22. Research in Higher Education
Paper
Reflection on Using Flipped Classroom in Teaching Mathematics and Statistics to Engineering Students
Elena Luchinskaya1, Galina Nilsson2
1Lancaster University, United Kingdom; 2University West, Sweden
Presenting Author: Luchinskaya, Elena;
Nilsson, Galina
This study presents a critical reflection on the use of the flipped classroom (FC) method in teaching mathematics and statistics to engineers, focusing on evaluating various aspects of student engagement. We based our analysis on the approach implemented by Lo and Hew [1] in their literature review on student engagement in mathematics flipped classrooms. This conceptual framework is rooted in the multifaceted nature of engagement, including behavioural, emotional, and cognitive aspects [2].
We applied this framework to two different FC formats. The first format follows a traditional approach, where students are provided access to the learning material in advance. The students go through it independently and then participate in learning activities offered in class. This traditional approach has been widely used and evaluated, presenting its own benefits and challenges. The second format is a modernised version of the traditional setting. In line with the traditional approach, students go through the learning material themselves; however, the lecturer summarises a topic in a weekly lecture and goes through examples presented in pre-recorded lectures on the board.
While the FC approach might be considered a well-known method [e.g., 3], it has not been widely used in teaching mathematics until recently. The available analysis of the effectiveness of this method in relation to student engagement doesn’t show consistent results [e.g., 1, 4]. What affects students engagement? What new ideas in implementing FC would be worth developing further?
During the Covid-19 pandemic, the higher education sector had to radically change the ways the majority of courses were taught to accommodate new realities. The vast number of courses went online creating favourable conditions for implementing and advancing the FC teaching method in a variety of subject disciplines, including mathematics-based courses.
Grounded in constructivist learning theories [e.g., 5,6], the FC represents one of the student-centred instructional models. In the FC environment, students are the builders of their knowledge. Initially, students familiarise themselves with new material outside the classroom and then build upon this foundation through adaptation and application of knowledge in in-class discussions, problem-based and project-based learning, and peer learning.
The objectives of this critical reflection are as follows:
- To evaluate the three types of student engagement in studying mathematics and statistics in the FC environment in two settings.
- To analyse the benefits and challenges academic staff face when using the FC in two settings.
- To propose recommendations on using the FC method in teaching mathematics and statistics.
Methodology, Methods, Research Instruments or Sources UsedThis paper presents the outcomes of the on-going collaboration between Lancaster University, UK, and University West, Sweden, focusing on the implementation of non-traditional teaching methods in mathematics and statistics [7-10]. It evaluates the outcomes of using the FC approach in two courses at University West, Sweden, during the first semester of the 2023-24 academic year.
The first course, ‘Statistics,’ was offered to second-year electrical engineering students, employing the traditional FC setting. Meanwhile, the second course, ‘Algebra and Trigonometry,’ targeted first-year engineering students. A total of 42 students enrolled in the ‘Statistics’ course, while 190 students were enrolled in the ‘Algebra and Trigonometry’ course. In both cases, the students were provided with new material on a weekly basis to independently prepare for the upcoming seminars.
Seminars were conducted twice per week, spanning two hours each session, over an eight-week period. First-year students were divided into four seminar groups. To evaluate student engagement, participants were required to complete a questionnaire comprising three parts. Each section featured a set of Likert-type questions designed to assess behavioural, emotional, and cognitive engagement.
The first set of questions delved into students’ participation, effort, and preparation for class activities. The second set aimed to gauge satisfaction with learning and motivation levels, while the final set focused on students' investment in learning, confidence development, and deeper understanding.
Additionally, discussions were held with the two course convenors to gain insights into their experiences with the FC methodology. These discussions aimed to provide supplementary qualitative data to complement the quantitative findings from the questionnaires.
Conclusions, Expected Outcomes or FindingsIn the study, 19 out of 42 students enrolled in the 'Statistics' module returned the questionnaire, highlighting strong engagement within the traditional setting. Students expressed significant learning through peer collaboration, effective communication with the lecturer, use of resources, and satisfaction with course organisation.
Among 140 first-year students, 68 responses revealed less coherence. While 80% expressed emotional satisfaction with course delivery, 80% were uncertain about cognitive engagement with the FC method allowing pacing of their own learning. Additionally, 30% were unsure about ease of communication with the lecturer.
Discussions with lecturers showed excellent student attendance. In 'statistics' course, the lecture used less group activities in class this time and focused more on going through solutions on the board. This was different from the previous year were the students were working in groups on solving problems. This might potentially affected student engagement and exam performance as the students were exposed more to passive learning.
