Tag Archives: PUFM

4 ~ Longitudinal Coherance

Longitudinal Coherance is the final of the four key aspects that Ma (2010) describes to be linked to having a profound understanding of mathematics.

Children need to be given the opportunities to develop confidence and coherence within mathematics. Having longitudinal coherence is when you can identify recurring themes and to see the relevance.

Wu (2002) describes longitudinal coherence as being able to see the interrelationships among topics. Seeing these relationships will allow for coherent development.

I believe longitudinal coherence to be when you have a fundamental understanding over mathematics as a whole. This allows you to explore and experience situations.

Ma (2010) describes Longitudinal Coherence to be using what has been learned during our mathematics journey to influence and support our current mathematical status.

3 ~ Basic Ideas

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Basic Ideas are the third of the four key aspects that Ma (2010) describes to be linked to having a profound understanding of mathematics.

Basic Ideas are ideas as they occur throughout mathematical learning which creates a solid foundation for future learning, Ma (2010).

When teaching mathematics the basic ideas should be highlighted to allow children to use these when approaching different situations. Children need to understand the basic ideas confidently to enable them to use these to help in more difficult questions/problems.

Ma (2010) believes that good mathematicians should be able to identify thee basic ideas prominent in topics to use them in future processes. Once the basic ideas have been learned they can then be use with knowledge to solve more complex calculations.

Bryce and Humes (2008) explain that having a ground knowledge of basic ideas means that you have a sound subject knowledge. We then need to use this knowledge to solve more complex calculations.

2 ~ Multiple Perspectives

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Multiple Perspectives is the second of the four key aspects that Ma (2010) describes to be linked to having a profound understanding of mathematics.

Multiple Perspectives is about knowing the base knowledge and concepts and understanding them to know when and where to apply them to new situations.

In schools, children should be taught different methods/approaches to use. Having single approach methods are no good to children, they need to be able to explore, Vale and Barbosa (2009). Children will learn more through trial and error as they are problem solving through exploration and discovery.

For teachers, teaching different methods will allow for equal learning opportunities. For students, this will cater for a variety of learning styles.

Multiple Perspectives allow for us to incorporate many skills such as; analysing, predicting, reflecting and evaluating. Having these skills will allow you to persevere with your situation until you have an appropriate answer.

Bryce and Humes (2008) both describe multiple perspectives to be having a problem, knowing what approach to use to solve it and why that approach would work best. It is about being flexible with your methods to adapt them accordingly to the situations.

1 ~ Connectedness

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Connectedness is the first of the four key aspects that Ma (2010) describes to be linked to having a profound understanding of mathematics. In this blog I will describe how I have developed to understand and interpret the meaning of connectedness.

Mathematics when taught at schools is not taught as an integrated subject but as a subject in isolation. When mathematics is not connected to real life children will find it difficult to link what they have learned to real life situations.

Children need taught mathematics through cross-curricular activities so they can experience mathematics as a whole. For example, STEM subjects (Science, Technologies, Economics and Mathematics) are so closely linked together therefore it should be obvious that these subjects are easily taught together with the natural link. These links should be highlighted to the children and used to their full potential.

MA (2010) describes connectedness to be having the ability to relate topics to one another. Having these connections allow you to use prior learning and knowledge and to apply these to new situations and contexts. Having the basic knowledge and understanding will allow you to work through new ideas and processes.

Harper (2015) described connectedness to be taking individual pieces of knowledge to make these into a unified body of knowledge. Tara was referring to having the basic understanding of the possible connections to link together with different situations.