Modeling the Model Diagram

I remember when I was learning to be a teacher, the math professor gave the class of trainee teachers a Primary 4/5 question. She wanted us to solve the question with model drawing. There were about twenty of us, with different backgrounds and age groups. The time given was 15 min. None of us managed to solve it. NONE. Mind you, all of us were university graduates. 

It's been almost 10 years since then and since then, I always believed that it does help kids with their Math. Unfortunately, most people I speak to, don't agree with me. There was a mother whom I met at a school's event recently who actually dissuaded her girl from drawing the model as she thought it was a waste of time. 

Audrey is P3 this year, and it's also this year that her teacher is requiring the class to do their models in the Math sums. I naively thought P3 Math means simple math questions = simple intro to model diagrams = a piece of cake. 

I was wrong. I should have known that the hardest thing to teach are always the basics. Audrey came home with a math worksheet one day, which required her to do her model diagram and solve the questions. It was already painful to see her come up with a diagram because she was quite particular about being neat and later erase all away because she didn't get it. After 30 minutes, she was still at the first (unsolved) question. I tried to do it slow with her, but she was not getting it. After a while, I gave up and basically did her homework with her. (I 'taught' and she wrote) Because we again had an unpleasant learning experience together, I felt lousy and was up the whole night thinking of what I could do to change things. 

We went back to basics  of the model diagram after school one day. So far it has worked for me. And in case you are one of those who were born too early for the model diagram method, see if this works for you. 

1) I did away with the drawing of the diagram

I used strips of construction papers (4 colors would be safe since so far, I haven't used more than 3 colors) of standard varying lengths. I halved a strip for the pink and further halved the lengths for the orange and blue respectively. Whilst the green I divided the paper into threes.

I did this for many reasons. Firstly, it was less time consuming for Audrey to present her model and secondly I'm not sure if it was just her, but she couldn't see at times that certain parts need to be the same (because it represents the same amount) and certain parts need to be longer proportionately to represent a greater amount.

2) She only shows me the diagram

This doesn't mean she doesn't solve the question, but my focus was really the diagram and not her working. The diagram is essentially a working and while she doesn't need to do her working, I still ask her what her steps are.

I got her to do on her white board from school since I really didn't want to keep wasting paper and I thought it was easier to erase any mistakes with the duster than the eraser.

3) Step-by-step intro to model diagram

With all my materials prepared, I had a step-by-step demo. I showed her an example, guided her on the next and let her do the second. She fumbles sometimes, but with practice she does get it.

In short, this is how you show it:

a) Translate line by line of the question to the diagram. (It helps to break down the question. If sometimes the first line does not help much, you can use the second line to help) 

b) Labeling  (It helps to understand the premise of the question)

c) "Layering": When comparing the strips, all similarities must be found in the model (it helps the child to relate to the question)

The above shows an example of how "layering" works. Comparing the first and third strips with the second, the difference is shown by the green and orange strips respectively. However, since the green is longer than the orange strip, it would also mean that the green strip consist of the orange portion inside it. Visually, it helps the child to see which has the most and by how much. 

d) Finally, indicate the question with a question mark (It helps to understand what we are finding out)

Here's an example:

There were 15 more pupils in Class 3A than in Class 3B. 20 pupils from Class 3B moved to Class 3A. How many more pupils were there in Class 3A than Class 3B in the end?

Starting from top left to right.

I always tell Audrey to approach the question line by line since most of the questions are pretty straight-forward. (There are some questions which you do not work on the first line, but because it won't be 'basics' I won't be talking about it here. If you do want to know how to do it, let me know, and I can always share it)

As you can see, she used the green strip to represent 20 pupils from Class 3B in the second picture and immediately did the "layering" step of placing it in the first strip as well. She then "moves" the 20 students to the first strip by adding another green strip to it, while indicating using a dotted line that the students have moved to the first class. (I would tell her to cover the bottom green strip so that she would remember that the 20 students are no more in that class, allowing her to see the 'excess' students  in 3A as compared to 3B)

Obviously, it's not possible to use the strips in a pencil and paper exam mode. Only after she is comfortable moving the colored strips, I would let her attempt drawing it out. 

Yes I know, the question mark for the diagram is missing :P

And I am proud to say, she is slowly becoming a little expert in model drawing. :P

I know it's a little wordy today… Nonetheless, I hope it has helped you to help your child a little. :) Let me know if it did!!!

P1 Math… The downfall of a P1 Parent...

