Math concepts are usually very abstract. To help us understand some of the concepts better, my teachers would (1) build on our existing knowledge of concepts that we learnt in secondary school, and also (2) share real-life examples with us so that we could better relate to the Mathematical concepts.

For Math, I learn better when there is an expert (teacher) going through examples and questions. Then it’s practice, and more practice. The scaffolding, expert guidance, and relating to real-life examples have made it easier for me to understand the abstract Math concepts.

In secondary school, I did a lot of note-taking and memorising. Coming from a school with tons of subjects every year (I was from a private school), it was hard for me as an average student to understand all the concepts, so the easiest thing for me was to memorise. I would read the textbooks on my own, write down notes and read them out loud so that I could remember them better. For Math, I had to do a lot of independent practice and revision. The nature of the lessons back in school was that the teacher would simply explain the topics with examples and then we would be buried with homework and practices. There was not much scaffolding or 1:1 tutoring from the teacher. Because of this, I had to come up with my own learning strategies. 

I also used to have study buddies. We would meet up almost every night nearing to our major exams to help each other out to explain concepts. I preferred learning from peers as compared to learning from teachers as I could understand them better with their relatable examples. 

My learning methods comprised a little bit of both Piaget’s and Vygotsky’s theories. Even though I did a lot of independent practice and learning in accordance with Piaget’s theory, I also learn well with scaffolding and rely on social interactions with my peers who were more knowledgeable than me, also known as MKO according to Vygotsky. 

 

 I remember I hate to be left alone to do self-reading (independent learning). I feel very insecure as I do not know how to learn from mere reading. I need to read many times to understand if no one is there to explain the content.

I learn best when I like the subject. Interest will motivate me to spend more time and effort in that subject. I feel that I am a visual learner, I need to see (be it picture, illustration, or video), feel and have hands -on experience. (Piaget’s theory on Direct/Concrete experience) A teacher explaining concepts and ideas in smaller chunk, repeat and reinforce important information will help me learn better than to talk for hours without checking on my understanding at all.  In addition, learning through games and friendly competition among friends help to make learning fun and less stressful for me. 
In primary school, my group of friends and I grew to love Chinese so much that we always asked for extra lessons. We started speaking and using the language more often. I remember that was how my Chinese teacher motivated us to be the top students. (Vygotsky’s theory on social interaction and language) 

When I was doing English Literature for O’ level, I was lucky to have a teacher who clearly knew about Vygotsky’s theory on ZPD and scaffolding. He was always around to guide and knew exactly where and how to assist. I am grateful and remember him till this day. He has made the learning so much easier for me.

 

Yes. The example I’m going to use is the Hands-on Sourdough making class by a famed baker. I attended this class with 2 other students. 

 

There was a huge emphasis on physical environment. The physical environment was well-designed and ignited a sense of intrinsic motivation in myself to learn; Each student had their own printed notes and workstation consisting of baking tools and ingredients. The physical environment thus enabled active exploration and maximized curiosity to take place, highlighting Piaget’s belief on self-discovery being crucial in one’s learning. 

 

The session started with a theory 101 lesson on sourdough. She tapped on our prior knowledge of how regular white bread, making references to our local bread brand – Gardenia, and mentioned that the key difference between the two was that in sourdough, it is naturally leavened with wild yeasts and not packaged yeast. Through this, my teacher applied the notion of Assimilation and Accommodation when introducing new material, enabling us achieve Equilibrium throughout the process. 

 

As my teacher went through the notes, she asked open-ended questions that paved the way for peer discussions between us 3 and took on the role of a facilitator. She was not quick to give answers and gave us time to reflect and think of solutions independently. After doing so, she led a whole-class discussion where each of us shared our thoughts. In doing so, I was able to learn differing opinions, and this heightened my learning experience. This is in line with Piaget’s view that the role of teachers is to provide appropriate learning experiences and materials to stimulate students to advance their thinking. 

 

Before the practical element of lesson started, my teacher assessed each of our ZPD when it comes to making Sourdough; She questioned on our past experiences on making sourdough, if any, and immediately I felt like she had a clear gauge on each of us can do, and how much help each of us would need in order to make sourdough. As 3 of us had differing levels of ZPD, with mine being the biggest (learning curve is the highest), my teacher provided me with the most support. First, she placed me directly next to her just so I could have the best view on the process – Autolyze, Bulk ferment and Shape. Second, after her demonstrations, she would pay more attention to how I replicate her steps and similar to the ‘I do, You do and We do’ method, she would attempt to correct my mistakes, if any and watch as I continue on independently. This links back to Vygotsky’s Zone of Proximal Development whereby one is only able to learn successfully under the guidance or in collaboration with a more knowledgeable other, in this case, it is my teacher. Such is thus, in line with Vygotsky’s theory of cognitive abilities being socially guided and constructed. 

