ED2652 Lecture Notes - Lecture 7: Australian Curriculum, Commutative Property, Number Sense
Mathematics 2: Number and Algebra
Lecture 6 – Week 7
Algebra and Algebraic Reasoning – Pattern, Equivalence and Function
• Competency Audit
o Start on time
o Calculator permitted
• Algebraic reasoning and algebra
o Algebraic reasoning/algebra is
▪ The understanding of pattern, function, and equivalence
▪ Generalised arithmetic which allows us to think about operations regardless of what the numbers
are
▪ relies upon an understanding of numbers and operations
▪ A sub-strand covered from P-10
• Algebra (Manly and Ginsburg, 2010)
o Full participation in today’s society involves a genuine grasp of the mathematical concepts that studying
algebra provides. Quantitative demands can be both complex and pervasive, reaching into an individual’s
daily life as citizen, worker, parent, and consumer. ... To be clear, although the skills and procedures of
algebra are important, it is often the more sophisticated understanding of mathematical relationships
imparted by algebra that is useful in navigating life’s decision-making challenges.
o The benefits of studying algebra are sometimes subtle. In the workplace, workers often are not aware
when they use an overarching mathematical concept. For example, researchers have shown that the
concept of proportionality was applied in nearly every workplace they studied (Hoyles et al. 2002; Marr
and Hagston 2007; Selden and Selden 2001).
o But few recognise that they are using “school math” because the mathematical ideas are so deeply
embedded into the context of the job. Adults often say they have never used the algebra they learned in
school. That may be true for the rote aspects of manipulating symbols, but they likely are using the
mathematical reasoning and problem-solving aspects of algebra unconsciously.
o Very young students can consider the commutative property of addition
▪ (a + b = b + a) and then later in multiplication (a x b = b x a)
• Malara & Navarra (2003)
o The distinction between arithmetic thinking and algebraic thinking in the early years’ context is best
defined as:
▪ 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)
• Big Ideas of Algebra
o Pattern
o Function
o Equivalence
• Australian Curriculum (p.2)
o Content strands – Number and Algebra
o Number and Algebra are developed together, as each enriches the study of the other. Students apply
number sense and strategies for counting and representing numbers. They explore the magnitude and
properties of numbers. They apply a range of strategies for computation and understand the connections
between operations.
o They recognise patterns and understand the concepts of variable and function. They build on their
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
Algebra and algebraic reasoning pattern, equivalence and function. Lecture 6 week 7: competency audit, start on time, calculator permitted, algebraic reasoning and algebra, algebraic reasoning/algebra is. Quantitative demands can be both complex and pervasive, reaching into an individual"s daily life as citizen, worker, parent, and consumer. In the workplace, workers often are not aware when they use an overarching mathematical concept. For example, researchers have shown that the concept of proportionality was applied in nearly every workplace they studied (hoyles et al. 2002; marr and hagston 2007; selden and selden 2001): but few recognise that they are using school math because the mathematical ideas are so deeply embedded into the context of the job. Adults often say they have never used the algebra they learned in school. Students apply number sense and strategies for counting and representing numbers. They explore the magnitude and properties of numbers.
