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Pamela Perger Margaret Thomson
Faculty of Education
The University of Auckland
A cross-curricular approach to teaching can provide children with realistic and meaningful contexts for learning. The value of this approach has been a point of discussion for over 50 years. Today, with the ever-increasing pressures on what teachers are expected to include in their classroom programmes, this approach is being viewed with fresh eyes. Integrating curriculum areas is not easy if the integrity of the individual curriculum areas is to be maintained. Mathematics has always been the poor cousin in integrated learning, either left out or catered for in only a superficial way. However the use of realistic contexts in other curriculum areas can be an opportunity for students to develop or practice mathematical understandings. The ability to recognise and make use of the natural connections that exist between different learning areas is a skill teachers require to make an integrated approach successful. When this is achieved it is a great gift to the experienced teacher who is confident in both teaching approaches and individual subject content knowledge. This paper explores ways in which mathematics can be integrated into a wider curriculum in New Zealand schools.
The following statement from the New Zealand Curriculum document reflects recognition of the crucial role mathematics plays in helping young New Zealanders understand the world and themselves.
By studying mathematics and statistics students develop the ability to think creatively, critically, strategically and logically. They learn to structure and to organise, to carry out procedures flexibly and accurately, to process and communicate information and to enjoy intellectual challenge (Ministry of Education, 2007).
The recent curriculum revision has resulted in a single document that for the first time includes Achievement Objectives across all curriculum areas. For the teachers of young children this reinforces a long-standing practice of integrating subject areas. Children in New Zealand begin school on their fifth birthday. Many of these children have early childhood experiences based on holistic styles of learning. This means that the first class in the compulsory sector can include children who expect their learning to make sense and relate strongly to their day-to-day lives.
Mandated curriculum areas for New Zealand Primary Schools (5 12 year olds) are Social Sciences, Health and Physical Education, The Arts, Technology, Science, Mathematics and English. New Zealand teacher qualifications require teachers to have a working knowledge that enables them to teach all curriculum areas at any level of the primary school. Pre-service programmes at the Faculty of Education at The University of Auckland include studies in each of the curriculum areas. An aim of the pre-service mathematics courses is to develop in future teachers the ability to recognise the opportunities for teaching and using mathematics in other curriculum areas, thus enabling them to present learning in a way that is meaningful to children.
The practice of teaching across curriculum learning areas has been a topic of discussion within the education field on and off for the last half century. Prior to 1990, curriculum integration was a widely accepted approach to teaching and learning both in New Zealand and the United Kingdom, but this changed in 1991 with the publication in the United Kingdom of a report on primary education by Alexander, Woodhead and Rose (since referred to as the three wise men) (Frankel, 2007). which severely criticised such integration. This criticism, combined with political pressures of the eighties and nineties in both New Zealand and the United Kingdom, resulted in a reversion to a single subject curriculum approach, with government initiatives that saw the Literacy and Numeracy Hours implemented in United Kingdom schools and the push for a focus on Numeracy and Literacy in New Zealand schools.
However, as the curriculum has been expanded and adjusted to cover new understandings about childrens learning and to address the changing world, teachers have found it ever more difficult to fit everything into the school day.
Lake (2001) noted that many teachers admitted to experiencing the feeling that there is just isnt enough time to get it all in or the school day just isnt long enough for all that Im supposed to do; it seems that every year there are more things added to the curriculum (p. 5). This pressure has led to a renewal of interest in integration, with teachers seeing it as an efficient way to handle the many demands placed upon their teaching time.
Sometimes, however, such an integrated approach excludes mathematics. Practitioners give several reasons for non-inclusion, the most common of which is the frequently stated belief that mathematics is an organised sequential body of knowledge that does not lend itself to being easily integrated with other curriculum areas and therefore must be taught in isolation. Some teachers lack confidence in their own mathematical knowledge, and this may prevent them from seeing opportunities to include mathematics in wider school learning.
An initial step for teachers wishing to incorporating mathematics into the wider school day is to include mathematics in daily routines. Routines such as calling the roll can provide an opportunity to discuss if more girls or boys are present, how many more boys are needed to equal the girls. If there are enough children to make teams of four for the physical education activity planned for later in the day. Children can also be involved in working out how much equipment is required for sports or art activities, ordering, collecting and giving out the equipment. Opportunities for older children to organise lunch sports tournaments and analyse sports results can also be found in the everyday life of the school. In New Zealand schools children can buy their lunch. They choose a selection of items from a set menu. Once children get into the upper primary children are chosen as class monitors who have the responsibility of taking the lunch orders, collecting and balancing the money before sending the lunch orders to the lunchroom. All of these activities happen each day within a school and provide opportunities for children to practice mathematical skills and reinforce mathematical knowledge.
