Day 6 - 31 August 2011

Today will be the last session with Dr Yeap and his wonderful Maths activities.

ASSESSMENT

I would like to share with my teachers the unorthodox way of assessing children’s Maths understanding. To bring the children outdoor as what Dr Yeap had shown at the Hort-Park.

 

From the Hort-Park Frame, he showed us many Maths concepts that could be applied. For instance, children can learn multiplication, division, addition and skip counting just by looking at this frame.  It would be a fun learning experience. 

 

This is a good example of incidental learning. We could also assess the children with questions of the Maths concepts that they have learned during the outdoor activities. He said that when assessing the children, need not be just paper and pencil. We can assess children through interviews and observations during activities in and out of the classroom.

MRT TASK

When we were asked to calculate the height between the level one and the basement of the MRT station I thought it was madness! However, with our short ruler, we managed!

Our group found that there are 62 steps and the height of each step is 15cm.

Therefore, the height between level one and the basement is 62 X 15cm =930cm. That is 9.3 meters!

STORY

The story about ‘How big is a Foot’ to introduce standard unit in length is funny. The children would love such story. Teaching (teacher) and learning (children) Maths could be a fun experience. We can use storybooks to relate to the Maths concepts.

Dr Yeap ended the day with the story about a butterfly. It is a heart-wrenching story. As educators, we must never shortchange our children by spoon-feeding them with answers without teaching them how to get the answers. We can do a lot of damage to a child if we do not go through the proper process. Just as the saying goes, 'Give a man a fish and you feed him for a day. Teach a man to fish and you feed him for a lifetime.'

Click on the  link to read the full story of the butterfly http://instructor.mstc.edu/instructor/swallerm/Struggle%20-%20Butterfly.htm

THANK YOU

Even though it was a 24-hour session, I have learned a lot about Maths. It is not only about numbers, it is a HOLISTIC APPROACH to develop oneself. In life, metaphorically, I do not want my children to be last in the queue. As it is, most of my children are living in a challenging situation and I hope I could help them to move up to the front of that queue. Thank you Dr Yeap for helping me to help others.

Day 5 - 26 August 2011

FRACTION

Another day of a 'mind boggling' session with fraction.

1. In 1 how many ¼ are there? (1 ÷ ¼ = 4)
2. In ¾ how many fourth are there? (¾  ÷ ¼ =3)
3. In ¾ how many ½ are there? (¾   ÷ ½    = 1 ½)
4. Tom has ½ liter of orange juice. He needs 5/7 litres of orange juice. How more orange juice does he need? 

I understand better when Dr. Yeap represents it with a model.

BLOOMS TAXONOMY

I learned about Blooms Taxonomy, a cognitive process that describes different level of learning and understanding – KCA- Knowledge, Comprehension and Application.  The teacher could assess the children’s understanding of the topic based on their knowledge, comprehension and application.

Find out more on this website http://www.kurwongbss.eq.edu.au/thinking/Bloom/blooms.htm

PICK’S THEOREM

 The area of the figure is related to the dots!

To find the area of the figure was another interesting activity that Dr Yeap gave us. He introduced the Pick’s Theorem in calculating the area of simple polygons. It was amazing to see the students’ calculation of the area of different shapes. It was found that the area of the figure is related to the dots!

Click on the link to find out more! http://www.geometer.org/mathcircles/pick.pdf

SPIRAL APPROACH

Dr Yeap told us that Singapore’s schools adopt the Spiral Approach curriculum (made famous by Jerome Bruner) whereby the children would be given many opportunities to encounter the topic without repetition. The children will learn the topic incrementally.

GRAPHS

We did Graphing using the clothes peg we got. Our group did a line graph that Mr Yeap said was not right, as it did not give a right representation. I learned different types of graphs; bar graph, pie graph and picture graph. Something new that I learned about graph is that when doing the bar graph the width must be equal.

Dr Yeap opened a whole new world of Maths to me. He went through a process to make us understand the word problems, slowly pulling it apart and then putting it together. He made us see the connection.

Day 4 - 25 August 2011

WORD PROBLEMS

 Dr Yeap came back with the number tricks. It was interesting to hear different ideas of how they get the students answers.  I realized that Dr Yeap always asked, ‘what other ways, are you sure?’ He made us think discuss with our friends and find out the answers. Teachers are to allow children to experience variations of Maths problems and to explore different ways to solve it and arrive to an answer. He made me laugh when he said do not be a COMMUNIST TEACHER because I had one all my school life!

NAMES TO REMEMBER

I supposed my teachers did not know about Zolten Diene the person who introduced about Maths variation, Jerome Bruner who introduced the CPA approach and Howard Gardner the multi intelligence approach.

For more information, please visit this website http://www.zoltandienes.com/?page_id=226

APPROPRIATE LANGUAGE INSTRUCTION

I learned that it is important to use the appropriate language when giving instructions to the children as the children may have a misconception of what being instructed. For example when using ‘ illegal’ language   in fraction: one out of four instead of one fourth. No wonder my brain got messed-up when it comes in doing fraction because I got all the illegal stuff.

