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    A design study to develop young children’s understanding of multiplication and division
    (2016) Bicknell, B.; Young-Loveridge, J.; Nguyen, N.
    This design study investigated the use of multiplication and division problems to help 5-year-old children develop an early understanding of multiplication and division. One teacher and her class of 15 5-year-old children were involved in a collaborative partnership with the researchers. The design study was conducted over two 4-week periods in May–June and October–November. The focus in this article is on three key aspects of classroom teaching: instructional tasks, the use of representations, and discourse, including the mathematics register. Results from selected pre- and post-assessment tasks within a diagnostic interview showed that there were improvements in addition and subtraction as well as multiplication and division, even though the teaching had used multiplication and division problems. Students made progress on all four operational domains, with effect sizes ranging from approximately two thirds of a standard deviation to 2 standard deviations. Most of the improvement in students’ number strategies was in moving from ‘counting all’ to ‘counting on’ and ‘skip counting’. The findings challenge the idea that learning experiences in addition and subtraction should precede those in multiplication and division as suggested in some curriculum documents.
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    Learning statistics at a distance.
    (2002) Curry, L.
    There is evidence from many leading statistics educators that students often find statistics a difficult subject to learn. This is often attributed to the abstract nature of the concepts and, in particular, to the change in thinking required to understand the theory of probability and its application in statistics. For mature-aged students, these difficulties may be compounded by lack of basic mathematical skills and anxiety about learning statistics. In addition, learning at a distance may increase the problems students have in obtaining good understanding of the concepts. In this paper the current literature relating to learning statistics is discussed, and some findings are presented from a qualitative study that aimed to record the feelings, opinions and experiences of a group of mature-aged students studying statistics in a distance environment. These findings are then discussed with reference to an existing framework described by Belenky, Clinchy, Goldberger and Tarule (1986) for understanding the way women come to know. The main findings of the study were the following: (1) Their lack of mathematical skills was the main reason that students were tentative about tackling a statistics course. Older students and those with little secondary education may have been particularly affected, (2) Anxiety was not so extensive as had been reported in overseas studies but is still an issue for statistics educators, (3) Almost all students saw value in having a compulsory statistics course in their degree and were aware of the need to interpret data presented to them in their study, work or everyday life, (4) The mature-aged students demonstrated good metacognitive skills and other learning strategies. Determination to succeed and high motivation were apparent, although many students found the course unexpectedly difficult, and (5) There was a variety of opinions about the effectiveness of available resources. Support mechanisms were deemed important, as was a face-to-face component in the statistics course and some flexibility in time frames.