A further step towards the integration of mathematics into the wider school curriculum occurs when teachers become aware of the value of placing mathematics into contexts that are interesting and relevant to children.
In order to make mathematics more meaningful and accessible for all learners, mathematics curricula frequently advocates the use of contexts. In this sense context refers to real or imaginary setting for a mathematical problem, which illustrates the way the mathematics is used. (Anthony & Walshaw, 2007, p114)
New Zealand teachers are well supported in this process. Every page of the curriculum setting out requirements in mathematics begins with the statement In a range of meaningful contexts children will . .( Ministry of Education, 2007, Authors italics) . The New Zealand Numeracy Project, which provides comprehensive teaching/learning material for number and algebra, insists that questions involving the mathematical operations of addition, subtraction, multiplication, division or proportion and ratio are presented to children in the form of word problems linked to a context they can relate to rather than a straight algorithmic form. Using the names of children in the class, questions such as Ray has $34, and gets $25 for his birthday. How much money does Ray now have? provides a context children can more readily relate to than when asked to solve 34 + 25.
The New Zealand Ministry of Education further promotes the use of realistic contexts by providing the Figure It Out series free to all schools. This series of childrens activity books (supported by extensive teacher notes) caters for six to twelve-year-olds across all of the mathematics curriculum strands. All the activities are based on contexts familiar to New Zealand children and one set of books in the series provides children with mathematical tasks based around one specific context. Figure 1 illustrates the range of mathematics covered by one such book: Under the Sea (Ministry of Education, 1997) written at Level 2 of the curriculum.
Figure 1. Overview of content of Under the Sea
Activity titleMathematical focusFlipping fishPatternsMeasure upMeasurementSea SymmetrySymmetryShapely sea creaturesMatching and making shapesTreasure troveUsing co-ordinatesUnder the wavesSolving story problemsFishing fancyWriting and solving story problemsStarry-eyedAdditionA Whale of a TimeTessellationFish fairRecording dataMega mazeMeasurement, Compass pointsFish formsPatternsScaling up Sequential patternsDeep sea divingMeasurementHorse racingSubtractionSea sheltersAddition, subtraction, multiplication, divisionTime it RightUnderstanding speedHot or Cold?TemperatureSea sortingClassifying and graphingFloating IdeasMeasuring mass and volume
This overview enables teachers to cover a wide range of mathematical ideas within a single topic, and relate the activities to work in science, social studies and the language arts.
As the experience and confidence of teachers develops, so does their ability to recognise opportunities to enrich childrens learning through integrating mathematics into the wider curriculum. The presentation of the 2007 New Zealand curriculum document facilitates, and appears to encourage, this integration. Although the overviews of all eight learning areas (Social Sciences, Health and Physical Education, The Arts, Technology, Science, Mathematics and English) are dealt with distinctly, all the achievement objectives (AOs) are presented in a pull-out form arranged in levels, so that teachers are able to see the entire set of AOs relating to a particular curriculum level. Further, one of the stated principles of the curriculum is coherence: the curriculum offers all students a broad education that makes links within and across learning areas (Ministry of Education, 2007, p 9) and all learning should make use of the natural connections that exist between learning areas (Ministry of Education, 2007, p16).
In order to integrate mathematics into the wider curriculum without losing the integrity of the mathematics, it would seem sensible to begin with the mathematical achievement objectives and then identify the naturally occurring connections to other learning areas. This approach moves beyond the use of a context to learn mathematics, instead embedding the mathematical learning into a wider field of understanding. Again, the Figure It Out series provides some excellent assistance to teachers. A recently-produced title in the series is Disasters Strike! written for children working at or beyond curriculum level 4. The teachers notes accompanying this activity book include specific references to achievement objectives in other curriculum areas, thereby greatly simplifying the task of planning an integrated unit of work. For example, an activity about earthquakes which requires students to sketch and interpret graphs on whole number grids which represent simple everyday situations (Algebra, level 4) also supplies cross-curricular links to specific achievement objectives in Social Studies, Health and Physical Education, and Science.
