puzzles; tasks that involve construction, sorting, patterning, and measurement. Each lesson should also include support for


learners who are experiencing barriers to learning, extension activities for learners who are coping well, as well as assessment activities. Both independent and small focus group session


activities must be observed (practical and oral), marked and overseen (written recording), by the teacher, as part of his/her informal and formal assessment activities. Teachers should constantly observe and track


learners’ responses (verbal, oral, practical and written) in learning and teaching situations. This enables the teacher to do continuous assessment, monitor learners’ progress and plan support accordingly.


Teaching Mathematics content General activities


Mental Mathematics Mental Mathematics is a crucial component in the curriculum. The number bonds and multiplication table facts that learners are expected to know, or recall fairly quickly, are listed for each grade. Mental Mathematics is used extensively to explore


the higher number ranges through skip counting and by doing activities such as ‘up and down the number ladder’. These activities help learners to construct a mental number line.


Mental Mathematics features strongly in both the Counting and the Number Concept Development sections relating to the topics ‘Number’ and ‘Patterns’. When doing mental Mathematics, the teacher


should never force learners to do mental calculations that they cannot handle – writing materials and/ or counters should always be available for those learners who may need them. Mental Mathematics should take place every day. Refer to page 128 of this Teacher’s Guide for mental Mathematics examples.


Problem solving


Problem solving allows learners to critically think and engage with problems, and develop their own mental strategies and cognitive approaches to using Mathematics. Problem solving, including those that include the basic operations, sharing and grouping, should be included in the daily Mathematics lesson. Each type of problem-solving activity needs to be presented repeatedly to the class. This enables learners to try different methods and uncover which methods work best for which types of problems. Problem-solving activities are best conducted when the teacher works in a smaller group (6–10 learners). The problem should initially be posed orally (e.g.


in a mat work session). Once learners can read, the teacher can supplement this process by giving the learners a written version, together with the oral exercise. Please remember that it is important to still pose the problem orally. The CAPS provides the types of problems suitable


for each grade and Content Area. Please refer to these for examples on problems, with which you can provide to learners throughout the year.


Counting


The average child will take several years to master them and learn to handle such numbers consistently, and be able to apply them correctly to a variety of everyday situations. Counting involves discrete variables, i.e. each individual unit or counter is counted as a separate and distinguishable entity or set (number) – for example, ‘How many counters are there in a pile?’ Counting is essential for learners in developing a proper concept of numbers, as it specifi es the size of a collection of objects (cardinal value). The ability to count is not acquired


spontaneously, but by imitating the actions of others. The learners will have to construct the connection between the repeating of arbitrary sounds and the size of collections. Learners should estimate before physically counting the objects. This estimation becomes more refi ned and sophisticated as a skill leading to a very accurate estimation of ‘How many?’. When the number is small (e.g. 4), the learner uses his/her visual perception to distinguish between three and four objects. However, once the number increases to beyond eight and ten objects, the learners can no longer rely on visual perception, but need to master the skill of accurate counting. Counting allows the learners to develop a true understanding of the conservation of number, e.g. the number is consistent regardless of how the counters are arranged spatially. Encourage learners to regularly count real objects.


Ask questions about the numbers of objects in a collection, the order of the count, the relative size and the comparison of two collections. This enables the learners to construct the important relationships which lead to the process of counting being usefully applied. Most errors made by learners in calculation are due to inaccuracy in counting, rather than in basic misunderstandings. Learning to count is not merely a matter of


reciting a string of number names, like reciting a nursery rhyme. It involves a number of additional features such as pointing at each object individually, as well as keeping a track of those objects already counted. The process of counting and assigning a specifi c value to each of the objects in the sequence is called the ordinal aspect of number (eighteenth, nineteenth, etc.). The fi nal step is for the learners to identify and know that the number upon which they end in the counting of a collection of objects is used to represent its actual size (the numerosity)


Guidelines to teaching in the Foundation Phase 9


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