T2W7

Other classes which are struggling with learning include 2N, 3N & 4N1. I feel that whatever strategy that we can use, it still depends a lot on teacher-student relationship. Pupils must have the trust in the teacher that the teacher sincerely wants to help them and that the teacher is patient and approachable.

I am confident to say that I have won the trust of a few pupils who started off to be very disrupting but now they are more attentive and eager to answer questions I raised in class. These pupils may still be a little noisy at times but they will automatically stop or even apologise when I turn and stare at them. Guess they just want attention from the teacher. In fact, they were made to stay back during recess time to finish up their seatwork with me at their side guiding them to complete the work. After a few staying back sessions, they have actually managed to complete their work in class within lesson times and handed them up to me immediately.

Praises worked well with this group of pupils as well. When they tried to answer questions and got their answers correct, I praised them (some praises used are "Very smart!", "I know you are good!") and that made them very proud of themselves. And this could be one reason why they were always very eager to answer questions (to show off to the rest of the class).

Of course there is also a group of pupils who are not disrupting in class and rather attentive but due to their weaker ability in Mathematics, they are struggling with two mathematics subjects. However, my teaching policy is not to give up on them even though sometimes I feel that they just "cannot make it". This is due to one year when I was teaching the weakest class both E Math (half of the class) and A Math (whole class), a few pupils proved to me that I made a wrong judgement on them. I tried to persuade them to drop A Math and to concentrate on improving their E Math as they just passed E Math exams with C6 and failed A Math exams badly with a score of 30+. They objected and assured me that they would do their best to improve. Hence, they persevered and I tried my best to help them. Eventually they obtained B3 for both Math subjects in their O Level exams. Maybe if they had dropped A Math, they might be able to obtain an A grade for E Math. But no matter what it was a great achievement for them and a great relief for me too :)

T2W6 - 3E2 (cont'd)

Went through class test with pupils on Wed. Surprisingly, all pupils were very attentive as I went through their common errors that they had made in the test (even the very disrupting pupils). This showed that though some of them are very irritating, they still want to learn. Hence, I feel that there is still hope for this class. Only thing is that they will only mature when they are in Sec 4 when they will be more focussed as they will be taking their O's. Now, most of them are just playful and easily distracted.

After a short discussion with their E Math teacher, we agreed that it will be good to split this class into 2 groups so that more attentive can be given to the weaker pupils (quite a number of them). But this is possible if there is enough resources to split them into 2 groups just like the 4E1 this year. Hence, for next term, there is a plan for splitting them but only for E Math. The splitting will be based on their Mid Year Exam results and they will be banded then so that the better ones can be stretched and the weaker ones can build on their foundation.

T2W6-3E2

Just finished marking the class test on Partial fractions & Indices for this class. My Gosh! Only 11 pupils out of 28 passed the test with 6 gotten borderline fail and the rest failed terribly. Those who failed had no recollection of what the 3 cases in Partial fractions are as shown in their workings. They could not even write down the general form for each cases! Considering questions on Partial fractions are rather standard, obviously many of the pupils did not bother to study for the test at all. It was quite disheartening as I have spent so much time trying to ensure that pupils were able to follow what were being taught in class so much so that not enough time for me to do revision for mid year exams with them.

The 2nd question was crafted such that the general form was given to them and yet many can only do up to performing long division to convert the given algebraic fraction into the sum of a polynomial and a proper fraction and could not continue correctly from there. Problems that most pupils had were basically algebra. They could not express the fractional equations into polynomial identities, eg. "(x^2-8x+44)/[(x+2)(x+2)^2]=A/(x+2) + B/(x-2) + C/(x-2)^2" after simplifying became "x^2-8x+44=A(x+2)^2 + B(x-2) + C(x-2)^2" or x^2-8x+44) =A(x-2)(x-2)^2 + B(x+2)(x-2)^2 + C(x+2)(x-2)".

The 3rd and 4th questions were on Indices. These 2 questions showed that even some of the better pupils could not obtain the answers correctly. This showed that the class did not grasp the concept of Indices well. This is always the case. Pupils "hate" Indices as they can get confused easily. Need to target their foundation in E Math Indices then. I tried explaining again how the laws of Indices arrived and pupils were able to understand. What they lack of is how to apply the laws of Indices and especially when they are given more complicated expressions to simplify. Guess I will have to discuss with the Sec 3 Math teachers to think of a better way to help pupils master the skills required in Indices. Maybe drill & practice would still be a better strategy to train them in doing Indices?

T2W5 - 3E2

Mid year exams is drawing nearer and I have yet to finish the last topic for 3E2 A Math due to the amount of time spent on disciplining some of the pupils and slowing down the pace as most of the pupils in the class are rather weak. But due to the shortage of time, I am sad to speed up the teaching in class and targetting only the most basics that are required from them to be able to do the minimum in the exam papers.

