GEOMETRY for TEACHERS |
This page is devoted to all materials related to the three-unit graduate course Geometry in the teacher's perspective. It shall include all slideshow presentations used in class, details of requirements, and other concerns exclusive to the class.
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COURSE INFORMATIONDownload the course syllabus for MATH 605: Geometry for Teachers at the right.
The document contains the Vision and Mission statements of the university, course contents, course requirements, and grading criteria. For questions, send Mr. Chua a message. |
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1 The Van Hiele Model of Geometric Thought |
November 26th, First Session |
Children whose geometric thinking you nurture carefully will be better able to successfully study the kind of mathematics that Euclid created. What has become as the Van Hiele level theory was developed by Dina van Hiele-Geldof and her husband Pierre van Hiele in separate doctoral dissertations at the University of Utrecht in 1957.
The model which includes five levels of geometric thought: visualization, analysis, abstraction, deduction, and rigor, describes the different levels of understanding through which students progress when learning geometry (Van Hiele, 1984). The basis of the theory is the idea that a student's growth in geometry takes place in terms of distinguishable levels of thinking. geometry instruction should be design with these levels in mind (Choi-Koh, 1999) The file at the immediate right of this text is the presentation in printable format. Download it for your personal use. |
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ACTIVITY ONE: Student's Level of Geometric Thought
Ask a Grade 10 student to answer the same test you worked with in the activity. Based on the answers in the paper, decide under which level in Van Hiele’s model the learner is under. Reason out why you have come into this decision. Give reference to specific items and answers in the test in your reasoning.
Follow the technical format: Letter-sized paper, Cambria-11, double-spaced, normal margin. Submit through email, [email protected] on or before December 5, 2016. Indicate "VanHiele's Model" as subject and upload your document as an attachment with the file name format LASTNAME_VanHiele's. A copy of the questionnaire may be downloaded above. |
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2 History, Sets, and Lines |
December 10th, Second Session |
The laws of nature are but the mathematical thoughts of God. For this fraction of the course, graduate students who are taking up the course on Statistical Methods are expected to develop the following learning competencies:
1. Review the idea of sets and apply them to geometric elements. 2. Explain how the Distance Postulate conveys an understanding of the relation between numbers and points. 3. Relate notions of distance between points to the Ruler Postulate 4. Develop the basic vocabulary of lines, segments and rays. |
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PROBLEM SET ONE: Sets, Conditional Statements, and Lines
The first problem set in this course will allow you to work with challenging problems relevant to the basic concepts in set theory and the firt four postulates on lines.
There is also an item that will seek to assess your understanding of conditional statements. Use the printed version of the document at the right as answer sheet and have it submitted on or before December 17th. For questions, send me an email or a text message. |
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3 Congruence Between TrianglesFor this chapter in the course on Statistical Methods, graduate students are expected to develop the following learning competencies:
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January 7th, Third Session
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PROBLEM SET TWO: Separation, Angles and Triangles, and Congruence
Revisit the site by January 13 for this new material to be uploaded. this should be submitted together with the paper reflection activity described in the succeeding webpage entry.
PAPER FOR REFLECTION (A Middle of the Term Requirement)
Mathematics educators and mathematicians believe that establishing the veracity of a statement is only one of many reasons for constructing or presenting a proof. INSTRUCTIONS:
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4 Lesson Study as Action Research
Improving something as complex and culturally embedded as teaching requires the efforts of all the players, including students, parents, and politicians... But teachers must be the primary driving force behind change. They are best positioned to understand the problems that students face and to generate possible solutions. In this fraction of the course, Geometry for Teachers, graduate students enrolled in the subject are expected to do the following:
1.Explain the potential of lesson study as an approach in improving teachers’ pedagogical practice. 2.Describe in detail the phases undertaken in conducting a lesson study. 3.Differentiate action research from other research designs. 4.Decide on a specific, Geometry-related learning competency in the K-12 Curriculum (G7-G10) that will take center in a lesson study cycle. 5.Formulate a specific (lesson study) research question based on the selected competency. |
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