Fractions are a fundamental component of the school mathematics curriculum, and most students achieve proficiency in these concepts during their elementary education. However, a significant proportion of students still encounter challenges in this area even after entering secondary education, necessitating additional support to prevent further…

It is well known that fraction knowledge is relevant for later success in mathematics. However, many students still face difficulties when dealing with fractions. Predictors of fraction knowledge have been widely examined. Systematizing "mathematical" predictors, whether their predictive contributions are direct or indirectly mediated…

When learning about fractions, teaching usually follows certain topics -- e.g. part of the whole, fraction equivalence, and size comparison. Not yet answered is whether students' conceptual and procedural knowledge of fractions is coherent between those topics. To answer this question, we performed a latent profile analysis of data from N = 1005…

This single-case study investigates the effectiveness of video modeling for teaching the Look, Ask, Pick (LAP) strategy to three seventh-grade students with learning disabilities. The participants watched video segments explaining the technique to solve fraction problems. Results from the intervention revealed substantial performance improvements…

Previous research on the role of prior skills like proportional reasoning skills for the development of mathematical concepts offers conclusions such as "more (prior skills) is better (for later learning)." Insights, which prior skill "level" goes along with which "level" of learning outcomes, may advance the…

This paper presents a replication study investigating the effectiveness of a strategy to assist students with learning difficulties in adding fractions. Drawing on the research conducted by Grünke et al. (2023), this single-case analysis extends the application of the "Look, Ask, Pick" (LAP) mnemonic technique initially introduced by…

Although the teaching of vocabulary in mathematics lessons is requested in content- and language-integrated lesson designs, the clarification of the specific lexical language demands is still an open question for many mathematical topics. In a content- and language-integrated lesson design towards understanding the concept of equivalent fractions,…

Fractions are an integral part of the mathematics curriculum. Most students acquire proficiency with these concepts during the course of their elementary education and are usually able to perform basic fractions operations when reaching middle-school age. However, a considerable number of students require extra help to not fall further and further…

Educational technologies in mathematics typically focus on fostering either procedural knowledge by means of structured tasks or, less often, conceptual knowledge by means of exploratory tasks. However, both types of knowledge are needed for complete domain knowledge that persists over time and supports subsequent learning. We investigated in two…

Background: Concerning students' difficulties with fractions, many explanatory approaches are based on the distinction between conceptual knowledge and procedural knowledge. For further research in this field, it is thus crucial to make these constructs accessible to valid measurement. Aims: In this study, we aim at developing a test instrument…

There is a general consensus that both conceptual and procedural knowledge are essential for students' mathematical development. A common argument is that differences in mathematical performance are caused by differences in conceptual and procedural knowledge. Therefore, it is important to investigate to what extent such differences in conceptual…

Empirical evidence exists that enhancing students' language can promote the mathematics learning of multilingual students at risk, whereas other target groups (e.g., monolingual students, successful students, both with diverse academic language proficiency) have hardly been considered. This cluster-randomized controlled trial (N = 589)…

Teaching simulations such as scriptwriting tasks offer a novel way to support pre-service teachers in gaining diagnostic competencies and in guiding students to work through difficulties. We first report on the theory-driven development of a scriptwriting task, specifically the theoretically-founded language- and accompanying content-related…

Pedagogical content knowledge forms the core of teachers' professional knowledge; it refers to knowledge about making subject matter accessible to students. Thus, the formation of pedagogical content knowledge constitutes a crucial issue for educational research and practice. We investigated the contributions of content knowledge and pedagogical…

Using multiple representations and changing between them is at the heart of the mathematics classroom; unconnected changes can, however, be obstructive for students' learning. In order to support students' learning with multiple representations, teachers have to link observed situation aspects with relevant professional knowledge, a competence we…