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Proof By Contradiction: Teaching And Learning Considerations In The Secondary Mathematics Classroom, Gregory Hine
Proof By Contradiction: Teaching And Learning Considerations In The Secondary Mathematics Classroom, Gregory Hine
Education Papers and Journal Articles
This professional practice paper is underpinned philosophically by the indisputable centrality of proof to the discipline of mathematics. Proof offers students the opportunity to deepen their own understanding of mathematical ideas, to construct and defend logical arguments, and to think critically about the veracity of mathematical statements. Such opportunities afford students key skills required for further study, and arguably for a myriad of careers. Proof by contradiction is a particular mathematical technique taught in Australian senior secondary classrooms (ACMSM025, ACMSM063) which will be explored in this paper. In particular, several worked examples will be outlined alongside implications for best instructional …
I'M Proud To Be A Toy Teacher: Using Cra To Become An Even More Effective Teacher, Derek Hurrell
I'M Proud To Be A Toy Teacher: Using Cra To Become An Even More Effective Teacher, Derek Hurrell
Education Papers and Journal Articles
The role of manipulative materials in mathematics can be a contentious one. It seems that in the mind of some teachers, manipulatives are fine in the early years but have no place in a rigorous maths classroom as the students get older. It is a topic worth our consideration.
Where We Were…Where We Are Heading: One Multiplicative Journey, C Hurst, D Hurrell
Where We Were…Where We Are Heading: One Multiplicative Journey, C Hurst, D Hurrell
Education Papers and Journal Articles
A journey into multiplicative thinking by three teachers in a primary school is reported. A description of how the teachers learned to identify gaps in student knowledge is described along with how the teachers assisted students to connect multiplicative ideas in ways that make sense.
Is It Time To Start Reconsidering The Teaching Of Time?, D Hurrell
Is It Time To Start Reconsidering The Teaching Of Time?, D Hurrell
Education Papers and Journal Articles
How students are taught about the difficult concept of time needs to be carefully considered, in terms of both the key aspects involved as well as the sequencing. Examples of concrete activities to support the teaching of time are included.
An Explanation For The Use Of Arrays To Promote The Understanding Of Mental Strategies For Multiplication, Lorraine Day, Derek Hurrell
An Explanation For The Use Of Arrays To Promote The Understanding Of Mental Strategies For Multiplication, Lorraine Day, Derek Hurrell
Education Papers and Journal Articles
This article provides a convincing argument for using arrays to promote students’ understandings of mental computation strategies for multiplication. Also a range of different examples that illustrate the benefits of arrays in the primary classroom are provided.
Australian Curriculum Linked Lessons: Reasoning In Number And Algebra, Lorraine Day
Australian Curriculum Linked Lessons: Reasoning In Number And Algebra, Lorraine Day
Education Papers and Journal Articles
In the Australian Curriculum: Mathematics "Number and Algebra are developed together as each enriches the study of the other". The content strands indicate what students should be learning and the proficiency strands indicate the types of learning experiences students should be exposed to in order to learn the content. Most of the content descriptors in Years F-6 algebra refer to a progression of patterning and finding unknowns in number sentences. We could see from this that there are two major themes running through the curriculum; that of patterns and relationships, and that of equations and expressions. These two aspects of …