Watching videos of a drawing hand improves students' understanding of the normal probability distribution.

Understanding normal probability distributions is a crucial objective in mathematics and statistics education. Drawing upon cognitive psychology research, this study explores the use of drawings and visualizations as effective scaffolds to enhance students' comprehension. Although much research has documented the helpfulness of drawing as a research tool to reveal students' knowledge states, its direct utility in advancing higher-order cognitive processes remains understudied. In Study 1, qualitative methods were utilized to identify common misunderstandings among students regarding canonical depictions of the normal probability distribution. Building on these insights, Study 2 experimentally compared three instructional videos (static slides, dynamic drawing, and dynamic drawings done by a visible hand). The hand drawing video led to better learning than the other versions. Study 3 examined whether the benefits from observing a hand drawing could be reproduced by a dynamic cursor moving around otherwise static slides (without the presence of a hand). Results showed no significant learning difference between observing a hand drawing and a moving cursor, both outperforming a control. This research links the cognitive process of drawing with its educational role and provides insights into its potential to enhance memory, cognition, and inform instructional methods.

Representational-mapping strategies improve learning from an online statistics textbook.

Using multiple representations is an important part of learning and problem-solving in science, technology, engineering and mathematics fields. For students to acquire flexible knowledge of representations, they must attend to the structural information within each representation and practice making relational connections between representations. Most studies so far have only attempted to help students connect between multiple representations in the lab or short-term classroom interventions, with the intervention largely separated from students' authentic learning. The present study developed a representation-mapping intervention designed to help students interpret, coordinate, and eventually translate across multiple representations. We integrated the intervention into an online textbook being used in a college course, allowing us to study its impact in a real course over an extended period of time. The findings of this study support the efficacy of the representation-mapping intervention for facilitating learning and shed light on how to implement and refine such interventions in authentic learning contexts. (PsycInfo Database Record (c) 2023 APA, all rights reserved).

Lower socioeconomic status is related to poorer emotional well-being prior to academic exams.

BACKGROUND: People of lower social status tend to have greater emotional responses to stress. The present study assessed whether lower social status was related to greater emotional responses in anticipation of a naturalistic stressor: academic exams among college students. METHODS: College students in an introductory statistics class (N = 252; 75.81% female; 18.41% Latino, 25.10% White, 43.93% Asian, 12.56% different racial backgrounds) completed two course exams as part of this naturalistic prepost-experimental design. They provided four reports of positive, depressive, and anxious emotion - one the day before and one immediately after each exam. RESULTS: As hypothesized, multilevel models (ratings nested within participants) predicting emotion indicated that students with lower mother's education had less positive emotion, more depressive emotion, and more anxious emotion the day prior to academic exams than students with higher mother's education (proportional reductions in variance [PRV] = .013-.020). Specifically, lower mother's education was associated with poorer well-being before but not after the exam. Exploratory models revealed that differences in emotion by mother's education were strongest for students with lower exam scores (PRV = .030-.040). CONCLUSIONS: Socioeconomic status may influence college students' anticipatory distress prior to academic exams, which may impact health and academic performance.

Instructed Hand Movements Affect Students' Learning of an Abstract Concept From Video.

Producing content-related gestures has been found to impact students' learning, whether such gestures are spontaneously generated by the learner in the course of problem-solving, or participants are instructed to pose based on experimenter instructions during problem-solving and word learning. Few studies, however, have investigated the effect of (a) performing instructed gestures while learning concepts or (b) producing gestures without there being an implied connection between the gestures and the concepts being learned. The two studies reported here investigate the impact of instructed hand movements on students' subsequent understanding of a concept. Students were asked to watch an instructional video-focused on the concept of statistical model-three times. Two experimental groups were given a secondary task to perform while watching the video, which involved moving their hands to mimic the placement and orientation of red rectangular bars overlaid on the video. Students were told that the focus of the study was multitasking, and that the instructed hand movements were unrelated to the material being learned. In the content-match group the placement of the hands reinforced the concept being explained, and in the content-mismatch group it did not. A control group was not asked to perform a secondary task. In both studies, findings indicate that students in the content-match group performed better on the posttest, and showed less variation in performance, than did students in the content-mismatch group, with control students falling in between. Instructed hand movement-even when presented as an unrelated, secondary task-can affect students' learning of a complex concept.

Removing opportunities to calculate improves students' performance on subsequent word problems.

BACKGROUND: In two studies we investigated whether removing opportunities to calculate could improve students' subsequent ability to solve similar word problems. Students were first asked to write explanations for three word-problems that they thought would help another student understand the problems. Half of the participants explained typical word problems (i.e., problems with enough information to make calculating an answer possible), while the other half explained the same problems with numbers removed, making calculating an answer impossible. We hypothesized that removing opportunities to calculate would induce students to think relationally about the word problems, which would result in higher levels of performance on subsequent transfer problems. RESULTS: In both studies, participants who explained the non-calculable problems performed significantly better on the transfer test than participants who explained the typical (i.e., calculable) problems. This was so in spite of the manipulation not fully suppressing students' desire to calculate. Many students in the non-calculable group explicitly stated that they needed numbers in order to answer the question or made up numbers with which to calculate. There was a significant, positive relationship between the frequency with which students made up numbers and their self-reported mathematics anxiety. CONCLUSIONS: We hypothesized that the mechanism at play was a reduction in instrumental thinking (and an increase in relational thinking). Interventions designed to help students remediate prior mathematical failure should perhaps focus less on the specific skills students are lacking, and more on the dispositions they bring to the task of "doing mathematics."

Exploring the practicing-connections hypothesis: using gesture to support coordination of ideas in understanding a complex statistical concept.

In this article, we begin to lay out a framework and approach for studying how students come to understand complex concepts in rich domains. Grounded in theories of embodied cognition, we advance the view that understanding of complex concepts requires students to practice, over time, the coordination of multiple concepts, and the connection of this system of concepts to situations in the world. Specifically, we explore the role that a teacher's gesture might play in supporting students' coordination of two concepts central to understanding in the domain of statistics: mean and standard deviation. In Study 1 we show that university students who have just taken a statistics course nevertheless have difficulty taking both mean and standard deviation into account when thinking about a statistical scenario. In Study 2 we show that presenting the same scenario with an accompanying gesture to represent variation significantly impacts students' interpretation of the scenario. Finally, in Study 3 we present evidence that instructional videos on the internet fail to leverage gesture as a means of facilitating understanding of complex concepts. Taken together, these studies illustrate an approach to translating current theories of cognition into principles that can guide instructional design.

The role of visual representations in college students' understanding of mathematical notation.

Developing understanding of fractions involves connections between nonsymbolic visual representations and symbolic representations. Initially, teachers introduce fraction concepts with visual representations before moving to symbolic representations. Once the focus is shifted to symbolic representations, the connections between visual representations and symbolic notation are considered to be less useful, and students are rarely asked to connect symbolic notation back to visual representations. In 2 experiments, we ask whether visual representations affect understanding of symbolic notation for adults who understand symbolic notation. In a conceptual fraction comparison task (e.g., Which is larger, 5 / a or 8 / a?), participants were given comparisons paired with accurate, helpful visual representations, misleading visual representations, or no visual representations. The results show that even college students perform significantly better when accurate visuals are provided over misleading or no visuals. Further, eye-tracking data suggest that these visual representations may affect performance even when only briefly looked at. Implications for theories of fraction understanding and education are discussed.