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This course will focus on the processes of understanding and learning the concept of function as a representation of covarying quantities. Our aim is to assist you in acquiring foundational reasoning abilities so that you are better equipped to provide coherent and conceptually focused instruction for your students’ continued mathematics, science and engineering course taking. We will explore various function models, including linear, quadratic and exponential. Written assignments will include problems and activities designed to engage you in “ways of reasoning” that should enhance your mathematical thinking and confidence in approaching novel mathematics tasks. Over time, your new knowledge and reasoning abilities should translate to your being more effective in supporting the learning of your students.
Classroom Rules of Engagement:
In addition to supporting you in developing a deeper understanding of big ideas, this course aims to enable you to communicate and reason more powerfully. Thus, we will emphasize class “rules of engagement” that will support your development in these areas. We will be stressing that you: 1) Speak meaningfully—relate formulas to the physical situation they model and base conjectures on a logical foundation; 2) Exhibit mathematical integrity-- don’t pretend to understand when you don’t; 3) Strive to make sense—persist in making sense of problems and your colleagues’ thinking; 4) Respect the learning process of your colleagues—allow them the opportunity to think, reflect and construct. When assisting your colleagues, pose questions that will help them to construct meaning rather than showing them how to get an answer.
Conversations and Explanations:
One of the most important abilities you must develop to be a good mathematics teacher is the ability to conduct conceptual conversations, with yourself and with your students. A conceptual conversation is one that has a diminished emphasis on technique and procedure, and an increased emphasis on images, ideas, reasons, goals, and relationships. The one thing we hope you develop through this course, and which we will value and reward, is the orientation to look for big ideas--to realize that mathematics is not about gettng answers to questions; rather, it is about developing insight into relationships and structures. We also hope to convey that solutions to sophisticated or complex problems emerge from understanding them deeply, not from memorizing and applying rote procedures. Click here for an example.
Homework:
Weekly homework will be assigned to support you in learning the big ideas that were discussed in class. At the beginning of each class, you will download your homework onto a flash drive. If you are not able to make it to class on time you need to email your homework to your instructor.
Final Project:
This will involve you in designing a curricular sequence for one of your classes, teaching this instructional sequence, and reflecting on its effectiveness. A detailed description of what is expected for the final project will be given to you during class.
Assessment
The instrument used to assess teachers at the end of the course consists of 10 pairs of questions relating to scenarios drawn from activities performed in the various modules. |