Sad also that there are a few pupils who are quite good in their A Math, have to bear with the slowness and the nonsense created by some of their naughty classmates. So as not to short change them, I always tell this small group of pupils to do more questions or some of the challenging questions when they have finished their work much earlier than the rest. As usual, I will always extend my stay in the class into the recess to answer some of their questions if they have any.

This term the class seemed rowdier than last term as I had actually flared up one day in this week and stopped my teaching to the whole class and targetted only selected pupils. The next lesson on the following day, I was able to teach for the first time in this term without any disruption from any pupils at all. They were all angels that day :) But I hold back my praise for fear that they will revert to the old self again for subsequent lessons.

Well, the subsequent lessons were still manageable though I had to send two boys out of the classroom on one lesson. Though I feel bad about it after that but sometimes we just have to sacrifice one or two to silence the rest.

Lesson Reflections

To constantly reflect on own lesson should be part and parcel of a teacher so that he/she seeks to improve his/her teaching in class so as to reach out to all the pupils in the class and to help pupils to achieve the learning goals the teacher has planned.

To pen down the lesson reflections helps a teacher to keep track of what he/she has carried out that has gone well or not gone well as planned. It serves as a mirror to the teacher's own teaching in class. It helps to develop the teacher as well.

A good lesson reflection should not just consist of reciting what has happened in the class but should have some of the following questions answered as well:

• What has gone well in the lesson?
• What did not go as planned?
• What has occurred during the lesson that was not expected?
• Did I achieve the lesson objectives?
• If not, what were the obstacles faced?
• Were the materials used appropriate and help to achieve the lesson objectives?
• Were the pupils engaged in their learning?
• To what extend has my pupils learned?
• Were the objectives clear and specific?
• Were my instructions clear?
• What were some of the challenging classroom management aspects?
• What could I do to improve this lesson and my overall instructional practices?

Giving feedback to pupils

I have been trying to give feedback to pupils in the following ways:

1. while pupils are doing seatwork:

• I will go round to check on their work and give immediate notice to pupils as to whether they have done correctly or not;
• especially when they have done wrongly, I will point out their misconceptions or where they have gone wrong;
• normally I don't tell them the correct steps, instead, I will point to them where their mistakes are and ask them questions that will help them to identify their errors which most of the times pupils are able to realise where they have gone wrong (giving pupils the ownership of their own learning)

2. marking their homework or tests:

• as I mark pupils' work, I will be able to identify some common mistakes make by most of them which I will then address as a class when I return their books or tests back to them;
• individually I try to write some comments or questions next to their mistakes to help them understand why the particular part is wrong; e.g. if correct answer is "x^2-12x+5=0" and pupil wrote "x^2-12x+5", I will circle the whole answer, put "=0" at the end and write "you have written down an expression and not an equation".

The above methods are just some ways I am trying to make my feedback to pupils as effective and meaningful as possible. I am still thinking for some better ways of writing down my comments on pupils' work as it is not the usual habits for a math teacher to write comments in a math problem.

T2W2 - 5N1 (Integration)

I started Integration with this class this term. After practising some basic integration, I proceeded to solving integration problems that require some differentiation and then using integration as the reverse process of differentiation to solve the problems.

At this point, as pupils have been practising techniques of integration, when they had to do differentiation again, some of them got the rules of both process a little mixed up. Hence, I had to give a number of such problems to them to practice doing both differentiation and integration in the same problem. After quite a few practices, I was glad that majority of them were able to do the questions.

In subsequent lessons, I will have to make them recall how to differentiate before doing more integration of functions.

Marking System & Feedback for my pupils' daily work

In the past, I gave one mark for each correct question that a pupils did in his/her daily work. This is quite meaningless as sometimes the working is correct but as answer is wrong due to carelessness. Hence, last year, I put in 2 marks for each question with 1 mark given to correct method and 1 mark to correct answer. Again this is quite meaningless as some questions have longer working. Hence, for this year, I tried a different way of marking. I mark my pupils' daily work similar to the way I mark in a test/exam paper. To me, this adds more meaning to my pupils as when they receive their marked work, they will be able to tell how many marks they can score for each question and how are the marks allocated for each question.

After attending the AfL workshop, I am more conscious in providing meaningful feedback to my pupils' assignment. In the past, I would just circle or underline the error and left the pupils to guess why. Now, I put a small tick at the correct step before the error and still circle or underline the error. Next, I try my best to write down at the side what is the error or a question for them to think about what is wrong with their working.