PART WHOLE,CHANGE,COMPARE

In the word problems I learned of 3 different situations: Part whole, change and comparisons. Examples:

1. There are 37 students in a class. 19 students are present. How many students are absent? –Part whole
2. Tommy had 37 marbles. He gave Peter 19 marbles. How many marbles left?-Change
3. I have $37; I have $19 more than you. How much do you have?- Compare

Important Note:In additions and subtractions I learned that units must be the same.

SHAPES

Dr Yeap proved to us that equal may not be identical and doesn’t look equal doesn’t mean not equal. It was an amazing experience trying to create rectangle and   triangle of different shapes to prove the point.

ENJOYABLE LEARNING EXPERIENCE!

Day 3 – 24 August 2011

VIDEO SESSION

 Today session we had a guest lecturer – Ms Peggy Foo. She showed us a video of a teacher conducting a Maths lesson and we are to observe and make comments on these areas:

-          sitting position

-          level of engagement/involvement

-          use of materials/manipulative

-          flow/sequence of lesson

-          communication(teacher-pupil, pupil)

-          classroom management

-          questioning techniques

-          attitudes/disposition of teacher

-          differentiation

OBSERVATION SKILL

After the feedbacks from the students of what went right and what went wrong and the areas that can be improved, she showed us a video of the same teacher conducting a revised Maths lesson after the feedbacks from the observers. We saw a mark improvement in the teacher’s lesson. The video made me to be more observant when I am observing my teacher teaching. I gives me the skills on areas to look for and be more analytical.

LESSON STUDY

This lesson study provided the teacher with constructive feedback for her professional development and growth. I think lesson study is great for teachers to exchange ideas and introduce strategies that can improve ones teaching. The teachers and children would benefit from this professional community collaboration.

NUMBER CONSERVATION

In the third case study, Ms Peggy showed a video of herself teaching number conservation to K1 children. The children were given 5 unifix to construct different structures. No matter what structure they made, the number will be the same.

That's me exploring unifix!

COMMUNICATION AND QUESTION TECHNIQUES

Ms Peggy communicated and engaged the children with questions. The children’s thinking was stretched when she asked them how many ways can be done to make different structure. They were also asked how the structures are the same and how are they different. I thought these questions were difficult for the K1 to understand. Nonetheless, I learned that the teacher plays a very important part in developing children’s learning. To facilitate, to scaffold, to challenge and design task for differentiation of capabilities would give all children the opportunity to learn and progress.

                                                             

VISUALIZATION - TANGRAM

I took a longer time to complete the tangram activity than I thought. I supposed my visualization skill is not that sharp. Some of my friends said that it was easier to form a triangular shape with the tangram than a square which I found otherwise. Nevertheless, I enjoyed the exercise very much!

Day 2 – 23 August 2011

GAMES TIME

Another thought provoking day. The game of Spinning wheel- Making the largest even number, taught us to look at the probability. Probability - a branch of Maths that gives a numerical value the chance of event happening. This game made us think the probability of the numbers that would result to the answers. Dr Yeap challenged us further with questions, “are you sure? Do you think so? 

When we played the ‘pick up sticks’ game, we were taught to use our observation skills. We are to observe the number patterns. What would be a good number or a bad number? We tried different ways to see the results.  After three games with my friends and prompting by Dr Yeap we then realize the patterns.

He said children should be given the opportunities to try different ways and to explore to find the answer. We are to look at the skills that the children could acquire when playing this game.

PROBLEM SOLVING-REASONING

Maths after all is about problem solving and we should use Maths as a tool. We so often give the children the questions and correct for them. We should give the children enough time to correct themselves, make connection and figure out what and how to do!

DIFFERENTIATION

Children have different level of intellectual and capabilities. Teachers should give differentiated instructions for children’s learning.

Dr Yeap showed us the ‘traditional’ way of doing the long division and using the language that my teacher used, I could help but laugh out loud. That was why I could not understand Maths. I just listen and did as instructed without understanding – my teacher must be a COMMUNIST with illegal license to teacher!

JEROME BRUNER-CPA APPROACH

Dr. Yeap modeled of how Maths should be taught.

He gave steps by steps instructions, using concrete materials or cutting papers, he would then make a representation by drawing on the board and finally in numbers. He said that what he showed us is the Jerome Bruner CPA Approach. It is a learning process from concrete, pictorial and then abstract. It is important that at the kindergarten level, when teaching Maths to begin with real objects (concrete) and then pictorial. At this level children learn Maths through representation.

I will always bear in mind that the ability to memorize is not a human strength. Maths is not about memorizing, it is about developing the children’s number sense (which my son said that I am lacking) L metacognition, visualization and generalization (patterns, relationship and connection).

Know more about Bruner: http://www.infed.org/thinkers/bruner.htm