Tom's+Blog+Lesson+Plan


 * Background and rationale**

An opportunity I discovered when facilitating virtual math classes, is in online conversations with students. The use of many mathematical symbols is very difficult in text. As a result, students need to be able to describe operations in words, developing a deeper understanding of mathematics.

This lesson can be adapted to any course in mathematics, but I would like to implement it first in my virtual algebra class. Courses including geometry, advanced algebra, and precalculus depend on a solid understanding of algebra concepts, so this lesson can be used in these classes, as well.


 * Standards addressed**

According to the National Council of Teachers of Mathematics (NTCM), http://nctm.org/resources/content.aspx?id=12622, ** Instructional programs from prekindergarten through grade 12 should enable all students to— ** Blogging offers an excellent opportunity to practice and strengthen these communication skills.
 * organize and consolidate their mathematical thinking through communication;
 * communicate their mathematical thinking coherently and clearly to peers, teachers, and others;
 * analyze and evaluate the mathematical thinking and strategies of others;
 * use the language of mathematics to express mathematical ideas precisely.


 * Lesson Objectives**

One of the concepts students learn in Algebra is “slope.” The objectives of this lesson are to be able to
 * describe and understand the concept of slope
 * provide examples of positive, negative, zero, and “undefined,” or vertical slope
 * apply the concept of slope to solve problems
 * express mathematical concepts in written language
 * evaluate the mathematical thinking or others.


 * Directions**

Students will respond to the following in a posting to the classroom blog: > - positive slope > - negative slope > - zero slope > - undefined, or vertical slope
 * 1) Explain “slope” to a classmate.
 * 2) Give a real-life example of each type of slope”
 * 1) For each example describe what is being measured by the slope.
 * 2) Describe how slope could be used to predict outcomes.

Each student must respond to the postings of two other students. In the first response, they will ask to clarify anything not understood. They will review item #4 and offer an alternative approach or an extension to the problem. In their second response, they will comment on another student’s response.

After all of the postings and responses have been completed, I will respond to each student, offering additional questions for consideration.

Finally, students will summarize what they learned in this activity and post to the class blog.


 * Assessment**

Students will be evaluated based on their participation. According to the February, 2008 issue of NCTM’s Mathematics Teacher, in the article “Online Discourse,” Randall Groth states that “teachers must be cautious about setting grading criteria for online conversations [to avoid writing] in a certain way to receive credit” (p. 425). Expectations for students, however, need to be established. In addition, this activity is an opportunity for me to identify any themes or trends in student responses and understanding. These themes can be addressed in subsequent class discussions.

The following rubric will provide students with expectations for this assignment and allow the assignment of a grade.


 * Math - Problem Solving : Communicating Concept of Slope ||
 * CATEGORY || 4 || 3 || 2 || 1 ||
 * Explanation || Explanation is detailed and clear. || Explanation is clear. || Explanation is a little difficult to understand, but includes critical components. || Explanation is difficult to understand and is missing several components OR was not included. ||
 * Mathematical Concepts || Explanation shows complete understanding of the mathematical concepts used to solve the problem(s). || Explanation shows substantial understanding of the mathematical concepts used to solve the problem(s). || Explanation shows some understanding of the mathematical concepts needed to solve the problem(s). || Explanation shows very limited understanding of the underlying concepts needed to solve the problem(s) OR is not written. ||
 * Mathematical Terminology and Notation || Correct terminology and notation are always used, making it easy to understand what was done. || Correct terminology and notation are usually used, making it fairly easy to understand what was done. || Correct terminology and notation are used, but it is sometimes not easy to understand what was done. || There is little use, or a lot of inappropriate use, of terminology and notation. ||
 * Strategy/Procedures || Typically, uses an efficient and effective strategy to solve the problem(s). || Typically, uses an effective strategy to solve the problem(s). || Sometimes uses an effective strategy to solve problems, but does not do it consistently. || Rarely uses an effective strategy to solve problems. ||
 * Working with Others || Student was an engaged partner, listening to suggestions of others and working cooperatively throughout lesson. || Student was an engaged partner but had trouble listening to others and/or working cooperatively. || Student cooperated with others, but needed prompting to stay on-task. || Student did not work effectively with others. ||
 * Mathematical Terminology and Notation || Correct terminology and notation are always used, making it easy to understand what was done. || Correct terminology and notation are usually used, making it fairly easy to understand what was done. || Correct terminology and notation are used, but it is sometimes not easy to understand what was done. || There is little use, or a lot of inappropriate use, of terminology and notation. ||
 * Strategy/Procedures || Typically, uses an efficient and effective strategy to solve the problem(s). || Typically, uses an effective strategy to solve the problem(s). || Sometimes uses an effective strategy to solve problems, but does not do it consistently. || Rarely uses an effective strategy to solve problems. ||
 * Working with Others || Student was an engaged partner, listening to suggestions of others and working cooperatively throughout lesson. || Student was an engaged partner but had trouble listening to others and/or working cooperatively. || Student cooperated with others, but needed prompting to stay on-task. || Student did not work effectively with others. ||