Son can ride a bicycle!

On 29 June 2014, last day of his P1 holiday, I was putting back a 12" steel kids bike given by a neighbour so that we can discard it for someone else to use. He hadn't had good time with this much heavier and taller bike while training wheels were fixed on, as he has been enjoying his wooden balancing bike much more. Thus, when he was asked a few days ago he said he didn't want this bike. However, as I put on the rear rack and the kick stand, without the training wheel, and asked again if he would like to ride on it, he said yes. So we went downstairs, to an open, flat and sheltered space.

There, initially I asked him to position the pedal so that he could start pedalling off. After some attempts, this didn't seem to work, partly because the chain kept dropping off with this sudden assert of force on the pedal. Ironically, another neighbourhood kid of his age, who hasn't yet able to ride a bicycle, suggested to push first then step on. So, he tried that and after some attempt, he could pedal and balance for more than 2 m. Upon see this, I concluded he has learned how to ride.

I think the short distance was mainly due to the chain was very loose and kept dropping off. Later, than I realized the problem was because when I fixed the rear wheel earlier, I didn't ensure the chain is taut, which is not necessarily when there is a rear derailleur, but this is a single speed bike, the first that I have ever meddle with. Now that this issue is resolved, I am eager to see him ridding a bicycle.

Update: Confirmed he can. The night this blog post was published, he showed his ability to ride a bicycle to my dad.

Maths or English?

Sometimes it is not easy to set questions that distinctively test on a single subject, especially when understanding the question that is expressed in some written words.

Here is a primary 2 question:

Natasha plants 6 trees on each side of a square garden. There is a tree at each corner of the garden. How many trees are there altogether?

Depending on different understandings, these may be the solutions given by students:
(a) 6 at each side and a square has 4 sides, 1 at each corner and a square has 4 corners. Thus, there are 6x4 + 1x4 = 24 + 4 = 28 trees

Guiding verses manipulating

A way to get someone to do things is to make him feels that that he wants to do it. In doing so, is he being guided or manipulated? What's the difference between guiding someone and manipulating someone so that the results is he willingly want to do something we desire him to do?

Sell your teaching skills online

Many things can be sold online now and I just come across BrightStorm (see ads above) that allows teachers to sell their lessons!

Re-considering my first job - as a tutor

I have found my backup income! Quoting from the report, Singapore emerging as 'tuition nation'

Physics tutor Phang Yu Hon has nearly 90 students and earns nearly 20,000 Singapore dollars (15,000 US dollars) a month, the report said. The 41-year-old gave up his research engineering job in 1994.

Probably without word of mouth, I imagine can get ~20 students and monthly ~S$ ... 4000 is quite nice. All thanks to the high pressure by teachers, who unshamefully asking parents to get tutors for their kids. Anyone interested for a mathematics tutor may check out my answers at Yahoo!Answers.

It isn't just the money. 20 students/week at 1.33 students/session, 5 days/week and 2 hours/session means about 3 sessions/day for 5 days/week, or about only 30 hour work-week.

Be careful how you ask a question

A JC friend returned from US to this region recently for a short visit. He is into research on student's thought process when learning math. I took a quick browse of his PhD Thesis and found an experiment by Cramer, Post and Currier (1993). I tested it out at Yahoo!Answers. However, it doesn't work as expected the first time. Then, I rephrase the way I present the question, and ... it works the second time.

I suggest readers to try it out first and see the results I got from Yahoo!Answers.

Sue and Julie were running equally fast around a track. Sue started first. When she had run 9 laps, Julie had run 3 laps. When Julie completed 15 laps, how many laps had Sue run?

Link to my experiments: Does your answer make sense? (for students)? and Quick, how many laps Sue ran?

Indeed, even in normal life events not necessary mathematical, the way we ask does affect the way the other party responds.

Do educators serve the students or their school?

Some JC classmates had a short "reunion" at the 1st month celebration of the daughter of one of them. A friend mentioned about the recent issue of a principal told 27 girls the school wanted 100-per-cent passes, and advised them to seek transfers to the Institute of Technical Education (ITE) since they were unlikely to do well in the GCE O levels.

