Blog Entry #7—NCTM Article, Summary and Evaluation

Writing: Choose a second article from the NCTM journal that you have subscribed to and read it. Then follow the format for Blog Entry #6 and write a summary and evaluation of the article.

Comments: Follow the directions for comments on Blog Entry #6.

Due Dates: Blog entries are due at the start of class on 3/26; Comments are due at the start of class on 3/29.

Blog Entry #6 — NCTM Article, Summary and Evaluation

Writing: Read an article from the journal that you subscribed to through your NCTM e-membership. Then follow the directions below to write a three-paragraph blog entry on this article.

Paragraph 1: Bibliographical information.
Write the bibliographical information for this paper. Follow APA formatting (for a brief overview of how to do this for a journal article, see the Purdue APA Formatting Webpage).

Paragraph 2: Summary paragraph of a main idea.
Your article contains one or two main ideas. You can identify a main idea because usually over half of the paper is devoted to describing, justifying and explaining the idea. Choose a main idea from the paper to write about. Identify the main idea in the topic sentence. Then use the remainder of the paragraph to describe the main idea and how the author is thinking about the idea. This summary paragraph should attempt to accomplish two things:

1. Accurately describe how the author is thinking about the main idea. Try to capture the important points that the author is making and remain true to the author's intent. Accurately reflect the author's points even if you disagree with them. Your summary should have at most one quote from the article, and then only if you think the author said something particularly well. All other content in the paragraph should consist of paraphrasing the author's ideas.
2. Communicate the author's thinking to someone who has not read the article. The people who read your blog entry will be interested in knowing what the author said, particularly because they are unlikely to have read the article themselves. Include enough detail in your blog entry so that it is not necessary for someone to have read the article in order to understand your summary paragraph.

Paragraph 3: Evaluation paragraph of the main idea.
This paragraph is where you get to weigh in on the main idea from Paragraph 2. Start with a topic sentence that summarizes the position you will take toward the main idea. Try to take on or address a big issue. Present a substantial argument by making at least three main points in your argument. To support your argument, include evidence from the article itself, from your own experience and thinking, or from other materials you have read about mathematics education or education in general. Maintain a professional and scholarly tone.

Commenting: Visit three blogs that have less than four comments for this particular entry. Read the entire blog, and then comment on the first paragraph. In particular, consider addressing some of the following issues:

1. Content: Did the (blog) author identify a main point and stick to addressing that main point throughout the paragraph? Did the summary paragraph make sense to you? Did it contain enough detail so that you understand what the main point was? What didn't make sense? What could the author have done to make the ideas clearer? Was it clear that the author proofread the entry before publishing it?
2. Voice: Did the (blog) author maintain a professional tone throughout the paragraph? Was it clear that the author was paraphrasing throughout the paragraph, being careful not to insert his or her own thinking? 
3. Structure: Did the paragraph have a topic sentence? Did it have a logical flow? Were there ways that the (blog) author could have structured the ideas so that they might have been clearer?
4. Interest: What else would you have liked to know about the main idea? What unanswered questions do you have? Based on the summary, are you interested in reading the article? Why or why not? (Note: Feedback to these questions may help the (blog) author recognize ideas from the paper that should have been included in the summary.)

Due Date: Blog entries are due at the start of class on 3/19; Comments are due at the start of class on 3/22.

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.

Blog Entry #3 — Benny and IPI

Writing: Write two paragraphs about Erlwanger's paper on Benny's understanding of fractions and decimals.

Paragraph 1: Write a description of what you think Erlwanger's most important point is in this paper.

• Describe what the main point is.
  
• Present the evidence that Erlwanger uses to make this point.

Use a topic sentence to start your paragraph. Make sure that you include enough detail about terms and ideas so that someone who didn't read Erlwanger's paper could understand the main point and the argument used to support it. Once again, you are trying to summarize Erlwanger's thinking, so do not include any of your own ideas. At the same time, don't just write a blow-by-blow account of the paper. Organize the ideas in a way that makes sense to you and is easy for a reader to follow.

Paragraph 2: Identify a part of his main point or argument that is valid for teaching mathematics today, and write a persuasive argument for why it is valid.

• Describe the part of the main point or the argument in Paragraph 1 that is still valid today.
• Explain why you think it is still valid.

Once again, your paragraph should start with a topic sentence. Although this paragraph reflects your own ideas and thinking, please maintain a scholarly tone in your writing. Feel free to include your own personal experiences or ideas from other papers you have read as evidence to back your claim. Include enough detail so that your audience can understand your experience or the ideas you are citing from other papers.

Please proof read your entry before you post it. Remember, approximately four people will be reading your entry, so be courteous and keep the errors in your writing to a minimum.

Commenting: Visit three blogs that you have not yet commented on. If a blog already has four student comments, please choose a different blog to comment on. Read the whole entry, but focus your comment on the second paragraph. Your comment should identify one part of the second paragraph that you think meets the assignment well, and one part of the same paragraph that could be improved. Some possible issues you might want to consider commenting on include the fllowing:

• Is there a topic sentence for this paragraph that adequately captures the point of the paragraph?
• Are all of the sentences in the paragraph related to the topic sentence?
• Is the idea that the author is arguing for part of the main point or argument that was identified in the first paragraph?
• Is the idea the author is arguing for adequately described?
• Does the author provide a compelling argument for the validity of the idea for teaching mathematics today?
  
• Is there something in the paragraph that weakens or detracts from the argument?
• Is there a way that the argument could be strengthened?
• Does the author fail to consider important evidence or ideas that contradict the argument?
  

The purpose of your comment is to critique the author's argument, not to argue for your own ideas about what is valid for teaching mathematics today. Do not propose an alternate point that should have been argued for instead of the one the author chose. Instead, work with the author's ideas and give feedback that can help the author write better in the future.

Due Dates: Entry due at start of class on Jan 25; comments due at start of class on Jan 27.