I am not a Math Professor, neither do I have a degree in Math. It may seem that I have a bone to pick with the math syllabus, but I don't. I just don't understand why certain methods make sense to the publisher, and certain methods don't make sense to the teacher?

So, here's one of the questions found in the P1 Math Workbook Part 2. Now in case you are wondering why these questions were solved with an addition sign, it was printed with it so the children had no choice but to solve it with the addition sign. 

(I'm sure it was so confusing that even the teacher marked the corrections wrongly for question 1)

There's just some things I cannot understand..

1) What is the purpose of the picture of 8 pears and a paper bag again?? (how does the bag even help me to solve the question???)

2) How would a teacher assess if a kid gives such a working? Should the 1 mark for working (which may not make sense to me) be given the mark or be marked 0? 

3) How does it make sense to solve it using an addition sign? Assuming if the question does not have pictures (relevant or otherwise), a kid would now need to think through a process like this:

Step 1:

8 (original) + ___ (bought) = 14 (now)

Step 2:

14 - 8 = ? 

Then wouldn't it be better to just teach step 2 direct? 

4) The intention of/for such questions. Are we encouraging a (forced) creativity in solving questions here? 

To be honest, I am not at all comfortable with this assignment. Can someone honestly tell me if the solution makes sense? Something maybe I have overlooked? 

I asked D to see if he could understand this… and even he couldn't explain it… (He's a man of few words… but this left him speechless)

But at this point, I'm just a frustrated parent. 

When a Picture says More than a Thousand words

The school term has started and so has my revision time with the kids.
Looking at last term's work, I wanted to do addition word problems with Audrey.
This week, instead of eggs, let me introduce our new character - Gingerbread Men!

This seems easy right? Ha! If only...

This (thank God) is not a question from Audrey's test, it's one of the questions we went through today.
To be fair, this is not a difficult question. I am sure suspect when teachers teach such questions, they would basically highlight the words "at first"and explain to them that it means finding out the number of items at the beginning. To do so, it would mean to add what is left and and is missing.

But here's what my dear girl did…

I'm not sure if you can see, but she struck 2 gingerbread men from the picture, and wrote as 6-2=4. (I don't even know to mark right or wrong)
After the egg incident, I have learnt it is more important (especially for kids) to understand rather than to be understood.
I asked her what made her do this way and here's her explanation:

There were 6 gingerbread men (Like why did they even draw that out?)
4 gingerbread were left.
So… She thought her working was supposed to be 6 - 2 = 4.
(I checked with D and he gave the same explanation as to why she could have done this way. Brilliant! My daughter is going to be a dentist too!)
I thanked her for teaching me something new and told her to take a break, since we would be continuing after dinner.

I tried to ask some friends whose kids are in Primary 1 to let their child try the above question. Basically I wanted to understand if their kids got it right or wrong, and if they did was it because they read the question or looked at the picture.

So one of my girlfriends got her daughter to try and she got it right. I asked did she solve it by reading the question or looking at the picture. She told me the former. She didn't even bother with the pictures.
Another two did the same thing as my girl… (okay now we got 2 more dentists!)

My concern, at this point, wasn't Audrey's train of thought. I was worried. Worried that she would not be able to proceed on questions when it didn't have any pictures (misleading or otherwise) and more importantly, that she will not be able to fit into what the system wants of her.

After dinner, I got her to redo the question again, this time, I covered the picture. I asked her to solve the question for me.

Just to showcase her artistic talent...

So I covered the pictures and she got the right answer. (did you know how loud my sigh of relief was????) I know why schools needed to provide pictures for word problems - for the consideration of other students who can't read.
However, through this one incident, I am not sure if the use of the pictures here has made matters worse. Or rather, the use of pictures has indirectly led to a failure of showing her concept understanding here.

SO if the kids generally didn't get it right because of the picture and if they get it wrong because of the picture… I'm trying to understand… does it mean:

1) Word problems should henceforth not have pictures?
2) If the child can't read, they shouldn't be given word problems?

It's sad that a good intention (picture in this case) didn't produce a good result.
Honestly, if I didn't have this incident with Audrey, I won't have known better as well. (Because I read the question instead of looking at the picture)
And if i were in the school management team, I won't have known that kids may be confused by the pictures and/or whether pictures should be drawn for word problems.
But instead of being critical of what has been done, I hope this post entry would create an opportunity to discuss on what could be done… after all, at some point, chances are your child will be going through the same education as mine.
So I'm posing to you readers, IF you were the setter, what can you do differently?

