How can we help teachers to implement mathematics “correctly” in preprimary school?

“Teachers are fundamental to the development of young children’s mathematical abilities” (Greenes, 1999:46). Few would argue with the rational idea presented by this quote, but the more daunting question it evokes is how are teachers to possess the skills necessary to develop young children’s mathematical abilities?

There is very little empirical evidence making a strong claim for the connection between teacher training and quality mathematical education in early childhood settings. One noteworthy research undertaking was initiated by the U.S. Department of Education in 2006, which investigated the extent that kindergarten teacher’s qualifications and instructional practices coincided with gains in

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reading and mathematics in students over the course of their kindergarten year, and how the instructional practices of kindergarten teachers related to their qualifications (Guarino et al., 2006). The researchers conclude that coursework in methods of teaching mathematics is positively associated with the use of practices that emphasise numbers and geometry, advanced numbers and operations, traditional practices and computation, student-centred instruction and mixed- achievement grouping in mathematics. These practices, in turn, are associated with higher achievement levels (Guarino et al., 2006:37).

Burchinal (2002:10) and his associates also investigated the link between informal teacher training (workshops and courses) and classroom quality, and conclude that caregivers with formal education who attend workshops regularly, are more sensitive in student-teacher interactions and provide better quality care than other caregivers, even when adjusting research results to accommodate differences related to teacher experience, adult-child ratios and type of classrooms (Burchinal et al., 2002:2). Workshops for teachers may therefore be an effective mechanism for improving child care quality.

One would assume that teachers with four year degrees will be more effective in instructing than unqualified staff. Research by McMullen and Alat into the connection between developmentally appropriate practices (DAP) in preprimary schools and the educational background of preprimary school teachers in Indiana revealed that participants with a four year degree or higher, adopted DAP more strongly as an overall philosophy in comparison with their less-educated peers (McMullen & Alat, 2002). However, another research project investigating the connection between teachers having bachelor degrees and the quality and academic outcomes of their preprimary school classes could find no correlation between the two (Early et al., 2007:558). It is also interesting to note that the Guarino et al. study (2006) provides no evidence of a direct relationship between the self-reported qualifications of teachers and student achievement.

Although making sweeping comparative claims between studies in the US and educational processes in South Africa would be irresponsible, the idea that preprimary school teacher training can be positively impacted by attending workshops/courses and not only by formal qualifications does breathe hope into the assumed problem of preprimary school teacher under-qualification in

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South Africa. Unfortunately, like most developing countries, teacher in-service training opportunities are quite rare for many South African teachers (Leu, 2004:1). The proposal of high- quality workshop training ties in with the goal of the Department of Education to improve the quality of Grade R teacher capacity by 2014 and beyond (DoE, 2012a:32).

As increases in teacher knowledge and skills, as well as changes in classroom practice are related to sustained and intensive professional development (Garet et al., 2001:936; Brendefur et al., 2013:193), quality teacher training workshops could have a direct influence on effective preprimary school mathematics instruction in our country, a notion that needs serious further investigation.

3.6 Conclusion

Preprimary school teaching is gradually being considered as paramount to the success experienced by the child in his overall academic journey (Barnett, 2008:1). Research has also strongly correlated mathematics achievement at a young age to academic accomplishment in later years (Duncan et al., 2007).

When considering South Africa’s dire state in mathematics performance in the international arena, the need for radical intervention is becoming critical (Bilbao-Osorio et al., 2013:261). One possible solution is intervention at the earliest possible level, thereby improving mathematical concept formation even before entering formal schooling, and thereby increasing the child’s chances of future mathematic success (Chard, 2008:12).

At a young age, intervention should be sensitive to the child’s need to play and to be engaged playfully in learning (Walsh et al., 2011). Allowing the child to self-discover mathematical concepts through free-flow play does pose some benefit to the child, but not all play appears to be equal when it comes to cognitive development (Sylva, 1993). There is strong evidence supporting the academic benefits of adult-guided play (Sylva, 1993:29).

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Literature suggests that teaching mathematical concepts playfully is ideally achieved through playing games (Ernest, 1986), using concrete apparatus (Cross et al., 2009:252), engaging in movement (Fedewa & Ahn, 2011) and using a learning set approach (Harlow, 1949). The time for intervention is in the preprimary school years, as this is a time of high brain plasticity (Berk, 2013:188), synaptic pruning (Nelson et al. 2008:24) and an ideal time for the scaffolding of developing executive function (Berk, 2013:282). One can even argue that based on empirical evidence concerning the mathematical competence of infants (McCrink & Wynn, 2004), preprimary school could already be regarded as too late to begin mathematical support. The preprimary school years are ripe with sensitive periods of development (Lillard & Jessen, 2003:6) and children are capable of advanced mathematical understanding at this time (Montessori, 1961:137).

The list of pre-mathematics concepts advocated by preprimary school curricula and programmes is exhaustive. This literature study focused on mathematical language, counting (including ordinal and cardinal numbers), seriation and ordering, classification and the oddity principle, measurement, number conservation, sequencing and patterning, shapes, spatial awareness and geometry, problem solving and basic arithmetic and working memory.

In an ideal world, teachers would have a fundamental understanding of all pre-mathematics concepts and pedagogically sound methods of instruction for teaching the preprimary school age. However, with the assumed under-qualifications of the majority preprimary school teachers in South Africa, training teachers through shorter workshops is a viable and necessary approach to uplifting the standard of our early mathematical education. Although arguably not as ideal as a full degree course, the possibility of workshop-based training is worth looking into as the most practical short-term solution to the tremendous gap in mathematics instruction at a preprimary school level in South Africa.

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