Course Guide - USAID Teacher Education Project

Later, when y is replaced by function notation f(x) students become confused thinkingthat this means "f" is multiplied by x since they recently have been introduced to thealgebraic format for multiplication such as 2x or ab.3. What is essential to know or do in class?a) Have a small group, then whole class, discussion about the article, “What DoStudents Struggle with When First Introduced to Algebra Symbols?”b) Have students work with familiar algebraic equations by using “n” as a variable todevelop patterns that illustrate how algebra can be thought of as generalizedarithmetic.4. Class Activitiesa) Begin the session by dividing students into small groups to discuss “What DoStudents Struggle with When First Introduced to Algebra Symbols?”, the article readfor homework, Assign each group Question 1 and one of the other discussionprompts. Ask them to discuss both the article as a whole and the questions theirgroup has been given. Allow about 8-10 minutes for the small group discussion.1) How does this article relate to the way you learned algebra as a student? Howcan x be both "the unknown" and a variable?2) What was your first instinct when solving the word problem about sharing money?Did you use arithmetic or algebra? What difference do you see between these twomethods? How might you help youngsters begin to shift from arithmetic to algebraicways of thinking?3) When you saw the two-column chart and looked for patterns, what did you see? Whattype of thinking led youngsters to come up with other patterns? Were those patternsvalid? Why or why not?4) When you saw the growth pattern in Figure 2, how did you extend the patternto find the number of sticks in Figure 25?5) What do you think of the author's comment that "Moving from arithmetic toalgebraic generalizations is a process that has been found to take time." If this isso, when should the "algebraicifacation" of arithmetic begin?6) How does the difference between the minus sign for the operation ofsubtractionand the negative sign for numbers less than 0 influence students’ work inalgebra?b) Have a large group discussion, starting with their overall thoughts of how theywere taught algebra. Did they "struggle when first introduced to algebraicsymbols"? Was algebra connected to arithmetic when they began studying it? Atwhat point did they notice a connection? Did they see algebra as generalizedarithmetic or as equations into which they substituted numbers in order to come up