I do hope you share your thoughts on this… if not, I hope, this will help you further understand how a normal 7 year old think. :)


added note: my friend told me that it's probably easier to let audrey learn how to give answers people want.. Maybe.. but I would also hope that from this post, people would also learn to accept what answers my child (and many other children give) because of the little things we as adults overlook. Will it change overnight, no. But will that make a difference to what you do with a child like this? Maybe… :)

Everyone's Favourite Topic - Eggs (An update on Math entry)

So just a few days ago, I blogged on the humbling lesson I'd learnt from my daughter's Math paper. (in case you didn't get to read it.. here's it… http://chellelifestory.blogspot.sg/2015/03/when-math-question-teaches-you-lesson.html)

When I started this blog (a week back), it had only a couple hundreds of views… but because of that entry, it became 6000+ (that post alone garnered 5100 views as of today). In another words it became viral. (Oh no… what have I done…) 

Because I posted it on Facebook, I had friends liking the post, commented on it and 2 (officially) shared it. But from there… somehow, it became 5000+ views from Singapore, 169 views from USA, 147 views from UK… the list goes on. (And as I write, the numbers are still increasing… like… how come people don't sleep one?)
I had friends who also privately messaged me and told me not to stop blogging and how much they enjoyed reading my blog (I was humbled… not as much as by the math question… but nonetheless still humbled) And because of that post, naturally they went on to read the next post on the outing to ECP… which is just a normal post that talked about mundane stuff. (now that was funny) Essentially they wanted to know, what did the school say (coming coming..)

From my Facebook page, I had many teacher friends who think that Audrey should not have been penalized. In fact, like me, they were pretty impressed by how orthodox her logic was… (okay because i didn't think that way… maybe that gene came from the dad) So to those who think the education system is hopeless, we got warriors in it who are trying very hard to prove otherwise. 

There were people who also commented that the answer should be 7. Their reason - whether it's broken or not, it's still an egg. (They are not wrong, but reading that made me want to slap them… only because they are my friends) True that, but we are not in a philosophy class.. so whether the glass is half full or half empty is really not the issue right now. 

There were also some who felt that because this is P1 Term 1's work and obviously, the children has been taught that whenever you see the term "left", the way to solve it is to use the subtraction method, hence if the student did not achieve the answer using that solution, the objective is not met and she should not be getting the score.

And that actually is the school's stand.

The teacher called me yesterday and in short, this is what she said:

1) Firstly, she really didn't see how Audrey got it at first and was quite surprised a child had interpret it this way

2) This was done in class and the students were taught that whenever they see "left", at this point, they should take the whole and take away a part of it.

3) The students are not expected to read word equations now, hence they had to minimize the words used and rely heavily on the diagram.

4) The question (while many argue is poorly set) is actually modified from their workbook (uh oh…. i hope now there won't be 4000+ people flipping through the P1 Math workbook and finding fault with it)

5) As a level they somehow agreed that because Audrey didn't meet their objective of the test, she can't be awarded the mark…

6) Ironically, however, if Audrey had put (4 +3 = 7) down as the working, and gave her answer as 4 she will get the mark instead of the comment Fluke! (Yes, we had to explain to her what Fluke is… okay the teacher explained that she thought it was only by chance that Audrey got it right) Oh in case you are wondering, it's because the child has understood part and whole concept… like a number bond?

Of course the protective parent in me didn't accept their explanation. (Please… I'm a Singaporean still… where can you find a singaporean who doesn't complain??) But I was very calm and told her to discuss with her level head/HOD again… (I didn't say I will resort to the press though… I mean like, does it still work nowadays???? )

And as a parent, these were my reasons:

1) In order to understand what was "left", the child understands it would be the unbroken eggs (And audrey has achieved that)

2) I asked her, if you gave a child $2 as daily allowance, and she spends $0.80 that day. Now if you had asked her, how much money does she have left, and she starts counting the remaining money in her wallet to give you the answer, should she be penalized? (Of course the teacher said no, but she said, in this case, the kids were taught that for such question to use subtraction to find the answer for left… which obviously contradicts point 6 above… that in a bit)

3) I also said if they had strictly wanted her to use subtraction, they could simply worded it as "Using a subtraction equation, find how many eggs are left." Then that would have minimize any chance of misinterpretation

4) If Audrey could come up with an easier and less careless alternative (Well it's definitely easier to add 3+1 than 7-3), why are we faulting her? Besides at national exams teachers are also taught to accept alternative answers and solutions should it make sense, why not now..

