To respond to global issues positively, education systems in higher education institutions play a significant role in empowering learners as well as promoting sustainable development goals. By implementing curricula that cultivate cross-cutting and transversal key competencies for sustainability, such as critical thinking, problem-solving, and collaboration, we prepare our pupils to become sustainability citizens, who not only sustain learning throughout their lives in various circumstances and across different disciplines but also engage constructively and responsibly toward any future world’s challenges through their dispositions, strategies, and skills. One such sustainable teaching methodology is known as the flipped classroom, an active-learning, student-centered, flexible, and multidimensional pedagogy. Our objective is to investigate the effect of such pedagogy on learners’ academic achievement and their attitude toward mathematics using both quantitative and qualitative methods. We cultivated sustainable learning in mathematics education for college freshmen ($n=55$) by exposing them to both the conventional teaching method (CTM) and flipped classroom pedagogy (FCP). By splitting them into control and experimental groups alternately ($n_1=24$, $n_2=31$) and by selecting the four most challenging topics in college algebra, we measured their cognitive gains quantitatively via a sequence of pre- and post-tests. The topics are factorization, rational expressions, radical operations, and applied problems. Both groups improved academically over time across all these four topics with statistically very significant outcomes $(p<0.001)$. Although they were not always statistically significant ($p>0.05$) in some topics, the post-test results suggest that generally, the FCP trumps the CTM in cognitive gains, except for the first topic on factorization, where the opposite is true with a very statistically significant mean difference $(p<0.001)$. By examining non-cognitive gains qualitatively, we analyzed the students’ feedback on the FCP and their responses to a perception inventory. The finding suggests a favorable response toward the FCP with primary improvements in the attitudes toward mathematics and increased levels of cooperation among students. Since these students are so happy to have control of their own learning, they were more relaxed, motivated, confident, active, and responsible in learning under the FCP. We are confident that although this study is relatively small in scale, it will yield incremental and long-lasting effects not only for the learners themselves but also for other role-takers in education sectors who aspire in nurturing sustainable long-life learning and achieving sustainable development goals successfully.

This article investigates the attitude toward mathematics among the students enrolled in the Foundation Year Programme at Nazarbayev University. The study is conducted quantitatively and an inventory developed by Tapia and Marsh II is adopted in this research. The inventory consists of 40 statements on the five-point Likert scale. Gender, specialization and final high school score in mathematics are collected. The number of valid returned questionnaires is 108. There are 55 males, 53 females, 73 Mathematical-Physics (MP), 22 Biology-Chemistry (BC) and 13 International Relations-Economics (IRE) students. Generally, they have a positive attitude toward mathematics, with the score mean and standard deviation are 3.999 and 0.531 out of five, respectively. We confirm a hypothesis on a positive correlation between previous high achievement in mathematics and favorable attitude toward it. The correlation value is r = 0.300, its effect size is medium and it is extremely significant (p-value = 0.0008 < 0.001). There is no significant difference between male and female students in terms of their attitude toward mathematics (t = 0.6804, p-value = 002489 > 0.05). There is a very significant difference between students who specialize in IRE and MP in terms of their attitude toward mathematics (F(2, 105) = 5.6848, p-value = 0.0045 < 0.01).

The nonlinear Schrödinger (NLS) equation stands as a cornerstone model for exploring the intricate behavior of weakly nonlinear, quasi-monochromatic wave packets in dispersive media. Its reach extends across diverse physical domains, from surface gravity waves to the captivating realm of Bose–Einstein condensates. This article delves into the dual facets of the NLS equation: its capacity for modeling wave packet dynamics and its remarkable breadth of applications. We illuminate the derivation of the NLS equation through both heuristic and multiple-scale approaches, underscoring how distinct interpretations of physical variables and governing equations give rise to varied wave packet dynamics and tailored values for dispersive and nonlinear coefficients. To showcase its versatility, we present an overview of the NLS equation’s compelling applications in four research frontiers: nonlinear optics, surface gravity waves, superconductivity, and Bose–Einstein condensates. This exploration reveals the NLS equation as a powerful tool for unifying and understanding a vast spectrum of physical phenomena.