| Instructor: Greg Crow, Ph.D. | Texts: Mathematics for Elementary Teachers: A Contemporary Approach 4th ed., Musser and Burger Mathematics: A Good Beginning 5th ed. Troutman and Lichtenberg | Table of Contents: Course Description Required Materials Course Background Course Philosophy and Approach Course Content Course Laboratories Course Methods Grading Policies The Final Examination |
| Class meetings:
TTh 9:55-12:30 |
| Office hours:
Rohr Science 220 |
Several recent national reports on mathematics education (see references [NCTM, 1989], [NRC, 1989], and[NRC, 1990]) agree that there have been significant changes in:
Our approach to mathematics for elementary teachers is based on a theory of teaching and learning mathematics called constructivism. Research in learning theory shows that students who learn mathematics effectively must be actively involved in the process, not just passive listeners/observers. In particular, in order to really learn and understand mathematical ideas and processes you must become deeply involved in activities such as exploring, discussing analyzing, explaining, conjecturing, defending, negotiating, testing, and evaluating. To do this you need good problems to solve, interaction with others on solutions, and opportunities to write your conclusions.
To be more specific, these courses are designed to help you:
The MTH 314, MTH 324 sequence includes the college-level mathematics and instructional methods needed to teach elementary school mathematics in ways consistent with the recommendations of the professional publications described above and with the California State Department of Education’s Mathematics framework [1992]. Material is selected for inclusion because teachers need to know it and understand it in order to teach elementary school mathematics effectively. Also, course activities and assignments are designed to assist you in gaining a deeper understanding of mathematics sufficient for effective teaching.
A teacher must help children develop these understandings, so this raises a question:
In both the classroom an lab we make serious efforts to integrate mathematics and methods as we deal with such issues in detail. For example, division of whole numbers is a mathematical concept that leads to a procedure for doing it. In mathematics the basis for teaching and learning procedures is always understanding the concept. This requires an instructional sequence involving children in activities that are progressively more abstract as follows:
For example, children will develop an understanding of the division of 12 by 4 (interpreted as repeated subtraction) by working with sets of 12 concrete objects in several specific problem-solving situations to develop and answer for the following questions:
Later children will circle and "take away" 3 sets of 4 froma set of 12 objects in their workbooks (pictorial work). Finally, they will write the symbols 12 4=3 to express this division.
Course labs will provide direct hand-on experiences to support learning and teaching elementary mathematics. Both lab and classroom experiences are designed to help you learn mathematics and learn to teach mathematics developmentally in a problem-solving environment. Class meetings will have a greater emphasis on development of mathematical concepts and procedures, while labs will have a greater emphasis on methods, materials, and activities for teaching mathematics to children. Specific goals for the labs include helping you learn
Use of groups. There is almost a century of research showing that academic achievements, productivity, and self-esteem improve dramatically when students work together in groups. This method emphasizes teamwork, cooperation and support by others, rather than isolation and competition in learning. For a thorough discussion, see the linked document on the Use of Groups.
Role of the instructor. There will be less direct lecturing than you may have experiences in other mathematics courses; many questions will be answered by helping you work through your own questions and difficulties. You will learn mathematics through active involvement - studying text material, solving problems, writing problem solutions, and discussing the material with others.
This way of learning mathematics may require some adjustment, but your patience and effort will be rewarded with a deeper understanding of mathematical concepts, methods, and procedures. This leas to confidence in your ability to do mathematics, to speak it, to write it, and to teach it.
Whenever the number of absences in a class, for any cause, exceeds the equivalent of one and one half weeks of classes, the professors send a written report to the Area Dean which may result in de-enrollment with a grade of "F" or "NC". A students is de-enrolled with a grade of "F" or "NC" if more than three weeks of classes are reported as missed.
Ultimately, your achievement in these courses will be proportional to your belief in the possibility of success and your willingness to give timely priority to course material and requirements. Some specific suggestions follow:
Review cards. Class tests and final exam will include problems and questions over material assigned in the texts, in other readings, or presented in class or lab.
For each test and the exam a "Review Card" may be prepared. You may write by hand (no typing, no Xeroxing, no reducing) any information you choose on the card (both sides may be used).
| One Exam | 175 points |
| Final Exam | 300 points |
| Individual Homework | 100 points |
| Quizzes | 125 points |
| Individual Total | 700 points |
| One Exam | 150 points |
| Group Quizzes | 75 points |
| Group Homework | 75 points |
| Individual Total | 300 points |
| A | B | C | D | |
|---|---|---|---|---|
| + | (87.5, 90) | (77.5, 80) | (67.5, 70) | |
| [92.5, 100] | [82.5, 87.5] | [72.5, 77.5] | [62.5, 67.5] | |
| - | [90, 92.5) | [80, 82.5) | [70, 72.5) | [60, 62.5) |
Grade components. The grade components are homework, attendance/involvement, quizzes, tests, and the final examination.
Other factors that affect grades are
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