In general, we think it is better for students to be told frankly and honestly which road might be better for them. The friend said, rather than at the end of the year a boss telling him he wasn't performing well, he would preferred to be told at the beginning that this job or career does not suit him, if the boss already confidently foresee it from his experience. Further, it would be better for a road map be shown at the various decision making junctions in a student life. This should reduce the wastage of resources for many to be trained in a profession but never practice it, and many who are practicing, but unhappily because they made the wrong choice when young.

However, for a principal do so because his school wanted 100% passes is ridiculous! Yet, this has been happening all along I think. My own experience is as early as before mid 80's where half of my class repeated a grade because, according to rumors, the school don't want high failure rates at O level while public is not informed of their passing rates at other grades. Nevertheless, most of them got into university compared to those who "luckily" and barely avoided the repeat.

When the alternative of taking only 3 A level subjects, Junior Colleges (JC) principals started to persuade students from taking 4 A level subjects. Someone I knew experienced that "coercing" when she started JC1 in 2005, but she insisted, which I did encourage her to. It must be some uneasy days or weeks for her to insist. The good news is that she achieved straights A's and distinctions, and also passed S-paper. There seems to be a struggle between being students' principal/teachers and being a school's principal/teachers.

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Generations of Virtue

It is nice to know that there are people proactively tackle the undesirable influence from the society and media, such as the Generations of Virtue. I have mentioned the similar in this post. Avoiding is not the way, and it can't work in this information era. Thus, it is important to prepared ourselves and the young ones in dealing with many potential undesirable influence.

Easy = Difficult

Recently weeks there are discussions on a difficult mathematics examination paper in this year PSLE.
It seems that some questions in it were difficult.

To me, there is not much different if an easy or a difficult question is set. If it is easy, then most will probably score. If it is difficult, then most will probably not score. Overall, it doesn't really affect my score/grade. Rather, I dislike easy question because I must make the efforts to do and get it right, whereas for a difficult question, I may choose to skip it but my score for it may be the same with many who spent time doing it yet didn't get it right.

Furthermore, I am one of those [selfish ones] who when spotted a faulty question will keep quiet and move on, since eventually the teachers have to void that question. I hate it when at later times, especially near to the end of the given time, someone raise the issue and the teacher announce an correction to the question. I think that is being unfair by making correction half way through an examination.

What matters is when a question is easy or difficult only to you or a small group of students. Otherwise, no problem.

Thinking further, I suspect it was the nice but unrealistic pictures that parents/teachers have given to students that causes some of them to be annoyed by not being able to score 100% due to some out of scope difficult question. I think this is an issue that should be addressed. The over ideal system in school is harmful in terms of getting students ready for the world. People who grew up in system-less environment probably have much higher ability to adapt and excel in the real world.

When they love to learn, they'll learn.

I like this phrase: When they love to learn, they'll learn. I found it at the SCORE! Educational Centers website that have Innovative Tutoring programs.

I had been a tutor for many years since my high school time. After a bad experience tutoring lower secondary levels (age 13-14), I only choose higher level students. Teaching and tutoring is easy, when students want to learn.

I wasn't good in motivating students, which I thought it is the parents' responsibility. However, most parents do not know how to do that. Making things worse, sometimes teachers and classroom environment de-motivate students from learning.

In a couple of months, I will be a father. Then, in a couple of years, children education will be my major concern as a father rather than as a tutor. I will surely be very interested to what SCORE! is offering. As my blog title put it, back2nature. Children naturally loves to play and have fun, and in doing so, they learn. Thus, the play and fun elements are fundamentally necessary in good education systems.

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Must Pythagoream Theorem be used?

This question is found in the Yahoo!Answers as one of the question designed to test knowledge of the Pythagoream Theorem.

1. Sam hiked 48 miles directly east and then 36 miles directly south. Find the shortest distance in miles from the point where he ended up to his starting point.
A. 60 miles
B. 36 miles
C. 48 miles
D. 72 miles

For me, MCQ question should not be solved by calculation because answers are suggested and the little time allocated, it is designed not to be calculated.

If it is used for training, it is better to demand students to think and explain briefly on all the 4 suggested answers, instead of ignore them, just work out an answer and search to see which of the suggested answer matches it.

