ED2652 Lecture Notes - Lecture 8: Mathematics Education, Commutative Property, Backtracking
Mathematics 2: Number and Algebra
Tutorial Eight – Week Eight
Equivalence
• Big Ideas
o Pattern
o Equivalence
o Function
• ICT in Mathematics
o Virtual manipulative
o Sits between Concrete and representational
• Functional Thinking (Siemon et al, 2011)
o In classrooms in the early years algebraic thinking entails:
▪ Making explicit the mathematics of pattern and extending these patterns to our number system
▪ Studying early functional thinking with a focus on the relationships between the operations, such as
the inverse relationship between addition and subtraction, commutative law for addition, and the
identities
▪ Studying the structure of the number system and operations, for example the meaning of equals
and the meaningful use of unknowns.
▪ It does not entail the manipulation of symbols.
o It is important that students understand (Warren 2015)
▪ Operations almost always change an original number to a new number.
▪ Simple real life problems with variables can be represented as ‘change situations’.
▪ Backtracking reverses a change and can be used to solve unknowns.
o Functional thinking focuses on the relationship between two (or more) varying quantities. In the early years
functions often involve following rules for consistent changes, and reversing the changes.
o These activities are enhanced with the use of representations such as function machines, and physically
acting out the change and reversing processes
▪ (Warren, Benson & Green, 2007).
• Elizabeth Warren (2015)
o Early Algebra
o Indigenous mathematics education
• Function Machine Activity
o Encouraging students to predict and justify supports their mathematical thinking and their ability to
communicate this thinking to others.
• Linking the learning
o Once students have a clear understanding of the concept of functional thinking, move to applying this
thinking to number situations.
• Use this opportunity to link multiple representations of the ‘change’. (eg. Number tracks)
o ‘What’s my rule?’ games can be used to introduce algebraic thinking by encouraging using words to
express generalisations. Can expand to two rule changes (more than one answer using different
operations).
find more resources at oneclass.com
find more resources at oneclass.com
