“One of the best ways for children to learn and understand much of the mathematics in the Primary School curriculum is for a teacher who understands it to explain it to them” (Haylock, 2010)
During this elective I am personally hoping to raise my confidence levels in mathematics by focussing on enhancing my profound understanding of fundamental mathematics. To have a profound understanding I will research and explore topics in a deep and thorough way.
The four main fundamental principles of mathematics are; connected, multiple perspectives, basic ideas and longitudinal coherence. To my basic knowledge I will explain my understanding of these concepts so far.
- Connectedness. When we are making connections for mathematical concepts and procedures to ensure that we are providing and constructing an appropriate level of understanding.
- Multiple Perspectives. Providing the opportunities to use various approaches to solve one solution. Being able to provide the correct explanations to these approaches by having a flexible understanding.
- Basic Ideas – Having a foundation of basic concepts/principles to use during all aspects of mathematics. For example, basic equations can be used even when getting more difficult formulae as you can substitute the required information.
- Longitudinal Coherence – Having achiveved a fundamental understanding of the whole maths curriculum to enable you to explore multiple different experiences.
Liping Ma (2010) explains the four key elements.
- Connectedness – ability to relate topics to one another so that you can build on prior knowledge to work through new processes and ideas.
- Multiple Perspectives – ability to use a variety approaches to solve mathematical problems. If you are successful in doing this, then you have complete knowledge of that topic.
- Basic Ideas – ability to identify the basic mathematical ideas which are prominent throughout maths topics and use these ideas to inform future processes.
- Longitudinal Coherence – what we learn from the start of our mathematical journey influences our current mathematical status regardless of how fragmented our previous knowledge may be.
