Learning Theories

A Critical Evaluation of Learning Theories in the delivery of 2nd Level Maths

In this paper I will examine the learning theories, that have a direct impact on my teaching practice and theories that could be incorporated so as to have a beneficial effect on the further development of my teaching practice. Why use theories to examine the effectiveness of teaching practice?, to quote “Webb”, 1996, Theory matters because without it education is just hit and miss, there will be no working foundation or basis to the discipline, even if this basis and foundation are constantly being argued over and in a state of flux.

The theories I will examine are Behaviourism, and Social Constructivism, I will explain the reasons for my choice alongside a discussion of the key principles of these theories as they relate to my own practice.

I am a maths teacher involved in offering 2^nd chance education to a variety of early school leavers both girls and boys between the ages of fifteen and twenty. For a variety of reasons, the students have not enjoyed successful outcomes from the mainstream Secondary School system. Small class size, early identification of learning difficulties, a fair but disciplined structure, has helped to ensure successful outcomes for these learners. The reduction of absenteeism, encouraging good timekeeping and behaviour, a positive work ethic, creating a warm and friendly atmosphere which is encouraging to learning and reducing to a minimum anti-social behaviour (bullying etc) are all goals that the effective use of aspects of behaviourism can help in achieving. It is with this in mind that I am exploring some of the strategies that behaviourism provides. 

What is Behaviourism

 Classical Behaviourism concentrated on external responses, to explore the crucial bond between stimulus and response, and it looked at observable behaviour. This emphasis on observable behaviour is understandable for the era; the classical behaviourists were working in, i.e. 1880’s to the 1940’s, as the workings of most mental processes were considered to be inaccessible at the time. 

 Behaviourists in the early period developed a series of experiments with animals, with which they attempted to prove, that you could “condition”, or train most animals including human beings by applying conditioning in the correct sequence and with reinforcing stimuli of the necessary strength or rigour and with enough repetition, you could bring about permanent changes in behaviour.  The long term results of experimental behaviourism resulted in a degree of consensus amongst some theoretical behaviourists as regards to its key principles. The principle of Reinforcement, employing positive or negative feedback in which the subject forms a strong association between the stimulus and the desired behaviour, is a key step, desired behaviours are rewarded causing their frequency to increase whilst undesired behaviours are punished causing their frequency to decrease.(Skinner 1938).

Neo-Behaviourists, such as Hull, Skinner and Benjamin Bloom, recognised the importance of learner’s internal characteristics, such as personality, motivation and habit. They therefore appear to be incorporating aspects of the Cognitive approach into the Behaviourist school. This could be contrasted to the classical behaviourist school, which focused only on the external manipulation of an organism (Pavlov). 

How can I effectively use Behaviourism in my Teaching Practice

My school has recently introduced a reward system, learners are  awarded  positive points, for good classroom work, positive involvement in classroom debates and discussions, good behaviour, attendance and timekeeping , a build up in positive points will result in time off, extra project work (fishing trips, bowling, cinema trips etc) .

Negative reinforcement is also used, for bad behaviour, poor attendance and timekeeping, negative points are given, resulting in a loss of privileges. A build up in negative points will result in suspension, and if not resolved, eventual termination. Some of the key principles of behaviourism are at work here, the principle of reinforcement, using both positive and negative feedback so as to from a strong association between the stimulus (good points- rewards) and the desired behaviour. Contiguity is used in that the rewarding of points is immediate, making the feedback stronger. Continuous good behaviour will result in a build up of positive points, resulting in more substantial rewards, encouraging repetition.

Behaviourism has influenced ideas about learner behaviour, modern curriculum planning and the teacher’s role in the classroom. With regard to planning and delivery of learning, I purposely employ many of these ideas, such as S.L.O’s (specific learning outcomes) which ties into tangible learning outcomes.

Benjamin Bloom’s “Taxonomy of Learning”, is a learning model that links external and internal behaviours by establishing “3 Domains”, or “Spheres of Learning”, the domains are the Cognitive, the Affective, and the Psychomotor. The cognitive domain (Bloom, 1956) involves knowledge and the development of intellectual skills. This includes the recall or recognition of specific facts, procedural patterns, and concepts that serve in the development of intellectual abilities and skills. The affective domain (Krathwohl, Bloom, Masia, 1973) includes the manner in which we deal with things emotionally, such as feelings, values, appreciation, enthusiasms, motivations, and attitudes. Eg, how we respond to criticism. The psychomotor domain (Simpson, 1972) includes physical movement, coordination, and use of the motor-skill areas. Development of these skills requires practice and is measured in terms of speed, precision, distance, procedures, or techniques in execution. 

