Wolfgang Schnotz

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.

This article investigates whether goal-directed learning of pictures leads to multiple mental representations which are differently useful for different purposes. The paper further investigates the effects of prompts on picture processing. 136 undergraduate students were presented maps of a fictitious city. One half of the participants were instructed to learn their map as preparation to draw it from memory as precisely as possible (PrepDraw), which should stimulate the creation of an elaborated surface representation. The other half were instructed to learn the map as preparation for finding the shortest traffic connection from various locations to other locations (PrepConnect), which should stimulate the construction of a task-oriented deep-structure representation (mental model). Within both experimental groups, one-third of the participants received the map without prompts. Another third received the map with survey prompts (stimulating processing of what is where), and the final third received the map with connect prompts (stimulating processing of how train stations are connected). In the following test phase, participants received a recognition task, a recall task, and an inference task. For recognition and recall, two surface structure scores (extent, accuracy) and two deep structure scores (extent, accuracy) were calculated. The inference task served also to indicate deep structure accuracy. The PrepDraw group outperformed the PrepConnect group in terms of surface structure related variables, whereas the PrepConnect group outperformed the PrepDraw group in terms of deep structure-related variables. Map processing was not enhanced by prompts aligned with the instruction, but non-aligned prompts tended to interfere with learning.

This study describes the problem solving behaviour of bilingual (German - Turkish) primary school students, their approaches and preferences while solving the word problems. Four different types of mathematical word problems (combinations, movement, subtraction and addiction) were given successively to four pupils (one girl and three boys) and their individual strategies during solution process were explored. After examining the students’ answers, four theme, namely language, effect of daily experience, recontextualizing the problem and the mathematical answer were listed. Generally, the students struggle to use the representations effectively with their problem solving strategies. This study would be valuable with giving detailed information about bilingual students problems solving strategies under free language environment and results would be helpful to researchers to conduct an intervention study that specially targeting to improve the problems solving strategies of bilingual children with an emphasize to rehearsal their reading skills and representation repertoire.

This paper presents the results of an empirical study on phrasal verbs with to come, to give, to go, to get, and to take and up, down, out as complements. Presuming that in many instances the overall meaning of PVs cannot be adequately inferred from the senses of their constituent parts (e.g., to make up for ⇒ to compensate), it is hypothesized that raising awareness for the underlying conceptual motivation of the verbs and the particles helps learners study PVs more efficiently. A quasi-experimental field study including a pre-/post-test design with both an experimental group (EG) and a control group (CG) was conducted in an authentic secondary school context in Germany. The participants were higher track ninth graders with L1 German. The corpus of PVs, the time of instruction (3 × 45 minutes) and the text material the students worked with were identical over both groups. Yet, only in the EG the students worked on the conceptual motivations of PVs. Different theoretical strands were used as a resource to develop CL-inspired teaching material (Mahpeykar and Tyler 2014; Rudzka-Ostyn 2003; Tyler and Evans 2003). The studies investigated a) the effect of CL-methods on retention and b) the transfer of CL insights to novel PVs. With regard to retention, the study could not statistically prove an advantage for the EG. However, statistical evidence was found that the EG outperformed the CG significantly on transfer ( p < .05).

Comprehension of graphics can be considered as a process of schema-mediated structure mapping from external graphics on internal mental models. Two experiments were conducted to test the hypothesis that graphics possess a perceptible surface structure as well as a semantic deep structure both of which affect mental model construction. The same content was presented to different groups of learners by graphics from different perspectives with different surface structures but the same deep structure. Deep structures were complementary: major features of the learning content in one experiment became minor features in the other experiment, and vice versa. Text was held constant. Participants were asked to read, understand, and memorize the learning material. Furthermore, they were either instructed to process the material from the perspective supported by the graphic or from an alternative perspective, or they received no further instruction. After learning, they were asked to recall the learning content from different perspectives by completing graphs of different formats as accurately as possible. Learners’ recall was more accurate if the format of recall was the same as the learning format which indicates surface structure influences. However, participants also showed more accurate recall when they remembered the content from a perspective emphasizing the deep structure, regardless of the graphics format presented before. This included better recall of what they had not seen than of what they really had seen before. That is, deep structure effects overrode surface effects. Depending on context conditions, stimulation of additional cognitive processing by instruction had partially positive and partially negative effects.