Here, obviously, B and C are wrong because from the question, Sam travelled 48 miles in one of the direction and both directions didn't make an angle of less than 90 degrees.

Thus, left with two possible answers A and D. Since 72 can be nicely expressed as 2x36, and if it is D, then probably you should have learnt another theorem about this nice feature. Thus, it is unlikely D.

So, assuming the MCQ is not faulty, and by considering the time and marks allocated ratio, it is wise to choose A and move on. When all is done, then can return to do checking with the left-over spare time. If the MCQ is faulty, it doesn't waste your time too since none will get it correct :)

Now, for the purpose of learning, it is better not just to calculate, but to figure out any nice pattern if the distance were 72 miles. By Pythagoream Theorem,
a^2 + b^2 = (2a)^2 ==> b^2 = 3 x a^2 ==> b = sqrt(3) x a ~ 1.7a > 1.5a ==> 1.5a < b, but
1.5 x 36 = 54 > b, thus distance cannot be 72. Alternatively, similar can be derived in a circle when a chord has same length as the radius, the chord that joins the other two ends of this chord and of the diameter that touches of this chord, is of length sqrt(3) x radius. Lastly, just a quick note, when using the standard way, it is faster to use mental calculation: 36^2 + 48^2 = (12x3)^2 + (12x4)^2 = 12^2 (3^2 x 4^2) = 12^2(5^2) = 60^2.

Argue or discuss

Person A wrote something. Person B disagrees, and conclude that A is trying to do something bad. A is curious to know why would B think that way. There are two ways, one way is to ask or question B directly how did he come to his conclusion; another is to put forth the reasons of A to see whether B still have the same conclusion and think that A is trying to do something bad. A uses second way, but B see it as trying to argue and refuse to respond.

I think argue is personal and destructive. If it is not personal, but objective, I think the above is call discussion. Discussion is a good way for learning and communication.

Why do we need 0-100 scores in marking test? Why not just a pass and fail grade? Better and accurate feedbacks help people to learn.

First impression

There has been talks recently on how much false information can be acceptable in resume. I think this is an area lacking guidelines. Potential employees try to give the best first impression. Good employers probably ignore all these gimicks. It is similar to guys trying to give good impression to girls, and the smart girls look at deeper contents, and vice-versa.

Personally, I prefer the old style of apprenticeship, with enhancement by the modern systematic evaluation methods.

Non-mathematical skills

Some non-mathematical skills taught in mathematical lessons

1. cancellation
2. change the sign
3. move the decimal points
4. move the term to the other side of the equation

Why mathematics teachers teach non-mathematical stuffs?

Recently, I gave tuition to secondary 1 students, and I think nowadays mathematics teachers are skipping steps, while last time only students skip steps.

For example, 3x + 6 = 18, and the next line we put 3x = 18 - 6.
Mathematically, we subtracted 6 from both sides because we want to single out the variable x.
However, this is usually not being taught, or it was just mentioned without any intention of teaching by assuming that students won't understand. As a results, I saw in student's workings this: above the first equation, there is an arrow from above the number 6 going across to the right side of the number 18. That is, what students have learnt was they just "move"/"throw"/"bring" the number 6 over to the other side, and "change"/"convert" the plus sign to a negative sign. What is this!!! Learning mathematics, or learning magical or pattern rules of manipulating symbols?

There are many more such non-mathematical stuffs that are taught in schools!

Lateral Thinking

Recently I just came across lateral thinking, although it was proposed some decades ago. I found my way of thinking is quite close to it. However, my experience is that not many are used to it. Most of us are more used to problem solving.

In a way, solving a problem is some how the minimal achievement. Much much more could be done with or without the problem being solve, and especially so when in situations where not even an existing problem could be recognized.

If relating to performance, it is like considering doing one's best as the minimal achievement, while performing more than required being the norm.

