Enhancing the mathematics achievement of Pasifika students: Performance and progress on the numeracy development project.

This paper reports on the analysis of data from approximately 30,000 Pasifika students whose teachers participated in the Numeracy Development Project (NDP) between 2002 and 2005. Most students' performance improved from the beginning of the year to the end, and performance and progress seemed to improve from 2002 to 2005. As a result, the gap between European and Pasifika students appeared to reduce fairly steadily over tune. These improvements coincided with changes in the composition of the cohort over time, most notably a reduction in the percentage of students from low-decile schools and an increase in the percentage of students from medium- and high-decile schools. Hence, it is difficult to conclude with any confidence that it is the NDP that is primarily responsible for the improvements. Although the gaps in achievement between European and Pasifika students were not completely eliminated, when these differences were put beside those found in other large-scale studies, it was evident that NDP differences were much smaller (a quarter of a standard deviation compared to a whole standard deviation). The use of an individual, orally presented assessment tool with an emphasis on explaining the strategies used to get answers, rather than a written test on which the number of correct answers is simply totalled, may help to explain the positive outcomes for NDP students

Supporting the development of number fact knowledge in five- and six-year-olds

This paper focuses on children’s number fact knowledge from a study that explored the impact of using multiplication and division contexts for developing number understanding with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. After a series of focused lessons, children’s knowledge of number facts, including single digit addition, subtraction, and doubles had improved. However, they did not always apply this knowledge to relevant problem-solving situations. The magnitude of the numbers did not necessarily determine the difficulty level for achieving automaticity of number fact knowledge

Developing young children's understanding of place-value using multiplication and quotitive division

This paper focuses on selected findings from a study that explored the use of multiplication and division with 34 five- and six-year-old children from diverse cultural and linguistic backgrounds. The focus of instructional tasks was on working with groups of ten to support the understanding of place value. Findings from relevant assessment tasks and children’s work highlighted the importance of encouraging young children to move from unitary (counting by ones) to tens-structured thinking

Using multiplication and division contexts to build place-value understanding

The paper describes a study with five-year-old children to explore how multiplication and division problems helped them to develop early place-value understanding. Two teachers taught a series of focussed lessons over two four-week periods. The children solved problems using familiar materials grouped in twos, fives and tens. By the end of the instructional period, virtually all children knew that two fives make ten; the majority could work with tens. Half of them could add tens and ones, fewer partitioned tens, and few could work with multi-unit processes. We propose a 5-level framework that describes developmental progressions in children's awareness of groups of five and ten as building blocks for place-value understanding

Using professional colleagues as interviewers in action research: Possibilities and pitfalls.

In this study of her university teaching practice in science education, an action researcher sought the collaboration of a colleague to address research design issues related to researcher bias. The colleague worked in another field of study (mathematics education) but was experienced in qualitative research, notably interviewing. Acting as an outside interviewer, the colleague used her skills related to the dynamics of interviewing and her knowledge of the content of the study to elicit pertinent information from interviewees about the effectiveness of the first author's teaching. The additional expertise enhanced the quality of the study considerably and highlighted how "two heads can work better than one". In the process both researchers gained appreciable professional knowledge from each other. The first author gained a greater understanding of the interview process while the second author acquired an appreciation of how pedagogical content knowledge (PCK) is viewed within the context of science, raising the possibility that there are some differences in the way that PCK is conceived within science versus mathematics. The collaboration also raised some unforseen issues that may have impacted on the nature of the findings. This paper discusses the positive outcomes of using a colleague as an interviewer in an action research project as well as some of the pitfalls that can also accompany such teamwork. Consideration is given to the issue of balancing the costs and benefits of this approach to data gathering

Deepening students' understanding of multiplication and division by exploring divisibility by nine

This paper explores how a focus on understanding divisibility rules can be used to help deepen students’ understanding of multiplication and division with whole numbers. It is based on research with seven Year 7–8 teachers who were observed teaching a group of students a rule for divisibility by nine. As part of the lesson, students were shown a way of proving why the divisibility rule for nine works, using materials grouped in tens and hundreds. After the lesson, students’ understanding of multiplication and division was considerably deepened

Children’s views of their teacher’s role in helping them learn mathematics

This paper reports on data from 183 nine-to eleven-year old children attending six Waikato schools. An analysis is provided of children’s responses to a question about their teacher’s role in helping them learn mathematics. Four major roles were identified, including mentor, classroom manager, transmitter of information, and arbiter of decisions. The implications for students’ mathematics learning of viewing their teacher in each of these roles are then discussed. The importance for teachers of recognising the ways they are perceived by their students is also considered

The mathematical content knowledge and attitudes of New Zealand pre-service primary teachers

This paper presents data on the mathematical content knowledge and attitudes of pre-service primary teacher education students. The assessment consisted of nine tasks, including 2-digit computations and proportional reasoning. Students rated their liking for mathematics at three time points: primary, secondary, .and when assessed. Fewer than half the students liked mathematics, currently. Those with positive attitudes tended to perform well on mathematics tasks, but some low scorers were positive and some high' scorers were negative about mathematics. Most students used algorithmic procedures to solve problems and several consistent misconceptions were identified. Performance was noticeably poor on adding common fractions and converting fractions to percentages using knowledge of common factors. The implications of these findings for Initial Teacher Education (ITE) providers are presented