Analyzing the Assessment Features of a Developmental Mathematics Course Towards Achieving the Quantitative Literacy Goal
Principal Investigator:
Erell Germia
Co-PIs:
Stefania Meza
Abstract:
Developmental mathematics courses are primarily offered to undergraduate students who may require intensive support in developing quantitative literacy crucial for career success. We explored how assessments in a developmental mathematics course offered at Kean University contribute to this quantitative literacy goal. Our findings show the lack of focus on quantitative reasoning, with assessments predominantly emphasizing rote calculations targeting a lower level of depth of knowledge. The assessments also underscore the power of interactive technological tools for students to make sense of the relationships between quantities. We offer suggestions advocating for emphasis on engaging students in quantitative reasoning.
Description of Research:
The integration of computers and interactive digital technologies revolutionized how math is taught and learned. Computers provide students with contextual information and exercises tailored to their level of understanding, offering feedback that encourages them to reflect on their thought processes (Papert, 1980). Digital technologies can offer a more dynamic approach to study the mathematics of change, particularly in graphical thinking and quantitative reasoning. Quantitative reasoning involves reasoning about the simultaneous changes between quantities, and is crucial for understanding interdisciplinary phenomena (Thompson & Carlson, 2017). Although quantitative reasoning is essential for students to develop and use in their future careers, it is often overlooked in traditional mathematics courses with class activities focusing more on symbolic manipulation than on understanding changes between quantities (Tucker, 1990). To promote quantitative reasoning, students should be engaged in dynamic interactions with tables, graphs, and other interactive artifacts (Panorkou et al., 2023). Web-based learning systems like MyLabMath play a crucial role in developing students’ quantitative literacy by providing interactive tools and resources that facilitate a deeper understanding of mathematical concepts and their applications.
In this presentation, we discuss our analysis of graphing linear equations tasks in a developmental mathematics course offered at Kean University. We examined the intersections of the Four Levels of Depths of Knowledge (Webb, 2002) and the two frameworks on dimensions of textbook analysis (Gracin, 2018) with the use of technology in computer-assisted instructions (Snelson, 2002). Then, we utilized the three theoretical foundations to create our Framework for Analyzing Graphing Linear Equations Tasks for our analysis. We analyzed seventy (n=70) evaluative assessments on graphing tasks in a MyLabMath developmental mathematics course in terms of its potential in developing students’ quantitative literacy and other curricular dimensions that may support such a student learning objective.
Our findings show that the tasks are lacking the intellectual opportunities for quantitative reasoning. Most of the tasks focus on mathematical computations and operations illustrating Level 1 of depth of knowledge. It is also evident that the tasks do not maximize the available technological tools for students to create tables and graphs while making sense of the relationships between quantities. Even when reasoning was measured in the task (n=1), students only worked on multiple choices from predetermined answers rather than allow them to express their mathematical reasoning about the concept. A developmental mathematics course is offered to students to develop foundational mathematics knowledge and mathematical reasoning that they may need in their future careers. Our argument includes offering opportunities for students to be engaged in the construction of mathematical relationships about quantities - to develop quantitative reasoning per se, that they often encounter on a daily basis. We suggest that the tasks should engage students in quantitative reasoning while they were asked to create tables of values and graphing coordinates. Future studies are needed to examine the pedagogical input of instructors and students’ construction of quantitative reasoning when provided with opportunities.