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Articles 1 - 19 of 19
Full-Text Articles in Education
The Importance Of Fractional Thinking As A Bridge To Algebraic Reasoning, Catherine Pearn, Max Stephens
The Importance Of Fractional Thinking As A Bridge To Algebraic Reasoning, Catherine Pearn, Max Stephens
Catherine Pearn
This presentation will discuss how Year 6 primary school students create algebraic meaning and syntax through their solutions of standard fraction problems. Sample solutions will show how students use best available symbols to move beyond arithmetic calculation and to create innovative chains of algebraic reasoning. Several efficient and successful multiplicative methods are used to achieve this goal—in contrast to less efficient methods, usually additive, which may work only with simple fractions. Teachers need to recognise the underlying algebraic meaning emerging from students solutions and help all students use more efficient strategies and build their own bridges to algebra.
Same Year, Same School, Same Curriculum: Different Mathematics Results, Catherine Pearn
Same Year, Same School, Same Curriculum: Different Mathematics Results, Catherine Pearn
Catherine Pearn
Year 4 students from a large metropolitan school in Melbourne were tested using the One Minute Tests of Basic Number Facts and a paper and pencil Number Screening Test developed by the author and colleagues. Observation of classes during the assessment procedures highlighted the vast difference in the students’ speed and accuracy when recalling basic facts and the types of strategies they used when solving whole number arithmetic tasks. When the results were analysed there were differences noted in the class results and when the results were presented to the teachers their reactions to these results varied considerably. This paper …
Creative Activities In Mathematics : Problem-Based Maths Investigations For Lower And Middle Primary : Book 1., Derek Holton, Catherine Pearn
Creative Activities In Mathematics : Problem-Based Maths Investigations For Lower And Middle Primary : Book 1., Derek Holton, Catherine Pearn
Catherine Pearn
Problem-based learning is a powerful alternative to drill-and practice or skills-based learning, especially within maths, but it can be difficult to source rich materials that engage an entire class. The Creative Activities in Mathematics series provides a wealth of investigations and open-ended active learning activities, designed to engage students with mathematics and develop their problem-solving, collaboration and mathematical skills. Book One provides 12 different class activities suitable for students in lower and middle primary school (Foundation to Year 4), along with teaching notes and staged lesson plans. Each activity is a whole-class investigation with open-ended answers that takes a particular …
Mathematical Thinking Of Preschool Children In Rural And Regional Australia : Research And Practice, Robert Hunting, Janette Bobis, Brian Doig, Judith Mousley, Lyn English, Joanne Mulligan, Marina Papic, Catherine Pearn, Bob Perry, Jill Robbins, Jenny Young-Loveridge
Mathematical Thinking Of Preschool Children In Rural And Regional Australia : Research And Practice, Robert Hunting, Janette Bobis, Brian Doig, Judith Mousley, Lyn English, Joanne Mulligan, Marina Papic, Catherine Pearn, Bob Perry, Jill Robbins, Jenny Young-Loveridge
Catherine Pearn
Results of a research project that investigated: early childhood educators' thoughts on young children's mathematical thinking and development; reviewed recent research literature on the mathematical learning and thinking of young children; and made this information accessible to early childhood educators at all levels. Sixty-four early childhood educators from regional and rural New South Wales, Queensland and Victoria were interviewed for the project. Questions focused on: children's mathematics learning; support for mathematics teaching; use of technology; attitudes to mathematics; and assessment and record keeping. [p.1]
Highlighting The Similarities And Differences Of The Mathematical Knowledge And Strategies Of Year 4 Students, Catherine Pearn
Highlighting The Similarities And Differences Of The Mathematical Knowledge And Strategies Of Year 4 Students, Catherine Pearn
Catherine Pearn
Research has shown that successful mathematics students use different types of strategies from those struggling with mathematics. Year 4 students were tested using the One Minute Tests of Basic Number Facts and a paper and pencil Number Screening Test developed by the author and colleagues. Observation of the students during the assessment procedures highlighted the vast difference in the students' speed and accuracy when recalling basic facts and the types of strategies they used when solving mathematical tasks. [Author abstract]
Working Out What Works, Kerry-Anne Hoad, John Munro, Catherine Pearn, Nola Purdie, Louise Ellis, Ken Rowe
Working Out What Works, Kerry-Anne Hoad, John Munro, Catherine Pearn, Nola Purdie, Louise Ellis, Ken Rowe
Catherine Pearn
The WOWW professional development program provides resources and training to support teachers to develop expertise in designing and implementing literacy and numeracy intervention strategies for students with or without learning difficulties. [Title page]
