Sketching the graph of mathematical functions using derivatives is a challenging task for undergraduate students who enrol for the first level of calculus course. Before graph plotting, students are required to perform a thorough function analysis using the concepts learned in differentiation. They are then expected to solicit the results obtained to sketch the graph. Nevertheless, the students face great difficulties in achieving this goal; and fail to relate the results obtained in the analysis and their representation in a graph. Their performance is thus negatively affected eventually. To overcome this cognitive gap, an innovative board game named Graph Puzzle (GP) is developed. It is intended to function as a manipulator to facilitate students in comprehending the inter-related algebraic, symbolic, and graphic representation of a function under the applications of derivatives, forming the corresponding procedural and conceptual knowledge. To measure the effectiveness of this board game, 84 undergraduate students who took this calculus course were given pre- and post-test before and after the learning session. An ANCOVA test conducted reveals a significant difference (F (1, 81) = 12.182, p = 0.001) between pre and post-test score in solving polynomial functions, whereas students’ performance in solving rational functions indicates no meaningful difference (F (1, 81) = 0.04, p = 0.841) of post-scores between control and treatment groups. From this standpoint, it is shown that GP has the potential to serve as a solution to the difficulties faced on graph sketching in calculus, particularly when dealing with polynomial functions.   Keywords: Visualization, Calculus, Embodied learning, Game-Based Learning, Graph Sketching

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Online learning has been a need for worldwide education systems due to Covid-19. It is essential to study the students' self-efficacy to determine online learning success. Research suggests that self-efficacy can boost student achievement, foster emotional health and well-being, and be a valid predictor of motivation and learning. The purpose of this paper is to examine the students' self-efficacy in Mathematics online learning using a reliable instrument adapted from the "Learning Self-Efficacy Scale (OLSES)" developed by Zimmerman and Kulikowich in 2016. The respondents consisted of 343 undergraduate students in Sarawak, Malaysia. This study's quantitative data analysis methods include descriptive and inferential statistics. The analysis reported that most of the respondents had moderate to high levels of self-efficacy, whereas most of them were comfortable with Mathematics online learning. Specifically, there was a significant relationship between students' self-efficacy and the domains, namely learning in an online environment, time management, and technology use. This study also found no significant difference in the mean scores of students' self-efficacy concerning gender, academic performance, and online learning prior experience. However, there was a significant difference in mean scores for students' self-efficacy across their online learning comfort levels. Further analysis indicated that students who were notably comfortable projected a significantly higher self-efficacy than those with an average or low comfort level. Although the students in this study mostly had moderate to high levels of self-efficacy, there is still room to improve and strengthen their self-efficacy, especially in their abilities and readiness to engage in online learning and thus in achieving good academic performance.

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