 

I see both Vygotsky and Piaget’s theories unfolding in my sourdough class. Some instances depict ‘Development precedes learning’ while other instances depict ‘Learning precedes development’. I developed both intrinsic and extrinsic motivation throughout the class despite having first experienced intrinsic motivation due to the physical environment. 

 

 

However in primary school there was a slight overlap in both Vygotsky and Piaget’s theories. Particularly in the lower primary there were still lots of direct instructions given in most of the lessons. My teachers would reinforce our concepts after every lesson and use basic logical examples especially for math. There was some influence of Vygotsky’s theories with leading questions by teachers and mini group work elements. As I grew older the classroom strategies were more aligned to Vygotsky’s Zone of Proximal development than Piaget. I was assigned my class based on my needs and grades. Particularly in upper primary and secondary onwards Vygotsky’s theory of scaffolding became more evident with teachers encouraging  group activities, peer tutoring and guided learning thus allowing me to be a more independent learner.

However, peer tutoring and guided learning involves lots of time and interest and involvement of peers. Particularly in my teenage years there was lots of resistance and disinterest in group work and often the time spent during discussions were unsupervised and futile. 
Rote learning was a common practise as a punishment or before exams and this did not benefit me in any way. My learning style leans towards a kinaesthetic and visual learner based on understanding rather than memorising.  I only understood and learnt this at a later stage as there was no emphasis to be aware of and benefit from one's learning style.

I could vividly remember how my Chemistry teacher taught us the concept to understand a periodic table easily. She broke down the information into different sections and categorised it according to the properties. She explained step-by-step on how to retrieve the correction information from the table, had few examples before letting the students to attempt the practice paper, used visual cards and coloured markers on visualiser to differentiate the elements on the periodic table. It took me a very short time to understand the period table and I aced at it back then in secondary school. The whole process of learning was closely guided with lots of teacher prompting.  I resonate it to Vygotsky's theory as it comprised of concepts Zone of Proximal Development (ZPD).  

I can also understand and remember better when teacher uses analogies and acronyms. They help to link new concept to what I am familiar (my existing schema) which is Piaget’s theory of Assimilation.

In my upper secondary days, I started to clear my doubts in mathematics with a friend who was very good in the subject. Whenever I could not solve a problem, she explained to me the concepts and changed my misconceptions. We discussed and solved the sums together. And I could understand her and started to perform better in the subject. I felt more confident and began to challenge myself to do more difficult problems. That was the turning point for me to start liking the subject. This method resonates with Vygotsky’s sociocultural theory of cognitive development, which emphasizes on two principles – More Knowledgeable Other and Zone of Proximal Development. 

In conclusion, I have realized that I learn best in a non-judgmental environment, through scaffolding and by asking a lot of questions.  

However, when I am introduced to something new that I might not have any frame of reference for, Piaget’s theory resonates more. An example would be experiencing disequilibrium while learning philosophy during my undergraduate programme. My worldview had to broaden to accommodate these new ideas and theories that often question my current understanding of the world. In this case, I would have to expand my schema to make sense of this knowledge. It is the disequilibrium that advances my understanding of what is taught. 

I was a lazy and somewhat difficult student in secondary school. In those 4 years, I remember having the same math teacher from start till end. She saw me fail in math till I manage to pull of a Bs and As for my maths in my final year in secondary school. Scaffolding and Zone of proximal development from Vygotsky were 2 prominent things that I remember happening with her. My class in general was weak in maths. So he scaffolded her lessons to really break things down for us to grasp the understanding and slowly and gradually increased it’s difficulty for us. For me, she was always the More Knowledgeable Other who constantly guided me through and made sure I was able to reach to the point of independently being able to solves the math problems. 

Then came polytechnic, one facilitator had always taken time to interact with as many of her students as she possibly could. Interacting about anything that interests the students. For me, she used to always check-in with me to see how I was coping with school and issues out of school. She shared with her about the prospects of the job and why she continued doing what she does. On top of interacting with me, she always had me doing my own journals. Posted me questions and asking me to write about what I thought about them. Sometimes about topics in school, sometimes about actions I have done. 

My mentor/supervisor during my internship was really the type who doesn’t like to spoon feed. He is really an advocate of experiential learning, which doesn’t really link much towards either Piaget or Vygotsky. However, what he does is. Once I have created an experience of doing something, and it has been created into a schema for me and I have become comfortable with that, what he does is, he puts me in disequilibrium. He pushes and challenges my schemas of what I thought I knew. For example, all activities that I have done was always done for school students and youths. That created a schema in my mind that these are all only for youths. When he realised that, he pulled me out of working with youths and got me to start learning about working with corporate clients. Thinking that I would be learning a whole array of new activities, this was when I was placed in a new situation. Doing the exact same activities that I would do for youths or kids as young as 8, 9-year-olds, now doing it for corporate adults as old as 50 years old! I was thrown off, not knowing if it was possible, how can I do something so ‘kiddish’ for adults so old! It was here that I had to make accommodation to what I already know and created a new schema in my mind.