SHARING TUTORING EXPERIENCES

Misconceptions

2011-04-25T16:26:00.001+06:00

Does your child studying in class 6 or 8 have the following MISCONCEPTIONS?

English:

The use of its and it's.....

The King Cobra is a large and powerful snake that swallows ____ prey. (Around half of both classes 6 and 8 children in a study used it's.)

A. it's
B. its'
C. its
D. it

Clarification: It's is contraction of it is, while its is a possessive.

E.g.

It's raining.

The dog is wagging its tail.

Math:

A thin wire 20 centimetres long is formed into a rectangle. If the width of this rectangle is 4 centimetres, what is its length? (Not even one fifth of the class 6 children in a study got this right, which means they did not understand the concept of perimeter.)

A. 5 centimetres
B. 6 centimentres
C. 12 centimetres
D. 16 centimetres

If we provide a diagram of the rectangle with the length (6 cm) and width (4 cm) indicated and ask class 6 students what the perimeter of the rectangle is, almost 90% would get the answer right (i.e. 20 cm). This shows students are used to such examples and not used to real life application examples that actually allow students to apply the concept to real life and understand the concept.

Science:

The best reason for including protein in a healthy diet is because it is the main source of ____________.

A. energy for the body
B. fiber for digestion
C. raw materials for cell growth and repair
D. vitamins for fighting diseases

(Majority of class 8 children in a study chose option A. This is a result of the general misconception that all food that we eat gives us energy for the body.)
________________________________________________
As Mr. Phurba Dorji had suggested, Ugyen took 4 identical pots and put an equal amount of soil in each of them. He planted bean seeds in pot 1, wheat seeds in pot 2, mustard seeds in pot 3 and apple seeds in pot 4. He kept them in the open and watered them equally for a month. At the end of the month he measured the height of the plants.

Through the experiment he was trying to find out which plant seeds ______________________________.

A. can grow in soil
B. can grow when kept in the open
C. grow the tallest
D. need more water to grow taller

(Most class 6 students in a study opted for A. This shows that these students were not clear about the objective of an experiment. They randomly selected options that refer to the factors mentioned in the question. They seem to have neglected the fact that some of these factors were made constant for all plant seeds and only one factor was measured in the experiment.)
_______________________________________________

KEY QUESTION: Are our children learning with understanding?

Are they just memorizing facts, rules, mathematical procedures and definitions and have no idea what they mean? Is their learning connected to real life? Are they being given opportunities to apply concepts and skills to real life situations? Are the tasks our children at school engage in authentic tasks from real life happenings?

We parents need to ask these questions for the sake of our children's education.

DIVISION by multiplication and subtraction

2010-04-17T17:35:00.002+06:00

I've decided to turn this blog into a platform for sharing the tutoring experiences I have with my children. It is dedicated to all parents in particular and also to teachers, most of whom I know struggle on a day to day basis in helping students learn in school despite limitations. I was a teacher once, however, had the fortune to actually teach in school for only a few years. Now, I'm hardly teaching per se but nevertheless engaged in teaching at home with my children. Of course, only when they approach me for help, which most of the time they do only when they're struggling with homework.

____________________________

Here's one of my experiences with tutoring my little son. Hope you like it and can use it.

My eleven year old son came to my side one evening and said, “Mummy, I didn’t understand this.” It was a math problem. Class Five. The title read ‘Division by multiplication and subtraction.’ The teacher had worked out an example for them and my son had it in his exercise book, but apparently he didn’t understand it.

The example worked out was for 9848 ÷ 8

I went through his textbook to check the method it promoted and then I started off like this:

“You have Nu.100. You want to buy sweets. Each sweet costs Nu.3. How many sweets can you buy with Nu.100? Let's try this first, tubga?"

We went through this process together, trying to understand ‘division’ as a real life business.

Me: OK, Chunu (that’s what I call my son), think of how many sweets you think you can buy.

Chunu: mmm… 10 sweets?

