Models... Not the super kind...

Sometimes, a bout of marking will give me ideas on what to write on. This time round, the math worksheets have given me some ideas about models.

Models - One of the mainstays of our Singaporean Mathematics learning system. This method has been around for a long time and yes, even I remember learning them when I was a student myself! A quick search on Wikipedia reveals that this came about in our syllabus in the early 1980s so I suppose that makes my cohort one of the pioneers who learnt this system! (If you don't know what the model method is all about, here is a link to help.)

I do concede that my students who draw models during tests do better. However, marking their worksheets and thinking about the way schools in Singapore have carried this out has made me wonder: Are we putting too much emphasis on the model method, in the wrong way? I know my school isn't the first to have the students draw bars and bars of models in their work, sometimes even writing up whole worksheets dedicated to the drawing of accurate models. I know I'm not the first teacher to underline and redraw their students' models and sometimes, giving up altogether and making them erase everything to start again.

However, I want to say that by doing so, we have to be clear on our reasons for doing so.

First, let us consider what the model is. For this purpose, I found a video by Dr Yeap Ban Har very useful. This video shows him giving a talk on 'Singapore Math' in UK and here he explains what the model is:

(PS: I studied the teaching of Math under Dr Yeap in NIE and I found him one of the most entertaining and passionate Math lecturers there. If you ever find a course conducted by him, I strongly suggest you attend.)

So now I know that they are really a tool, or in his words, "a mere excuse... to develop visualization ability" and to provide a stepping stone to the algebra they will eventually encounter.

Which also makes me wonder why on earth some schools would force their students to draw models for every single problem sum, even deducting marks for models drawn wrongly even if the equations are correct. Isn't that like checking to see if you were counting on your fingers in the way that they want? Yes, it is an important tool for understanding but at the same time, there are other problem solving methods out there. Just as some kids would understand better through model drawing, there are also kids that understand just as well without the models. (Or worse, be led into misunderstanding the problem because of the model being drawn wrongly)

Another issue is the accuracy needed in drawing a model. Other than the lines having to be straight, the units have to follow mathematical logic as well. For example, if Robert has 3 times as many units as Stella, you cannot draw a model where Robert's 3 units are equal in length to Stella's 1 unit. This may lead students into developing a flawed understanding.

Yet I'm sceptical about making my students draw and erase until they draw perfect mathematical models. Remember that the syllabus is about developing problem-solving skills, not about mathematical drawing skills. Do we really have to make them draw all their models from scratch? Can we not, for example, provide blank rectangles for them to start the thinking process and then add on their own model drawings?

So as a summing up:

- Models are a method for teaching, amongst many others
- We teach them so that the students can visualize problems better (and there's a fine difference between problems and problem sums, I feel, but that's another topic for another day)
- We are not teaching them so that our students will be accurate artists
- Maybe there are other ways to let them use the model method, without making them draw everything from scratch
- Maybe we can also teach them, they have a choice to use it or not

Anyway, if you have become intrigued by Dr Yeap, here is another video where he talks about Singapore Math.

What do you think about the Model Method? Comment below!

We are Not Happy... Why? The 1-yr-old BT vs the 10-yr-old Old Maid

I've been going through the blog archives looking for inspiration for new blog posts. When I did so, I realised that some of the old entries dated back to my NIE days! Talk about feeling old!

I read through a couple and I felt even older. The voice that was being projected in the blog archives really sounded younger and more energetic. Compare that to now, when the words I type now seem to crawl across the screen. Ah, youth...

One post that caught my eye was this old one: We are Not Happy... Why? At the time, a number of complaints had appeared in the now-defunct Tomorrow.sg website about the things making them unhappy in the industry. I read through the post and wondered: Had things changed enough in the 10 years since I last wrote that post? Let's compare then:

The 1-yr-old BT vs The 10-yr-old Old Maid

BT:
" it is NOT the children that is causing the dissatisfaction, but all other things like the leadership, the administration, the non-curriculuar activities."

