ED2652 Lecture Notes - Lecture 7: Australian Curriculum, Equals Sign, Weighing Scale
Mathematics 2: Number and Algebra
Tutorial Seven – Week Seven
Equivalence
• Questions from reading
o Explain why the use of balance scales and correct terminology are important if students are to develop an
understanding of the connection between equality and balance
▪ Concrete material – allows students to gain a better understanding of meaning
▪ Describing what is happening in front of you → increased sense of vocabulary
▪ Terminology will help them later on in their development and assessment
• Three Big Ideas in algebra
o Pattern
o Equivalence → Use the word ‘balance’ with students
o Equations
• Equal Shmequal
• The equal sign
o The equal sign (=) does not mean ‘answer’
▪ 2a + 8 = 24, the answer is not 24 → We need to find a
▪ The equal sign (=) does mean “equivalence”
o Understanding that the equal sign signals a relationship between quantities, that it isn’t just a prompt to
“give the answer,” has been shown to offer lasting benefits as students move into the more abstract areas
of mathematics in algebra and beyond.
▪ Knuth, Stephens, McNeil & Alibali, 2006
• Rittle-Johnson, Matthews, Taylor, and McEldoon, 2011
o Younger children - the equals sign means you need to find a ‘sum’ or ‘answer’.
o As children progress the equals sign as meaning the same value is on both sides
▪ e.g., c = a + b and a + b = c + d.
o Following this, the equals sign is seen relationally so students may accept
▪ e.g. a + b = b + a
o These three views are not necessarily hierarchical or mutually exclusive (McNeil, 2008) and they commonly
coexist depending on the context and format of presented number problems.
• Freiman and Lee (2004)
o Number sentence problems in the form of a + b = d + c and a + b = _ + c or a + b = d + _ consistently
caused difficulties across year levels.
• Carpenter et al. (2003)
o found that when solving 9 + 6 = __ + 5, students may put 15 in the blank space because they consider
that the equals sign means “find an answer”.
o Alternatively, other students, may assume the sequence of symbols in the number sentence as unimportant,
and may put 20 in the blank space.
• Concrete Items
o Scales
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