T1W9 - 3E2

Wow this class was getting noisier and restless each day. Worse still, some of the pupils were always changing place and their seating plan was still not confirmed after one month of planning. Hence, I could not take it anymore and stepped in to change their seating. Within a week, I changed their seating plan twice and this second attempt seems better so far. Will need another week to monitor.

This class of pupils are very talkative and a handful of the boys just cannot sit still. Hence, teachers teaching this class must be very firm and have to keep reminding them the class rules. However, all of them want to learn though some of them are really lazy to do work. Hence, they need to be push. Some strategies that I used for this class have work rather well so far.

It just happened that their A Math lessons are normally just before recess time. Hence, if I have to wait more than 5 mins before they are all ready for lesson to start, I will release them 5 mins late for recess. Releasing them late happens at least twice a week ... sigh ... and you may think it is not right, but it works well as the class will ensure that the noisy ones are quiet and not disrupting so that the class can be released on time. What's more, all the pupils are able to be very attentive as I do my teaching and they will really wait for me to give them the signal that they can be released before they start moving out of the class for their break.

When I give exercises as seatwork cum homework, they will also have to show me that they are able to do at least one of the questions before I release them (one by one) on time for recess. This method works well so far as the lazy ones become very hardworking (at that moment) trying their best to do the work correctly so that they can go off for recess on time.

For a few weaker yet lazy ones (usually only one or two of them) who do not write down anything or attempt at least one question, I will make them stay on in the class and help them with the first question, clarify their doubts or misconceptions before releasing them.

Though this class of pupils are noisy and mischievious, I can tell that majority of them if not all want to learn and they want to do well. This is seen by their enthusiasm to get confirmation from me that they have done the work correctly. Sometimes, I feel that they seem to be attention seeking but this attention-seeking behaviour is constructive to their learning as they lack the confident to say that their concept is correct. Because of their eagerness to ask and clarify their doubts, I don't dread going into the class to teach and I don't mind if I can't be on schedule as when I teach at their pace, I am able to keep majority of them interested in A Math which is often seen as an abstract subject that is very difficult to learn.

5N1 AM (T1W9 - Appln of Differentiation: Rate of change)

Started teaching topic and pupils find this topic tough. This is partly due to pupils being weak in Mensuration and they do not like to do questions that are very wordly (one characteristics of NA pupils - language). To help them tackle questions on Rate of Change, I taught them to identify information from keywords in the questions, write them down in mathematical notations and how to piece them together with the help of Chain rule.

For example, the question will always have one rate of change given, say "the rate at which x is increasing is 5 cm/s". Then pupils will write this as "dx/dt = 5". Next, they will have to identify what the question wants them to find, say "find the rate of increasing of the volume". Then pupils will have to write down "dV/dt = ?". They will then write down using Chain Rule a relationship between dV/dt and dx/dt : dV/dt = dV/dx*dx/dt ---(1). From this eqn, they will see that they need to find dV/dx as dx/dt is already given. So to find dV/dx, they need a formula relating V and x which is normally a formula they already know or given in the question. After getting the formula, they will get their dV/dx and then substitute it into (1) and BINGO they have answered the question.

Normally after showing one to two examples, the pupils and I will write down the essential general steps to solving similar question on the topic taught so that they have some basic steps to follow as they do other similar questions as practice.

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.

5N1 AM (T1W3 - Differentiation)

As I had grouped A Math lessons of this group with the E Math lessons of the rest of the pupils in their class, I see this group every day except Thursdays which really help me to teach them with small chunks of concept each time. Unlike past 2 years when their A Math lessons were tagged with DT/FN lessons and I see them twice a week. Now, they need not recall what had been taught a week ago but just a day or two ago. This year, a number of them (especially CY and YB) had also changed their attitudes towards A Math homework given to them as they did their homework dutifully and handed up on time.

Strategies I used in class that has been working well with these pupils so far:
1) constant practice on the similar types of questions before introducing new formula/rule/concept;
2) presentation of their solutions of their homework/seatwork on the whiteboard (These kids were very enthusiastic in learning and majority of them were very eager to present their working on the whiteboard);
3) individual attention in class when they are doing their seatwork;
4) last but not least, praises for good work done.

As I introduced Chain Rule, Product Rule & Quotient Rule to them, I found they were able to use the rules effectively. They were only a bit confused when it comes to simplifying expressions that involve square root. Hence, more practice on such question will be given to them.

This group really brightens my day up!

T1W3 (Sec 3E E Math SRP - Module 1: Algebraic Manipulations)

I had the first session of E Math SRP with the Sec 3E on Monday, 19 Jan 09. The group that I am taking are pupils scoring E8 or F9 in their 2008 Sec 2E Math SA2. It was a fruitful session as pupils in these group were very motivated to do the worksheet created.