Old Maid:
10 years on, I don't think this has changed at all! I still find satisfaction in coming to the classroom. However, I still feel like the administrative duties are an interference to my real work with the students. In fact, with experience came added responsibilities that I had to quickly learn how to adapt to. I handled them with mixed results, some I felt turned out all right in the end, some I could not handle well and became disasters bigger than what they began with! 

The general feeling I get from other teachers regarding admin work and leadership seems to be the same: Something that came along with the job and that had to be tolerated. People that weren't keen on tolerating them just dropped out and became tuition teachers or left the industry altogether. 

What I found frustrating was when all this affected the teaching work. At such times, I was teaching very boring lessons because I didn't have the time to plan my lessons properly. It became easier with time, because I started to collect classroom activities and created some of my own as well. As time went by, I became more familiar with the syllabus and the activities for each topic. So what was said to me as a BT really came true: It really does get easier. 

My advice and viewpoint on this: Unfortunately, NIE doesn't train productivity, time management and people skills. Pick them up on your own and spend some precious time reading up and finding a system that works for you because you will need it more the longer you are in teaching. Always spend time brushing up on what you know of the syllabus and any teaching strategies. 

BT:
"I feel as if we are expected everyday to do more and more and more for the children, but only for that few extra peanuts. [and not gold-plated ones, to boot]"

Old Maid:
To really see if we are doing more and more for the children, you have to know the changes that have taken place in the system since then. 

First, by now all should know that hiring has frozen, especially if you notice the lack of Mrs-Chong-esque TV advertisements. Next, you should also be aware of the grand change in the English syllabus known as Stellar and Peri, otherwise the next paragraph won't make sense to you. Maths has also seen some topics being dropped out though I also see more emphasis on higher order problem solving. 

I feel that if you only look at the number of worksheets issued under Stellar and the topics dropped from Maths, you may feel that there's not that much work to do. However, I do feel that more actual teaching is expected. Forget teach-less-learn-more, it seems to be teach-more-learn-more, with holistic assessments all thrown into the mix. The good of all this is that the system has become more student-centric and is a lot more forgiving of each individual child's unique mix of strengths, talents and weaknesses. This is a long way from the system that I grew up under.

Something that has not changed though, I'm still waiting for my gold-plated peanuts, haha. Although the Connect plan comes very close to this, the 3 years waiting for it can sometimes be quite a pain, I admit.

BT:
"I hope our suffering is not caused by our own silence. There is only so much that we can all take to a certain point. Why allow others to put you past that point?"

Old Maid:
Some teachers obviously found dingy solutions to their own suffering, as evidenced by the number of sex-abuse cases that have come up in the news, more and more in recent times. [Thankfully, they make up a small number of the total teacher population] 

Social media has changed the game in this arena. We share more stories of what we go through online on Facebook or Twitter (or Blogger!) The more these stories get shared, the more the public has become more aware of what we go through in order to educate our children. I get a lot of sympathy from other people when I tell them I'm a teacher! They usually tell me, "Teachers do a lot, don't they?" Yes, everyone, they do. 

And this helps, because then a lot more people become more willing to speak up for us when we feel like we cannot. Take what happened when the news came out that they were willing to charge teachers for using the school carparks. I read through the comments section and was touched to see members of the public expressing outrage at such a move. 

As the movie said, though, "with great power comes great responsibility". Now that we have more outlets to express ourselves, another responsibility also falls on us to use that power wisely. The Internet is a great place for FB-scrolling and looking for cute gifs of cats, yes, but it can do that much more for us by giving us a place to speak up. We are no longer just limited to those outlets blessed by MOE, but we can create soapboxes of our own from which to speak from.

However, if we cannot express ourselves well, if all we do is complain in bad English, make fun of our heads or students, then no one will ever take us seriously when we have something serious to complain about. I would tell my BT-self of the past that yes, things will change in the future. We can break out of our own silence, but you will find that by doing so, you have an even greater onus to research your facts, gather your information before speaking up with a viewpoint.

