Challenge
An equity gap exists for historically underrepresented students in entering or completing STEM degrees. Part of this difficulty is that the STEM pre-requisite mathematics course of Calculus often forms a barrier for many students to overcome, reducing the likelihood of advancing into higher education in STEM topic fields. This is especially true for underrepresented students at both the university and community college level.
The traditional precalculus and calculus sequence often presents procedural knowledge in a linear fashion. The linearity in class structure becomes a series of barrier to student learning since falling behind at any stage critically impacts students’ performance at subsequent stages. This traditional format also obstructs the flow of ideas and prevents students from developing the cohesive and interconnected personal view of the subject that allows for generalization to real world applications that future creative pursuits in STEM fields require. We introduce calculus differently. Topics in these courses are segmented allowing us and the students to focus on the process skills needed utilizing a given range of available questions. These questions are scaffolded with different cognitive strategies and tutorials to make understanding not just how to solve the question but what the answer means when you do.
Project Design
This project reconceptualizes how calculus is taught and aims to provide a wide and inclusive STEM gateway for a diverse future generation of engineers, mathematical scientists, physical and biological scientists, and medical scientists.
The project’s goal is to help students understand the mathematical principles fundamental to Calculus so that they have a strong intuitive grasp of the mathematical theory, and so that they can solve STEM problems involving continuously varying quantities. In this project, we will develop an e-Book to implement a novel series of principle-based calculus concepts with revised content, video tutorials, and active learning pedagogy to meet these educational goals.
The e-Book “Principles of Calculus” entirely reimagines the role of pre-calculus and single-variable calculus in STEM education. It comes with a STEM pedagogical focus and formatting on differentiation, integration, and sequences and series by organizing along the following principles: (1) finite approximation, (2) local linear approximation, (3) higher order approximation, and (4) integration. Because the principles interact, the sequence is necessarily nonlinear and nonlocal in design, it allows for focusing the students’ attention and thinking about the processes they are exploring.
The development of this new program is guided by educational research and will utilize spatial learning strategies, supplemented by self-paced micro-tutorial videos, and guided by interactive worksheets. All learning materials are organized to support student engagement at different learning levels and foster a growth mindset through adaptive technology. All learning materials are also formatted to be both scientifically and culturally relevant to students.
The materials developed under this project will be shared as Open Educational Resources. It will enable instructors to lead a year-long course on calculus and to launch their students into successful STEM majors. After the initial period of development and piloting, this project will offer professional development opportunities for educators across California to review our materials and to potentially adopt our resources as part of their own reimagined STEM pathways.