Blog Entry #5 — Students Learning without Algorithms

Writing: In this paper, Warrington describes how her students learn how to divide fractions without first being taught the invert and multiply rule. Write two paragraphs in response to this paper.

Paragraph 1: Describe the advantages of teaching mathematics without telling the students the procedures or even the right answers. For each advantage, refer to a specific event in the paper that illustrates that advantage. Note that it is appropriate not only to include the advantages that Warrington identifies, but also any additional advantages you notice.

Paragraph 2: Describe the disadvantages of teaching mathematics without telling the students the procedures or even the right answers. If there is evidence in the paper that illustrates a particular disadvantage, use that to support your argument. Be sure to explain the disadvantages in enough detail so that your readers can understand what the disadvantage is.

As always, follow the guidelines for good academic writing (topic sentences, scholarly tone, proofreading, etc.)

Commenting: Visit three blogs. For each blog, read the entry and then leave a comment. Your comment should include at least the following:

1. Something that you and the author both agree about, and why you agree with the author.
2. Some area in which you think differently from the author and why. This may either be a point the author makes that you disagree with, or an additional point that you think is important but is not included in the author's entry. Make sure that you respond respectfully by hedging and using "I" messages.

Due Dates: Entry due at the beginning of class on February 17; comments due at the beginning of class on February 19.

Blog Entry #4 — von Glasersfeld and Constructivism

Writing: Write a two-paragraph entry about constructivism. The first paragraph should describe what von Glasersfeld meant by "constructing knowledge." You may want to address some of the following issues:

• The reason(s) von Glasersfeld chose the term "constructing" knowledge rather than "acquiring" or "gaining" knowledge.
• A description of what it means to construct knowledge.
• The role that experience plays in constructing knowledge.
• The conditions under which we construct knowledge.
• The reason(s) von Glasersfeld referred to knowledge as a "theory."
• The reason(s) von Glasersfeld talked about knowledge as being "viable" rather than "correct."

For the second paragraph, discuss one implication of constructivism for teaching mathematics. In other words, imagine that you believe in constructivism, and describe one thing you might do in your own teaching of mathematics as a direct result of this belief. Describe the implication in enough detail so that your audience can understand exactly what you would do. Also explain why this implication is compatible with a constructivist perspective.

As usual, be sure to use topic sentences for both paragraphs. Also, be kind enough to proofread your entry.

Commenting: Visit three student blogs. If a blog already has five comments for this entry, choose a different blog. Read both paragraphs. Then comment on the author's implication. Some of the things you might consider discussing are the following:

• Is the implication clearly described?
• Does the author adequately explain why the described action follows from a belief in constructivism? 
• Do you agree with the author?
• Are the elements of writing present, such as a topic sentence, a logical flow in the argument of the paragraph, a scholarly tone, etc.?

Due Dates: Entry due at the beginning of class on February 10; comments due at the beginning of class on February 12.