During week 3, we learnt about 4 psychological theories of learning, namely behaviourism, cognitivism, constructivism and humanism. Despite the fact that we have learnt about these theories in our previous semesters, but this revision lecture had provided me some insights about how can we apply these learning theories in a mathematics classroom setting. In this reflection, I would like to focus on how the theories of **behaviourism, cognitivism and constructivism** help to inform my teaching practice.

Behaviourists suggested that learning occurs when there is a change of behaviour, and that the behaviour has to be measurable in nature. In my opinion, behaviourism theory has contributed to the field of education in terms of construction of learning outcomes. Learning outcomes could be one of the important elements in teaching, where teachers communicate learning intention to students before the class begins. When we construct a learning outcome, we follow the behaviourists theory where the terms used have to be observable and measurable. For example, students are able to **recite** times table of 4 with **100% accuracy**. Reciting is the behaviour that we want our students to produce, and the accuracy of 100% is measurable when students recite the times table.

In cognitivism, Vygotsky (1978) claimed that learning occurs through social interaction between a child and a MKO (more knowledgable others). In essence, a teacher or a tutor is needed to scaffold their learning. According to Vygotsky’s Social Development Theory, it was suggested that each child has their own **Zone of Proximal Development** (ZPD), where it is essential for teachers to identify where the learner is. After identifying the learner’s level of difficulty, the teacher provides **scaffolding**, so that the learner is able to perform a task with the help of a teacher, and gradually able to perform a task without any guidance.

Below is a picture of how Zone of Proximal Development and scaffolding works:

Lastly, I would like to talk about the constructivists approach of teaching and learning. Constructivists proposed that learners can **construct their own knowledge** and that is how learning becomes more meaningful and relevant. Teachers are encouraged to practice the role of a **facilitator**, where opportunities of exploration are to be provided to learners, and teachers being part of the co-construction of knowledge with them. In accordance with the constructivists learning theory, Dewey (1938) claimed that **experiential learning**, defined as ‘learning by doing’, can make learning more visible to students. This is because they learn with concrete experience, observe and reflect upon their experiences, make sense and construct their own concept of the idea and eventually test it in new situations. This is known as the Kolb’s (1984) reflective learning cycle. In my opinion, this might be a challenging approach for the in-service teachers, who have taught for many years in the education field in Malaysia, to adopt. Though the teaching method is relatively new to them, I think that teachers should be given appropriate support and training to practice it, as it will make learning more engaging for our 21st century students.

I am currently working as a part-time tutor at a learning centre, where Singapore Primary School Mathematics Curriculum is used. I was teaching a Year 4 student, student X, the concept of **area**, specifically **areas of triangle**. Firstly, I introduce to student X that all triangles have a base and a height, and those are the information we need to calculate areas of triangles. I then introduce the formula to student X, base x height x 1/2. There were a few subtopics in the particular chapter, such as finding the areas of basic triangles, as well as the shaded areas. I guided student X through the practices by providing adequate amount of scaffolding. For example, I modelled to him the steps to calculate the area for the first few questions in each exercise. Then, I provide him the opportunity to apply the skill on his own.

I gave student X significant amount of drill and practice, where repetition of learning occurs. As behaviorism theory suggested, I assumed that student X has already mastered the skill as he was able to produce the intended behavior. I stopped providing scaffolding as he demonstrated that he can perform the skill without my guidance while doing the exercises. After one week completing the exercises on the particular topic, I allowed him to proceed to the “Review Practice”. Surprisingly, he still needed my assistance in calculating the areas after one week of learning. I asked what did he remember about calculating areas of triangles, and he was able to tell me the formula. However, I realized that his weakness was that he could not identify which are the base, and the height. As the questions given in Review Practice was a little more challenging and required wee bit more of critical thinking, student X was not able to complete it on his own.

After identifying his weakness, I used some triangular-shaped concrete materials, and printed some colored triangles, with different ways of indicating the base and height, to show him in order to enhance his conceptual understanding on this topic. Instead of just using printed worksheets, I provide student X the kinesthetic bit of learning, where he was allowed to touch and learn. Then, I let student X to continue with the Review Practice. After the concrete experience of learning, he was able to complete it with a little help from me!

Having such tutoring experience has made me aware that scaffolding is not as simple as merely providing assistance to students. In my opinion, there are a few essential steps before we are able to provide scaffolding effectively. For example, we must identify what level the student is at, how much knowledge the student have and have not grasped, as well as the student’s preferred learning style. All these information will allow us, as teachers, to create a clearer picture of the student’s learning ability, and eventually knowing how much and what kind of scaffolding do we provide.

Having said that, it might be impossible to scaffold all 22 (average number) students in a class, and it could be near to impossible to provide different level and different way of scaffolding to all 22 students. Therefore, what I would do in the future is to group my learners into similar learning abilities, or perhaps group them with the skill that they are weak in, and provide scaffolding accordingly. In my opinion, this method could work more effectively as compared to scaffold them individually, as this helps to promote the child’s social development too.

Below is a picture that shows some effective scaffolding strategies. The picture was retrieved from http://www.mshouser.com/teaching-tips/8-strategies-for-scaffolding-instruction. Click in to read more about **SCAFFOLDING**!

References:

Dewey, J. (1938) Experience and education (New York : MacMillan).

Kolb, D. A. (1984). *Experiential learning: Experience as the source of learning and development* (Vol. 1). Englewood Cliffs, NJ: Prentice-Hall.

Vygotsky, L. S. (1978). *Mind in society: The development of higher psychological processes*. Cambridge, MA: Harvard University Press.