5) How come we can accept 4+3=7 (award 1 working mark for that) and give 1 mark for the answer 4? I mean if the child puts 3, and still get 1 mark for working, how is that even understanding the question? It doesn't make any sense at all right?

6) Finally, I told her, considering the above, if the school insists that she is wrong, what values are we telling the child? That because Audrey doesn't conform to the norm, she should not be rewarded? Or because she didn't meet the KPIs of the test, she is wrong? (how would a 6 year old know so much?) In short, I told her that it is not about the marks, but what message we are telling the child by marking it wrong.

See I may be a strict parent with high expectations, but I am a very protective one as well, especially when it comes to her development. If I did my part as a parent, I won't allow anyone to create a mess out of it.

To which, she told me she will discuss with her level coordinator again and get back to me… soon. This is the last week and I really hoped that they could explain to Audrey this week since it's all fresh in her mind. (So don't worry there will be another update on that)

BUT guys, before you condemn the school/teacher, or saying that it's ridiculous (come on admit it) the intention of the post was really NOT to declare war against the authority (it seems like it's a trend these days, but it's really not my cup of tea). It is also not to scare parents to see how hopeless the education system is or how the teachers should go back to NIE or try taking national exams again or whatever... (There are MANY dedicated teachers in the service who work very hard to look after a stranger's child while they can only pray that someone will look after theirs… and no… the tax you pay don't pay for their salaries because hello… they pay tax too!)

That blog entry was only humbling because it was only by taking time in the quiet moments of the night, looking from a 6 year old's point of view, and hoping to understand it better, did I realize that I had overlooked her alternative suggestion (which is not wrong!) 

Audrey wasn't misunderstood because her parent, i.e. me (this once) did it. But there's other kids who may not have been given another chance and even had their answers laughed at because, to us, it didn't make sense. 

Unfortunately, they could be your child/student. My question is, when the time comes, would you then, have celebrated his/her small successes or condemned him/her like the rest of the world?
The objective was then to say, yes they are kids and they may see things differently, but no, it may not be wrong.  

With that, I hope the essence of the entry was not lost. 

When a Math question teaches you a lesson on humility...

My (not so) little girl came home yesterday with her first English and Math tests. She scored 15/20 for both. The teacher commented that she could have done better if she had read the instructions properly.
I agreed with the teacher. I flipped through the papers in front of her to see what her mistakes were. They were mainly careless mistakes which could be avoided if she had put in greater effort while doing her test.

I told her immediately I was not happy with the results. I told her it's a shame that she got this grade because of her carelessness. (I'm not sure which is worse… to do badly because of carelessness or because they are clueless) From all my posts, I am sure you will know that I am not a person who will lower my expectations because she is my daughter. In fact, by doing so, I think she would only learn to expect second best for herself… from her work, life and even her future partner.

After the (mild) scolding, I told her to go and sleep after saying goodnight and apologizing for her poor performance. While putting the youngest to bed, my dear girl went under her blanket and was completely quiet. I knew immediately she was in tears. (Well… that's what I do when I don't want anyone to know I'm crying…. and… she IS my daughter after all) I waited for her to calm down, pulled the blanket aside, with both my hands on her face, I looked straight into her eyes and told her I love her no matter what the score was. She was still someone I was proud of and with her ability, she deserved to do better. She teared a little and with a kiss, she went back to bed.

This whole episode made me reflect on whether I had passed the test as a parent myself.

I wanted to see how other parents coped with this and I tried to google on articles or sharing about parents who have discussed the times when their kids didn't perform as well as expected. Hmm.. interestingly while there are tons of articles talking about behavior, hardly any site talked about this.

D had dinner with some friends last night and when he came back, I showed him the papers.
Unlike me, he tends to be the more relaxed parent. Not that he has low expectations of the kids, he just didn't think it was something we should sweat about. Unlike me too, he looked at the paper as a whole, not at the mistakes Audrey made. Laughed and said okay. (Really so difficult to say more than one word????)

When the kids slept and all was quiet… I looked through the paper again. This time at the small successes that I may have overlooked earlier. Audrey got her concept of addition (2 and 3 numbers) right… She understood how to form sentences with the words in different order… She wrote neatly… She completed her paper in the given time. :)

I looked for the things that I should look at as a parent, not a teacher… And then I saw this….
There's this question that she got wrong. The question asked how many eggs are left. I'm sure many of you, just like me, at first glance, not understand what she was thinking about. There's 7 eggs, 3 broke, why on earth should she put 3 + 1 = 4?

