Development of graph inventory

This project focuses on investigation of university students understanding of graphs. Graphs are an important and universal scientific tool, but the results of physics and mathematics education research strongly suggest that students often do not develop sufficient understanding of graphs through standard instruction. The research will be conducted on two student populations: first -year university students of physics at the University of Zagreb, Croatia and the University of Vienna, Austria. Student difficulties which will be detected in these two populations will be analyzed. In the first stage of the research an instrument consisting of eight sets of parallel questions from mathematics, kinematics and other contexts (twelve multiple choice items and twelve open ended items), developed by the Physics Education Group at the University of Zagreb, will be used. Prior research of that group has shown that the instrument is valid and its use on first year mathematics and physics students at University of Zagreb has already helped detect important student difficulties with graphs and allowed comparison of student understanding of graphs in different contexts. The use of the instrument will now be extended to first year students of physics at University of Vienna. Students explanations provided with the answers to test items and those obtained through the semi-structured interviews, which will also be conducted with some of the tested students, will be used as the basis for further improvement of the test items and for the construction of a new two- tier instrument on graphs. The new instrument will be administered to ca. 650 students at the University of Zagreb and the University of Vienna and its functioning will be evaluated with Rasch analysis. In addition the new instrument will be administered to 100 students at University of Ljubljana and at Free University of Berlin. The purpose of the new instrument would be to enable physics teachers and university physics faculty to quickly detect the prevalence of the students main reasoning difficulties in analyzing graph slopes and areas. The new instrument is intended to be used as the pre- and posttest. It will have the advantage of being easier to administer and analyze than the existing instrument, and yet to provide important information on student reasoning. As such it could help university faculty to quickly evaluate student understanding as well as the efficiency of the teaching on graphs. It is planned to publish the results of the research in open access journals and to present them at several physics teachers meetings and international conferences.

Scientific data are very often communicated through graphs, because they allow the skilled user to quickly recognize and extract important features of the data set under analysis, such as trends, rates of change etc. Students are introduced to graphs through different school subjects, but mostly through mathematics and physics. The main aims of the project Development of Graph Inventory were to investigate Austrian first-year university students understanding of graphs, as well as their main reasoning difficulties in analyzing graph slopes and areas, compare those with data from other countries, and develop a new two-tier diagnostic instrument on graphs.In the first stage of the project an existing instrument on graphs with 24 items, requiring written explanations of answers, was administered to 417 first-year physics students at University of Vienna and to 74 first-year physics students at University of Zagreb in October 2014. The results were compared to the results of 385 first-year students at Faculty of Science, University of Zagreb from October 2010. The overall trends in difficulties of conceptual areas in the test were very similar and data showed only small discrepancies between these two groups of students. The Rasch analysis indicated stability and reliability of the instrument. In the second stage, the new two-tier instrument has been developed using questions from the previous instrument as well as constructing some new ones. The second tier in each question substituted students written explanations and procedures. The new test consists of 24 two-tier items and is convenient to administer and much less time consuming to mark than the previous one. The test provides the insight in student difficulties with graphs and their underlying reasoning and can also be used as a research tool in the field of physics education. Knowing student difficulties may contribute to improvement of instruction on graphs and to a better understanding of this important topic among students at high-school and university level.