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This was an introductory lesson to complex numbers given to the top stream ordinary level class. For this lesson I had prepared a PowerPoint presentation to show the students. The lesson began by drawing on the student's prior knowledge of the different number systems and then presented them with a new type of number - the imaginary number. I explained to the students how and why this type of number was created. I continued the lesson by introducing complex numbers to the students and the methods for adding, subtracting and multiplying them by a real number. The learning outcomes I specified in my lesson plan were achieved and the students were well engaged in the class material. There were no behavioural issues in the class.
Strengths in my teaching:
I was pleased with the layout and sequencing of my lesson plan and this was also acknowledged by my supervisor. I had given lots of thought on how to introduce complex numbers to the students in a clear and concise way. I was aware that this was a new topic that students had never encountered before and so I decided to introduce it by referring to their prior knowledge of number systems. I feel that by being thorough in my lesson planning results in a more structured lesson and it also helps to keep the flow of the lesson going.
The variety of teaching methods I incorporated within the lesson helped to keep the students engaged and interested in the material being taught. I used lots of questioning throughout the lesson to ensure that the students remained involved and active in their own learning. My PowerPoint presentation displayed plenty of examples in a clear manner and the students found them easy to comprehend. However my supervisor did point out that the some of the slides contained too much text and he advised that I minimise the amount of text on screen. This was something that Bonnie Long also outlined in her Ed Tech classes.
My supervisor noted my enthusiasm and lively approach in the classroom. I was energetic in the way that I carried myself and in my explanations and this led to an interactive classroom atmosphere. My explanations were clear and given in a step-by-step way which ensured that the students followed the material.
As noted by my supervisor, I gave lots of praise and encouragement to students throughout the class. I feel that this helped to boost the class morale and build confidence among the students, thus promoting higher student participation within the class. Also, giving praise and encouragement will help to spur students to think and make connections between complex numbers and other areas of maths.
In using regular informal assessment strategies such as questioning and observation, I was able to monitor and evaluate the students understanding of complex numbers. Students responded well to the pertinent higher and lower order questioning and they were able to make connections between complex numbers and algebra. When doing their written work I walked around the classroom to ensure that the students understood the material being taught. While my supervisor commended my classroom presence he suggested that I stop and talk with the students, particularly the weaker ones, so that I could check their progress and assist them with any problems they may be having.
As noted by my supervisor, I gave an effective recap at the end of the lesson. I questioned specific individuals and ensured that a variety of students got to answer. Students were able to recall the material learned at the beginning of the lesson and the different rules applicable to the addition, subtraction and multiplication of complex numbers.
Weaknesses in my performance:
My supervisor made a number of suggestions on how to improve my introduction of complex numbers to the students. He recommended that I introduce the lesson by providing the students with simple linear and quadratic equations to solve so that they would discover the impossibility of attaining the square root of a negative number. In this way, students would acquire a better understanding of why imaginary numbers were invented and it would allow for greater class participation. It was also suggested that I give the students a brief history on when and who invented imaginary and complex numbers as this would show the students the development of these numbers through the eras. These are things that I will definitely introduce to my future lessons.
To ensure that the students understood what imaginary numbers are I could have provided them with more operations to compute before moving on to complex numbers. This would have made the transition from the operations of imaginary numbers to those of complex numbers easier for the students to comprehend.
My supervisor noticed on several occasions throughout the lesson that I directed my questions towards certain students. This is something I never realised I did and I will be much more aware of it in future classes. I feel that the questions I asked were good ones which would really stimulate student thinking and understanding had I given all of the students a chance to answer them and not just a specific individual!
I did not relate the topic of complex numbers to the real world and I was unaware of this until it was pointed out by my supervisor. For the students benefit, I should have connected the application of imaginary and complex numbers to real life situations. Students would have gained a greater understanding of its relevance in areas such as electrical engineering, signal processing and in applications of optics. Therefore in order to spark the student's interest in complex numbers I will make sure mention their significance in tomorrow's lesson.
One student ask me a question about what 'in the form a + bi' was. Although I answered his question I could have spent another minute to explain this to him properly and then assess his understanding to avoid any future confusion about this. My supervisor advised that I use simple vocabulary in my lessons so to avoid student confusion.
I did not make use of all the teaching resources available to me within the classroom. As the PowerPoint presentation is reflected onto the whiteboard I have limited space on it to write explanations. For this reason I should have made use of the blackboard in the room. It would have permitted my explanations to remain visible for the duration of the class and allowed both them and the PowerPoint to be on display simultaneously.
I will strive to prepare a varied range of teaching and learning resources and strategies that I can implement in the classroom. I will also ensure that I make full use of all the teaching aids available to me. This will help to generate the interactive and discovery based learning environment that I am aiming to create in my classroom. I do not just want my students to be able to manipulate rules; I also want them to be able to establish logical deductions about maths. As Roger C. Schank says "The job of a school and a teacher is to serve as the catalyst for discovery" 
I will continue to give praise and encouragement to my students as it makes them feel worthwhile and comfortable in class. In turn they will be more eager to participate in the lesson. Also, I will encourage them to take an active role in their own learning by encouraging them to think and make connections, and to learn from their fellow students.
While I feel that my distribution of questions to the class is improving, I need to improve upon the style of questioning that I employ. I must implement a more open style of questioning so that all of the students feel included and so that it will get them to think about what is being asked. I have learned from my lectures on the PGDE that when direct questioning is used, students' concentration levels drop and they become more passive in the class. My teaching and learning notes in the PGDE will be a good reference point for me to refer to and continue to improve my questioning technique.
I will make more an effort to relate questions and class material to the students own life's and to the real world. This will help to capture the students' interest as well as highlighting to them how their school education is important after they finish school.