Whole Number Knowledge And Number Lines Help To Develop Fraction Concepts, Catherine Pearn
Whole Number Knowledge And Number Lines Help To Develop Fraction Concepts, Catherine Pearn
Catherine Pearn
Many researchers have noted that students' whole number knowledge can interfere with their efforts to learn fractions. In this paper the authors discuss a teaching experiment conducted with students in Years 5 and 6 from an eastern suburban school in Melbourne. The focus of the teaching experiment was to use number lines to highlight students' understanding of whole numbers then fractions. The study used a screening test and interview using number lines to probe students' understanding of fractions as numbers. By using whole numbers on number lines first, the interview questions clearly helped many students to connect whole number and …
Mathematics Recovery : Frameworks To Assist Students' Construction Of Arithmetical Knowledge, Catherine Pearn
Mathematics Recovery : Frameworks To Assist Students' Construction Of Arithmetical Knowledge, Catherine Pearn
Catherine Pearn
Mathematics Recovery was the outcome of a three-year research and development project at Southern Cross University, conducted in 1992-5. The project received major funding from the Australian Research Council and major contributions in the form of teacher time, from regional government and Catholic school systems. Over the 3-year period, the project involved working in 18 schools with 20 teachers and approximately 200 participating first-grade students. MR can be regarded as consisting of two distinct but interrelated components. One component concerns an elaborated body of theory and practice for working with students, that is, teaching early number knowledge. The second component …
Why You Have To Probe To Discover What Year 8 Students Really Think About Fractions, Catherine Pearn, Max Stephens
Why You Have To Probe To Discover What Year 8 Students Really Think About Fractions, Catherine Pearn, Max Stephens
Catherine Pearn
Many researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. This paper examines the persistence of whole number schemes among 14 year-old students who appear to have successfully mastered routine algorithms for working with fractions. Uncovering whole number thinking among such students is therefore difficult, and is illustrated through the use of several probing interview tasks, revealing quite different forms of whole number thinking. These forms of thinking can give correct answers also making it difficult for teachers to identify incorrect thinking about fractions. Representations of fractions using number lines can assist in …
Probing Whole Number Dominance With Fractions, Max Stephens, Catherine Pearn
Probing Whole Number Dominance With Fractions, Max Stephens, Catherine Pearn
Catherine Pearn
Children's whole number schemes can interfere with their efforts to learn fractions. To what extent do these schemes persist for secondary school students? This paper reports on the development and piloting of an interview designed to identify and probe inappropriate whole number strategies for working with fractions among secondary students. The interview showed that these strategies are still prevalent among Year 8 students. Among others who use appropriate multiplicative strategies the interview showed that some of these are still not confident in challenging instances of inappropriate whole number thinking. [Author abstract]
The Development Of Mathematical Strategies In The Early Years, Catherine Pearn
The Development Of Mathematical Strategies In The Early Years, Catherine Pearn
Catherine Pearn
Current research has shown that children develop a repertoire of mathematical strategies by progressing though five 'counting stages'. These are: perceptual - students are limited to counting those items they can perceive; figurative - students count from one when solving addition problems with screened collections; initial number sequence - students can now count on to solve addition and missing add-end problems with screened collections; implicitly nested number sequence - students are able to focus on the collection of unit items as one thing, as well as the abstract unit items; explicitly nested number sequence - students are simultaneously aware of …
Fractions : Using The Measurement Model To Develop Understanding, Catherine Pearn
Fractions : Using The Measurement Model To Develop Understanding, Catherine Pearn
Catherine Pearn
Several researchers have noted how children's whole number schemes can interfere with their efforts to learn fractions. An Australian study found that children who were successful with the solution of the rational number tasks exhibited greater whole number knowledge and more flexible solution strategies. Behr and Post (1988) indicated that children needed to be competent in the four operations of whole numbers, along with an understanding of measurement, to enable them to understand rational numbers. The workshop session described in this paper was a 'hands-on' session that focused on the use of paper folding, fraction walls and number lines to …
Assessing Rational Number Knowledge In The Middle Years Of Schooling, Catherine Pearn
Assessing Rational Number Knowledge In The Middle Years Of Schooling, Catherine Pearn
Catherine Pearn
