypothetico-deductive) and its practical implementation is based on the science of learning: multiple intelligences and multiple representations, collegial work, learning communities, and formative assessment with constructive feedback. Also ISLE’s library of tasks helps students develop various abilities used in the practice of science, mathematics and engineering, including the ability to represent knowledge in multiple ways, design experiments to formulate and test hypothesis, account for anomalous data, evaluate reasoning and experimental results, and communicate. A part of ISLE resources is a website with more than 200 videotaped experiments supported by questions that can be used for data collection, pattern recognition, model building and testing, and analysis of anomalous data (http://paer.rutgers.edu/pt3). In addition, there is a validated set of rubrics that can help students self-assess their mastery of these abilities. (Examples of rubrics are provided below; all of them are available at http://paer.rutgers.edu/scientificabilities). These tasks and rubrics have been developed as a part of an NSF project. They have been used in introductory college classes, teacher preparation classes and in professional development of middle school science teachers. ISLE’s summative assessments indicate that the curriculum is very effective in helping students master: (1) traditional physics content (learning gains of .56 on the Force Concept Inventory, post-test scores of 73% on Conceptual Survey of Electricity and Magnetism), (2) problem solving skills (ISLE students scored on average 76% correct when traditionally taught students scored 61% correct on the same 8 problems chosen by the professor who taught the traditional class), and (3) in helping them acquire scientific abilities.

The strengths of the ISLE system and the ALG curriculum is the repeated process though which students acquire knowledge and abilities. ISLE students begin each conceptual unit by observing simple, carefully selected phenomena (called observational experiments). They look for patterns in their observations and produce qualitative explanations based on these patterns. To find these patterns they analyze their observations using different representations, learning to reason in ways that are natural to their own learning styles. They then use their own explanations to make predictions about the outcomes of new experiments (called testing experiments, see an example at the end of this section). Based on the outcomes of their testing experiments, confidence in their explanation increases, or it needs revision, or it is rejected.

This process is then repeated only this time using quantitative mathematical representations—using “progressive differentiation” (e.g. from qualitative understanding to more precise quantitative understanding of a particular phenomenon), which involves a simultaneous focus on the structure of knowledge to be mastered and the learning process of students. During this quantitative stage, students solve context-rich problems using multiple representation techniques. Students learn to represent processes in multiple ways and to check for consistency of the representations—for example, the consistency of a free-body diagram and the application of Newton’s second law in component form to an object involved in some process. In labs students design their own experiments to test principles quantitatively and qualitatively and solve challenging experimental problems. Once students have developed enough conceptual knowledge, they can use that knowledge to understand and analyze a variety of modern technology, including devices such as: motion detectors, global positioning software and hardware, fiber optics technology, cell phones, force probes, electronic scales, analogue and digital galvanometers, magnetic field probes, spectrometers, and digital cameras. It is important to note that during all stages of this process students work cooperatively and learn to come to a consensus in terms of what they observed, how to explain it, and how to test the explanations. Student reasoning is heavily scaffolded by the curriculum materials, which suggests materials and questions for the analysis of observational experiments and testing experiments, guides students through the invention of new physical quantities, and provides data to help students find relationships between the quantities.

In The Physics Active Learning Guide (Van Heuvelen & Etkina, 2006) is a set of activities that follow the ISLE philosophy and can be used in a college classroom. all activities are grouped into 4 categories in each chapter: qualitative concept building and testing, conceptual reasoning, quantitative concept building and testing, and quantitative reasoning. It is this repeated structure that allows student to see how science ideas are built on evidence, tested by evidence, and applied to practical life. Additionally it builds mathematics knowledge by engaging students in data analysis, pattern recognition, proportional reasoning, unit conversions, measurement, algebraic representations, linear functions, integers, estimation, significant figures, charts and graphing, algebraic mean, vectors, trigonometry, rates, symbolic representations, etc.

ALG activities form a natural sequence of concept building and formative assessment at progressively more difficult levels, allowing them to be used at different levels of mathematical and physical sophistication – starting with qualitative and quantitative concept building and testing in middle school, which involves use of appropriate pre-algebra and algebra reasoning skills and then moving to reasoning that involves more complicated algebra-2 concepts.

ISLE naturally and strongly supports the perspectives on the 4 lenses of learning environments supported by the National Science Foundation. As we mentioned above, learning of ISLE students has been studied at various levels – using standardized tests, traditional problems, and performance assessments. The results indicate that the students do learn physics content as well and better than students taught though other reformed curricula, much better than students taught traditionally, and they acquire a vast array of scientific abilities.

The ISLE system and ALG activities have been successfully implemented in the calculus-based physics for regular engineering majors and engineers at-risk, in algebra-based courses for science majors, in physics methods courses for future physics teachers, and in professional development workshops for middle school teachers.