Teacher knowledge of students and enactment of motivational strategies in teaching the concept of functio

This research linked educational psychology and mathematics education to investigate how a teacher used his knowledge of students in designing and implementing mathematical tasks related to piecewise function and composition of functions. The study revealed that the teacher ("Mr. Algebra") faced many challenges in the implementation of mathematical tasks because students had not mastered early algebra concepts. Additionally, students carried with them some incomplete formal learning about function evaluation, constant functions, and domain and range, which made learning piecewise functions and composition of functions more difficult. The study employed various frameworks of mathematical tasks, Self-Determination Theory, and motivational design approaches.;Additionally, this research employed Keller's (2010) ARCS Instruments, Course Interest Survey and the Instructional Materials Motivation Survey. On these instruments, students were asked to give their teacher a score based on how the teacher: (1) captured and maintained student attention ; (2) established that material is relevant to their lives; (3) built their confidence using such strategies as scaffolding and feedback; and (4) provided satisfaction for students to know that the material will be useful to their lives after the course ends. The analysis based on these ARCS Instruments showed that students were not fully motivated to learn mathematics because they perceived the course material irrelevant to their lives. Moreover, the analysis of student motivation based on Self-Determination Theory showed that there were differences in student motivation that required flexibility in teaching strategies. Even though students had lost their motivation to learn mathematics at an earlier grade the teacher played a role in renewing their motivation.;Also, the study revealed that mathematical tasks the teacher created were of high cognitive demand but students were willing to perform their best because they felt the teacher related to them. However, they did not perform well because they had not mastered previous course materials. Students at the college level continue to encounter difficulties with the concept of function such as those documented in earlier research. Therefore, intervention in Algebra (pre-function concepts) in teaching and learning is beneficial to help students be success at that level and move students to learning and application within and beyond Algebra.