  I have used methods to combine these three spheres of learning in my daily practice, for eg, in teaching Maths in Electronics, I initially teach Ohms law and Faradays Law (specific facts) which is associated with the cognitive domain, this is then related to the Psychomotor domain by concentrating on procedural learning, precision and technique is required in designing electronic circuits and using these as the building blocks to create real working electronic circuits. The affective domain is addressed by the sense of achievement and enthusiasm installed in the learners by their success at creating working circuits.

When introducing new subject matter, I make use of “Gagne’s”, nine key Instructional events, by gaining the learners attention, I attempt to hold their interest by stating the session’s objectives, I will emphasise the SLO’s for this material. I will remind the learners how this material ties into what has gone before and its place and importance to the overall aims and goals of the programme, helping to make the structure of the learning more transparent.  I will explain the new material by employing a variety of teaching aids, using a whiteboard, a variety of computer programs via an overhead projector with audio, which helps in the explanation of subject matter in co-ordinate geometry and geometry.

Some of the activities I use to help learning to take place are the use of handouts with questions; this provides feedback to help me evaluate learner progress. The use of feedback is also critical in the planning of future learning, have the learning objective being achieved, or will these topics have to be revisited if only surface learning has taken place.  I see some of the more positive aspects of behaviourism at work here, in encouraging good behaviour in adolescent and less mature learners, research has shown that Adults need less behavioural control than children, a form of conditioning is at work, here but it is has a overall benign goal.  As the Learners mature and become more responsible and the subject matter they are dealing with grows in complexity, where there is a need for the development of problem solving skills, originality of thought and acquisition of concepts, the use of behaviourism to achieve these goals becomes difficult, therefore a different pedagogical theory needs to be examined.

What is Social-Constructivism?

Social constructivism is a learning theory that applies the general theory of constructionism into social settings, (school groups, work groups etc) such as it allows groups to construct knowledge for one another, it helps create a structure for collaborative working by creating a small culture of shared artefacts with shared meanings, it emphasises the importance of culture in learning.  When a learner is immersed within a culture of this sort, he or she is learning all the time about how to be a part of that culture on many levels. Its origins are largely attributed to Lev Vygotsky. 

 It is these attributes of Social constructivism that have also made it the focus of attention as a suitable theory for successful online learning.

 In infants, communication between the mother and infant is a pre-requisite to the Childs acquisition of concepts and language. (Vygotsky 1934). It is argued that communication and dialogue are key aspects in facilitating meaning, which is critical in the process of deep-learning. Vygotsky again explored a field related to this which he called the Z.P.D or Zone of Proximal Development, it is with the help of this concept that he emphasised that only a certain limited amount can be learned by the student in a solitary manner. 

Educational Implications of Social-Constructivism

Am I already using Social-Constructivism in my teaching practice? And can its role be expanded?

Constructionism sees learners as constructors of meaning where learning is seen as an active process in which learners are attempting to construct new meaning; it examines the cognitive processes by looking at what learners do with information to develop this raw information into knowledge.  In teaching Maths after a grounding in theory, I employ the use of projects, where students work collaboratively to create their own statistical surveys based on a topic that they want to research, working with their own peer groups, Learners may use class room discussions, interviews or questionnaires to gather the data on which there data research assignment will be based, the information gathered will then be  sorted and collated so that it can be  accurately used to produce statistical graphs and charts that will  show their research findings and may have some  real-life applications.

Project work also has the advantage that it allows peer-tutoring to take place, and peer-tutoring if used effectively (and not dominated by a member or members of a group) can increase self-esteem, allow confidence building to take place and help develop social-skills. It allows for the exploration of topics from the students perspective this can help in clarifying understanding and for more intrinsic deep learning to take place.

If the initial barriers of shyness and lack of self-confidence can be overcome, peer assessment can become a valuable tool in student learning, as it allows students to develop the criteria for making judgements and evaluating their own performance.

 Many constructionist ideas originated in the ideas of Jean Piaget who theorized that as children learned they actively made theories or mental models about how the world around them worked. These mental models grow and adapt as new information is added to them. If the new information is fundamentally different than what has come before, it may not be incorporated in an existing model and an entirely new mental model is created to deal with the new circumstance, these profound changes in how people think are called paradigm shifts, major events like emigration or war may make an individual completely rethink pre-conceived attitudes and ideas. 

