CONNECTIONS TO LEARNER’S WORLD / SEE MATHEMATICS AS WORTHWHILE

The promotion of connections to the learner’s world, or the importance of seeing

mathematics as worthwhile, is also prioritised in this document. This is shown on the first page, where the practice of ‘embedding’ mathematical processes in meaningful contexts is mentioned, as well as in the section regarding ‘crucial factors’ – where the use of

“meaningful problems” is advocated (p. 5). Finally, in the ‘guidelines for practice’ section, this indicator is again brought to the fore as the document calls on teachers to make mathematics “meaningful and relevant” (p.19). This is reiterated throughout the nineteen pages of Part 1, and is highlighted through stating children should:

“experience Numeracy as a purposeful, meaningful and sensible activity” (p. 2) (emphasis added); and experience it as “meaningful, interesting and worthwhile” (p. 3); the desire to encourage children to use mathematics to “make sense of their world” (p. 4) (emphasis added); and to use their understanding of learnt mathematics to “solve meaningful problems” (p.14) (emphasis added).

It can be argued from the above analysis of Part 1 of this teacher’s guide that the five productive learning dispositions are not only encouraged, but seen as fundamental in the

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effective teaching and doing of mathematics across the content areas and topics. This is in line with the intended CAPS curriculum, and many instances of teacher practice guidelines are mentioned herein – although not detailed, a general idea is conveyed to the teachers around how to create an environment, and what sort of activities to conduct, in order to foster the development of these learning dispositions.

The CAPS document analysed in 5.2.1 above gives educators a template of outcomes that need to be reached by learners, and the Numeracy Handbook analysed in 5.2.2 serves to support the CAPS, by providing support to teachers on how to implement the outcomes. The ANA: 2013 Diagnostic Report and 2014 Framework for Improvement adds a third ‘leg’ to this teaching support structure, and is similarly analysed below.

5.2.3: Annual National Assessment: 2013 - Diagnostic Report and 2014 Framework for Improvement

This document, utilising the identification of problem areas and concepts, provides specific intervention strategies for educators in order to “inform all levels of the education system of specific areas of Language and Mathematics knowledge and skills which learners...found to be challenging” (p.6).

This document is significant in the teaching and learning of Mathematics as it is a) the most recent documentation involving school performance levels, and b) it is intended to be used in conjunction with the other two documents in the long-term efforts of improving

mathematics teaching and learning in the Foundation Phase. Although Grade R is not

represented in this document (Grade R children do not participate in the ANA’s), it remains a significant document as the recommendations arising from the results are considered across grades, content areas and topics, and the Grade 1 results could have implications for Grade R. However, as discussed in chapter 3, we should guard against Grade R becoming a

‘watered down’ Grade 1, as assessment strategies have the potential to push work down through the grades in order to attain higher results later on (e.g. introducing Grade 1 work earlier in order to spend two years covering content, instead of gradual progression through concepts and contexts).

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The following table summarises the suggestions made to enhance the effective teaching and learning of mathematics, in relation to key productive disposition development, in 2013 in Grades 1-3:

Discussion:

Again, it can be noted that the section of this document dealing with suggestions of how to enhance the effective teaching and learning of mathematics, the five indicator categories of learning dispositions are encouraged, and are offered as practical ways of addressing the most serious shortcomings in Foundation Phase Mathematics learning. The fact that this sample only spans two pages, yet yields multiple examples of productive disposition

development is another indicator of the promotion within policy of these ‘habits’ in teaching and learning.

There is an even spread of frequency amongst the first three indicator categories, with two statements each, and again amongst the last two categories, with one statement each.

1: RECIPROCITY:

Two statements refer to ‘reciprocity’ in this document, one relates to affording children the opportunity to “explain (in their own words) their solutions/methods” (p. 10); whereas the

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second relates to the different forms of ‘reciprocity’. Both verbal and non-verbal methods of communicating are discussed in that “problem-solving should be an oral, practical and written activity” (p. 11).

2: PLAYFULNESS / RESOURCEFULNESS:

Again, two statements referring to this indicator category are present, specific mention is not made to the terms ‘playfulness / resourcefulness’, but rather the document encourages teachers to make use of “routine and non-routine problems” (p. 11) and to demonstrate “a variety of techniques to solve any one problem” (p. 11). This points to the importance of exposing learners to the availability of multiple techniques and methods which can be utilised when tackling mathematical concepts, a key way of encouraging ‘playfulness /

resourcefulness’.

3: RESILIENCE

The two statements which relate to this indicator category first deal with taking

“responsibility” (p. 10), and secondly with “different cognitive levels” (p. 11). As discussed earlier under section 3 of the CAPS document, this refers to teachers extending learners by exposing them to more difficult work, and not assuming that they can only handle the most basic work. And through the exposure to challenges (and through the learner’s subsequent successes), ‘resilience’ is developed.

4: CONFIDENCE / SELF-EFFICACY

The one statement related to this indicator category encourages the development of

‘confidence / self-efficacy’ amongst learners through affording them the opportunity to

explain their own solutions (p. 10). No further references or explanations around this indicator of key productive learning dispositions is present.

5: CONNECTIONS TO LEARNER’S WORLD / SEE MATHEMATICS AS WORTHWHILE

Although the one statement present in this document which refers to this indicator category speaks specifically to “Geometry and Data-Handling” and not all aspects of mathematical teaching and learning, it is nevertheless important in its encouragement of teachers to use

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“readily available resources” (p. 10), with the presumed objective to apply abstract mathematical concepts to the real world.