In the case of first-year students attending the summary lectures, lecture attendance was notably high, however, seminar attendance was comparatively low. Typically, students engage in problem-solving activities either individually or in groups during seminars, seeking guidance from tutors when needed. The lower seminar attendance suggests that students may have grasped the material well enough without collaboration with peers.
Reflecting on these findings, repeating examples may enhance understanding and application of new concepts, while group work fosters active engagement, positively impacting exam performance. It's evident that using a variation of learning activities in class could positively impact different types of student engagement.
The pandemic has accelerated changes in the way we teach our students. Transitioning to more flexible, mixed modes of teaching practices will provide opportunities to create a more engaging and motivating learning environment that reflects the rapidly changing world we live in.
References1.Lo, C.K. and Hew, K.F., 2021. Student engagement in mathematics flipped classrooms: Implications of journal publications from 2011 to 2020. Frontiers in Psychology, 12, p.672610.
2. Fredricks, J. A., Blumenfeld, P. C., and Paris, A. H. (2004). School engagement: potential of the concept, state of the evidence. Rev. Educ. Res. 74, 59–109. doi: 10.3102/00346543074001059
3.Akçayır, G. and Akçayır, M., 2018. The flipped classroom: A review of its advantages and challenges. Computers & Education, 126, pp.334-345.
4.Yang, Q.F., Lin, C.J. and Hwang, G.J., 2021. Research focuses and findings of flipping mathematics classes: a review of journal publications based on the technology-enhanced learning model. Interactive Learning Environments, 29(6), pp.905-938.
5.Felder, R.M., 2012. Engineering education: A tale of two paradigms. Shaking the foundations of Geo-Engineering education, pp.9-14.
6.Loyens, S.M., Rikers, R.M. and Schmidt, H.G., 2009. Students' conceptions of constructivist learning in different programme years and different learning environments. British Journal of Educational Psychology, 79(3), pp.501-514.
7.G. Nilsson and E. Luchinskaya, A Reflection on Using Two Models of Supplemental Instruction in Teaching Mathematics for Engineers. In Strømmen-Bakhtiar, A., Helde, R. and Susen, E., 2021. Supplemental Instruction: Volume 2: Student Learning Processes. Waxmann Verlag.
8.Nilsson G. and Luchinskaya E. “Developing Competences Using Problem-based Learning: a Case Study of Teaching Mathematics to Computer Science Students”, Journal of Research in Teacher Education, 2007, No 3. pp. 13-21.
9.Luchinskaya E, Nilsson G., Kristiansson L. “Increasing university students’ motivation to improve maths knowledge in a workshop environment”. ECER 2014, Porto, Portugal, 2014.
10.Luchinskaya, E., & Nilsson, G. (2009). Using problem-based and peer-assisted learning in teaching mathematics to university students: Focus on competence development [Paper presentation]. European Conference on Educational Research (ECER 2009), Vienna, Austria.
22. Research in Higher Education
Paper
Study Profiles of First-year University Science and Mathematics Students: Who Are at Risk of Dropping Out?
Henna Kevarinmäki1, Jake McMullen1, Tommi Kokkonen1, Vesa Korhonen2
1University of Turku, Finland; 2University of Tampere
Presenting Author: Kevarinmäki, Henna
Dropping out of studies is a large issue for the university, society, and often for the individual. While dropping out could be a positive issue for students who find a better-suited profession or study field, it admittedly also has negative effects, such as losing financial aid and time, and experiencing more unemployment and lower incomes than persisters (Davies & Elias, 2003; OECD, 2019). From an institutional perspective, universities’ funding is usually dependent on the number of graduates, so aside from the wasted resources, dropouts have a direct effect on universities’ funding. The drop-out issue is greatest in STEM fields, where the drop-out rates are the highest and where it is especially important to obtain more workforce to answer the needs of the quickly developing technology industry and to solve global issues such as climate change.
Drop-out is a complex phenomenon where both an individual’s internal factors and external factors interact with each other, eventually leading to the decision to drop out. In Heublein’s model of drop-out, the internal factors include aspects such as study behavior and motivation, and external factors for example study conditions and guidance (Heublein, 2014). Heublein argues that for the study programme to be successful, these factors should align and alter respectively. Though plenty of empirical research has been done and theoretical models built, existing empirical evidence still has limitations. Previous research often approaches the issue from a variable-centered perspective, which may prevent the identification of the smaller at-risk subpopulations and understanding the complex interrelations behind drop-out. Existing research also lacks a multi-variable perspective which is vital in a multi-faceted process of dropout. As well, attention should be paid to differentiating between types of dropouts and gaining information from the context of different countries’ education systems. A better understanding of the phenomenon could help the work of reducing dropout rates.
