Conceptualization of Learning

In this class, I will attempt the teach each and every student to the best of my abilities. Every student learns differently; however, the process of learning, in reference to Mathematics, can be grouped into for categories: allegorization, integration, analyzation, and synthesization. Students who learn by allegorization need ideas to be expressed through concrete mediums and require some time to think about these ideas. Allegorizers use knowledge of concepts they previously learned to understand the new material and they tend to approach each problem in a similar fashion. There are also students who learn by integration and they also need ideas to be expressed through concrete mediums but require some type of physical effort to understand the material. Integrators also compare new material to known concepts, but may not understand how the two are related. They also use their own “common sense” to understand the new material and to distinguish it from the older concepts. Another group of students might learn by analyzation; that is, they need very detailed explainations of the material and think about these ideas using logic. They understand how the new concepts and the old concepts are related; however, they may not realize exactly what makes the two concepts different. Finally, there are a group of students who learn by the synthesization of the ideas. These students are very abstract in their thinking and develop their own unique strategies. They approach problems in new ways but have to put forth physical effort to understand the ideas.

Conceptualization of Teaching

In order to facilitate the learning processes of each individual student, I will explain and demonstrate the new material in different ways. I will tell you the basis of the concept, how the concept works, the origin and use of the concept, and how to use this concept in multiple situations. First, I will explain the problems and how the concept works. Second, I will guide you through the process of working each individual problem. Third, I will explain how this problem relates to real world situations and how the material works logically. Finally, I will require you to work the sample problems with me and to work sample problems on your own.

Each individual problem will be approached in both a concrete and abstract manner and will utilize active and reflective strategies. First, I will explain how the problem works in theory and the logical process involved in solving the problem. Second, I will demonstrate how the problem works in a real world application. Third, I will allow a few moments for each of you to think about the problem and to understand how the concept works. Fourth, I will give you a sample problem to work on your own and then we will check that problem before we move to a different problem using the same concept.

Goals for students

I will expect a lot out of my students. Students should be able to demonstrate that they understand the basic concepts by applying the correct concept to the problem, employing the correct method, utilizing the correct process, and correctly processing the arithmatic. These goals should be reached in homework, tests, and classroom participation.

Conceptualization of Grading

When grading a test, I will look to see if the student is meeting the goals I set out. First, for each problem I will look to see if the student applied the correct concept; that is, the student must at least use a concept from that chapter to work the problem. Second, the student must use the correct method associated with that concept; that is, the student must use the proper formula or method to begin solving the problem. Third, the student must logically solve the problem using the correct process; that is, the student must place the correct numbers in the correct places and begin solving for the answer. Fourth, a demonstration of knowledge of arithmatic must be utilized to complete the problem; that is, the student must be able to add, subtract, multiply, divide, and use the basic mathematical operations to arrive at the answer. For instances where students will be asked to solve for the exact answer, calculators will not be used and students are required to solve the problem manually. Finally, providing the correct answer must be present to receive all the point. For the most part, each section of solving the problem will be worth one point. Only one point will be deducted per problem for mixing a positive or negative number or miscalculating numbers in one section which results in an incorrect answer; that is, if the student demonstrated knowledge of the processes but made a mistake early in the problem and arrived at the wrong solution, then the student will receive most points for correctly working most of the problem and using the correct concept and method.

When grading homework, I will be looking for effort, not correctness. Students will not have to hand in homework. Before the start of each class, I will walk around the class and have each student briefly show me their homework. Students who school above 85% on a tests will receive a “free homework ticket.” This ticket allows the student to miss or skip the basic application problems section only, approximately half of the homework problems. This is a reward to students who do well on tests. Students who score less than 70% on their tests will be asked to rework problems on their test correctly and turn it in for up to five extra points.