Conclusion......?

BT: "So by now I guess I'll be in this line a very long time. Is it going to be worth the ride?"

Old Maid: "Put it this way: You will go through a lot of pain. You will struggle through some really bad days and you might even cry on some of them in your cubicle when no one is around. There will be days when you feel like crying in class, there will be days you feel like you will never be a good teacher, there will be days when you feel like you will never finish all the paperwork. There will be days your head will yell at you for the things you didn't know you had to do. There will be days you will feel like you see no end.

But on some days, you will make the children smile and laugh. You will sit next to a crying child and comfort him/her till they feel they can go on with school again. You will have hilarious times in class and if you are really lucky, you will that child who couldn't spell his name correctly in P1 walk up on stage in P6 and you will swell with pride even if you hadn't taught him for the last 4 years.

If you feel that those are worth more than all the other stuff, then you just might make it."

A Rough Guide To Writing Exam Papers

One of the most difficult things for me in this job is setting exam papers. Over the years, I feel like I've set enough papers to write assessment books for each level! Admittedly, setting papers is not my strong point and unfortunately there are no TRAISI courses to teach you how to do this. I learnt how to do them along the way, as part of the job and I picked up a few pointers to help me. Hopefully it helps you too!

1. Gather your materials - TOS, SOW, old exam papers
The Table of Specifications (TOS) and Scheme of Work (SOW) are vital documents for any exam setter. The first tells you what kinds of questions should be in the exam, for example, how many comprehension questions or grammar cloze questions. You might think that such things would be the same throughout schools in Singapore and the general format might be the same for the upper primary. However, there may be subtle differences. One school may decide to include more higher order math questions than another. The TOS should make this clear.

The SOW is just as important because it tells you what material the students would have covered up till the examination date. Again, this would vary from school to school and supplementary materials may differ. A detailed SOW would also be useful because it would also reflect the learning objectives for each unit. One such SOW for English may list out the vocabulary items and their expected usage. If you refer to the SOW for paper setting, you would not set questions that are out of the syllabus or that have not been covered.

As for old exam papers, they are useful as a question reference but don't think you can simply erase the old questions and replace them with new ones. I made this mistake once when I was setting one for the first time. I forgot to ask for the TOS and instead set the paper according to an old exam paper, only to find out to my horror that the exam format had changed and I had to reset the paper all over again! Don't do the same mistake I did and always ask for a TOS!

2. Start picking at nits
Everything about the paper must be up to par. Make sure all questions are arranged neatly in line. Check that you used the correct cover page and font. Measure your diagrams to check for mathematical accuracy. You can also print out a copy of your paper to ensure your scientific diagrams can be seen clearly. ( You would be surprised how different they look from your computer screen. ) Remember to update your answer key if you change any questions. Compare your paper with an approved previous exam to see that you have written instructions correctly, or put the check boxes correctly. It is tedious work but if you find it and correct it yourself, someone else won't have to tell you so.

3. Take all criticism in your stride
After you have handed your paper up, the next stressful moment is getting it back. That's when you get it back with all the corrections you have to do by yesterday. Your head should also go over the paper with you to explain the rationale for certain corrections or to clarify her expectations. Maybe the question you thought was a killer turned out to be too easy?

It can be demoralizing the first few times to see so many corrections in a piece of work. Don't sweat it. Most of the time, your head isn't being personal when this is done. Sometimes at the HOD level, they are more aware of the different standards from level to level and they have to adjust whatever work you send in. I always get corrections in my papers and I also see colleagues more experienced than I am get back a paper with tons of corrections too. It's normal for anyone so just take it in your stride and use the experience to learn how a paper should be set.

