Introduction
The study of Voigt et al. (2020) fuses a flipped classroom’s at-home video and in-class curriculum components. This is done by using design heuristics that enable students to critically think about mathematical problems on their own before working on the task in a group setting. Voigt et al. (2020) demonstrate how components of the written and hidden curriculum were influenced by elements of the instructional design theory of Realistic Mathematics Education and Culturally Responsive Pedagogy. They also illustrate how those factors were then experienced by the students as part of the enacted components of the curriculum. The study’s backdrop is a two-week classroom teaching experiment for 27 calculus students at a Norwegian institution covering trigonometry and vector concepts. This paper aims to provide an alternative version of Voigt et al. (2020) study using Cobb et al.’s (2003) description of design experiments.
Understanding Design Experiments
To begin with, it is critical to understand the design experiments proposed by Cobb et al. (2003). According to Cobb et al. (2003), “design experiments are pragmatic as well as theoretical” in orientation in that the methodology’s core focus is the study of function, both that of the design and the consequent ecology of learning. Even while design experiments are carried out in a variety of contexts that differ in both type and scope, they are all held to the same emphasis on function in a realized context. For example, the teacher-experimenter and student one-on-one design studies, in which a research team holds a series of lessons for a small group of students. A learning ecology is intended to be created on a small scale so that it may be thoroughly researched.
There are also experiments conducted in classrooms where a research team works with a teacher (who may also be a research team member) to take charge of instruction. Moreover, experiments in preservice teacher development where a research team organizes and analyzes the education of future teachers are part of design experiments. In addition, design research experiments can include studies on in-service teacher development that involve collaboration between researchers and teachers to foster the growth of a professional community. Experiments in restructuring schools and school districts where a research team works with educators, administrators, and other stakeholders to support organizational transformation are also implemented in design experiments.
The goal of design experimentation is to create a body of knowledge about how people learn. Additionally, to obtain more information about tools that are used to facilitate that learning, whether it be for the benefit of an individual student, a classroom community, a professional teaching community, or an entire school or school district taken as an entity (Cobb et al., 2003). The study of Cobb et al. (2003) sees learning processes broadly, taking into account not only the development of social practices that are pertinent to learning but also concepts like identity and interest.
A design experiment is carried out in a small number of settings due to practical considerations, but it is clear from the concern for a theory that the goal is not to merely look into how to promote new types of learning in those particular contexts. Instead, the study team views a few key components of the learning that is envisioned as well as the mechanisms to enable it as paradigmatic examples of a larger class of occurrences (Cobb et al., 2003). For instance, in the case of a one-on-one design experiment, the overarching theoretical objective might be to create a psychological model of the process by which students gain a thorough understanding of specific mathematical concepts, as well as the kinds of tasks and teaching methods that can facilitate that learning.
An Alternative Method
Voigt et al. (2020) demonstrated how design theories could be used to develop a richer flipped classroom model. They show that such classes provide an opportunity for students to critically evaluate how flipped classes can be designed in a way that values the variety of student experiences. And goes beyond a transferable model of learning by connecting the material presented in the video lectures with their classroom experiences (Esperanza et al., 2021). However, the study has some shortcomings that can be eliminated in future studies. For example, the sample size of 27 students is too large for the design experiments research as Cobb et al. (2003) wrote that such experiments should be done with a smaller sample size. Twenty-seven students may be divided into groups for the study by Voigt et al. (2020).
Another limitation is that the study did not fully explain Realistic Mathematics Education and Culturally Responsive Pedagogy theories and their further implications. These theories design researchers to plan and build classrooms that give students a variety of challenging assignments and plenty of chances to contribute both individually and in groups (Schallert et al., 2022). Once these requirements have been accomplished, the research focuses on the development of students’ thinking over time and aims to pinpoint both successful and unsuccessful instances, improving the appropriate designs in light of them. The teaching phase and the retrospective analysis both test and examine the effects of adjustments.
As an alternative method for the study of Voigt et al. (2020), it seems that identifying specific aspects of the case and focusing on curriculum products and design principles would be the better approach. Design studies frequently serve as testing grounds for innovation. The goal is to introduce new kinds of learning in order to research them and look into the potential for educational progress. As a result, there is frequently a large gap between conventional forms of schooling (which may be investigated using a naturalistic approach) and those that are the subject of a design experiment. The design created in advance of an experiment makes use of earlier research and makes an effort to capitalize on its empirical and theoretical findings. When compared to purely naturalistic research, the engineering of the learning forms being researched gives the research team some degree of control.
In addition, the researcher is more likely to come across pertinent aspects that lead to the establishment of a certain type of learning and become aware of their interrelationships if they are working to support that form. The study of complicated phenomena like learning ecologies is inherently impossible to fully specify all that takes place. Therefore, it is even more crucial to identify in the design specification between elements that are the subject of the inquiry and those that could be incidental, auxiliary, or taken for granted as background conditions.
For instance, justification standards in the classroom might be taken for granted in a study of young children’s arithmetic development, with a focus instead on conceptual growth. As an alternative, the primary focus of the inquiry may be the evolution of norms (Cevikbas & Kaiser, 2020). The methodology’s core concept is the utilization of earlier research to define a design and support the distinction between central and auxiliary conditions. The conditions for creating hypotheses are created through design experiments, yet these theories must still be put in danger. Design experiments, therefore, always have two sides: a prospective face and a reflective face. All empirical studies should be familiar with these two faces, but the shapes they take in design trials are relatively specific.
On the prospective side, designs are put into practice with an assumed learning process in mind, along with ways to assist it in order to scrutinize the specifics of that process. By taking advantage of opportunities that present themselves as the design develops, another equally crucial goal is to encourage the formation of additional potential pathways for learning and growth. Design experiments are hypothesis-driven studies that frequently involve multiple levels of analysis on the reflecting side. The initial design is an assumption about how to accommodate a specific learning style that will be put to the test. However, more specialized conjectures are often framed and tested during the course of the design research.
Conclusion
To conclude, the study of Voigt et al. (2020) illustrates the importance of the flipped classroom through design heuristics that help to motivate students to think about mathematical problems critically. In terms of design research, it fails to control sample size and address the theories fully. Detecting specific aspects of the case and focusing on curriculum products and design principles are suggested as an alternative method for this study. Working systematically through the large, longitudinal data sets created during a design experiment is a key obstacle in doing retrospective analysis in order to get reliable results. In order for other researchers to comprehend, follow, and evaluate the analysis, it is crucial to be clear about the standards and types of evidence used for drawing particular sorts of inferences.
References
Cobb, P., Confrey, J., diSessa, A., Lehrer, R., & Schauble, L. (2003). Design Experiments in Educational Research. Educational Researcher, 32(1), 9–13. Web.
Cevikbas, M., & Kaiser, G. (2020). Flipped classroom as a reform-oriented approach to teaching mathematics. ZDM Mathematics Education, 52(7), 1291-1305.
Esperanza, P. J., Himang, C., Bongo, M., Selerio Jr, E., & Ocampo, L. (2021). The utility of a flipped classroom in secondary Mathematics education. International Journal of Mathematical Education in Science and Technology, 1-34.
Schallert, S., Lavicza, Z., & Vandervieren, E. (2022). Merging flipped classroom approaches with the 5E inquiry model: a design heuristic. International Journal of Mathematical Education in Science and Technology, 53(6), 1528-1545.
Voigt, M., Fredriksen, H., & Rasmussen, C. (2020). Leveraging the design heuristics of realistic mathematics education and culturally responsive pedagogy to create a richer flipped classroom calculus curriculum. ZDM Mathematics Education, 52(5), 1051-1062.