טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentMarmur Ofer
SubjectUndergraduate Student Learning during Calculus Tutorials:
Key Memorable Events
DepartmentDepartment of Education in Science and Technology
Supervisor Professor Boris Koichu
Full Thesis textFull thesis text - English Version


Abstract

The research focuses on student learning in undergraduate calculus large-group tutorials. The learning is examined in relation to both student affect, as well as the instructional context in which the learning takes place. The research goals are to gain a better understanding of how to design frontal-style tutorials that create a positive learning-experience; identify learning opportunities that enable students to be actively engaged learners in class; and gain a deeper understanding of the role affect plays in student learning.

                                                                                     

To address these goals, a theoretical construct of Key Memorable Events (KMEs) was conceptualized as part of the research. KMEs are classroom events that are perceived by many students as memorable and meaningful in support of their learning, and are typically accompanied by strong emotions, whether positive or negative. Accordingly, the research addressed the following questions:

         What are tutorial events that serve as KMEs for students?

         What are the possibilities for student learning afforded by these KMEs?

         How do these KMEs relate to the teaching that takes place?


The research was performed in two stages. The preliminary research utilized a design-experimentation methodology to examine the feasibility of designing successful lessons based on the creation of several KMEs. This led to the main research, in which the research questions above were examined in “regular” instructional settings. The research was constructed as a multiple-case study. The main corpus of data consisted of stimulated-recall interviews with 36 students in relation to eight filmed tutorials.


The main findings of the research are:

         Identification and categorization of eight KMEs: Surprise; Heuristic-didactic discourse; Suspense; Bridging; Engaging questions; Undigested symbols; Leaving theoretical loose ends; and Overarching connections.

         The identified KMEs were associated with the following learning opportunities: heuristics on how to approach a challenging problem; evaluating the correctness of a given solution; sense-making of mathematical symbols; connecting between analytic and intuitive modes of thinking; real problem-solving behavior which includes failed attempts; exposure to common mistakes; and creating connections between different mathematical topics. The learning in the KMEs was typically concentrated on thought-processes and knowledge that could be generalized for future problems, rather than merely focused on a solution-oriented end result.

         Successful lesson designs generally went through 1-2 initial KMEs that created tension, raising student engagement and anticipation, and concluded with a subsequent KME that generated resolution around a mathematical goal for learning.

                                       

As a practical contribution, KMEs may serve as a methodological tool to examine classroom learning, as well as a tool for lesson design. They can be utilized as indicators for invariant aspects of a lesson that consequently allow instructors to “fill” them each time with varying mathematical content. As a theoretical contribution, the KME concept supplies an added layer to our understanding of learning by creating a hierarchical differentiation of events regarding their contribution to the learning, whilst putting emphasis on memorable “snapshots” of a lesson. Additionally, the KME concept may supply insight into the transition between emotions experienced during a mathematics lesson, and how these develop into more stable attitudes and beliefs towards the subject.