Mathematics Part 2: Producing literate and numerate children

Literacy is a complex, multi-faceted concept that changes as society changes. The ability to cope with a wide range of texts requires more than the ability to read the words. It requires a full understanding of the key concepts underpinning ideas and the ability to interpret a variety of symbolic, spatial, and quantitative texts.

Shifts in literacy requirements have expanded to include the ability to read, interpret, and act upon a much wider range of texts. The vast majority of commonly encountered texts during the course of daily life require a degree of quantitative and spatial reasoning. The mathematical knowledge most commonly required is some form of understanding of rational numbers (any number that can be expressed as a fraction) and proportional reasoning.

An increasing amount of information is shared in a digital format, therefore there is an ever increasing need for people to be numerate, not just able to carry out set procedures. Being numerate requires an understanding of basic arithmetic, the properties and manipulation of whole numbers, and rational numbers. It requires using number sense to reason whether answers are correct. When a point is reached in solving a problem, knowing which operation or formula is required is still essential, but completing the procedure has been superseded in reality by technology.

The mathematics learning area has statistics in the title making clear the increasing importance of that branch of mathematics, a branch which is not confined to the mathematics but used widely in many learning areas.

One of the achievement objectives is headed: Statistical Literacy:

The changes in literacy requirements are forcing the need to change the way mathematics is taught. An instructional understanding of mathematics, in which the focus is on right answers to familiar problems is no longer sufficient for the literacy requirement. To be fully literate, a person needs to understand the mathematics and statistics embedded in the context.

New Zealand Curriculum (page 12):

Key Competencies: Language Symbols and Texts:

‘Students who are competent users of language, symbols and texts can interpret and use words, number, images, movement, metaphor and technologies in a range of contexts.’

Mathematics is part of literacy and literacy part of mathematics. Successful problem-solvers require deep mathematical understanding comprising mathematical knowledge, reasoning ability, and heuristic problem-solving strategies (problem-solving that employs a practical method not guaranteed to be perfect, but sufficient for immediate goals). Familiar or common problems make use of procedures that can be learnt. Unfamiliar problems (which is where most problems start, otherwise they would not be problems) must either be turned into familiar problems or solved using ‘first principles’ which require conceptual understanding of the mathematics.

Problem-solving is a ‘messy business’ with the solvers moving forwards and backwards, reasoning, making connections, and engaging in productive struggle or ‘controlled floundering’ as they work their way to a solution.

Haste should not enter into the process of problem-solving – value should be on persistence

New Zealand Curriculum (p. 10):

Students will be encouraged to value:

  • Excellence, by aiming high and persevering in the face of difficulties
  • Innovation, inquiry and curiosity by thinking critically, creatively, and reflectively.

There is a balance to be achieved between the extremes of the pendulum. Providing students with challenging problems and not allowing time within programmes for learning specific procedures, means students will always be having to reinvent the mathematics. Progress is slowed down and knowledge gaps increased, reducing the opportunity to make necessary connections. These gaps hinder the development of conceptual understanding resulting in children finding mathematics a frustrating and ultimately defeating experience.

The number system works by delaying the teaching of standard algorithms and focusing on the mental strategies necessary to prior conceptual understanding. When, however, mental methods of solving become an end in themselves, as demanded by the GloSS assessment, they become just another procedure confusing children’s conceptual understanding of the number system.

In today’s world, technology can be used to carry out basic mathematical procedures. To know if the result provided by the technology is reasonable, students need to be able to make a reasoned estimate. A reasoned estimate requires, at the most basic level, a conceptual understanding of the whole number place value system and recall of addition, subtraction, multiplication, and division facts. However, it needs to go much further, the conceptual understanding of the number system must be expanded to include rational numbers and the decimal place value system (which came 1500 years after the base 10 whole number system, invented as a business tool to replace fractions which were found difficult to work with).

It is only when this level of conceptual knowledge and understanding has been reached can proportional reasoning skills be used. The majority of texts and situations where mathematics is applied in daily life require proportional reasoning skills – home budgeting, following sports teams, analysing data, and vocational matters.

I asked a data analyst if she could give one piece of advice to primary teachers of mathematics.

Her response was immediate and simple: ‘Estimate more and calculate less’.

The barrier between literacy and numeracy is an artificial one created by schools.
Professional learning needs to focus on encompassing and connecting literacy and numeracy as tools for learning. Teachers, to prepare children for positive and productive citizenship, need to develop in them, a deeply connected conceptual knowledge of mathematics, reading, writing, speaking, and listening.

The more teachers know, the more connections they can make. Focused and timely gathering, analysis, interpretation, and use of information are part of the continuing process of the interaction between teaching and learning. And the deeper the understanding, the more able teachers are to undertake evaluation decisions to raise children’s achievement.

New Zealand Curriculum (p. 41):

‘Teaching and learning programmes are developed through a wide range of experiences across all learning areas, with a focus on literacy and numeracy along with the development of values and key competencies.’

Charlotte Wilkinson is an independent education consultant (MOE Accredited #654) and resource developer (The Wilkie Way, Pearson Mathematics, Primary Mathematics Assessment Tool [Available from http://www.edify.co.nz]) specialising in Primary Mathematics

http://www.thewilkieway.co.nz

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One Response to Mathematics Part 2: Producing literate and numerate children

  1. Ian Skipper says:

    Greetings Kelvin

    All teachers / principals etc need to read these 2 postings and discuss at their next staff meeting!

    Regards

    Ian

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