Me: OK..so if you buy 10 sweets, how much would that cost?

Chunu: (works it out on paper)

10 sweets x Nu.3 = Nu.30

Me: Good! So, Chunu, if you buy 10 sweets, you will have how much money left over?

Chunu: (works it out on paper)

               100
               –30
             _______
                  70
             _______

               70 mummy! I have 70 ngultrum left!

Me: Can you buy more sweets?

Chunu: Yes. I have Nu.70 left.

Me: So, how many sweets do you think you can buy?

Chunu: mmm…. (struggling)

Me: When you bought 10 sweets, you spent 30 ngultrum, right? How much is double of 30?

Chunu: mmm… (works it out on paper)

            30
          +30
          ____
           60
         ____

Me: This is the same as…..? (I write on his paper, next to his addition)

          30 x 2 = 60

        So, Chunu, if you got 10 sweets with Nu.30, how many would you get with Nu.60? Use
        mulltiplication, tubga?

Chunu: mmmm…(works it out on paper)

            10 x 2 = 20

            Mummy…20 sweets!

Me: Yes! Good!

        So, Chunu, if you buy 20 sweets, you will have how much money left over?

Chunu: (works it out on paper)

             70
            –60
          _______
               10
         _______

             10 mummy!

Me: Can you buy more sweets?

Chunu: Yes. I have Nu.10 left.

Me: So, how many sweets do you think you can buy?

Chunu: mmm…. (struggling again)

Me: You have Nu.10 left. Each sweet costs Nu.3. 10 ..... 3 ….. think….. how many sweets can
       you get?

Chunu: mmm… (works it out on his fingers)

           3 …..+3 =6 …….+3 = 9 ……+3 = 12

Me: You have only 10, right? Would you be able to pay 12?

Chunu: No! 9! (works it out on paper)

              3 x 3 = 9

Me: So, Chunu, if you buy 3 sweets, you will have how much money left over?

Chunu: (works it out on paper)

               10
               –9
          _______
                1
          _______

                      1 mummy!

Me: So, how many more sweets do you think you can buy?

Chunu: mmm…. No! can't buy...

Me: Why?

Chunu: Only Nu.1 left ... one sweet Nu.3

Me: Good! How many sweets were you able to buy in total with Nu.100?

Chunu: (works it out on paper)

                 10
                 20
                   3
              ___

                 33
                ___

                        33 sweets!

We then converted the above process into the division format below:

Each sweet costs:              I have:                                       I can buy:
Nu.3                                  Nu. 100                                     10 sweets
                                                - 30                                       10 x 3 = 30
                                              _____
                                                   70
                                                - 60                                      20 sweets
                                              ______                                  20 x 3 = 60
                                                    10
                                                    -9                                       3 sweets
                                              ______                                    3 x 3 = 9
                                                      1

                                                                                             10 + 20 + 3 = 33

The answer: I can buy 33 sweets and will have Nu.1 left over.

Me: So, my dear Chunu, now let’s do 9848 ÷ 8.

9848

-8000                            1000 x 8 = 8000
______
1848                            100 x 8 = 800
- 800
______
  1048                            100 x 8 = 800
- 800
______
   248                                20 x 8 = 160
- 160
______
     88                                10 x 8 = 80
-    80
______
        8                                 1 x 8 = 8
-       8
______                           ___________
        0
                                       1000
                                         100
                                         100
                                           20
                                           10
                                             1
                                     ________
                                       1231
                                     ________

The answer: 1231

My son was excited when he got the answer correct, while I wondered if he understood what he did. He had been given three divisions to complete as homework. He did them all without the need for much guidance from me, so then I started wondering if he was actually getting it.

________________________

DARN! I had the above processes laid out beautifully in proper mathematical formats, but just couldn't get them pasted here. Didn't know what to do, so this is the best I could manage. Looks not very mathematical to me. Hope those who try to go through this post is able to understand. Best of luck!

an article

2010-03-15T13:17:00.000+06:00

For those teachers and others interested in the intrigues of maths teaching and learning, here's an article
by Steven Strogatz. Hope you find it useful, insightful and interesting. I thank Bhutanese Blogger for sharing this with me on my other blog.

