## Posts Tagged ‘Equals sign’

**Key points**:

- Algebra is a third of the Malaysian Secondary Mathematics curriculum.
- The article lists a large range of sources relating to misconceptions in the understanding of algebra. It states that, because algebra is an extension of previously acquired mathematical learning, it is linked to the use of symbolic representations and that “Warren (2003) felt that understandings of basic arithmetic operations could assist sucessful transition from arithmetic to algebra.”
- “Students use the equals sign in both contexts: arithmetic and algebra. The concept of the equals sign in the framework of arithmetic is that of a ‘do something’ signal (Bodin & Capponi, 1996). Many students tried to add “= 0″ to algebraic expressions when they were asked to simplify (Kieran, 1997).”
- The article cites Booth, 1981, as a refernce for children not understanding the idea of a letter as a variable, and they rather see each letter as representing a digit.
- The article looks in detail at a range of errors (12 types) made by students. The examples given are from the secondary curriculum and so may not apply to any errors made by children in a primary school – but a worthwhile source to help identify the sorts of errors that could be made.

**Main Reference**:

- Lim, K. (2009) ‘An Error Analysis of Form 2 (Grade 7) Students in Simplifying Algebraic Expressions: A Descriptive Study’
*Electronic Journal of Research in Education Psychology*, Vol. 8, No. 1, pp 139-162

**Key points**:

- “Early algebraic thinking in a primary context is not about introducing formal algebraic concepts into the classroom but involves reconsidering how we think about arithmetic.”
- “arithmetic thinking focuses on product (a focus on arithmetic as a computational tool) and algebraic thinking focuses on process (a focus on the structure of arithmetic) (Malara & Navarra, 2003)”
- “The aim was to assist 5 year-olds to come to an understanding of the structure of equations, and in particular the use of the equal sign.”
- “When asked to find the unknown for 7 + 8 = ? + 9, many students express this as 7 + 8 = 15 + 9 = 24.”
- “Three add 2 is different from 4 add 2. There is a different number on each side. Three add 2 is not equal to 4 add 2. It is different from 4 add 2″. Arithmetic thinking is required when computing the value of the two expressions. Algebraic thinking is required when placing the appropriate language between the expressions. Equals is only applicable if the two expressions are equivalent, that is, have the same value.”
- “It is interesting that both Brianna and Ethan spontaneously introduced symbols as short hand for the object:
*p*for pears and*b*for bananas or an iconic picture of each. In the secondary context this is commonly referred to ‘fruit salad’ algebra where the letter stands for an object instead of variable, and is thinking that we want to discourage.**For example, a common misconception in the secondary context is that 3**In the early years it is important to make the distinction between how we verbally describe number problems and how we represent these problems with symbols. While we say, “Three cars and five trucks,” the convention is to represent this as 3 and 5. Number sentences are made up of numbers.”*a*+ 3*b*stands for 3 apples and 3 bananas instead of*a*and*b*standing for any number.

**References**:

- Malara, N., Navarra, G. (2003) ‘ArAl Project: Arithmetic pathways towards favouring pre-algebraic thinking.’ Bologna, Italy: Pitagora Editrice.
- Warren, E., Mollinson, A., Oestrich, K. (2009) ‘Equivalence and Equations in Early Years Classrooms.’
*Australian Primary Mathematics Classroom,*Vol. 14, no. 1, pp. 10-12