Home-education, also known as home-schooling, is an educational choice made by families to facilitate learning at home rather than in school. Research by Rothermel (2002) and Rudner (1999) shows that, on average, home-educated children far outperform school-educated children on standard mathematics tests. But at present, no study has yet investigated the key reasons behind this phenomenon – indeed, no research has taken an in-depth look into the ways in which parents facilitate the learning of mathematics at home and the resultant effects on their children’s mathematical development. Therefore, in this study, we will consider the nature of mathematics education through the eyes of the home-educating parent and their children. \ud Through questionnaires, this research examines the relationship between the educational and mathematical beliefs of home-educating parents. Parental views are compared with the children’s perceptions of the home learning environment, their mathematical beliefs and their mathematical understanding. Furthermore, the children’s mathematical understanding is addressed through consideration of their responses to a series of mathematical questions set within the context of Key Stages 1-3 of the National Curriculum. To obtain the research sample, home-educating families from across the United Kingdom were contacted via the Internet, and information was collected through both email and postal response. From the parental data, three categories of home-educator were highlighted: (1) Structured, (2) Semi-Formal and (3) Informal (as described by Lowe and Thomas, 2002). The children’s questionnaire responses were then analysed, using illustrative case studies to demonstrate how different home-educating approaches of their parents could result in different perceptions of mathematics and mathematical learning in the children. For example, children learning via a ‘structured’ approach were less likely to be able to measure their own level of mathematical ability than children from the other families; they also mentioned limited resources and less independence when learning mathematics. \ud When examining the children’s assessed work, selective case studies, together with detailed analysis, revealed a strong link between the home-educating approach and the problem-solving strategies of the children. Children from structured families were often competent when solving more routine, ‘calculation-type’ problems, but less able to adapt their knowledge to problems that required a ‘deeper’ understanding of the concept. Children from families where the parent themselves had a mathematical background (e.g. mathematician or mathematics teacher) typically used formal mathematical reasoning in their work. On the other hand, children learning from ‘informal’ families (where emphasis was placed on ‘child-directed’ learning) seldom used ‘standard procedural’ type approaches to solve problems, but instead displayed a range of creative strategies. \ud The findings suggested that a home-educating parent’s conception of mathematics not only influenced the way in which they attempt to teach mathematics but also their children’s mathematical beliefs and learning style. Furthermore, there was evidence to suggest that certain home-educating approaches encouraged a ‘type’ of mathematical understanding that could be applied in a range of situations, whereas other approaches, particularly where both the learning materials and interaction with others was restricted, resulted in a more limited level of mathematical understanding
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