MATHEMATICS FROM THE EARLY YEARS AND BEYOND

MATHEMATICS FROM THE EARLY YEARS AND BEYOND

Featured - August 8, 2015

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In South Africa we have been bombarded with news items on how badly our children are doing in international benchmarking tests of mathematics (and science). Those of us who work at the Pre-Primary level of education are well aware that the results of the children at prep and college levels will not improve if we do not focus on the correct teaching of maths concepts with the three to six year old children.

Early mathematical experiences have to be presented in kinaesthetic and concrete ways, leading to semi-abstract activities in Grade 0. We do not favour worksheets for young children and concentrate on ‘hands-on, brains-on’ learning.

Many young children enter Pre-Primary school with knowledge of counting, numbers and shapes and while we consolidate these skills it is also important to expose our children to more challenging content. Young children are ready to learn more advanced concepts as long as they are presented in an engaging and developmentally appropriate manner. This does not equate with ‘pushing down’ the curriculum content to younger and younger children.

‘All children are capable of learning and should regard themselves as competent learners.’(Dockell 1995) Negative parental views and feelings about maths must not be passed on. Never let your child feel negatively about maths, or any other subject, because you were not good at it. For example, saying, ‘Don’t worry, I was no good at maths either’ or ‘Girls are not good at maths, I wasn’t, will give the child reasons to believe that maths is beyond them too.

“Children who feel confident in themselves and their own potential have a head-start to learning” (Ball 1994)

Parents have a vital role to play because the years before a child commences schooling are critical to their learning, including the learning of numeracy. The foundations of this effective early learning are achieved through play based activities. Play is the work of children.

Some activities you can do to promote the acquisition of maths concepts:

  • Sing number songs and rhymes
  • Count out everyday item such as plates and cutlery for supper, potatoes for cooking, biscuits for tea.
  • Match how many times you clap with items such as bottle tops.
  • Bake with your child and count and measure together as you prepare the ingredients.
  • Draw attention to numerals on gates, cars, busses etc.
  • Share out sweets, cakes etc. amongst the family or have teddies tea parties and do the same. (division)
  • Divide fruit, veg and cakes into pieces and talk about halves and quarters. (fractions)
  • Work out how many sweets we need if everyone is to get two. (multiplication)
  • Match, identify and count coins. Give coins to spend on small items in the shop.
  • Compare the sizes of clothes and shoes that the family wears and arrange them in ascending and descending order.
  • Sort and match socks.
  • Arrange things such as toys, bottles and cans in size order.
  • Sort toys into sets as you tidy up. Eg dolls, cars, puzzles.
  • Match sets of toys. Two cars and two dolls.
  • In the bath, provide plastic containers and discuss, full, half full, empty etc.
  • Play simple board/dice games such as ludo that involve associating a number name to a square.
  • Play dominoes

Many parents will proudly tell you that their child can count to ….. Counting is a rote memory skill unless it can be applied to objects. Here are a number of key principles that have to be mastered:

  • Each item is counted only once. (the one-to-one correspondence principle)
  • Each number picks out a specific numerosity.
  • Number words must be recited in the same order, (stability principle)
  • The last number word in a counting sequence represents the numerosity of the set. (cardinality principle)

By the time your child is 2-3 years old he already knows how to track very small numbers and can differentiate between markedly different quantities so start by working on the number words 1-2-3. Progress is slow and it could take nine months to a year to really comprehend the difference in meaning of these three numbers before you move on to 4. Progress will be faster from here.

The tracking of American, British and Canadian children found that children who entered pre-school with a strong grasp of numeracy, counting, relative magnitudes and ordinality achieved better maths scores in later years and that these skills were more predictive of general scholastic achievement than were language, attention or social skills. (Duncan et al 2007)

At Pre-Primary we work on the following maths concepts, at an age appropriate level, through the use of movement, concrete objects and only in Grade 0 at a semi-abstract level.

  • Counting
  • One to one correspondence
  • Addition and subtraction
  • Linear and solid shape
  • Spatial relationships
  • Sorting and classification
  • Measurement of size, mass, volume, time
  • Patterns and sequences
  • Symmetry
  • Data handling

All these concepts are linked to everyday applications in as many ways as possible, to make maths meaningful. The use of Smartboards and tablets is also enabling children to consolidate their concrete concepts at their own level and pace. Good practise does not permit asking children to learn something now, with difficulty, something they will manage more easily later. Nor does it include the teaching of isolated maths skills through memorisation, rote or the reliance on worksheets.

At around the age of seven, children move on to more abstract maths skills but still have the need of concrete tools to acquire new concepts. We believe it is important to track both our teaching levels and the children’s abilities against international benchmarks so the following tools are used:

SIAT
The SIAT [Schools International Assessment Test] is compiled and administered by the University of New South Wales, Australia. More than two million students in numerous countries worldwide write these tests annually. It is compulsory for our Grade 4, 6, 8 and 10 students at CrawfordSchools and Trinityhouse Schools to write these tests in Mathematics and English. Students in other grades may opt to write these tests and the subject of Science is offered as an additional option as well.

The purpose of writing these tests is twofold:

  • These tests benchmark our students’ performance and progress against international standards
  • More importantly they serve as a diagnostic tool which reports on the individual student and group strengths and weaknesses in specific subjects. These results inform teaching and promote the development of application of skills required to problem solve, reason and to think critically.

IMSO
In the 1990s, Indonesia realised that for their country to develop to its full potential they would need Mathematics and Science graduates upon whom their economy could leverage. They decided to have a Mathematics and Science Competition at Primary School level to foster and identify mathematic and scientific thinkers. Based on the success of their strategy and the impact it had on developing mathematicians and scientists in Indonesia, neighbouring countries asked if they could participate, and thus the IMSO [International Mathematics and Science Olympiad] for Primary Schools was born.

CrawfordSchools and Trinityhouse Schools have participated in the Olympiad since 2009. The purpose of our participation is to align our highly reputable initiatives in Mathematics and Science with those of international standards. Countries competing in IMSO from year to year have included China, India, Indonesia, Iran, Malaysia, Nepal, Philippines, Singapore, South Korea, Sri Lanka, Taiwan and Thailand. This year the 11th IMSO returns to its roots in Indonesia, Bali where our 22 students will participate in an international arena of similarly talented peers, not only for their individual schools, but for ADVTECH and as representatives of South Africa too. We believe that the Olympiad encourages an invaluable life-long and life-wide experience for our students and teachers.

Next time you read or hear derogatory articles on the state of South African maths, please be assured that the ADvTECH Schools have the matter well in hand and your child is benefiting from a world standard education. By working with the school, you can foster a love of maths that will significantly influence subject and career choices later and set your child on the path of success.