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.

Blog Entry #2 — Relational and Instrumental Understanding

Writing: Skemp's distinction between two different types of understanding is still frequently referenced in mathematics education today. Write a paragraph that compares and contrasts these two types of understanding. Your paragraph should include some of the following things, although not necessarily in this order.

• A definition of each type of understanding.
• How the two types of understanding are related. (Are they mutually exclusive, contain some of the same things, etc.?)
• Their advantages and disadvantages.

Your paragraph should start with a topic sentence that reflects the content of the paragraph. Instead of following the order of ideas above, your paragraph should be organized in a way that makes sense to you. The purpose of this paragraph is summarize Skemp's ideas, so while the organization should come from you, all of the content should come from Skemp's paper, and should accurately reflect his thinking. Lastly, do not quote anything from the paper. Instead, state all of the ideas in your own words.

Commenting: Visit three different blogs, preferably blogs that you didn't comment on last time, read the comparison paragraph, and then write a comment that includes the following parts:

• One part of the paragraph that you think meets the assignment well. It may be that you like the way that the person defines the two types of understanding, or the logical structure of the paragraph. 
• One part of the paragraph that you think could be improved. For example, this could be a place where the author failed to follow directions or where ideas are not expressed clearly. Remember to hedge in your comments and to use "I" messages.

If a blog already has five student comments on it for this particular blog entry, please select another blog to comment on.

Due: Entries due by the beginning of class on January 15; comments are due by the beginning of class on January 18.

Blog Entry #1 — Your Take on Mathematics Education

Although you have never taken a course in mathematics education before, you have already formed a lot of ideas about mathematics and mathematics teaching and learning through your experience in school mathematics classes. For your first writing assignment, I would like you to answer the following questions.

1. What is mathematics?
2. How do I learn mathematics best? Explain why you believe this.
   
3. How will my students learn mathematics best? Explain why you think this is true.
   
4. What are some of the current practices in school mathematics classrooms that promote students' learning of mathematics? Justify your reasoning.
   
5. What are some of the current practices in school mathematics classrooms that are detrimental to students' learning of mathematics? Justify your reasoning.
   

When you visit three blogs to read and make comments, your comment should include 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 responses. Use hedging language, such as "perhaps," "maybe," "I wonder," to soften the tone of your response and to be respectful of the author's ideas.
   

Due Date: Entries due by class on Jan 6; comments due by class on Jan 8.