4. Hide
I would not recommend ever setting your paper in a public setting. You might say that you need your Starbucks frappe to help you do your work, but have you considered that your students, who will be taking your exam, may be drinking at that Starbucks outlet too? Even if you go to the other side of Singapore from where your school is, you never know if you would meet a parent, school or head while you are there. Worse, they might be looking over your shoulder while you type and you might never find out until the truth blows up in everyone's faces. Order that frappe to go and hide in the privacy of your own home to do this piece of work.

Luckily I never learned this lesson the hard way, but I have encountered parents and students while marking in public areas. If I was setting papers instead, I might have gotten into trouble if one student suddenly brags on Facebook about how he really earned his marks.

Hope this short list helps some of you out there. It is not meant to be a gospel of exam setting and I'm pretty sure there are points I might not have thought of or situations that haven't happened to me [yet]. Share with us if you have any other pointers for others!

Using Positive Reinforcement in Class Management

Positive reinforcement is something that has been talked about many times in NIE, in seminars and in schools. In case your memory about NIE courses is a bit hazy, here's a definition I got from Google:

"In operant conditioning, positive reinforcement involves the addition of areinforcing stimulus following a behavior that makes it more likely that the behavior will occur again in the future. When a favorable outcome, event, or reward occurs after an action, that particular response or behavior will be strengthened."

So if you do something good for your students after they do something, that behaviour will be strengthened and they are more likely to repeat it in class.

At this point, I know some will be skeptical as to whether it really works. I don't blame them. When I was a beginning teacher, I was given a particularly rowdy class in one year. I tried to teach as they had trained me in NIE only to find the kids unresponsive or worse, behaving even worse. Like how I tried to talk nicely to a student who had yelled at me in class only to have him yell at me more. Then I yelled at him for yelling and he finally stopped. 

Not my best moment, I know, but be nice, I was a beginning teacher then. Also, I won't be surprised if many other teachers, beginning or experienced, learned that same thing in the classroom: That being 'fierce' works.

Then after a few years of this, I was, frankly, sick of it. I was falling ill at the start of every school year from yelling at them, I felt my blood pressure go up and ultimately, I wasn't feeling very happy at work. 

So I changed, and it worked. My classes became calmer and I didn't get as many sore throats as I used to. 

(Sounds like a miracle cure? Well, of course, because you are reading in one sentence what I had to practice over a number of years to reach an approach that felt right to me and I have conveniently glossed over all the painful times that something didn't work or when something I did led to even more chaos. Remember: It takes time.)

What worked for me? 

1. Every teacher should have a signal to tell the class to quieten down and listen. I made it a point to praise the first child to do so instead of scolding the last ones who don't. This works like a miracle for lower primary classes.

2. I clearly told the class what I expected them to do and praised the ones who did it. In another class when I wanted them to sit in a circle, I told them I wanted a circle, I used hand signals to show them where I wanted the circle to be and I told them that they had to be seated quietly to be ready. 

Obviously when the class starts doing this, there will be massive chaos. I would walk around to help and I would also keep an eye out for children who had done as I had asked and point out what they had done right. Most of the class will get it. If the stragglers didn't, I helped them, because my goal wasn't to catch those who didn't get it, it was to help them do the behaviour I wanted.

3. I found that non-verbal cues worked just as well as verbal ones. Even a simple thumbs-up was enough to fill a child with pride. I've also seen cards and toys being used.

4. Loads of teachers give stamps and points for work done in class. They also took them away for bad behaviour. I generously gave points for good behaviour and took them away only when the behaviour was preposterous. I also did this when I was holding competitions in class, so I would award a group a point for a correct answer and another point for good behaviour, ie, sitting quietly, cheering on their classmate etc etc. 

5. I changed my language to point out most of the good stuff my students did. When I had a class doing group writing, even if there were tons of mistakes, I tried to look out for something good. ("I like this part because...") Even when, er, there was nothing to be found, I tried to phrase it in a way to show I was helping the student. ("I'm going to help you make this better."/"I think it would be better if......")

