T1W8 - 3E4 (Nature of Roots of Quadratic Eqn)

Spent quite some time on helping pupils understand the relationship between the discriminant of a quadratic equation and the nature of its roots by doing the IT worksheet in the A Math Workbook. As the CD provided by the workbook could not work well. I changed to the use of graphmatica and the calculator. They work as well too. After completing the worksheet, pupils were the ones who concluded how discriminant affects the roots of the eqn.

At the same time, they were also able to observe that the sign of the coefficient of x^2 affects the shape of the graph. They were the ones who came up with the conclusion that if the coeff of x^2 is positive, then the graph is a U-shaped curve while negative coefff of x^2 is negative the curve is N-shaped.

Through their own discovery, they are able to remember concepts better. Though it is time consuming to conduct such lesson, it is a worthwhile investment of time. The subsequent lessons (which require pupils to use their newly acquired knowledge to solve related problems) were able to be carried in faster manner.

Assessment for Learning

Assessment for Learning (AfL) provides information for both teacher and pupils to progress towards learning goals.

In AfL,

Teachers
- reflect on the purposes of assessment;
- use strategies to assess pupils’ learning;
- plan how pupils will receive feedback, how pupils are involved in assessing their own learning and how they will be helped to progress further.

Learning activities
- incorporates assessments and provides information for future learning plans;
- must show the learning outcomes of the pupils;
- must not be biased;
- have learning goals and criteria used in determining the quality of achievement that must be understood by pupils;
- not only assess pupils’ learning but also encourage deeper learning;
- have assessment integrated in the teaching and learning and not separated from them.

Feedback given to pupils must
- help them improve further;
- motivate them;
- aim at the personal achievement of the standards and not used as a comparision with peers;
- be clear and constructive on the strengths and weaknesses of the individual.

Pupils
- learn to be responsible for their own learning (through the use of self-assessment and peer assessment strategies and the emphasis is on the how to improve further);
- are provided with opportunities for them to strive for their best.

T1W7 - 3E2 (Symmetrical Properties of Roots of an Eqn)

When I started this topic, I used the whole of one period to show pupils how to obtain the results: given x^2 + (b/a)x + (c/a) = 0, sum of roots = alpha + beta = -b/a & product of roots = alpha * beta = c/a. As the proof was rather abstract, majority of the pupils in the class were lost as they could not understand the proof at all.

Hence, the following lesson I tried a different approach. I created a worksheet that required pupils to discover general forms for sum of roots & product of roots with 4 different quadratic eqns. For this lesson, pupils dealt with numbers instead of a, b and c. After completing the worksheet, all of them were able to write down the sum of roots and product of roots given any quadratic eqns. I did not even need to explain to them why the reason for the ‘minus’ sign in as they deduced the formula on their own. I was really happy that this method worked for them. Thus, I was able to carry on the lesson on deriving another eqn using the sum of roots & product of roots from the first eqn.

T1W6 - 3E2

Pupils were tested on Polynomial Identities & Remainder Theorem on Tues, 10 Feb 09. All of them passed the test with 2/3 of them obtained full marks and a few with near full marks. I am really happy for them. The way I conduct my lessons with this class seems to work well :)

What I always do in class:

1) At start of lesson, ensure that all of them have their textbooks and notebooks on the table.
2) We will first recall what has been taught in the previous lesson.
3) An example will be shown before pupils attempt more similar questions.

For example,
- Pupils will state Remainder Theorem and I will write the theorem on one side of the whiteboard.
- We then go through an example by doing it together on the board.
- Next, pupils will work on more problems taken from the textbook.

4) Feedback will be given to them as they attempt the questions.

For example,
- While they are doing their work, I will walk round to check on everyone of them and answer questions from those who are in doubt.
- Sometimes, some pupils will come forward to me to help them check their working when they are not sure if they are doing it correctly or if they cannot get the correct answers.
- As I check their working, I don't always tell them the correct steps right away. Instead, I will point at the step/s that they make mistake and ask them to check and tell me what is wrong with the step. (It is always good for pupils to be able to spot their own mistakes rather then depending on the teacher to tell them. When the ownership is in their hands, they remember better.)

T1W5 - 3E4 A Math (Cubic Exp & Cubic Eqns)

This class has completed Chap 1. To stretch them further, they were tasked to try Qns 14 & 16 of Review Questions 1 from their textbooks. These 2 questions require them to prove before solving the cubic equations.

I got a pupil to come up to present the proving part of the 1st question. She tried but was not confident of doing it so I allowed her to get one of her classmates to come forward to help. As the 2 were doing on the whiteboard, I went round the class to see what the rest had done. Some did not do anything as they were not sure how to start as they told (but I suspect they did not prepare at all). As I went round, I spotted some common errors.

Some pupils wrote -2^2 when the correct way of writing is (-2)^2. Quite a no of them thought that -2^2 is the same as (-2)^2 with both answers as 4. Hence, we had a discussion on the difference between the two. It was a good discussion as I helped them to clear their misconceptions.

T1W5 - 3E2 A Math "SRP"

Had a second A Math "SRP" session with my 3E2 pupils on Monday. Revised with them by solving a pair of linear and non-linear simultaneous equations before administering them a diagnostic test on this topic.

For the revision, I gave them a question and asked them what were the steps they must do. They were able to tell me that they must make y the subject with the linear equation (they were able to identify which is the linear equation) and then substitute into the other equation. Hence, I left them to complete the question and went round to check their steps as they wer working on it. Pupils who could solve the question were then given the diagnostic test first so that they could leave the class once they had completed the test.

It was heartening to see the enthusiasm in them to complete the work and start with the test. Guess the idea of leaving early motivated them to complete the work quickly and correctly :)

All of them passed the test except for 2 so these 2 knew that they will continue their A Math "SRP" with me :) The others will have to passed the next class test on Polynomial Identities & Remainder Thm if they want to be out of the "SRP". Hopefully this will help in making them be serious and work hard for the coming test.