We approach this issue using a person-centered approach to examine the study profiles of first-year university students. We aim to identify distinct patterns of students’ study orientations across dimensions of motivation, learning approach, and experienced stress. In this study, we explore what type of study profiles can be identified from first-year science and mathematics students and whether the profile membership is related to first-year grade point average (GPA). The variables included are interest, self-efficacy, surface learning approach, and academic stress. (Korhonen, 2014; Korhonen & Rautopuro, 2019; Lastusaari, 2018; Widlund et al., 2023). All variables are related to students’ study processes and recognized as being connected to drop-out, and they are malleable variables that the universities have a chance to affect (Condren & Greenglass, 2011; Haarala-Muhonen et al., 2017; Heublein, 2014; Jesús et al., 2022; Kehm et al., 2020; Lastusaari et al., 2016; Parpala et al., 2010). Possible at-risk profiles are observed and discussed.
Identifying plausible profiles helps institutions get a picture of the new students and their support, information, and teaching needs. Intervening with the risk elements at an early stage could prevent dropouts. It also adds important information on the large and yet unclear phenomenon of drop-out, especially from the perspective of the crucial STEM fields and the first study year, and from person-oriented and multi-variable perspectives, also including both self-reported and student register-based variables.
Methodology, Methods, Research Instruments or Sources UsedThe data consisted of 177 first-year Finnish university science and mathematics students’ survey answers and grade point averages (GPAs), collected in spring 2023. The self-reported items, interest, self-efficacy, surface learning approach, and academic stress, were used to explore the study profiles, and GPA was used as a direct measure to validate the profile memberships. Interest and self-efficacy were measured with an instrument, originally designed to measure mathematical motivation (Widlund et al., 2023) as the expectancy-value theory’s beliefs and values (Eccles, 1983), and then developed to fit university science and mathematics students. Both interest (α=0.903) and self-efficacy (α=0.858) were measured with three questions, measuring students’ interest in their major and their beliefs about their abilities to perform in their studies. The surface learning approach was measured with a modified version of the ChemApproach -questionnaire (Lastusaari, 2018), originally designed to measure chemistry students’ four different learning approaches, now developed further, ending up with four questions measuring the surface learning approach (α=0.841). Academic stress was measured with an instrument developed in the Campus Conexus -project (Korhonen & Rautopuro, 2019). One question was removed to increase the internal consistency of the measurement, ending up with a four-question solution (α=0.839). All questions were answered on a Likert scale of 1 (Completely disagree) – 5 (Completely agree). Confirmatory factor analysis confirmed the structures of the constructs. All measures were formed by calculating the means of the questions.
Latent profile analysis with a three-step method was conducted with the variables interest, self-efficacy, surface learning approach, and academic stress, and finally grade point average (GPA) as an auxiliary variable. First, the number of profiles was obtained by fitting latent profile models iteratively to the data, starting with two and continuing up to six profiles. The best-fitting model was identified by interpreting fit indices. The analysis was conducted four additional times to check robustness. Second, the students were assigned profiles based on the class membership probabilities. Finally, logistic regression analysis and ANOVA were conducted to observe the connection between the profile membership and GPA.
Conclusions, Expected Outcomes or FindingsThe model with five different study profiles was identified as the best fit. The profiles were named respectively: “well-performing, interested” (55.8%), “lower-performing, interested” (19.8%), “high-performing, interested” (11.5%), “lower-performing, uninterested” (7.4%), and “well-performing, uninterested” (5.4%). The “well-performing, interested” and “high-performing, interested” profiles seemed to not have any major issues in their studies, as they had high interest, mediocre-to-high self-efficacy, low surface learning approach, mediocre-to-low stress, and mediocre-to-good GPAs (M=3.55, SD=0.92 and M=3.09, SD=0.70). The “lower-performing, interested” profile seemed to struggle with all aspects other than interest, having low self-efficacy, and high surface learning approach and stress, and a lower GPA than most of the profiles (M=2.92, SD=0.73), indicating that this profile would benefit from support offered by the university. The two smallest profiles came across as at-risk groups, as both “lower-performing, uninterested”, and “well-performing, uninterested” had low interest, indicating they are not interested in the field they are currently studying. In addition, the former had low self-efficacy, and high surface learning approach and stress, and the lowest GPA of the profiles (M=2.62, SD=0.75), indicating that also their learning habits would need some improvement. These students will most probably end up dropping out if not intervened by the university. The latter, however, didn’t seem to have other challenges than the low interest, as they had high self-efficacy, low surface approach, and high GPA (M=3.46, SD=0.50), indicating that these students may eventually transfer to another study field. The at-risk groups could benefit from the university actively communicating about possible specialization fields and professions, and positive environmental and societal impacts offered by the current study field, helping the students find the motivation towards the study field.