This sounds easy, but remember, this is after a number of years of tears, frustration, yelling. Even when I thought I got it, I would still make mistakes, so I'm warning you first:

Make sure you are praising for something the child has done out of his/her own effort. Do not, for example, praise them for work done by their groupmates, work they completed by copying from another student, or work that has obviously been done with an adult's help! That only reinforces to the child that I can get recognition by stealing other people's efforts!

Also, and this has been said countless times in countless literature, praise the child for effort spent and progress made, not for the result achieved at the end and not by saying, "You are so clever!". Firstly, because you don't want to demotivate the weaker students for not achieving the same high marks as their peers. Secondly, you don't want to scare the pupils away from trying harder and only do things that they think is easy for them to achieve.

Remember at the end, you want to give the students the confidence to succeed and you also want to give yourself a break. I had a very miserable time when I felt I had to yell at my class everyday, but after change, I found I was much less frazzled at the end of the day and I also had a better relationship with my later classes. It does take time to find a style that works for you but I can assure you that when you do, it works out better in the long run. 

Term 2 is the Best

It's Week 3 of the term and I'm already looking forward to June! How is everybody doing? I find that Term 2 is one of the best terms of the year. It's at a good level of 'busyness' that is manageable for everyone and usually this is the term when I can still carry on my NY resolutions (like sleep 7-8 hours each night and exercise regularly) before everything becomes too chaotic. Here are my reasons why...

Term 2 is the Best

1. Settled-down Students
In Term 1, many students are still reeling from the shock of waking up in the morning at 6. Many of them would also have to get used to a new form teacher's routines. There would be some struggle between handling the new workload and the new teacher. This is also the time when they are most likely to try and 'test' the new teacher to see how much they can get away with. For a teacher, class management would be critical during this period as how you react towards them may determine how smooth your year with this class is!

By the time Term 2 comes around, the students are already settled down to school routines and know the conduct and behaviour that is expected of them. If you have already set your foot down firmly in Term 1, managing the class should be easier in Term 2.

2. Lighter workload
The workload for teachers is still relatively low compared to the mayhem of exam preparation in Terms 3-4. In Term 2, you would be preparing the students for half a year's work to be tested in SA1. Compare this to Term 4, where you may be revising a year's work for SA2. The issue of timing also comes in, which brings me to the next point...

3. Less school days in Semester 2 
Many teachers feel very harried during Semester 2 and this is also the period where you see everyone deep in piles of marking. Why does it feel so? That's because there are significantly less days to cover work in Semester 2 than in Semester 1 and a simple calculation illustrates this.

Assume that School A carries out CA2 in Week 9. If we assume that English is on a Monday followed by the other subjects, that leaves 8 weeks to prepare. Factor in the National Day holiday, which loses one day due to public holiday, the day before, because that's a half day and the day after, which is a school holiday. Now we have 3 days potentially lost from the school calendar. Subtract 1 more day for Youth day and that's almost a whole week gone! So we are left with 7 weeks for CA2!

Then in Term 4, again assume that School A carries out SA2 in week 8. Assuming English is on Monday, that leaves 7 weeks for preparation. Subtract 1 week for PSLE marking and you now have 6 weeks. Subtract another 3 days average for public holidays, you now have 5.5 weeks for SA2! That's 5.5 weeks to cover Term 4 topics and revise the past year's work! Has the panic set in yet??

Most schools would be aware of this shortfall in days and this should be covered in their SOW in various ways. Some may start Term 3's work right after SA1 in Term 2 and Term 4's work in Term 3. The SOW should also be planned to take into account of this.

Teachers may handle this by... Going into fervent and frantic marking sprees. :D Well, whatever works. Keep your spirits by remembering that after all that, the December holidays beckon after that. And to prepare, keep yourself healthy now in Term 2 by sleeping well and exercising and eating well. I cannot guarantee you would be able to do that after June!