Digital monitoring of fraction learning: Adapting a test for knowledge of fraction subconstructs - Schadl, Constanze; Lindmeier, Anke (Proceeding of the 46th Conference of the International Group for the Psychology of Mathematics Education, 2023)
Fraction learning is a central yet difficult topic in mathematics education. Hence, formatively monitoring fraction learning is important. Despite a sound research base from paper-based studies, findings on fraction learning are still difficult to use in practice, as mathematics teachers have limited access to test materials, for example. This contribution presents the first results of a study that explores the feasibility of digital testing with n = 231 sixth graders. It focuses on the psychometric quality of fraction tests that have been adapted to a digital format and their suitability for repeated testing. The findings indicate similarities but also differences compared with the paper-based tests. The two tests indicate to be parallel and hence suitable for the digital monitoring. The implications of our findings for school practice are discussed.
CRIS-Team Scopus Importer:2024-10-02

MODELLING PROPORTIONAL REASONING SKILLS IN LEVELS WITHIN A DIGITAL SETTING - Schadl, Constanze; Lindmeier, Anke (Proceedings of the International Group for the Psychology of Mathematics Education, 2022)
Proportional reasoning skills are central for fraction learning which, in turn, is an important aim in secondary mathematics education. In an effort to better understand students’ proportional reasoning and its relation to fractions, previous research has used paper-based tests and succeeded in modelling proportional reasoning skills in levels. However, so far these findings cannot be used by teachers because of the high effort involved with paper-based testing. In this report, we explore the applicability of digital methods to address this issue with data from fifth graders (n = 93) in a mode study. Despite of a need to adapt the instrument for the digital assessment, we observe similar levels based in IRT modelling as in the paper-based settings. The findings inform the further development of digital assessments to support fraction learning.
CRIS-Team Scopus Importer:2024-10-02

Preparing for Digital Learning Monitoring in the Fraction Context: Assessment of Students’ Prior Knowledge According to Evidence-Based Cognitive Models - Schadl, Constanze; Lindmeier, Anke (International Journal of Science and Mathematics Education, 2025)
Regularly assessing students’ learning using evidence-based cognitive models can enhance learning by supporting teachers’ monitoring and scaffolding decisions. In the case of mathematics, this is considered especially essential for topics renowned as being complex for students, like fractions. Although previous findings from paper-based studies yielded sophisticated cognitive models, they were not consistently related so far to evidence-based assessment approaches. Also, as paper-based testing appears resource-consuming, its practical use is hindered. Addressing this gap, we developed instruments for digital evidence-based assessment. This paper focuses on the psychometric quality of two tests assessing prior knowledge of fractions: symbolic multiplication and division skills (SMDS) and proportional reasoning skills (PRS). Using item-response-theory-methods to analyze data from N = 147 fifth graders, the digital SMDS-test showed good reliability and validity. The findings suggest a specific item subset suited as an efficient short test. Regarding PRS, further adaptation of the digital format is advised.
CRIS-Team Scopus Importer:2025-02-17
Keywords: Cognitive model; Evidence-based digital assessment; Item-response-theory-methods; Proportional reasoning skills; Symbolic multiplication and division skills

Searching for efficient and informative instruments to digitally monitor fraction learning: putting tests for fraction subconstruct knowledge and informal fraction knowledge on the test bench - Schadl, Constanze; Lindmeier, Anke (Frontiers in Education, 2024)
Fractions are a relevant yet complex topic of school mathematics. Fortunately, educational research issued rich knowledge of central concepts and associated difficulties for students. Using this knowledge for monitoring learning and formative assessment could support students’ learning process. However, access to apt evidence-based tests is restricted, and paper-based testing limits their practical usability. The digital adaptation of paper-based tests may address these challenges due to affordances like automated test scoring. Further, digital tests may facilitate repeated test use necessary for monitoring and formative activities. The present contribution focuses on fraction subconstruct knowledge and informal fraction knowledge and is part of a systematic research effort to transform paper-based tests into a digital format. With two cross-sectional studies in Grades 6 (N = 233) and 5 (N = 271), each with three measurement points, we investigated the psychometric properties of adapted digital parallel tests regarding their suitability for repeated testing. The internal structure of the adapted digital tests proved to be comparable to that of the original paper-based tests in many, but not all, aspects. Parallel tests were found to be sufficiently parallel. The findings for the two focused constructs support that systematic efforts lead to usable tools for students’ fraction learning. The discussion considers how this supports the transformation of research findings to support the adoption of formative assessment.
CRIS-Team Scopus Importer:2025-04-01
Keywords: (informal) fraction knowledge; digital assessment; IRT-scaling; learning progress; psychometric quality

Who Struggles with which Demand? Using Level Models to Understand Interindividual Differences in and Relations Between Facets of Fraction Knowledge - Schadl, Constanze; Ufer, Stefan (International Journal of Science and Mathematics Education, 2025)
Dealing with fractions is a central and complex topic in mathematics learning. Existing theoretical models of fraction knowledge and skills describe central knowledge facets and roughly characterize procedural demands. However, it is still unclear how to describe students’ levels of fraction knowledge and skills with explicit reference to the mastered contents and how to understand relations between skill facets using these levels. Based on two datasets with 751 sixth and seventh graders, a structural model with three facets is investigated: knowledge of fraction subconstructs, fraction arithmetic skills, and fraction word problem-solving. These facets build on each other in existing models of fraction knowledge and many fraction curricula. Levels for the three constructs are characterized by more or less prestructured fraction demands and the complexity of numerical information. Linear relations between conceptual and procedural fraction demands are investigated in detail concerning the level descriptions, confirming that conceptual demands show a more substantial contribution to procedural demands than vice versa. Further, the results underline the complexity of fraction word problems demands and that mastering them may require at least the lower levels of knowledge of fraction subconstructs and fraction arithmetic skills. The results provide a basis for learning trajectories and different formative activities in school practice, which may also be relevant for mathematics teacher education.
CRIS-Team Scopus Importer:2025-05-16
Keywords: Conceptual and procedural demands; Explanatory models; Fraction learning; Level models; Structural model