Multifaceted variable approach: What can we learn from student errors Salma Tahir, Michael Cavanagh,

1
Multifaceted variable approach What can we
learn from student errors?Salma Tahir, Michael
Cavanagh, Mike MitchelmoreCentre for Research in
Mathematics and Science EducationMacquarie
University, Sydney, Australia
2
Overview

• Brief description of research
• Student errors in Phase I
• Student errors in Phase II
• Possible Reasons
• Suggestions and discussion

3

Real life contexts
Phase I
Graphical , tabular and algebraic representation
Patterns for generalisation
4
Phase 2
5
SAMPLE

• 4 graded Year 7 classes in one girls school
• Experimental group Sets 2 and 4
• Comparison group Sets 1 and 3

6
Phase I

• 13 x 50-minute lessons over 3 weeks (Patterns,
  linear algebraic expressions and some functions)
• 40-minute written test
• Student interviews after test

7
Phase II

• 27 50 minute lessons (linear graphs, number
  properties, addition, subtraction, multiplication
  and division of algebraic expressions).
• Algebra test and student interview.
• 850 minute lessons (linear equations).
• Mid term test.

8
Errors regarding variables in algebra test_2008
9
Manipulation errors in algebra test_2008
10
Errors
11
Errors

• p2p33p39p
• p33p
• p33

12
Errors

• 3a12-5a10a
• 3p69p
• 6by2-2by4by2
• 15a-5a10a2

13
Errors regarding algebraic manipulations

• Conjoin terms
• Incorrect order of operations.
• Incorrect cancellation.
• Fraction errors

14
Errors in Midterm test_2009
15
(McGregor Stacey, 1997)

• Use real situations to formulate equations and
  describe situations algebraically
• Use complex problems which can only be solved
  using algebra
• Develop a thorough understanding of number
  properties

16
Suggestions (Falle, 2007)

• When to conjoin terms(algebraic multiplication)
  and when not.
• Encounter arithmetic expressions in different
  equivalent and unclosed forms.
• Use of formal language in class.