ReferencesCondren, M., & Greenglass, E. R. (2011). OPTIMISM, EMOTIONAL SUPPORT, AND DEPRESSION AMONG FIRST-YEAR UNIVERSITY STUDENTS Implications For Psychological Functioning Within The Educational Setting [Book]. In G. Reevy & E. Frydenberg (Eds.), Personality, stress, and coping implications for education (p. 133). Information Age Pub.
Davies, R., & Elias, P. (2003). Dropping Out: A Study of Early Leavers From Higher Education. Research Report RR386. Institute For Employment Research (IER).
Eccles, J. (1983). Expectancies, values, and academic behaviors. In J. T. Spence (Ed.), Achievement and achievement motivation (pp. 75–146). W. H. Freeman.
Haarala-Muhonen, A., Ruohoniemi, M., Parpala, A., Komulainen, E., & Lindblom-Ylänne, S. (2017). How do the different study profiles of first-year students predict their study success, study progress and the completion of degrees? Higher Education, 74, 949–962. https://doi.org/10.1007/s10734-016-0087-8
Heublein, U. (2014). Student Drop-out from German Higher Education Institutions. European Journal of Education, 49(4). https://doi.org/10.1111/ejed.12097
Jesús, E., Simón, L., & Gijón Puerta, J. (2022). Prediction of early dropout in higher education using the SCPQ. Cogent Psychology, 9. https://doi.org/10.1080/23311908.2022.2123588
Kehm, B. M., Larsen, M. R., & Sommersel, H. B. (2020). Student dropout from universities in Europe: A review of empirical literature. Hungarian Educational Research Journal, 9(2), 147–164. https://doi.org/10.1556/063.9.2019.1.18
Korhonen, V. (2014). Opintoihin kiinnittymisen arviointia kehittämässä - Nexus-itsearviointikyselyn teoreettista taustaa ja empiiristä kehittelyä: Vol. B:3. University of Tampere.
Korhonen, V., & Rautopuro, J. (2019). Identifying problematic study progression and “at-risk” students in higher education in Finland. Scandinavian Journal of Educational Research, 63(7), 1056–1069. https://doi.org/10.1080/00313831.2018.1476407
Lastusaari, M. (2018). Persistence in Major in Related to Learning Approaches - Development of a questionnaire for university chemistry students [Doctoral thesis]. University of Turku.
Lastusaari, M., Laakkonen, E., & Murtonen, M. (2016). ChemApproach: validation of a questionnaire to assess the learning approaches of chemistry students. Chemistry Education Research and Practice, 17(4), 723–730. https://doi.org/10.1039/C5RP00216H
Organisation for Economic Co-operation and Development. (2019). Education at a glance 2019 : OECD indicators (p. 493). OECD Publishing. https://doi.org/https://doi.org/10.1787/f8d7880d-en.
Parpala, A., Lindblom-Ylänne, S., Komulainen, E., Litmanen, T., & Hirsto, L. (2010). Students’ approaches to learning and their experiences of the teaching-learning environment in different disciplines. British Journal of Educational Psychology, 80(2), 269–282. https://doi.org/10.1348/000709909X476946
Widlund, A., Tuominen, H., & Korhonen, J. (2023). Motivational Profiles in Mathematics - Stability and Links with Educational and Emotional Outcomes [Manuscript submitted for publication]. https://doi.org/10.31234/osf.io/ugrpy
22. Research in Higher Education
Paper
Exploring Cloud Physics with Graph Theory: Representing and Analysing Conceptual Understanding
Julien-Pooya Weihs1,2, Vegard Gjerde3, Helge Drange1,2
1Geophysical Institute, University of Bergen, Norway; 2Bjerknes Centre for Climate Research, Bergen, Norway; 3Department of Physics and Technology, University of Bergen, Norway
Presenting Author: Weihs, Julien-Pooya
This study investigates the evolution in conceptual understanding of cloud physics among learners from diverse academic backgrounds, using the mathematical framework of graph theory.
