MAT 764—Fall 2005—Hendrix 1

Class Agenda

Thursday, September 8, 2005

Tentative Schedule of Activities:

2:00 PMBrahier Discussion of Questions from Chapter 1

Let’s look at the questions you answered in Chapter One. You decide if there are ones that we should talk about and exactly what aspect.

2:20 PMLearning Styles Inventory Discussion

Why did we use this instrument on Tuesday? What can it tell us about ourselves? About our students? About teaching and learning in general? Would you recommend giving such an instrument to students? Why or why not?

Here are some links to learning styles articles, inventories, and analyses. Did you follow any of the links and read more about learning styles? How does this pertain to mathematics teaching and learning?

2:30 PMTextbook Reading—PSSM Chapter Three—Standards for School Mathematics

How does the content presented in this chapter compare to your own school or educational experience? Do you feel that these “standards” guided the mathematics instruction that you experienced? Which one standard sticks out in your mind the most? Why? In what ways do you see that standard within teaching and learning mathematics? Did you learn about or think about something new in mathematics teaching and learning from reading this chapter?

2:50 PMBrahier: Discussion of the ideas in Chapter Two

(I’m sure that we will continue this discussion on Tuesday!)

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

Rooted in the research of Jean Piaget

A philosophical stance that represents more of a gamut of thought than a single position

A philosophy of teaching and learning, NOT an instructional strategy and certainly not a single one!

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

  • 1.
  • 2.
  • 3.
  • 4.

Inductive versus Deductive Teaching

3:10 PMDiscussion of the NCTM Standards Project

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

Assignments for Thursday:

Metalesson—should be able to post them in HTML now on the website—all of you have posted files to this server before (conics GSP files in MAT 334). Let me know if you experience difficulty.

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.

Assignments:

  • 1. MacGyver Math: Create your own problem—ONE MacGyver-like problem—an important concept that we take for granted, but has deeper significance than we first realize. Write up the problem AND a solution (explanation) in HTML. Save on your hard drive for later
  • 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.
  • 3. Brahier, Chapter 2 Discussion Questions, p. 58—#’s 3, 4, 5, 6, 7