Teaching College Mathematics
This ability involves being informed of the current state, guidelines and standards for the teaching of mathematical sciences, understanding the mathematical core ideas a student should develop and knowing strategies of active learning. Also, it includes using technology to promote understanding and assessing student learning. Then, it naturally implies applying this knowledge to design curriculum and learning activities, create effective learning environments and foster mathematical thinking among students.
Description
To develop this competency I participated in the class "Teaching College Mathematics". The course is designed for future faculty members who expect to teach courses in the mathematical sciences. The main objectives for the learners are discovering the recent research related to the teaching and learning of the mathematical sciences at the collegiate level and applying the acquired knowledge to their own practice.
You can check the syllabus of the class to know all the details. In a nutshell, we completed weekly readings and reflections, lead and participated in discussions, and engaged in group activities and projects. Discussion topics included our own teaching and learning experiences, the current state and guidelines of mathematics education, the core principles of mathematical understanding, and strategies for implementing active learning in math lessons. We also developed a personalized framework for designing mathematical tasks and, working in groups, created example lessons based on these frameworks.
Each student led a discussion on a topic of personal interest. Topics covered included mathematics self-efficacy and intervention practices, adult learners, trauma-informed approaches to mathematics instruction, the role of undergraduate learning assistants in classroom pedagogy, student–teacher relationships, and generative AI in education, the latter was co-led by me and a fellow student.
Reflection
I wrote the following paragraph at the beginning of the class:
I hope to use this class as an opportunity to improve my teaching philosophy and move beyond relying on my own personal experiences. By deepening my understanding of educational theory and engaging in peer discussions, I would develop a broad and solid comprehension of my teaching methods. Also, I struggle with being accountable when I work for and by myself. This class will provide the structure and accountability I need to stay focused on reading the materials and developing a portfolio and a teaching project. I am prepared to work hard and sincerely on the assignments and projects. I will actively participate in the discussions with my peers and overall do my best in the class.
I consider that I did achieve my goal. I greatly benefit from reading the suggested papers and reflecting on them. The readings were enriched by the opportunity to share my thoughts and reflections with my peers. Overall, I found most activities to be meaningful experiences in this class that indeed deepened my understanding of educational theory and helped me acquire a better understanding of my own teaching and my future teaching project.
For example, from 2015 CUPM Curriculum Guide to Majors in Mathematical Sciences , I learned about the current guidelines of math education as well as the learning goals for students learning mathematics. I found the text to be relevant, pertinent, realistic, personalized and caring. I am amused by the idea that most of the current Mathematics’ departments in and out of the USA follow this or similar guidance when developing and articulating the guiding goals of their program. Moreover, each program is encouraged to create objectives according to their context. A math department in rural Pennsylvania should not be a copy of Oxford’s math department and viceversa. Additionally, it gave me context of the classes I am teaching in MSU. I would like to have these guidelines in mind when I am designing and executing a lesson.
I was captivated by two readings about Lectures in Advanced Mathematics: Why Students Might Not Understand What the Mathematics Professor Is Trying to Convey and Teacher Knowledge for Active-Learning Instruction: Expert–Novice Comparison Reveals Differences . My main highlight is how we as instructors should develop knowledge and skills necessary to effectively implement active learning strategies. For example, we should identify the elements that we want the students to find most meaningful in a lecture and intentionally highlight them in our lessons. At the same time, it is crucial that we have the time and space to experiment, take risks, and even fail in the process of developing such learning strategies.
Overall, this course was an enriching experience that deepened my understanding of mathematics education while expanding my perspectives as both a learner and an educator. I want to continue improving my practical skills, theorical knowledge and my enthusiasm to achieve my goal of being a mathematics professor.
Artifacts & materials
Below, you will find a selection of the work I completed in class.
This includes the framework I developed for designing mathematical tasks, which is intended to guide the creation of meaningful activities to learn mathematics in a class. The framework highlights three central dimensions: cognitive goals, which focus on skills students are expected to develop such as mathematical thinking and reasoning, communication skills and technology use; content goals, which considers the mathematical concepts, professional development and interdisciplinary connections being explored and pedagogical decisions, that involve the instructional choices, tools, objectives and structures for effectively implementing the task. In addition, the file includes an example of a mathematical activity that has been analyzed and evaluated using this framework. This example illustrates how the framework can be applied in practice, showing the ways in which theoretical principles can be translated into instructional implementation.
Also you will find my summaries and reflections on some papers I reviewed about AI tools in mathematics education. For each article, I provide an introduction, a summary of the main ideas, a critique, and a personal reflection. The papers include:
- Roles and Research Trends of Artificial Intelligence in Mathematics Education , a bibliometric mapping analysis and systematic review that explores the role and research trends of AI in mathematics education by searching for the relevant articles published in the quality journals. This systematic review, which precedes the birth of generative AI’s, showcases the landscape of applications of AI in education that is far broader and more diverse than generative AI tools.
- ChatGPT: A revolutionary tool for teaching and learning mathematics , a study that examine the perspectives and experiences on the use of ChatGPT in teaching mathematics. The findings of this investigation propose a number of avenues for research that ought to be explored in order to achieve educational goals through the cooperation of human tutors and machines like ChatGPT.
- Using ChatGPT as a proof assistant in a mathematics pathways course , a research that examined the capabilities of ChatGPT as a tool for supporting students in generating mathematical arguments that can be considered proofs. In this study, students engaged with ChatGPT to evaluate and revise their original proof attemptsvusing the AI’s feedback.