Cloud physics is an inherently multidisciplinary area of research, and therefore also of teaching in higher education. Challenges related to the understanding and modeling of clouds influence one of the main uncertainties in climate models [1], as well as a range of other areas, like affect aircraft operations and remote sensing technologies. Cloud physics education therefore represents a key aspect in atmospheric science education and, more widely, in geoscience education [2]. Recent academic efforts have addressed the difficulties encountered by learners in the discipline [3, 4, 5, 6], yet more is to be done to connect these with the conceptual structure of cloud physics.
Graph theory is an established field of mathematics, but the use of graph structures in education is relatively new [7, 8, 9, 10, 11], offering new perspectives to discipline-based educational research. Graph structures are networks of nodes connected with edges, and in our case networks of concepts from cloud physics connected with directed arrows by the participants of our study. The algorithmic power of graph theory affords characterization of both the mathematical graph structure and the role of the nodes that compose it. In this study, participants hand-drew concept maps depicting the life-cycle of a cloud, reflecting their understanding of cloud physics. We coded the maps according to thematic analysis and transformed them into graph structures in Python.
A "map of cloud physics" is created, depicting the joint graph representation of all participants. Studying this representation presents a novel way to look at the field and inspires a series of follow-up investigations to inform the disciplinary teaching and learning practices. We present sub-graphs based on the participants' academic experience. While Novice represents the group with no formal academic exposure to cloud physics, a comparison of the Adept and Advanced groups highlights the main changes induced by an increasing experience in the discipline. We represent the core knowledge of each group, corresponding to the nodes and edges of highest consensus, using a hierarchical structure. We also compute the groups' agreement with regard to the predecessors and successors of the used concepts, and define a new node-level metric measuring these quantities.
The evolution of the computed metrics through the experience-gradient provides a diagnosis of both the changes occurring along a learner's journey in cloud physics, and of the structure of the discipline and its inherent conceptual complexities. Overall, our results both qualify and quantify the epistemological shift in the description of the life-cycle of a cloud, from the general physics of the water cycle to detailed description of cloud microphysical processes, as learners mature in their understanding of the discipline.
Our findings can be used by lecturers to tailor their teaching towards the identified expert-like concepts, and by students to anticipate the main complexities in the field during their learning process.
(As our work in this study is very graphical, for both visualisation and analysis purposes, the above explanations would undoubtedly profit from a few visual inputs, which we would be happy to provide to the reader upon request.)
Methodology, Methods, Research Instruments or Sources UsedWe collected concept maps from 117 participants from five different academic teaching and research institutions in Norway between Nov 2022 and Sep 2023. The participants were asked to graphically depict the life-cycle of a cloud, from the early conditions for formation to their dissipation, using around ten minutes for the exercise. The instructions were to draw and label nodes representing scientific concepts, and connect them with unlabeled directed arrows wherever they seemed appropriate. The information collected from the participants informed about their disciplinary field (six disciplines of STEM), academic level (bachelor, master, PhD, researcher), and experience with cloud physics (Novice, Adept, Proficient, Expert).
The concept maps were coded according to thematic analysis (with thematic saturation reached at about 110 concepts) and converted to graph structures via the creation of adjacency matrices in Python. The joint weighted graph of all the collected data presents a “map of cloud physics” reflecting the collective understanding of all the participants. Setting threshold levels of consensus on edges reveals valuable substructures on this map. A 3D web-visualization allows to navigate the map and highlight specific areas according to criteria set by the user.
We computed graph-level metrics such as density, diameter and intertwinement for each participant, and created box-plots of these metrics according to the participants’ disciplinary field, academic level and cloud physics experience. Grouping the participants according to their experience with cloud physics led to the largest variance of graph metrics, motivating clustering the data into Novice, Adept, Proficient and Expert groups. A further grouping of Proficient and Expert into Advanced was also introduced.
We identified for each group a “layer-structure” in their collective graph according to consensus threshold values set on edges. The layers of highest consensus correspond to the core knowledge of each group, which we represent using a hierarchical structure that indicates the optimized way of navigating their sub-graphs. For the Advanced group, the core knowledge sub-graph can directly be used to inform teaching and learning.
