MAE3270 Module 10 - Lecture 1

Chapter 1: Introduction

• Content of the lecture:

  • What is algebra

  • Development of algebraic thinking across the Australian Curriculum

  • Linear versus non-linear relationships

• Algebra comes from the Arabic word "aljabr"

• Number sentence example: 5 + ? = 7

• Students need to add 2 to 5 to equal 7

• Encourage students to consider questions with multiple digit answers

Chapter 2: Algebraic Thinking

• Introduction of formal algebraic notation in later years of primary school

• Algebraic notation is a language used to describe patterns

• Common misconceptions about algebra:

  • Not taught in primary school

  • Collection of arbitrary rules

  • Method to be rote learned

  • Has limited usefulness in the real world

  • Consists of simply replacing numbers with letters

• Development of algebraic thinking in the Australian curriculum

  • Patterns and algebra from foundation through year 10

  • Linear and non-linear relationships from year 7 through year 10

• Algebraic thinking emerges from activities in number, measurement, and algebra

• Students need to use materials, models, diagrams, and tables to understand patterns

Chapter 3: Patterns in Algebra

• Algebra is a mathematical system used to generalize certain mathematical operations

  • Algebra uses letters to stand for numbers

• Algebraic thinking leads on from students' early learning about numbers and patterns

  • Students with good knowledge of patterns and arithmetic operations are successful at learning algebra

  • Poor grasp of fundamental arithmetic can lead to difficulties in algebra

• Patterning in algebra in year 3

  • Number patterns resulting from performing addition and subtraction

  • Examples of number patterns: increasing by 5 each time, decreasing by 3 each time, adding 3, subtracting 6

  • Number patterns can start at any number, not just those familiar from times tables

• Incorporating ICT in algebra

  • Using number trains to increase or decrease by a certain amount each time

• Middle years focus on patterns and multiplication

  • Understanding and memorization of multiplication facts

  • Solving word problems involving multiplication or division

  • Using equivalent sentences involving addition and subtraction to find unknown quantities

Chapter 4: The Equal Sign

• Students need to make sure both sides of the equal sign are equal

  • Example: 5 + 3 = 10 - ?

  • Answer: 5 + 3 = 8

• Equal sign can represent equivalents in algebra

  • Number balance can be used to highlight the equality of both sides

• Common misconceptions about the equal sign

  • Children see the equal sign as an instruction to perform an operation

  • Children may put the wrong number in the box when asked to solve an equation

  • Using the equal sign as a device for connecting calculations is mathematically incorrect

Chapter 5: Upper Primary Algebra

• In middle/later years, patterns in algebra involve fractions, decimals, and whole numbers

  • Describing, continuing, and creating patterns with fractions, decimals, and whole numbers

  • Using equivalent sentences involving multiplication and division to find unknown quantities

• In year 6, continuing and creating sequences involving whole numbers, fractions, and decimals

  • Describing the rule used to create the sequence

  • Exploring the use of brackets and order of operations (BIMDAS)

• Patterns and sequences involving fractions, decimals, and whole numbers are interrelated with the number and place value sub-strand