Personal Learning and Development

(Student ID: 201122240)

A personal record of gained skills and experience with evidence.

On my placement I was able to work with students ranging from 11 to 16 years old all varying in attainment. I gained an insight of the different behaviours through supporting classes but also through discussions with teachers. Before a lesson, each teacher would discuss which child require more support to ensure I supported the students who required it. These discussions with the staff often became the most important parts of my day.

Teaching Probability

My placement provider wanted me to support teachers and the students rather than teach classes myself. This would allowed me to see all age groups study but also ensure that their studies are not interrupted by a lesson taught by an unqualified teacher such as myself. I was given the opportunity to support one student who arrived after the lesson began. This student had missed the introduction of a new topic so I was required to catch them up on the work to ensure the student did not miss vital mathematical knowledge. As the student arrived late, I was able to witness the class teacher teach the topic before I taught it myself, something that benefited me as it allowed me to understand the concept and method of how to teach the topic before i taught it.

As the lesson was an introduction to probability, the first example included a spinner with numbers 1 to 4 and a dice with numbers 1 to 6. I explained what probability was then asked the student to copy and fill in a probability table with all the possible number combinations. I talked them through the process to ensure they conceptualised the information rather than just follow a procedure. I then asked the student to count how many probability combinations are available and explained that this in what all probabilities in this set of data will be out of. To work out how many times the number 6 will come up is the same as working out the probability of rolling a 6 out of the 24 different possible combinations.

To help the student understand the possible totals of the number spun on a spinner and the number rolled on a dice, I asked the student to write the total of the various number combination on top (the numbers written in red on top of the co-ordinates in example below). The student was then asked to work out the probability for rolling and spinning a total of 6 which would be 4/24 simplified to 1/6. This was what the teacher had taught so far so I stopped my explanation here and asked the student to follow the same instructions for the other examples displayed on the board. I continued to sit with the student to ensure they understood the topic, then allowed them to work independently while I helped other students.

*Below is a colour coded example of the work completed with the student with explanation where required. This is not the students work, it is a replica of the work completed.*

Probability, I find, is a hard to explain and teach but easier to answer questions on. Because of this opinion, it was important for me to ensure the student understood what I explained. Furthermore, as this teaching session was unplanned, I made sure understood what I was explaining before I taught the student. This experience was interesting as it was something I had not completed previously. The fact that it was unplanned was really helpful as I was able to test my own understanding and ability to teach under pressure. Therefore, the experience was enjoyable as I was able to test my autonomy and ability to work under pressure.

Skills Developed

As discussed in my placement aims, I had not worked in a secondary school prior to this experience so I was not sure what to expect. I wanted to develop my experience of working with children and young people to ensure I understood how different year groups vary in characteristics and knowledge. I developed my leadership skills as I was required to support all children in mathematics lessons ensuring children behaved and completed the majority of the work set for them. I expanded on my team working skills as I worked alongside different members of staff who, through observation and questioning, taught me the possible issues and solutions to ensure students remain focused. Furthermore, I developed my time management and organisation skills as I took two buses to arrive at my placement school.

This placement allowed me to develop many skills and discovery a variety of ways on how to become an effective teacher through various observations and student supporting opportunities. This experience, while it was different to previous school placements, was also the most challenging for me as supporting teenagers is something I require more confidence in. It allowed me to grow and enjoy working with teenagers, taking away skills which will be useful throughout my teaching career.

Annotated Bibliography

Conceptual VS Procedural Teaching and Learning

Ball, L., D. 1988. Unlearning to Teach Mathematics. For the Learning of Mathematics. 8(1), pp. 40-48

It was understood that teachers often enter the field of teaching with an understanding of how they think children should be taught based on personal experiences. This study was conducted to help some trainee teachers understand the importance of teaching a correctly to ensure personal understanding and the ability to ensure students understand as well. This article showed how hard it can be to learn a new topic or a pre-learnt topic from a different angle. Understanding different perspectives is important to ensure the students understand the concept as well as the problem-solving procedure.

McCormick, R. 1997. Conceptual and Procedural Knowledge. International Journal of Technology and design Education. 7(1), pp.141-159

This article considered the use of conceptual and procedural teaching in technology subjects. Technology while it is a stand-alone subject, it brings in concepts from other subjects such as mathematics, science and computing. This article helped me understand that in some situations, teaching the procedure may be the easier option but it is still important to show alternative processes to help students understand the concepts behind them.

Rayner, V., Pitsolantic, N., and Osana, H. 2009. Mathematics Anxiety in Perservice Teachers: Its Relationship to their Conceptual and Procedural Knowledge of Fractions. Mathematics Education Research Journal. 21(3), pp.60-85

This article discussed the relationship between persona experiences of mathematics learning to the anxiety of mathematics teaching. It was discussed that teachers often use own experiences to influence their teaching techniques. If teachers were taught conceptually, they suffered less anxiety for teaching mathematics than teachers who were taught mathematics procedurally.  This study helped understand the longitudinal effect conceptual or procedural teaching can have on an individual allowing me to see the importance of teaching to ensure the student understands the concepts rather than just knows how to solve a problem.

Surif, J., Ibrahim, N. H., Mokhtar, M. 2012. Conceptual and Procedural Knowledge in Problem Solving. Procedia – Social and Behavioural Sciences. 56(1), pp. 416-425

This article discusses the use of procedural and conceptual learning for chemistry in Malaysia. It is discussed that conceptual learning is necessary to understand chemical substances and their properties while procedural learning is necessary for problem-solving. The study conducted involved 200 students in 4 different schools and it was discovered that students were using alternative routes to find a solution rather than understanding the chemicals or the procedures. This article showed me that is students are not taught the correct methods and are supported to understand the topic, then they will result in guess work where they sometimes might get the right answer. This process will not help students and it will negatively affect their education as they would be learning incorrectly.

Tevfik, I., and Ahmet, I. 2003. Conceptual and procedural Learning in Mathematics. Journal of the Korea Society of Mathematics Education Series D. 7(2), pp.91-99

The use of procedural and conceptual teaching varies in different countries. This article discussed the use of procedural teaching in one Turkish school where achieving the correct answers and gaining a good grade was the main aim for students. Where marks are concerned, if learning the concept behind a process will not provide the student with the answer to a problem, the learning the concept is not necessary. This article helped me understand that teaching varies in different countries and the aims of learning and educating students also varies. While conceptual will help understand a topic, the understanding of a topic is not seen as necessary for some students in turkey and is therefore seen as irrelevant.

Images Used

ed place. 2020. Outcomes and Probability (3). [Online]. [Accessed: 22/04/2020]. Available From:

Kalai, G. 2017. TYI 30: Expected number of Dice throws. [Online]. [Accessed: 22/04/2020]. Available From:

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