Happy reading...

school initiative

2010-03-15T11:24:00.000+06:00

One of the things I long to see or hear of is a school's own initiative - could be related to any one of the following areas/problems/issues that instantly come to my mind:

teaching problems (e.g. large class and student activities)
low parental/community participation in school processes and development
child friendly school environment (non physical)
child safety in school (support system)
professional exchange among teachers
monitoring of teaching
monitoring of learning
remedial system for slow learners
support system (e.g. counselling) for children with problems
support system for the school
exchange programme between schools (e.g. remote and urban, east and west)
etc etc etc

We often tend to view every initiative as something needing government budget. I would say this isn't necessarily true. I would add it is possible to mobilize resource support from the local community, so long as the community is convinced of the need and the benefit to their children. But, of course, schools have to be given some autonomy to be able to take initiatives. I'm not sure if our government schools have this and how effectively they could use the autonomy if they had it. I just wish schools realized the need for 'autonomy' and the importance of using it for desired benfits to children rather than their own selfish benefits. If they realize this, it could be debated/discussed at the annual education conference for support from management at the district level and headquarters. The reality is that there's only so much that the government/ministry/districts can do for schools. What the schools implement with the children is what matters at the end of the day and so much of the implementation can be made easier if directly linked to the grass root level.

The core of the school system is leadership and team building. If the core is strong with a good understanding of what's best for the school, taking initiatives would be easier and made possible. Some people might remark that I say all this so easily, not being inside the school system. Let me clarify that I was inside the system as a teacher when faced with the problem of textbooks not delivered to school on time and teaching aids not available. I remember having to wait for the Bhutan History textbooks in the late 1980's when they were written for the first time. It was no point grumbling or complaining, I thought to myself, so I discussed the matter with my students. I had spotted a calendar with pictures of the eight manifestations of Guru Rinpochhe at a shop. I could've bought it myself, but that wouldn't have been sustainable. So, instead, I and my students decided each one would contribute Nu.2/-. The class captain was responsible for collecting the contribution and I was responsible for buying a copy for each section from the shop. Several of our learning objectives were achieved with the help of the calendar, in the absence of the textbook. Likewise, I would work very hard in preparing teaching aids and thinking of the best ways of making my students understand concepts (one of the most difficult being the solar system, I remember!). Above all, I was very determined NOT to exploit or bully my students and I stood by that very firmly. For instance, students would come running across the ground when they saw me approaching with a heavy bag over my shoulder. They would compete with one another to carry my bag, but I never ever allowed any one of them to carry it for me. A simple thing as this matters because every simple and small thing has big impact on the values we grow up with and exhibit in society as adult citizens. We adults (teachers included) miss the point when we make little children rush to a shop nearby to buy a packet of cigarrette or bottle of beer or doma or when we invite them to our quarters during the weekend to do our household chores free of any charge. We miss the point and then wonder why these children have grown up to love or enjoy smoking, drinking, chewing doma, bullying, etc. We don't realize we actually failed to provide them with an envirnment conducive to their safety and positive development. We look to the external for support and assistance when many of the things are just a matter of we ourselves being conscious of our duty and moral responsibility. From this perspective, initiatives are possible and if there is objection from the ministry/district for whatever reason then I would say it is not to be given up but communicated explicitly and clearly why it is good for the school. Who knows? One school's initiative could be replicated by many other schools. Now, wouldn't that bring a sense of pride to the initiator? On the other hand, there might be no need for a uniform initiative across all schools in the country given the different local needs (such as, between urban and rural, remote and semi-urban, etc).

great!