Success in Numeracy Education (SINE) is the major numeracy approach being implemented in Victorian Catholic schools. SINE is designed to assist teachers to identify the mathematical understanding of the students they teach and to develop activities to help all students to progress at their relative level of understanding. Two components of SINE have been piloted and implemented: SINE Prep to Year 4 and SINE Years 5 and 6. This paper focuses on work with fractions being undertaken as part of the pilot program for SINE Years 5-8. There has been considerable research into the difficulties experienced by students learning fractions …
Additional Assistance : Counting, Duality And Compression Of Number And The Counting Slide, Mary Delahunty, Catherine Pearn
Additional Assistance : Counting, Duality And Compression Of Number And The Counting Slide, Mary Delahunty, Catherine Pearn
Catherine Pearn
At the beginning of 2000 the principal and staff of St Catherine's, Moorabbin, Victoria, instituted an additional assistance mathematics program within their school to support those children identified as being at risk in the early years. Children in Grade 1 and Grade 2 were the focus for withdrawal and support and were offered three sessions a week withdrawal and some whole class skills activity sessions for the year. Classroom needs was the focus for Grade 3 and children who were specifically targeted in relation to place value and the laws of mathematics received one session per week withdrawal for two …
Procedures Or Concepts : Confusion In Young Children's Development Of Mathematical Understanding, Catherine Pearn
Procedures Or Concepts : Confusion In Young Children's Development Of Mathematical Understanding, Catherine Pearn
Catherine Pearn
This article provides an overview of research investigating the mathematical understanding of young children involved in the Mathematics Intervention program.
Empowering Classroom Teachers For The 21st Century: Meeting The Challenge Of Advancing Children's Mathematical Development, Catherine Pearn
Empowering Classroom Teachers For The 21st Century: Meeting The Challenge Of Advancing Children's Mathematical Development, Catherine Pearn
Catherine Pearn
In this paper, the specific concerns for literacy and numeracy as we enter a new era are addressed through a discussion of an innovative mathematics early intervention program, which the author and classroom teachers have developed and applied. 'Mathematics Intervention' is an innovative program developed by three classroom teachers to identify, then assist, children in year 1 'at risk' of not coping with the current mathematics curriculum. The program incorporates assessment tools and learning activities based on recent research about children's early numerical learning. It develops the basic concepts of number upon which children build their understanding of mathematics. All …
The Importance Of Efficient Strategies In Developing Numeracy In The Early Years, Catherine Pearn
The Importance Of Efficient Strategies In Developing Numeracy In The Early Years, Catherine Pearn
Catherine Pearn
A mathematics intervention program has been established at Elm Primary School for children at risk of not succeeding with Grade 1 mathematics. The program is based on current research that shows that children become numerate by progressing through five counting stages. The development and results of clinical interviews used for testing are discussed along with strategies that have been used to assist children overcome common difficulties identified by the testing. The importance for classroom teachers to be able to identify each child's strategies and thus their counting stage is stressed as a starting point for numeracy teaching in early years. …
Megan: 'Seventeen Take Away Sixteen? That's Hard!', Catherine Pearn
Megan: 'Seventeen Take Away Sixteen? That's Hard!', Catherine Pearn
Catherine Pearn
This paper focuses on results from testing for the Mathematics Intervention program. To determine whether students participating in the Grade 1 Intervention program maintained the progress made during the program, students were also tested when in Grade 3 or Grade 4. The main aim of this testing was to determine whether an intervention program at Grade 1 can assist students to develop flexibility in their mathematical thinking, enabling them to develop their own strategies and to be less reliant on rules and procedures. The assessment method used for the testing at both Grade 3 and Grade 4 and at the …
Mathematics Intervention, Marguerite Merrifield, Catherine Pearn
Mathematics Intervention, Marguerite Merrifield, Catherine Pearn
Catherine Pearn
A Mathematics Intervention program has been established at Boroondara Park Primary School for children 'at risk' of not succeeding with Grade 1 mathematics. The program is based on current research that shows that children become numerate by progressing through five counting stages. The development and results of clinical interviews used for testing will be discussed along with strategies that have been used to assist children overcome common difficulties identified by the testing. The importance for classroom teachers to be able to identify each child's strategies and thus their counting stage will be stressed as a starting point for numeracy teaching …