Node-level metrics were then computed for each group, in particular right/left-eigenvector, betweenness, and out/in-degree centralities. Expanding on the degree centrality measures, we created a new metric that quantifies the agreement of a group on the successors and predecessors of a node. A study of the rate of change of these node-level metrics across groups highlights the concepts becoming central, and thus important, in the conceptual understanding of these groups as their disciplinary experience increases.
Conclusions, Expected Outcomes or FindingsOur analysis shows that the agreement on the origins and effects of the concepts Adiabatic Cooling and Heterogeneous Nucleation increases with experience, indicating an increasingly precise understanding and knowledge. This agreement decreases with experience for Evaporation, Rain and Shortwave Radiation, making us suggest that these concepts have an inherently more complex role within the storyline of a cloud.
We also show that the importance of specific concepts such as Droplet Growth and Convection increases with experience in explanations of more advanced learners, whereas that of more general concepts such as Water Mass and Condensation decreases. Convection, Droplet Growth and Maturation also gain importance as bridges enabling the flow of information in the graphs of more experienced groups of learners.
The hierarchical graph of the Advanced-group reveals a three-part structure of cloud physics: 1) the atmospheric physics and thermodynamics, from an ascending mass of moist air to droplet nucleation; 2) the aerosol physics behind cloud formation; and 3) the mechanisms behind droplet growth and ice crystal nucleation during the maturation phase of the cloud. Such a result can be used as a recommendation to introduce the topic sequentially in a teaching and learning setting.
Using concept mapping narratives as a proxy and the theoretical framework of graph theory, differences in understanding of cloud physics in groups of varying experience have been quality-tested and quantified. We believe that the methodology developed within this study has the potential to be applied to other disciplines of the STEM curriculum, and could thus inform their teaching and learning practices. The visual representation of a discipline through a large and dense network could, in particular, form a helpful tool for both teachers and learners. The applied methodology makes structures emerge from large "maps", and reveals how increasing experience in a discipline changes how learners navigate them.
References[1] Morrison, H., van Lier-Walqui, M., Fridlind, A. M., Grabowski, W. W., Harrington, J. Y., Hoose, C., Korolev, A., Kumjian, M. R., Milbrandt, J. A., Pawlowska, H., Posselt, D. J., Prat, O. P., Reimel, K. J., Shima, S. I., van Diedenhoven, B., & Xue, L. (2020). Confronting the Challenge of Modeling Cloud and Precipitation Microphysics. Journal of Advances in Modeling Earth Systems, 12(8). https://doi.org/10.1029/2019MS001689
[2] Cervato, C., Charlevoix, D., Gold, A., & Kandel, H. (2018). Research on Students’ Conceptual Understanding of Environmental, Oceanic, Atmospheric, and Climate Science Content. In K. St. John (Ed.), Community Framework for Geoscience Education Research (pp. 17–34). National Association of Geoscience Teachers. https://doi.org/10.25885/ger_framework/3
[3] Davenport, C. E., & French, A. J. (2019). The Fundamentals in Meteorology Inventory: Validation of a tool assessing basic meteorological conceptual understanding. Journal of Geoscience Education, 68(2), 152–167. https://doi.org/10.1080/10899995.2019.1629193
[4] Gopal, H., Kleinsmidt, J., Case, J., & Musonge, P. (2004). An investigation of tertiary students’ understanding of evaporation, condensation and vapour pressure. International Journal of Science Education, 26(13), 1597–1620. https://doi.org/10.1080/09500690410001673829
[5] Handlos, Z. J., Davenport, C., & Kopacz, D. (2022). The “State” of Active Learning in the Atmospheric: Sciences Strategies Instructors Use and Directions for Future Research. Bulletin of the American Meteorological Society, 103(4), E1197–E1212. https://doi.org/10.1175/BAMS-D-20-0239.1
[6] Petters, M. (2021). Interactive worksheets for teaching atmospheric aerosols and cloud physics. Bulletin of the American Meteorological Society, 102(3), E672–E680. https://doi.org/10.1175/BAMS-D-20-0072.1
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[8] Selinski, N. E., Rasmussen, C., Wawro, M., & Zandieh, M. (2014). A method for using adjacency matrices to analyze the connections students make within and between concepts: The case of linear algebra. Journal for Research in Mathematics Education, 45(5), 550–583. https://doi.org/10.5951/jresematheduc.45.5.0550
[9] Tatsuoka, M. M. (1986). Graph Theory and Its Applications in Educational Research: A Review and Integration. Review of Educational Research, 56(3), 291–329. https://doi.org/10.3102/00346543056003291
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