MAT 764—Fall 2004—Hendrix 2

Class Agenda

Thursday, September 9, 2004

Tentative Schedule of Activities:

2:00 PM Activity—How Far? How Fast? How Many? How Much?

What did you learn from this activity? What was the point in doing this activity?

2:20 PM Brahier Discussion Questions from Chapter Two

What did you learn about psychology of learning mathematics in this chapter? Here are some talking points:

According to Skemp (1971), “problems of learning and teaching are psychological problems, and before we can make much improvement in the teaching of mathematics we need to know more about how it is learned” (p. 14).

Did you read anything that related to our MacGyver problems?

Bruner’s Stages of Representation—enactive, iconic, and symbolic

Van Hiele levels of Geometric Reasoning—visualization, analysis, informal deduction (ordering, comparing), deduction, rigor (more abstract understanding)

Cognitive Science—Romberg, Carpenter, Fennema, and many others

Constructivism—as a philosophy of learning or learning theory

v  Rooted in the research of Jean Piaget

v  A philosophical stance that is more a gamut than a

v  Four main tenets of constructivism, from Peterson, P. (1994)

o  1.

o  2.

o  3.

o  4.

Inductive versus Deductive Teaching

Textbook Reading—PSSM Chapter Three—Standards for School Mathematics

Which one standard sticks out in your mind the most? Why? In what ways do you see that standard within teaching and learning mathematics? Do you feel that these “standards” guided the mathematics instruction that you experienced in school?

3:10 PM Discussion of the NCTM Standards Project

You will each be assigned a content standard and a process standard to unpack.

Assignments for Tuesday:

v  Metalesson

v  Read: Begin Reading your sections of the Standards. Peruse Chapters 4 & 5, but focus on your specifically assigned sections of 6 & 7. Start with the two standards that you will work on as a group. Short article on equity from Mathematics Teaching in the Middle School.

v  Assignments:

o  1. Have you completed your MacGyver Problem and posted it?

o  2. Concept Attainment Activity—Create a concept attainment activity similar to the example on page 49 of the Brahier text. You may use whatever concept in mathematics you wish to build this activity. This is an exercise in building an inductive learning activity. Post it on the web, with a link to answers. Be careful not to place the answers on the activity itself.


Standards Curriculum Group Project

Each person is assigned two distinct sections of the Principles & Standards 2000 online document to present to the class. In Principles & Standards 2000, there are two distinct sections: (1) principles and (2) standards. Principles are underlying philosophies about school mathematics, learning and teaching that influence everything we do in the classroom. The Standards are subdivided into Process and Content Standards.

Each person is assigned one process standard and one content standard, as chosen in class. With each of the two standards, you are to become the class’ expert on those two standards for both grade strands, 6-8 and 9-12. Your final report should include the following, organized however you feel is useful as a cohesive website:

v  Summarize the major thrust of each standard. What is the importance of that standard in the current reform milieu of teaching and learning mathematics?

v  What are the major characteristics of each standard in relation to the middle school grades? What are the specific benchmarks of learning that are appropriate for the middle grades in that standard? Describe and “unpack” these standards in your own terms—taking ownership of the concepts and ideas—without just quoting the documents’ language directly.

v  What are the major characteristics of each standard in relation to the high school grades? What are the specific benchmarks of learning that are appropriate for the high school grades in that standard? Describe and “unpack” these standards in your own terms—taking ownership of the concepts and ideas—without just quoting the documents’ language directly.

v  Compare and contrast these principles and standards to the North Carolina Standard Course of Study. How do they relate? Where are there differences? What are your opinions about what you read in this articulation? Cite any references needed.

v  Each person is to choose a high school mathematics text or high school mathematics materials (Integrated Mathematics Project, Mathematics Modeling our World, University of Chicago School Mathematics Project, etc.) and evaluate the curriculum/text in terms of your content & process standards. Do the curricular materials reflect current recommendations in mathematics content and instruction? To what degree? In what ways? Give a general description of the curricular materials/text, and then focus in greater detail on chapters that correlate with your assigned standards—both content & process. What is the quality of the content of these chapters? How age-appropriate are the activities in relationship to NCTM Standards and the NC Standard Course of Study? What supplementary materials are provided and what else is needed? Is this a text/curriculum package from which you would be able to teach effectively?

v  Most importantly, for each content/process standard, provide an example of mathematics or classroom interaction that demonstrates the intent & meaning of the standard. One good example that demonstrates depth is better than a mile-wide collection of shallow examples. I.e., pick one content topic from your standard and design a lesson activity. Your group will “teach” this lesson activity in class on the due date of the project (to be decided in class together). This will be part of a growing body of examples that you will wish to continue to build over the course of the semester.

v  The summary and analysis of your content & process standards should be online in your course website folder. There should be an overall webpage for the project of the class that links to each individual summary or instructional activity. The mathematics lesson activities that exemplify your assigned standard should also be online. Everything should be in HTML format.

v  You will receive next week a more detailed rubric for the project that reflects the categories described above. The project is worth 20 % of your grade, and that will be translated into 200 points. 100 points will reflect your summary & analysis of the standards and comparison with the NCSCOS; 30 points will reflect your summary and analysis of the curricular materials (text); 50 points will reflect your lesson activity and presentation; and 20 points will reflect the quality of the project website.

v  You will do one pair of standards as a cohort, and that will help you prepare for your own standards portion of the project. That collaborative effort will also be graded on the same 200 point scheme, and averaged into your project grade as 1/5 of the weight.

My Content Standard:

My Process Standard:

Agreed Due Date: