Obstacles to Developing Symbol Sense

· Differences between natural language and algebraic expressions.
Ex: 4+2x is read right to left but processed left to right.

· Multiple meanings attached to letter symbols
Ex: single unknown numbers, general numbers, varying quantities

· Cognitive difficulty in translating words to algebraic expressions
Ex: For "s is eight more than t" many students write t=s+8

Important Facets of Strong Symbol Sense

· Knowing when to use symbols and when not to…do not rush to symbolize

· Interpreting the meaning of symbols used in different contexts
Ex: for y=mx+b, constructing different meaning for x and y than m and b

· Upon inspecting an algebraic operation, can predict the form of the result
Ex: knowing that (x-1) + (x+1) will result in 2x

· Scanning an expression or formula and being able to make rough estimates of emerging patterns in numeric or graphical format
Ex: values of 2p+3 for natural numbers p will lie on a straight line and increment numerically by 2

· Scanning a table or graph, or interpreting verbal statements, and identifying the likely form of the symbolic expression
Ex: reverse of the previous point, seeing a line or a table of values that increment by a constant value, can predict a symbolic form of mx+b

Recommendations for Attention to Symbol Sense in the Classroom

· Use visual representations before symbolic ones

· Capitalize on opportunities to guide students towards using symbols without rushing or forcing them!

· Engage students in bridging activities between numbers and symbols

· Exploit the use of equivalent expressions for sense making of a situation

· Have students relate expressions and equations to the original context of the problem

· Ask student to undo processes involving symbols

· Take advantage of technology to help transition from letter as unknown to letter as variable