E.g. most students are happy when the their answers to a maths problem is the same as the given answer. This actually is just the minimal achievement. One may solve the problem in more than a way. One may reason out why solving it in another way is wrong. One may discover any redundant information given in the problem. One may transform the problem into a more difficult and challenge oneself. In so doing, the student is truly fulfilling the purpose of a student, which is to learn, not just with a false "worker" mentality by just "producing the solutions/answers" to their "bosses" aka teachers.

tests and exercises

A friend commented that her kids will get zeros for their spelling tests the next day if she is not free in the evening to coach them. I feel something not proper here. What are tests for? If they were for the teacher to know the progress of their students, then when the results of the students include effort from their parents and others, the teacher will miss out those students in need of more coaching. I think students and parents of young kids should be explained clearly on how the education system works.

What are the differences between various tests, exercises and exams? Exams are basically for the purpose of qualifying someone's ability. Thus, one strive to score, by all sort of ways, including churning out good answers even without understanding it, and hiding any signs of 'blurness' about the subject.

On the other hand, exercises are for the purpose of evaluating the performance of the teaching and learning process. Thus, very different from exams, one should be very honest, reflecting whatever understanding he has gained through the lessons within the teaching system, specifying the source of knowledge if it were not from within the system. At the same time, the teachers are to figure out ways to improve on the teaching/learning process, instead of just wonder what's wrong with the student.

Tests are the confusing ones. These are conducted in a more controlled way than exercises such that a more unbias evaluation can be achieved. However, many tests have their scores affecting the final qualifying process, which introduce bias since student will hid their weakness and give answers they recognise as correct, but don't understand. A way to reconcile is not to view tests as evaluation tools but trainings and simulation practices to prepare students to perform well in exams.

Personally, I prefer more evaluation sessions, exercises and tests, and minimal qualifying sessions, exams and tests. Evaluation sessions aim to improve the whole teaching/learning system, benefiting the school, teachers and students. Qualifying sessions are for practical reasons such that other organisations can use to select their preferred students. However, the sad news is, most organisations find many of these qualifying sessions are not really suitable for them, and the more resourceful ones will conduct their own assessment. I think objectives of an educational institute should focus more on teaching rather than qualifying. It is also fairer for an independent qualifying institute, and more effective for the employer or higher institute to conduct qualifying sessions for the incoming cohort.

Fairness in exam

Recently there is a hooha in the primary 6 Science examination in Singapore (PSLE). Some students sob while doing the paper with ‘difficult’ questions as complained by these students and their parents. For me, there is nothing much to worry about when there is a very difficult question in the examination paper, because probably most will lose the marks for the question. Similarly, there is not much to cheer about when there is a very easy question because almost all will score the full mark for that one. Thus, I suspect that the problem lies in the attitude that they believe and expect full marks if they have put in the sufficient amount of preparation. Thus, for those who have put in more than sufficient efforts and who believe that they are entitled to full marks if there is no fault from them during the examination, they probably have felt being cheated or the situation is very unfair to them.

Should the examination system be perfect with total fairness? I prefer not. Considering the education in school as the preparation process for students to survive in society, it should not differ from the actual world too much. The real world is not fair, surely not in perfect state. Although the school should provide a protected environment for students to experiment and explore and learn, it should not be too protected and over perfected such that students will find it quite tough when they eventually have to live in the outside world.

Neural networks

I just read an article about the up bringing of children. There is a discussion about the two extremes, caning and reasoning, and also some mixtures of the two. I might have mentioned before, another article I read some months back stating that it might not be so much dependent on the method, but the consistency of the rule or standard that underlines the method. For example, when on different occasions, a child acts in a particular desirable or undesirable way and he/she receive different reactions or responses from the parents, the child will be confused, find contradictions and inconsistencies.

Actually, many computer scientists and engineers should be very familiar with this phenomenon. For a number of decades, artificial neural networks (ANN) were implemented using mathematical models. On class of these ANN needs to be trained in order to perform in an acceptable way. The training effectiveness depends on the training data. If there were substantial portion of the training data has error, the ANN will probably not able to fulfill in role.

Now, we have to know that ANN is an artificial version of the neural network that scientists found in brains. I agree that brain is not the whole of a human being and therefore let alone the neural network in our brain. However, if the neural network in a child brain is fed with wrong training data by giving them different or even contradictory reactions and responses to the same behavior, then the that neural network will not be trained properly. This would result in the child behaving in a way that we label as undesirable.

So, may be some engineers and some psychiatrists should start working together for a better parental guideline in the up bringing of children.