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Quantitative reasoning (QR) is a key part of biology. Here, we apply the theoretical framework of student noticing to investigate into how students learn QR in an intro bio lab course. Using observations and interviews, we characterize what students notice when working with QR, their depth of noticing, and the factors that shape their noticing. 

For serious games on education, understanding the effectiveness of different learning methods in influencing cognitive processes remains a significant challenge. In particular, limited research addresses the comparative effectiveness of serious games and videos in analyzing brain behavior for graph structure learning, which is an important part of the Science, Technology, Engineering, Math, and Computing (STEM+C) disciplinary education. This study investigates the impact of serious games on graph structure learning. For this, we compared our in-house game-based learning (GBL) and video-based learning (VBL) methodologies by evaluating their effectiveness on cognitive processes by oxygenated hemoglobin levels using functional near-infrared spectroscopy (fNIRS). We conducted a 2×1 between-subjects preliminary study with twelve participants, involving two conditions: game and video. Both groups received equivalent content related to the basic structure of a graph, with comparable session lengths. The game group interacted with a quiz-based game, while the video group watched a pre-recorded video. The fNIRS was employed to capture cerebral signals from the prefrontal cortex, and participants completed pre- and post-questionnaires capturing user experience and knowledge gain. In our study, we noted that the mean levels of oxygenated hemoglobin (delta HbO) were higher in the GBL group, suggesting the potential enhanced cognitive involvement. Our results show that the lateral prefrontal cortex (LPFC) has greater hemodynamic activity during the learning period. Moreover, knowledge gain analysis showed an increase in mean score in the GBL group compared to the VBL group. Although we did not observe statistically significant changes due to participant variability and sample size, this preliminary work contributes to understanding how GBL and VBL impact cognitive processes, providing insights for enhanced instructional design and educational game development. Additionally, it emphasizes the necessity for further investigation into the impact of GBL on cognitive engagement and learning outcomes. 

Backward transfer is defined as the influence that new learning has on individuals’ prior ways of reasoning. In this article, we report on an exploratory study that examined the influences that quadratic functions instruction in real classrooms had on students’ prior ways of reasoning about linear functions. Two algebra classes and their teachers at two comprehensive high schools served as the participants. Both schools drew from lowsocioeconomic urban populations. The study involved paper-and-pencil assessments about linear functions that were administered before and after a four- to five-week instructional unit on quadratic functions. The teachers were instructed to teach the quadratic functions unit using their regular approach. Qualitative analysis revealed three kinds of backward transfer influences and each influence was related to a shift in how the students reasoned about functions in terms of an action or process view of functions. Additionally, features of the instruction in each class provided plausible explanations for the similarities and differences in backward transfer effects across the two classrooms. These results offer insights into backward transfer, the relationship between prior knowledge and new learning, aspects of reasoning about linear functions, and instructional approaches to teaching functions.