Example | The feature it is an example of e.g. everyday maths or an intellectual pursuit | Rank these examples according to the importance you place on them |
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Adults regularly use aspects of logical thinking in their organisation and decision making processes, doing mathematics can develop cognitive ‘muscles’ such as proportional reasoning, pattern-spotting and visualisation. Mathematics lessons have the potential to teach learners how to think, preparing them not only for specific everyday contexts or commonplace careers, but also for unexpected moments, and in preparation for jobs that do not yet exist. | ||

Developing fluency with numbers by practising simple problems that have immediate applications, such as students being able to work out how many cans of fizzy drink or bars of chocolate they can buy with the cash they have. | ||

Encouraging public interest in mathematics, and ultimately to ensure its continuation by bringing up the next generation of mathematicians. | ||

Mathematics develops statistical understanding that allows learners to test and weigh up many political claims and can develop an understanding of probability that assists learners in making sense of risk, chance and prediction. By working mathematically students can build up a cognitive toolbox that can help them function as a full member of a modern, democratic society. | ||

The reason that many people have for learning mathematics is that without a mathematics qualification they will be excluded from many professions. The higher the qualification in mathematics that someone has, the greater their earning potential. | ||

Many professions rely on good mathematical knowledge. Nurses use formulae to calculate safe dosages; account managers use formulae when setting up spreadsheets; and special effects organisers use them to calculate safe distances when working with pyrotechnics. Thus practising writing and reading formulae is vital preparation for employment, since the ability to express relationships symbolically and work with algebra is essential in so many careers. |

the differences between high-effect and low-effect teachers are primarily related to the attitudes and expectations that teachers have when they decide on the key issues of teaching – that is, what to teach and at what level of difficulty, and their understandings of progress and of the effects of their teaching.

Good teachers of mathematics have a connectionist (Askew et al., 1997) view of mathematics, not teaching discrete chunks of mathematics but supporting students in seeing how each topic draws on and extends the ideas that they have worked with before. Being a connectionist teacher also requires you to think about how the mathematics that your students are learning is part of the real world and why learning is important to them not just later when they are employed but at the age they are now.

What happens if your students make a mistake when answering a question? Is the mistake quickly moved on from or is it explored and celebrated because it gives the class an opportunity to learn more? Do you ask for conjectures or only for answers? Do you want to know what your students think or just what they know? Students are especially reluctant to reveal their lack of confidence in their knowledge in mathematics, where they often consider there is one right answer and one right way to get to it. Tackling such ideas is a vital part of enabling your students to learn well.

Effective mathematics teachers use students’ descriptions of their methods and their reasoning to help establish and emphasise connections and address misconceptions.

Highly effective mathematics teachers have knowledge, understanding and awareness of conceptual connections within and between the areas of the mathematics curriculum. This means that if students are not making progress they have alternative explanations and representations that can be used to ensure success.

Effective teachers of mathematics do not just help their students to convert from a fraction to a decimal; they also demand that they think about when one should be used in preference to the other, or whether the two forms of representation are always equivalent. Students who habitually make such connections use efficient strategies for all purposes including mental arithmetic. (Hattie, 2012)

If we are to develop in young people the ability to move towards capability as mathematicians, then we should spend less time on projecting our ideas about what it means to ‘be mathematical’, and more time ‘being there’ in the mathematical situation – mathematical be-ing. (Wiliam, 1998, p.6)

The national curriculum for mathematics aims to ensure that all students: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that students develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

the ability to solve problems is at the heart of mathematics. Mathematics is only ‘useful’ to the extent to which it can be applied to a particular situation and it is the ability to apply mathematics to a variety of situations to which we give the name ‘problem solving’.

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