1. MH513: Developing Mathematical Proficiency: Algebra (6-8) Dr. Numeroff-Martin Week 4: Seminar 4 The Real Meaning of Equal

2.  Identify a one-week unit plan from a credible online source or textbook. The unit must last for at least 5 consecutive teaching days and be able to stand alone as a mini-unit of instruction. The unit may cover any area of algebra covered in this course at any of the middle grade levels (grades 6-8) you desire. However, the unit must employ either manipulatives and/or technology tools. Algebraic Unit Analysis Due in Unit 6

3. Algebraic Unit Analysis  You will write an analysis describing the important algebraic thinking in the unit you selected for analysis. Include a discussion of pedagogical issues, based on research, of using the unit with middle grade mathematics students. References to NCTM Principles and Standards, course-reading materials, unit source material, and at least two (2) additional research-based articles are required. The paper must follow APA guidelines. Due in Unit 6

4. Algebraic Unit Analysis * Description of the algebraic unit (1-2 pages) * Include a reference to the source of the unit. * Describe the grade level and course where the unit could be used. * Describe the materials used (e.g., manipulatives, technology). * Describe the prerequisite skills and concepts that are essential for students to be successful in this algebraic unit. * Analysis of the algebra and algebraic thinking students may use in this unit (2-3 pages) * Describe the important algebraic thinking in this unit continued… Due in Unit 6

5. Algebraic Unit Analysis * What habits of mind could be fostered through this unit? * Reference the NCTM Principles and Standards as well as course reading material and research literature. * Discuss pedagogical issues of using this unit with students (2- 3 pages) * What is the role of the teacher? * What do you anticipate learners doing? * What questions should be posed to get students to think algebraically? * Reference the NCTM Principles and Standards as well as course reading material and research literature. Due in Unit 6

6. The Real Meaning of Equal An understanding of the concept of equality is vital to successful algebraic thinking and is one of the big ideas of algebra about which students should reason. Thinking of the equals sign operationally is a common interpretation of many elementary school students. Children in the elementary grades generally think that the equals sign means that they should carry out the calculation that precedes it and that the number after the equals sign is the answer to the calculation.

7. The Real Meaning of Equal “The equal sign is a symbol that indicates a state of equality exists and that the two values on either side of the equals sign are the same. It does not mean that the answer is coming or that the answer is on the other side of the sign.” (Mann, 2004) Mann, R L. (2004). Balancing act: The truth behind the equals sign. Teaching Children Mathematics, 11(2), p65-69.

8. The Real Meaning of Equal Students need to change their thinking from “the answer is” to the “is the same as” mode of thinking – a symbol of equivalence and balance. How can you help students understand this meaning?

9. Thank you… for attending the seminar. If you have any more questions or comments you can always email me at: Dnumeroff@kaplan.edu Have a wonderful week : )