She didn't get the right answer because of "fluke". She got it because she saw the solution differently. She took the 3 eggs from the left and added to the 1 egg on the right to give the answer. Like what I mentioned in the email to the teacher, the standard way of marking didn't make room for a different way of solving the question. (Aren't you amazed how kids can surprise you at times?)

I'm fine if the teacher not reconsider accepting her way of solving the question… but I did mention to the teacher to be less ambiguous with the question should they not be ready to accept a different style of  answering.

Audrey has 'humbled' the teacher in me. While it doesn't discount the other careless mistakes she made, it does feel good to be proven wrong by her. :) (Okay… maybe if Ms. Smart Alec keeps doing it, it may not feel that good..)

When she came back from school today, I told her I appreciated her for seeing things from another point of view (I mean isn't this what we are encouraging nowadays) and that I actually learnt something new from her. She just smiled and continued doing her work assigned to her today. :)

With deeper reflection, I never asked her how she felt about getting such results. While I felt it was not good enough and I was very clear in showing my displeasure, she may have thought otherwise. Her feeling good at getting 15/20 is not a bad thing. In fact, just because she felt good getting 15/20, it doesn't mean she won't want to get a better score. So, while she got 15/20 for her test, I failed for mine.

That's the thing about Parenthood… Just like life and love, it's a mystery. It doesn't come with any manuals (since each child is different).. We can only pray that we don't screw up too much. I thank God that He has given kids an amazing ability to overlook the shortcomings of their parents no matter what… Isn't that after all His message to us too? :)

Looking back at Term 1...

Audrey has (almost) survived term 1 of school.

I remembered that she lost her wallet on the first day of school. I didn't know she lost it until at night when I asked for it. She didn't know where she lost it, how much she had inside and didn't feel bad losing it. (Winner.)

Knowing me, that was definitely not going to sit well with me. First, I didn't like the fact that she was completely nonchalant about it. Second, she didn't even tell me until I asked for it. I could have easily given her another wallet, but I didn't. Yes, she's my child but that doesn't mean that she needs not be responsible of the things given to her.

As a result, I placed her pocket money in a small ziplock bag. I could tell that she definitely felt the consequence of not looking after her things. The next day, she came home with her pocket money - in her ziplock bag. 

The following day when she came home, her ziplock bag had a tear. I saw it, but I kept quiet. Audrey asked that night if she could use a wallet instead, before I could say anything else, she told me she will not lose her wallet. I agreed and till now, she still has her wallet with her. (Well done girl!)

D felt I had been too harsh with her. He felt that I should have told her the importance of looking after her stuff rather than just going straight to a plastic bag as a wallet. My argument was the fact that she was unconcerned about losing the wallet, and not the act of losing it.

However, because I was the one who disciplined her, D decided not to overrule that.

In the middle of the term, Audrey came home with her Math workbook. Parents are required to sign it as a form of mid term review. She generally has gotten all her work correct, except some of it was done untidily. Her numbers were big and unsightly. Though it was marked, I told her to erase her work and redo it - neatly. I have seen her work before and she is capable of neat work. I emailed the teacher and told her to not accept any work from Audrey if it was ever done untidily. (The teacher must be thinking what's wrong with me…) Since then apparently her teacher told me her work has improved.

My rationale is that if she can do it before, she is definitely capable of doing it again and no one should discount it.

Time passed quickly and very soon it will be the first term's holidays. Audrey enjoys school life so far. Her usual recess meals are either sushi (mainly) or noodle soup. Out of the $2 ($0.40 goes to savings and tithings) she is given, she only spends $0.60-$0.80 a day. (She saves the rest when she comes home) Her "best" friend is Annabelle. Given her height, she is still second in class. (Like how is it possible you think… well… It is). She enjoys her netballs on Thursdays (I still don't understand why I had to pay $80 for this CCA for the whole year). 

Most days, when she comes home, she sits down 2 hours with me doing either English, Math or Chinese papers. (Yes it's only term 1, but she's not complaining… and I really don't see how it's different from putting her in tuition classes like berries or enrichments). I am proud that she can sit, without procrastinating, and finish her work. (I tell her this too… and all she did was smile widely) At least, I take ownership and make the effort to sit with her as well. 

Of course, again, different parents have different believes in this and maybe I am a tiger mum… So I guess different parents would have different views on it. 

I am sure Audrey is looking forward to the holidays, which we planned for a staycation and all. After all, all work and no play makes Jack (in this case Audrey) a dull boy (girl).

Let's hope that when it comes to the boys, I won't be strangling myself...