The implications for the successful implementation of this theory in practice depend greatly on the cultural context, in which it is to be used in. For Learners from a disadvantaged socio-economic background, for eg some of the Youthreach students I teach, some aspects of this theory could be employed but with very strict monitoring, as a group many students maybe be hostile to new positions and values, they are not familiar with, also some students would have a prior history of being critical and mistrustful of some subjects on the curriculum.

The learner’s ability to make sense of information and to turn it into useful knowledge is greatly enhanced in Social-Constructivism. The use of social-constructivism as a learning theory, helps to reflect on the importance of culture in learning, this is linked to the significance of, “important others”, as learning mediators. I also make use of a mentoring system in my daily work, each teacher is mentor to a group of seven students, the mentoring programs are designed to offer support to students on program completion, personal issues, confidence building and transitioning to further education or the workforce.

To use my own context, I would see aspects to this theory, having a positive impact, with older more mature students, who can be guided to achieve their goals, through a mix of independent learning, collaborative learning and group project work.

To refer back to Vygotsky, and the Z.P.D. he emphasised that only a certain limited amount can be learned by the student in a solitary manner.  While much more can be learned and internalised more effectively by support from the teacher and also critically by the students peers. This can be in the form of collaborative learning; this can take many forms, from being laboratory or classroom based, to external work. Within the framework of this theory, the teacher helps to propel the student forward by offering suitable material, encouragement and prompts; this is described as “scaffolding”, or critical supports to help the student to the next higher level. It is also important that teacher supports are only temporary, so as to encourage independent learning. 

Collaborative learning is an integral part of the Social Constructivism paradigm, focusing on the concept that, thinking does not exist independently of the world, or of other people.

Collaborative learning is integral in Communities of Practice, which are groups of people who share a process of collective learning in a shared domain of endeavour, by setting up or encouraging the creation of these communities in an educational context, using the techniques of PBL and project work it is believed that this will foster a deeper understanding of a subject, for eg, “Project Maths”, and encourage students to apply their knowledge to real-life situations in an exam setting, as opposed to memorising material to get through the test.

While particular emphasis is placed on the development and use of information processing, logical thinking and problem-solving skills, the new approach will also stress the importance of students developing their skills in communicating and working with others. These are important core skills which are transferable across the curriculum and contribute to effective lifelong learning. 

 I have introduced elements of self-directed and Problem Based Learning into my Maths curriculum, but this must take into account discipline issues, serious lack of confidence as regard problem solving skills and quite often a lack of basic maths concepts, also an unwillingness to work in a mature fashion in a collaborative manner is another barrier. I can see Project Maths as being a very useful in that it is designed to teach maths in a way that promotes better understanding of mathematical concepts and the everyday relevance of the subject.

References: 

Bloom, B. (1956, p 2) “Taxonomy of Learning”,

Carlile & Jordan, (2004-9.  p 1).“condition”, or train most animals including human beings by applying conditioning in the correct sequence”

Carlile et al (2004-9, p 2,) Contiguity and repetition Learning outcomes. 

Faraday, M. & Henry, J. (1831) Faradays Law.

Gagne & Medsker (1996. p 3)  “Gagne’s”, nine key Instructional events. 

Hull, Skinner, & Bloom, B. (1956. p2) Neo-Behaviourists, recognised the importance of learner’s internal characteristics, such as personality, motivation and habit “external manipulation of an organism” (Pavlov).

Krathwohl. Bloom. Masia. (1973, p 2) The affective domain.

Lave, J. & Wenger, E et al (2006), “Communities of Practice”. 

Ohm, G. (1827, p 3) Ohms law,

Piaget, J. (1938) “theorized that as children learned they actively made theories or mental models about how the world around them worked”.

Simpson, (1972, p 3) The psychomotor domain

Skinner (1938). Reinforcement, employing positive or negative feedback in which the subject forms a strong association between the stimulus and the desired behaviour, is a key step, desired behaviours are rewarded causing their frequency to increase whilst undesired behaviours are punished causing their frequency to decrease.

Thorndike (1911. p 2) “the principle of reinforcement” 

Vygotsky (1934)  “In infants, communication between the mother and infant is a pre-requisite to the Childs acquisition of concepts and language”. “Z.P.D or Zone of Proximal Development”.

Webb (1996. p 1) “Theory matters because without it education is just hit and miss, there will be no working foundation or basis to the discipline”.