2010-03-05T10:30:00.000+06:00

I was watching BBS just a few days ago and I came to know that a school in Dagana had used the EEC electoral method to have their school captains elected. I think that's a great initiative and very timely, given our recently instituted democratic system. And, to share with you, the same idea was adopted by the Royal Thimphu College (private) last semester (July-December 2009), that was actually its first semester, to have the Student Government members elected from among the Student Body by the Student Body for a term of one year. There are also other student representatives (club coordinators, services coordinators, academic representatives, etc) that are elected by the Student Body.

What this example tells us is that it is not just the lessons conducted in class that provide learning opportunities to students, but also the way the school is organized. If out there it is democracy, then in here (school, college) also it has to be democracy. Similarly, if happiness matters out there so does it matter in here (school, college). If a school makes the attempt to adopt 'happiness' as its theme, then it would to quite an extent make the effort to introduce/innovate ideas and systems within the school to ensure the students and teachers are happy. We need not even wait for people from outside the school to dictate to us what to do to keep the school happy.

Students get confused when there are contradictory notions within the school system and between the school and home/community/society. I would reckon it is the responsibility of school leadership to bridge any such gap to the extent possible.

good news

2010-02-21T15:19:00.000+06:00

I read in a recent local newspaper (forgot which and when exactly) that the Ministry of Education is planning on opening a website for schools to share ideas. It was mentioned that remote schools in particular would benefit from this. It was indeed a pleasant surprise! Great! I hope it works and I hope this blog site, if any progress, will supplement/complement government efforts.

GNH mathematically

2010-02-08T21:37:00.000+06:00

I thought I'll begin with my favourite subject - mathematics. I do not claim to be an expert teacher. I cannot be as I taught only for a very few years. I can only claim to be a conscientiously creative teacher with the potential to turn ordinary every day happenings into teaching lessons. I am inspired by one of my professors, Jim Parsons, whom I'll always cherish as an unconventionally jolly good magical teacher and writer.

Coming back to the subject, I chanced upon RICE and it got me thinking about problem solving. This is what I gathered from a 2008 presentation by a certain Cynthia Lanius.

Slide 10

“A problem-centered approach to teaching mathematics uses interesting and well-selected problems to launch mathematical lessons and engage students. In this way, new ideas, techniques, and mathematical relationships emerge and become the focus of discussion.”

Slide 11

Problems are “starting points for serious explorations, rather than tasks to be completed.”

Slide 12

"Misunderstanding, confusion, and being wrong are natural parts of problem solving, and being able to recognize that you are wrong can be just as valuable as knowing that you are right. But the process of reaching that answer, struggling, being wrong, trying something else, is what is called learning."

Let's look at a problem for exploration, adapted from Cynthia's presentation.

Slide 14

Choden has a large piece of paper. She tears it into two equal pieces, and hands one to Megraj. She continues to do this; tearing the paper she has left into two equal pieces, handing one to Megraj.

a) After two tears, how much of the original paper does Choden have left? How much does Megraj have?

b) After three tears?

c) After four tears?

d) After twenty tears?

e) After infinitely many tears?

Adding some geometry to it for richer exploration, we could present the problem like this.

Slide 16

Choden has a large isosceles right triangle. She tears it into two congruent triangles that are similar to the big one, and hands one to Megraj. She continues to do this; tearing the triangle she has left into two congruent triangles, handing one to Megraj.

a) After two tears, how much of the original triangle does Choden have left? How much does Megraj have?

b) After three tears?

c) After four tears?

d) After twenty tears?

e) After infinitely many tears?

Now, if we were to adapt this lesson to discuss and solve GNH-related concepts and values, how might that be possible? Let's think and share ideas....

The cross-curricular theme of GNH

2010-02-02T20:28:00.000+06:00

Maybe we can begin with the cross-curricular theme of Gross National Happiness (GNH). I think it is important first of all for ALL teachers in our country to clearly understand the concept of GNH. So, let's begin this blog of sharing of ideas among teachers with trying to understand GNH at a common level.

Anybody wish to try explaining GNH?