Mono- and Multi-Representational Learning of the Covariational Aspect of Functional Thinking

Using multiple external representations is advocated for learning in STEM education. This learning approach assumes that multiple external representations promote richer mental representations and a deeper understanding of the concept. In mathematics, the concept of function is a prototypical content area in which multiple representations are used. However, there are hardly any experimental studies investigating the effect of learning functional thinking with multiple representations compared to learning with only one form of representation. Therefore, this article reports on a quasi-experimental intervention study with students from Grade 7, using three measurement time points. The study compared the multi-representational learning of functional thinking with both tables and graphs with mono-representational learning with either tables or graphs. The results show that multi-representational learning led to advantages in learning qualitative functional thinking. However, in quantitative functional thinking, learning with both graphs and tables did not result in higher learning gains than learning exclusively with graphs. Furthermore, students were better able to transfer their knowledge from graphs to tables than vice versa. The results also indicate that multi-representational learning requires more time than mono-representational learning but can lead to higher learning gains. In sum, the results show that the effect of learning with representations is a complex interaction process between learning content and the forms of representation.

Cognitive Load Implications for Augmented Reality Supported Chemistry Learning

This paper presents a study about augmented-reality-based chemistry learning in a university lecture. Organic chemistry is often perceived as particularly difficult by students because spatial information must be processed in order to understand subject specific concepts and key ideas. To understand typical chemistry-related representations in books or literature, sophisticated mental rotation- and other spatial abilities are needed. Providing an augmented reality (AR) based learning support in the learning setting together with text and pictures is consistent with the idea of multiple external representations and the cognitive theory of multimedia learning. Using multiple external representations has proven to be beneficial for learning success, because different types of representations are processed separately in working memory. Nevertheless, the integration of a new learning medium involves the risk to hinder learning, in case of being not suitable for the learning topic or learning purpose. Therefore, this study investigates how the AR-use affects students’ cognitive load during learning in three different topics of organic chemistry. For this purpose also the usability of AR learning support is considered and the possible reduction of the influence of the mental rotation on learning success will be investigated.

One Instructional Sequence Fits all? A Conceptual Analysis of the Applicability of Concreteness Fading in Mathematics, Physics, Chemistry, and Biology Education

To help students acquire mathematics and science knowledge and competencies, educators typically use multiple external representations (MERs). There has been considerable interest in examining ways to present, sequence, and combine MERs. One prominent approach is the concreteness fading sequence, which posits that instruction should start with concrete representations and progress stepwise to representations that are more idealized. Various researchers have suggested that concreteness fading is a broadly applicable instructional approach. In this theoretical paper, we conceptually analyze examples of concreteness fading in the domains of mathematics, physics, chemistry, and biology and discuss its generalizability. We frame the analysis by defining and describing MERs and their use in educational settings. Then, we draw from theories of analogical and relational reasoning to scrutinize the possible cognitive processes related to learning with MERs. Our analysis suggests that concreteness fading may not be as generalizable as has been suggested. Two main reasons for this are discussed: (1) the types of representations and the relations between them differ across different domains, and (2) the instructional goals between domains and subsequent roles of the representations vary.

Engaging Young Children with Mathematical Activities Involving Different Representations: Triangles, Patterns, and Counting Objects

This paper synthesises research from three separate studies, analysing how different representations of a mathematical concept may affect young children’s engagement with mathematical activities. Children between five and seven years old engaged in counting objects, identifying triangles and completing repeating patterns. The implementation of three counting principles were investigated: the one-to-one principle, the stable-order principle and the cardinal principal. Children’s reasoning when identifying triangles was analysed in terms of visual, critical and non-critical attribute reasoning. With regard to repeating patterns, we analyse children’s references to the minimal unit of repeat of the pattern. Results are discussed in terms of three functions of multiple external representations: to complement, to constrain and to construct.