There are some conference papers and journal articles which look at the role of real life objects (try keyword searches such as: three dimensional aids, manipulative materials, educational materials).
I have listed some examples of references below along with an E-librarian question about the role of relevance or learning in context in mathematics. Try your own keyword searches of some of the information sources suggested.
Also included, some clips from Teachers TV and an article from the BSRLM about context in mathematics.
I hope this helps.
The role of context in linear equation questions: utility or futility?
KS2 Maths - Geometry
Hungary - Primary Maths
British Education Index
NOTE: For information about accessing full text articles please read this TTRB article: Access to full text journal articles
Mental models in manual weight comparisons between two objects of different size. Themes in Education, December 2005, vol. 6, no. 2, p. 151-167, ISSN: 1108-5908. Hakkarainen-Olavi.
"Participants in the study were 272 pupils from the fifth grade, 288 pupils from the seventh grade and 276 pupils from the ninth grade. All children attended comprehensive school classes in the greater Helsinki area."
Tuckshop subtraction. Mathematics Teaching, July 2007, no. 203, p. 3-7, ISSN: 0025-5785. Duke-Roger, Graham-Alan-T, Johnston-Wilder-Sue.
"The paper focuses on a three-phase teaching programme referred to as EIS which represents three ways of understanding mathematical ideas: enactive (physically handling objects which embody concepts); iconic (based on pictures of the concept); and symbolic (where the concept is represented through conventional mathematical notation)."
Should you show me the money? Concrete objects both hurt and help performance on mathematics problems. Learning and Instruction, April 2009, vol. 19, no. 2, p. 171-184, ISSN: 0959-4752. McNeil-Nicole-M, Uttal-David-H, Jarvin-Linda, Sternberg-Robert-J.
"The article describes an experiment in which pupils were given word problems to solve, using perceptually rich notes and coins or bland notes and coins (experimental conditions) or no notes an coins (control condition)."
Promoting Repeating Patterns with Young Children--More than Just Alternating Colours!. Australian Primary Mathematics Classroom, 2007, vol. 12, no. 3, p. 8-13, pp. 6, 5 refs., ISSN: 1326-0286. Papic-Marina.
"Patterning is an essential skill in early mathematics learning, particularly in the development of spatial awareness, sequencing and ordering, comparison, and classification. This includes the ability to identify and describe attributes of objects and similarities and differences between them. Patterning is also integral to the development of counting and arithmetic structure, base ten and multiplicative concepts, units of measure, proportional reasoning, and data exploration. The importance of early algebra and patterning is reflected in current curriculum frameworks in pre-school and primary years both in Australia and internationally. This article describes some teaching/learning experiences from a recent intervention study on patterning with 4-6 year olds. It was designed to encourage children to "see" the structure of patterns and to symbolise, represent, and transfer patterns from one mode to another. Children were exposed to complex repetitions and to patterns as rotations and translations. They developed their skills in seeing similarity and difference between attributes of objects. Through these experiences children were enabled to observe more than one attribute of pattern at one time: colour, number, shape, and orientation. The results of the study provide some direction for the teaching and learning of patterns and algebra in the transition to and in the first years of schooling. (Contains 3 tables and 2 figures.)"
Developing an understanding of the concept of area. Australian Primary Mathematics Classroom, 2007, vol. 12, no. 4, p. 4-9, ISSN: 1326-0286. Muir-T.
"When asked to calculate the area of a particular shape, one student responded by asking, 'Is that the outside or the inside?' while another student replied, 'I think it's the one where you put a little 2 next to it'. Both of these responses indicate a lack of conceptual understanding of area and reinforce the research findings that students commonly confuse area and perimeter and that many primary and secondary school students have an inadequate understanding of area and area measurement. This article describes a learning sequence undertaken by the author with a Grade 3/4 class which focused on developing an understanding of the concept of area and was consistent with Tasmania's curriculum documents which advocate that the core content for Standard Three should introduce students to area by covering shapes and objects. The recommended structure for teaching measurement topics up to, but not including formula or application, was incorporated into the learning sequence."
Using spatial skills to interpret maps : problem solving in realistic contexts. Australian Primary Mathematics Classroom, 2007, vol. 12, no. 4, p. 14-19, ISSN: 1326-0286. Lowrie-T, Logan-T.
"One way of providing upper primary school students with the opportunity to engage in realistic activities is to ensure that mathematical concepts and ideas can be taught and expressed in contexts closer to students' own experiences. In this investigation the authors consider the influence that a genuine artefact has on students' spatial reasoning. The authors have found that students are more likely to utilise a range of spatial skills to complete mathematics tasks when they are deeply engaged in an activity. The authors use artefacts that the students can readily relate to in everyday situations in order to enhance the authenticity of the classroom activity. Activities such as these allow students to embed themselves in the situation and thus help them make sense of mathematical ideas through spatial reasoning. Such skills and processes include building and manipulating mental representations of objects, perceiving an object from different perspectives and interpreting and describing physical environments. Spatial reasoning is especially useful in creating and reading maps, planning routes, designing floor plans, and creating art. The authors argue that the activity described promoted students' spatial sense-making by creating opportunities to use a range of problem-solving tools to complete an activity that required the interpretation of information in various (visually rich) representations; and, visualise manipulate and construct spatial arrangements within scenarios that encourage the use of out-of-school knowledge and experiences. By representing their solution in another way the students were able to consider information and solutions from a different perspective; provide concrete representations that made it easier to see and interpret their solutions; and, reflect upon their solutions and make judgments about their efficiency and practicality."
Making maths marvellous with manchester and manipulatives. In 'ConnectEd maths : MAV's 45th annual conference, Thursday 4th and Friday 5th December 2008, La Trobe University, Bundoora' edited by J Vincent, R Pierce and J Dowsey, pages 402-411. Brunswick Vic : Mathematical Association of Victoria, 2008, ISBN: 978-1-8769-4999-0. West-Gabrielle.
"In the mathematics classroom, everyday colourful objects and items that are found around the house or classroom can become useful tools for engaging students in a variety of learning experiences. Well thought-out, 'good' questions along with 'open' investigations should be an integral part of these experiences. Then mathematical concepts - number, algebra, measurement, space, chance and data - can be interwoven and connected through sensory and physical activities to support the building of students' thinking and understandings."