Emergent Maths stems from the belief that the best teaching comes from a simple philosophy that no child comes to a lesson “empty”. All children have an inherent mathematical knowledge of sorts upon which it is possible to build. (For those sceptical of such a belief try getting two pre-school children to share 3 sweets between them and you will soon find out they have a well developed knowledge of division!) In this sense we are able to build on concepts and ideas that are already well embedded within a child’s own thinking. This style of teaching is diametrically opposed to the discrete teaching of skills where the information flow is one way from teacher to pupil and the child is left to “decode” the teacher’s methods rather than developing their own. In the past this approach has often led to a situation where a child may understand what they have to do but not necessarily understand what they are doing.
Spelt out in simple practical terms this may mean that whereas in the past we “taught” children decomposition when we felt they were ready and able to grasp the concept, now we would give them the problem and ask them using their own previous knowledge how they might solve any given equation. In practice this results in both a richness and variety of strategies that the children use as they seek solutions to the problems the teacher sets.
Many “emergent maths” lessons will start with an open-ended task that allows children simply to explore and play around with patterns within numbers. As children present their own thoughts and ideas the teacher has ready access to a number of teaching points but crucially they have come from the children and therefore are fully embedded in the child’s own thinking. The teacher may pick up on one of these and either consolidate a learning objective from the Numeracy strategy or extend and build on the class’ own thinking by taking the concept one stage further on.
The key features of such a lesson are that the agenda and objectives are not necessarily set by the classteacher. The teacher is providing an open-ended activity that all children can access at their own level as a starting point for the mathematics. The Maths then “emerges” from the children’s own working.
Fundamental to the whole process is the fact that the children are in control of the learning up until the point where the teacher may extend their thinking. The activity poses no threat, treats them as a fully-fledged mathematician and allows them to learn through their own learning style and thought processes. The art of quality teachingis to gauge where and when to intervene to build on the children’s own thinking. “Excessive intervention is a major error” (Karen Murris)
This is not curriculum delivery where teachers assume they are the guardians of a body of knowledge that must be imparted to the children. Instead children are given the mantle of the expert and encouraged to explore freely and without fear in an arena where they feel totally in control. The flow is not teacher to child or knowledge base to empty vessel. The key principle underlying this philosophy is that children don’t come to lessons empty but bring with them a rich source of mathematical concepts that teachers can draw out and build upon. “The wise teacher does not ask you to enter the house of his wisdom. He leads you to the threshold of your mind” (Kahil Gibran)
The flow is therefore from child to teacher where the child is demonstrating concepts in which they feel secure, challenged to extend these ideas into new areas of learning and where finally a teacher may extend that thinking by channelling and guiding the children’s thoughts through strategic intervention. However this latter stage should wherever possible continue in the same emergent vein. So that the key is not “Yes very good now let me show you a better way” but “what about if we had to? …… What would happen if? The radical nature of this teaching style is that the teacher is not there to impart a body of knowledge but to pose strategic questions and set challenges that take the children on in their own thinking. “The teacher is no longer to be seen as the sage on the stage but as the guide from the side”
This teaching style requires teacher to develop not only a new mindset but also a greater level of higher order teaching skills. Didactic teaching is relatively straightforward in the sense that as long a classroom has a modicum of control information can be readily imparted to children whilst they passively seek to imbibe the knowledge that is delivered. An emergent classroom requires teachers to make snap decisions with regard to the direction of the lesson at any given moment. For this to operate successfully they must have a secure knowledge base in any given curriculum area. They must seize opportunities for learning as they arise and develop high quality questioning skills not only to challenge the more able and self-assured children but also to draw out the opinions of the less confident child. The success of this style of teaching rests on the teacher’s ability to create a classroom culture where children feel able to take risks without fear of ridicule and where making mistakes is seen as a necessary part of the learning process.
It goes without saying that this approach naturally legislates against consistent use of textbooks and worksheets as this presupposes an agenda set by the teacher (the school here has no textbooks). The philosophy of emergent maths presupposes that the objectives for any given lesson will arise from the children and in that sense a flexible approach is required with regard to the consolidation of concepts gained. Good teaching will establish a framework that leads naturally towards a learning objective within the Numeracy Strategy. So the teacher may set up an open-ended lesson that focuses on mental strategies in multiplication yet leaving the detail of which strategy is selected to the children as their own thinking develops through the lesson.
The keyfeature for both teacher and child in an emergent lesson is that of questioning. The teacher seeks to pose questions that will elicit further and deeper thinking from the child. Whilst the child must rely not simply on open questions but on developing questions that increase understanding and take their own enquiry further.
A key element in the success of this philosophy is the ability children have to take ownership of their own learning, which in turn enhances confidence and self-esteem. No longer is Maths seen as a secret body of knowledge that is held by the teacher. Instead children can engage in rich mathematical thinking accessed at their own level confident that there are, in the first instance, no wrong answers, only ideas and concepts that can be explored and refined with their peers or by the teacher.
Similarly there is enough quality thinking, social skills and general quality learning being developed for the Maths content to be removed and for the lesson to stand as a learning process in its own right. The skills the children are acquiring such as creating hypothesis, discussing ideas with others, integrating other people’s views into their own thought processes are all generic skills they can transfer into any curriculum area, and indeed, into life in general. The thinking skills that the government is seeking to promote through the Curriculum 2000 document are able to flourish naturally in this environment. Here children are able to develop enquiring minds and are able to take their work forwards, independently from the teacher, as they develop and build on their own mathematical ideas.
In this sense the current trend towards “problem solving” is not deep enough. Children need to be taken to a level where they engage first hand with concepts through “problem creating and problem posing” where they are actively engaging with Mathematical patterns and relationships first hand and setting their own agenda for their learning. Through this they are becoming true independent learners and the curriculum is increasingly becoming “child driven” not “objective driven”. The emergent teaching style starts with where the child is at and seeks to use the objectives as scaffolding to take a child forward in their own understanding. This is diametrically opposed to the current trend of imposing teacher led objectives and rigid lesson planning upon children.
Finally good sound teaching philosophy is not bound within the confines of discrete subject areas. If it is true that children to learn more effectively through an emergent style of teaching then it should permeate all areas of the school’s curriculum. The school’s Teaching and Learning policy seeks to address this issue.
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