# Vakdidactisch Onderzoek

## Learning of physics and mathematics concepts in an integrated STEM curriculum.

To solve the complex problems faced by our society, an increasing numbers of STEM (Science, Technology, Engineering, Mathematics) professionals are needed. Moreover, such a society requires STEM literacy for all its citizens. Education therefore increasingly focuses on STEM education. In doing so, it faces some problems of its own, e.g., students' low perceived relevance of STEM, a significant number of students in STEM programs in secondary education who do not want to pursue a STEM program in higher education, the difficulty to achieve deep understanding of STEM topics, a decrease of students' performance in STEM fields, a need for a research-based STEM framework, a need for qualitative learning materials, etc. With these challenges in mind, the education research community is putting its efforts into studying integrated STEM (iSTEM), in which the integration between the various STEM disciplines is a proposed solution to address these issues.

In Flanders (Belgium), the STEM@school project aimed at contributing to this research by developing a framework, designing learning materials, and performing qualitative and quantitative research on the implementation thereof in Flemish secondary schools. As part of the STEM@school project, this dissertation cooperated with the development of the framework, studied 9th grade students' learning of discipline specific concepts in an integrated curriculum, and investigated their ability to link concepts between physics and mathematics. We investigated how fluent students are in transitioning between graphs, formulas, and tables (their representational fluency), as well as their conceptual understanding of linear function problems in kinematics and mathematics, and compared these between an iSTEM group and a control group. Furthermore, we assessed and compared students' conceptual understanding in kinematics.

The main conclusions from this research can be summarized as follows.

- Concerning the specific topics of representational fluency and conceptual understanding in kinematics and mathematics for linear function problems, the iSTEM instructional approach from the STEM@school project resulted in level of performance which was highly similar to the regular instructional approach.
- Furthermore, we show that students experience more difficulties in kinematics compared to mathematics on comparable questions. We established that the type of linear function and the representational transition have an important effect on students' performance. Additionally, we found an asymmetry in the direction of the representational transitions containing a formula for the direct linear relationship in mathematics.
- Our results show that the slope is the most problematic concept in kinematics and that the y intercept is the most problematic in mathematics. Furthermore, we found a strong presence of confusions when determining the slope of a linear graph, which almost all occurred in kinematics and nearly none in mathematics. In addition, we identified three distinct categories of confusions and observed that students rarely change representation to solve a question.
- In kinematics, students from the control group reason with steepness more often and STEM students make more use of correct strategies and significantly less of the incorrect strategy compared to the control group.
- Concerning the understanding of kinematics, our study shows a small gain in students’ performance for the iSTEM group, which was particularly the case for the concepts related to vectors. Furthermore, our results show that students' understanding in kinematics is very low in both groups, strongly implicating that further improvements to the learning goals and the curricula are necessary.
- Specifically for our detailed topics, it can be concluded that the iSTEM approach succeeded in achieving similar or improved student performance and that further improvements are necessary.

## Blending of mathematics and physics: student reasoning in the context of the heat equation

Many physics concepts are described in terms of mathematical structures. As such, proficiency in mathematics is required to understand and describe physical phenomena, and being able to combine mathematics and physics is a prerequisite to become more proficient in physics. However, research shows that combining mathematics and physics is often a problem for students. In this project we investigate how undergraduate physics and mathematics students combine mathematics and physics in an upper-level course on partial differential equations (PDEs), specifically the heat equation. In this equation, the physical process of heat flow is described using advanced mathematics, hence it provides very good opportunities to investigate problems regarding blending of mathematical and physical concepts. ‘Blending’ is central to our theoretical framework: conceptual blending (Fauconnier and Turner, 1998).

The goal of this project is two-fold. First, there is the goal to develop a deeper understanding of reasoning processes when students combine mathematics and physics. We thereby will start from the conceptual blending framework. We investigate particular instances where students encounter difficulties when describing heat flow using the heat equation. The second goal is to develop teaching and learning materials that address these difficulties and explicitly support students in their blending process.

## SLOPE – Studying Learning Opportunities in a Planetarium Environment

Despite the long history of research on planetariums, there are many questions unanswered about the role they can play in educating various kinds of audiences and in supporting their interest in astronomy. Planetarium displays can prevent or remedy misconceptions about crucial notions of space, astrophysical phenomena and the universe as a whole. The Planetarium in Brussels offers a diverse educational program both for the public and for schools. In this project, we will focus on the activities that the Planetarium offer to students in the last two years of secondary education. These activities typically take the form of one school trip to the Planetarium. This visit aims at enriching the traditional school based (geography) lessons, by exploiting the unique visualization possibilities in the dome to enhance student learning.

Whether these Planetarium visits are effective in terms of student learning, and which features of the visit in general and the visualization in particular may contribute to this effectiveness, is not clear, however. In the proposed project, we will first investigate to what extent the unique Planetarium setting supports the learning of a selection of astronomical and astrophysical concepts by upper secondary school students. In a second phase, we will try to improve students’ learning processes and outcomes by enriching and optimizing the existing program and test its effectiveness. The ultimate goal is to design a research-based learning environment for astronomical and astrophysical concepts by fully exploiting the unique visualization possibilities of the Planetarium.

This PhD project builds on expertise from the staff of the Planetarium that will be combined with research expertise in astronomy/astrophysics, physics and geography education and educational psychology available in KU Leuven.