These pupils are not extremely weak in Algebra. I feel that the Sec 2E Math teachers had done a good job by giving these kids a good start in learning Algebra. What constitutes to their poor results could be due to carelessness or not simplifying expressions to the simplest form or maybe not enough one-to-one attention given to them to address their misconceptions.

Some observations I have made:
1) quite a no of them were very careless especially when they multiply by negative numbers. A number did not simplify further after expansions;
2) all of them were able to use the "smiling face" method to do expansion and a few of them were able to use the algebraic identities to expand terms in the form (a+b)^2, etc.;
3) some got confused when it came to expansion of 2 algebraic expressions which contained more than 2 terms.

Actions I had taken:
1) as the class was quite small, I could go to every one of them to give them feedback on their working;
2) I went round one by one, checked some of their working and marked all the questions they had attempted and addressed mistakes that they made;
3) I praised them when they did correctly.

From the session, I feel that these kids want to learn and they want to do well in Math. What they are lacking in is personal attention in coaching them with the learning of Math. Some how, I feel that these batch of Sec 3E pupils, though weak and slower, have the potential to do well as they have very positive attitudes towards learning. Hence, I hope all teachers teaching them will help them to work towards maximising their potential and hopefully adding value to their learning.

My 2008 4E A Math Classes

Last Monday, 12 Jan 09, was the release of the GCE 'O' Level results. Some pupils from my 4E1 class did well as what they had expected but some did not. It is always sad to see some pupils so upset due to the results not up to their expectations especially from a good class like 4E1.

As for 4E4, many of them who did turn up for the A Math papers last year did not managed to pass the subject but at least they tried their best. However, I was glad to see that many of them had managed to pass their E Math and obtained an option to a polytechnic course as this class was a very worrying class last year when more than half of the class did not pass any of the school's internal E Math Exams since Sec 3.

The most rewarding feeling that I got was when some of my pupils came up to me to thank me for all the help that I had rendered to them last year. Some even sms-ed me later part of the day thanking me for the extra time I had spent last year to help them clear their doubts in A Math. It is always this appreciation that I get from my pupils that keep me going when the teaching gets "tough". At least, I know I have made an impact, though not that great, on the lives of these pupils :)

3E2 AM (T1W2 - Simult Eqns)

Given a 1-qn class test on simult eqns to class on Tue and had the scripts marked on the same day. Out of 39, 15 pupils failed the test. Common mistakes made by these 15 pupils:

1) when making y (or x) the subject from the linear eqn, the signs were mixed up hence resulting in getting wrong answers;

2) though some pupils can substitute linear eqn into non-linear eqn, they could not simplify the quadratic eqn obtained when fractions were involved.

The test showed that pupils who failed are weak in simplifying algebraic fractions. These pupils need to work on the skills before they are able to solve simult eqns well. Hence, I have arranged to meet up with these 15 pupils the following week for remediation. During the remediation, more simult eqns will be given to them for practice. In the mean while, arrangements are made for most pupils in the whole level who are identified for E Math SRP this week to practice on simplifying algebraic expressions and indices.

3E4 AM (T1W1 - Simult Eqns)

Very nice class. Girls are quiet and boys are shy except for two boys - one likes to ask silly qns & another rather cheeky :)

Noticed 2 VH pupils - one needs brailling while the other needs enlarging. Both were very attentive in class. I tried to read out word by word as I presented solution to a qn so that the one pupil who needs brailling will know exactly what was written on the board through hearing.

3E2 AM (T1W1 - Simult Eqns)

The pupils in this class are of mixed abilities. First impression: a few pupils seems to have higher ability in mathematics but quite a handful are rather weak as seen from their blank looks as I presented to them the solution to solving a pair of simultaneous eqns involving a linear eqn and non-linear eqn.

Problems faced by them: unable to simplify complicated algebraic expressions (including algebraic fractions). Hence, I needed to check their working and even guiding them step by step to derive the answers during lesson.

Although a handful of them are rather weak but they showed positive attitudes towards learning as they enthusiastically tried solving the simultaneous eqns and kept coming to me for assistance. I actually had the urge to teach them elementary mathematics instead. Hence, I need to think of a way to help them so that their enthusiasm will not be lost as they proceed to learn more topics in A Math.

However, A group of girls were rather inattentive as they kept giggling and not attempting to try. I had to go to them to ensure they started their work. To my surprise, these girls are student councillors! I need to be more stricter with this group.

To assess the pupils' ability, I am giving them a test (only one question: to solve a pair of simultaneous eqns) on coming Tues.

5N1 AM (T1W1 - First lesson of the year)

Glad to see my 5N1 A Math pupils again. Seeing them warmed my heart greatly as they greeted me with smiles and laughters. But sad to say that one pupil has intention to drop A Math. I managed to ask her to continue for the experience.