While number and algebra appear to be the most obvious areas of integration, the other strands within the mathematics curriculum provide many opportunities for cross-cultural work. Some excellent resources approach mathematical concepts through stories and games. Children learning geometry can be introduced to its applications through such stories as Whats Your Angle, Pythagoras by Julie Ellis, while the story Jim and the Beanstalk by Raymond Briggs discusses measurement concepts in a humorous version of a traditional story.
Teachers who are committed to the integrated approach may feel confident enough to take a final step into planning fully integrated units of work where mathematics is an important part of a study, but not the major focus. Figure 2 illustrates an example based on a New Zealand childrens book.
Figure 2. Cross-curricular Achievement Objectives
Fifty-five Feathers
(Brown & Taylor, 2004)
A story about how Pukekos concern for his friend Gecko who is always cold in winter sees him visit the Wise Old Tree for advice. The advice he is given is to collect fifty-five feathers to make him a cloak. The story follows Pukeko as he collects the feathers from the various New Zealand native birds.Level 2Curriculum Achievement ObjectivePossible Context / ActivityMathematics and Statistics
Use simple additive strategies with whole numbers Using addition / subtraction strategies with numbers up to 100Science
Life Processes - Recognising that all living things have certain requirements
Ecology recognise that living things are suited ti their particular habitat.
Evolution explain how we know that some things from the past are now extinct.Conservation - Study of New Zealand native wild life (birds and plants) and the need to preserve it.TechnologyPlanning for Practice outline a general plan to support the development of an outcome.
Brief Development Describe the outcome they are developing and identify the attributes it should have
Outcome Development and Evaluation select and develop an outcome in keeping with the identified attributes.Design and make a cloak for Gecko
Health and Physical EducationSafety Management
Identify risk and use safe practices in a range of contexts.
People and Environment
Contribute to and use simple guidelines and practices that promote physically and socially healthy classroom, schools and environments,Keeping ourselves health in Winter English
Speaking Writing and Presenting Ideas - Select, form and express ideas on a range of topics.
Language Features use language features appropriately, showing some understanding of their effects.Design and present a poster or pamphlet on the topic - conservation of New Zealand wild life / birds
Practitioners are quick to point out that integration is not an easy option; not all concepts can or should be integrated and careful consideration needs to be given to retaining the integrity of individual subjects within an integrated approach. As Burgess (2004) notes, integrated units can be difficult and time consuming to plan and demand high levels of skill in terms of curriculum subject knowledge and teaching methods.
However, teachers who embrace such an integrated approach to teaching and learning mathematics are adamant that childrens learning is enriched.
Across all curricula, opportunities to explore authentic applications that arise out of real-life contexts can have a significant and sustained impact on student knowledge, attitude, self-esteem, independence, and confidence (Alton-Lee, 2003)
References
Alton-Lee, Quality teaching for diverse students in schooling: Best Evidence Synthesis. Wellington: Ministry of Education.
Anthony, G., & Walshaw, M. (2007). Effective pedagogy in mathematics / paanugarau: Best evidence synthesis. Wellington: Ministry of Education.
Briggs, R. (1970). Jim and the beanstalk. London: Penguin Books.
Brown, B. & Taylor, H. (2005). Fifty-five feathers. New Zealand: Reed.
Burgess, H. (2004). The primary strategy: A chance for a whole curriculum. Education 3-13, 32:2, 10-1.7
Ellis, J. (2004). Whats your angle: Pythagoras? Watertown, MA: Charlesbridge.
Frankel, H. (2007). Another way of working. Times Educational Supplement 12 October.
Hunter, R., & Scheirer, E. (1988). The organic curriculum; Organizing for learning 7-12. Sussex, UK: Falmer Press.
Lake, K. (2001). Integrated curriculum. School Improvement Research Series. Retrieved 4 April 2008 from HYPERLINK "http://www.nwrel.org/scpd/sirs/8/c016.html" www.nwrel.org/scpd/sirs/8/c016.html
Ministry of Education. (2007). The New Zealand curriculum for English medium teaching and learning in years 1 13. Wellington: Learning Media.
Ministry of Education (2003). Figure it out: Disasters strike. Wellington: Learning Media.
Ministry of Education (1999). Figure it out: Under the sea. Wellington: Learning Media.
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