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The world around us is not compartmentalised or fragmented, nor are experiences and activities entirely independent of each other. This mixture and blend of experiences are all inter-related and make up the tapestry of life. On a similar note, the taught curriculum should reflect this integration to more effectively engage young learners in an educational process which consists of largely complimentary areas of learning.
Integrated learning is far from a new concept but until recently mathematics has struggled to integrate successfully with other subjects.
Whilst there is no singular educational model that can be adhered to, the premise remains; that of taking several subjects and integrating them with one another with the aim of learning becoming enhanced exponentially across all involved subject areas. Mathematics has such a broad scope of application it is entirely appropriate that it should be integrated prolifically across a range of subject areas.
Integration works more effectively when there is a clear point of focus for curricular areas to target. This synergy of subject areas with a specific goal can then complement each other in a much more valuable manner.
Advantages of integration include:
Can benefit pupils in understanding and appreciating links between subject disciplines, and a better understanding of how this relates to life.
It can alleviate planning pressure on teachers.
Curricular ideas are connected.
Boundaries sometimes related to teaching a specific discipline can be eschewed.
It can provide a valuable tool for reinforcement.
More meaning and relevance can be taken from the learning experience.
Some disadvantages include:
Additional planning of programs is required in order for different subjects to be co-ordinated and to run concurrently. This also means that a close regard to context and time is essential if the integration program is to be effective. If this is not considered then the effect can actually become detrimental.
The purity of some subject areas (including the actual scope of the discipline) can become confused or lost if attention is not paid.
More expertise is required on behalf of the teachers in order to maximise learning by effective integration.
The use of questioning in a constructivist environment.
'In order to protect pupils' self-esteem and develop self-confidence, it is important that questioning takes place in an encouraging and supportive atmosphere' (Kyriacou, 1986).
Constructivism is a theory about how people learn based on scientific study and observation. It states that through a process of experience and reflection we develop (or construct) our own understanding of the world. New experiences are reconciled with previous ideas and understanding, sometimes altering previous beliefs and sometimes becoming disregarded as irrelevant compared to these previous beliefs.
Questioning is important when adopting a constructivist approach to teaching. Through pertinent questioning educators can assist students in the construction of their knowledge rather than reproducing lists of facts for memorisation.
Questioning pupils is an important tool in assisting inquiry based learning activities and problem solving.
Constructivist teaching should inspire the students' natural curiosity and desire to learn how things work. Learners should be engaged by applying their existing theories and experience and ultimately forming valid conclusions based on their findings.
(Brooks & Brooks, 1993)
The use of play in a rich environment.
The physical environment holds great power for teaching potential. The environment can affect mathematical learning and teachers should take great care to consider how their classroom space can be arranged in order to promote children's mathematical learning experience.
(Carol & Galper, 2001)
The mathematically rich learning environment can be further enhanced with play, providing puils the opportunity to view and engage with mathematics whilst seeing adults apply these techniques in real-world scenarios.
Providing a mathematically rich learning space can improve the pupils mathematical skills by rote.
'In adult-guided classrooms, teachers provide scaffolding by introducingâ€¦ materials in the play centres and discussing with children how to use materialsâ€¦ The students in those classrooms, in turn used more printed materials with attention to their printed aspects and produced more printed materials than students in classrooms with no specific teacher guidance' (Gunn, Simmons & Kameenui, 1995).
The on-going nature of assessment and planning for teaching.
The process of identification, interpretation and addressing the learning of students is the essence of assessment. The purpose of assessment is principally to provide information on the progress and on-going achievement of learners in order to establish a direction for future educational programming.
It is crucial to report this assessment in order to inform and support further teaching via the provision of important feedback to the pupils themselves, their other teachers and their parents.
Assessment in the classroom is a key element of developing learning strategies.
In a competitive world which is quickly changing it is important to develop citizens who are competent and capable of independent and flexible thought. It is also important that these citizens can think for themselves.
Certain assessment strategies are more suited to particular syllabus outcomes than others and it is important for teachers to develop relevant strategies which are appropriate to the subject or method which they are employing.
(Black & Wiliam,Â 1998)
Mathematical content knowledge.
It is important for teachers to develop a sound understanding of their subject. When teaching mathematics it is crucial for teachers to not only develop an understanding of important mathematic concepts but they should also be able to explicitly appreciate the connections on a fundamental level between what they are teaching and what they are learning.
Teachers of maths should have a deep understanding of procedures, concepts and reasoning skills that are appropriate and central to the nature of the elements they are teaching.
It is essential that maths teachers know how to connect and represent mathematical ideas whilst effectively communicating them in an appropriate manner.
Students should have confidence in the educator's understanding of the subject and conversely learn to appreciate the diversity, power and utility of the subject.
The teacher should be able to convey these ideas effectively and understand student thinking in terms of questioning, strategy, misconceptions, etc. whilst addressing these issues in such a manner that it supports and promotes pupil learning.
(Kilpatrick, et al., 2001)
The use of relevant curriculum documents.
The use of hands-on resources and manipulative's.
Developmental domains, dispositions and learning styles.
'It is very important to realise that within any mathematics set there will still be marked differences in the mathematical attainment of pupils. It is essential that the teaching takes account of these differences and is responsive to the needs of individual pupils. It should not be assumed that the same teaching approach will be necessarily suited to all in the group' (Cockcroft, 1982) _REFERENCE