Contents
Preface
How to use HOTmaths with this book
Acknowledgements
Partย 1 Contemporary Issues in Learning and Teaching Mathematics
Chapter 1 Introduction:ย the learning and teaching of mathematics
Introduction
Key terms
Mathematics for the twenty- fi rst century
Mathematical profi ciency and the Australian Curriculum
Theories about how students learn mathematics
Student engagement in learning mathematics
Summary
Chapter 2 Language and mathematics
Introduction
Key terms
Why language is important
The mathematics register
Language in the classroom
Technical communication
Summary
Chapter 3 Making mathematical connections
Introduction
Key terms
The importance of making mathematical connections
What are mathematical connections?
Teachersโ practices in promoting mathematical connections
Science, technology, engineering and mathematics (STEM)
Putting activities into practice
Summary
Chapter 4 Using technology in mathematics education
Introduction
Key terms
Why use technology in the teaching and learning of mathematics?
Mathematics software
Devices used for teaching, learning and doing mathematics
Mathematicsย online
Summary
Chapter 5 Inquiry-based learning
Introduction
Key terms
Student-centred learning in mathematics classrooms
Teaching strategies that foster student- centred approaches
Problem solving and modelling in mathematics classrooms
Inquiry-based learning in mathematics classrooms
Collaborative and cooperative learning
Summary
Chapter 6 Gender, culture and diversity in the mathematics classroom
Introduction
Key terms
Gender in the secondary mathematics classroom
Culture in the secondary mathematics classroom
Special needs learners in the secondary mathematics classroom
Summary
Chapter 7 Assessing mathematics learning
Introduction
Key terms
Why assess?
What is assessment?
Guidelines for creating assessments in secondary mathematics
Providing feedback to students
Summary
Partย 2 Learning and Teaching Key Mathematics Content
Chapter 8 Number and algebra
Introduction
Key terms
The unknown, pronumeral and variable
Algebraic expression problems
The classification of linear equations
Teaching and learning linear equations in a hierarchical level of complexity
Algebraic problem- solving in real life contexts
Transferability of algebraic problem-solving to the science curriculum
Summary
Chapter 9 Measurement and geometry
Introduction
The importance of learning geometry
The importance of learning measurement
Key terms
The concept of geometric proof
The concept of transformation
Using technology in measurement and geometry
Summary
Chapter 10 Statistics and probability
Introduction
Key terms
The need for data and its collectionย
Descriptive statistics, tables and graphs
Tabular and graphical displays
Probability
Putting it all together:ย statistical inference
Summary
Chapter 11 Functions:ย a unifying concept
Introduction
Key terms
Functions and their settings
Functions at the transition
Developing functions through the early secondary years
Functions in the senior secondaryย school
Summary
Chapter 12 Calculus
Introduction
Key terms
Troublesome knowledge, threshold concepts and concept image
What students need to know before beginning calculus
Derivatives
Reversing the process:ย anti-differentiation and integration
Summary
References
Index