Reflection

The most impactful thing that I have learned from this module is the different activities introduced during the lesson. for example, the my favourite activity is still the poker card activity whereby we had to sort the cards in a method so that it turns out to be like a magic trick to encourage children to learn number words. I was so impressed with the activity that i carried out with the children for a few days. To tell you the truth, I was very pleased with their response. The K1 and N2 really taught it was magic! The K2 was really smart, at the end of the trick, they were able to tell me immediately that it was not magic and that it can be done by sorting and placing the card according to a method. I was quite pleased to hear such response from them as I did not expect them to figure out the trick so quickly.

Lastly, I feel that this course has provided me with information and resources to plan for an enriching mathematics lesson for my children. Also, it made me realise the need to constantly provide children with opportunity to imagine, visualize and problem solve the thinking process. For instance, when I was teaching my N2 children about shapes using their body, I asked them to think about forming a circle using their body. The children came up with two ideas in total.

Firstly:

  The children suggested this method of making a circle using their body.

The second method:

One of the children suggested using hands to form a circle.

After the lesson, it really made me feel that it is important for children to problem solve themselves as they will be able to conceptualize concepts and create their own understanding of ideas. thus, they would be better able to grasp the concept further and build a stronger foundation at the end of the day. As the saying goes, it is the process and not the product that is important.

Geomatric

When the activity was first brought to us to figure out the area of a pentagon, I was lost and rather in fear. I have always been weak at maths and geomatry was on my "most hated concept list" as I could nv realli visualize or find a reason or statement that makes me understand the rules of geomatric. I guess my spatial sense was not very developed at that point of time. However, as Mr Yeap and my classmates goes through the solutions and methods to approach this activity, I was able to pick up and understand and see the relationship much faster than I expected. I was even able to relate certain relationships that I have learned previously in primary school! I guess that's what makes it easier as I had certain knowledge on the topic and now I am just refreshing or rather assimilating and accomodating the concepts that I have learned previously. Thus, I feel that as teachers, we should plan according to the van Hiele levels of geomatric thought as this will help children to develop their spatial sense as we will be able to plan accordingly and appropriately to their developmental level. Last but not least, as Van De Walle explains, consistent introduction of experiences with shapes and spatial relationships will help children to develop spatial sense (2010, p. 400).

Reflection on Practice

Two things that are already practice in pre-schools:

1.Learning the relationship of more, less and same.

This concept is usually taught when children are of 4 years of age. It is an important concept as children will be able to relate and see for themselves the relations of numbers and exposing them to counting on. It also helps them to understand the meaning of more and less. This is usually taught using concerete materials such as counters and picture cards to impart this concept.

2.numeral writing and recognition

As mention in the book, the common practice for children to learn to write and recognise number is by repeatedly tracing numerals, writing them in the air, on the board and tracing them on sand.

Two things that are not common practice in pre-school:

1.Dot cards as a model for teaching number relationship

So far, it is not a common practice in Singapore for teachers to make use of dot cards to teach number relationships and counting. We tend to use items such as flash cards with pictures of dogs, cups and etc to aid in children's counting or concrete materials such as buttons or counting cubes.

2.Part-part-whole

Again, part part whole is not taught adequately in our local context with dot plates. concrete materials such as counting cubes and fingers tend to be used to teach part part whole. Our local context tend to focus on only teaching part part whole with addition of the same number. For instance, 5+5=10, 4+4=8 and 3+3=6 instead of 4+5=9.

Reflection on chapter 7

After reading the chapter, it brought me back to the days where I had attended a mathematic module in Australia for 3 months. I was first introduced to the use of calculators in the classroom during the first lesson and I was amazed by how they had integrated and implemented the calculator as a tool and part of the curriculum. The textbook has clearly depicted the same effectiveness and how calculator act as a tool to aid in children's understanding of the concepts such as counting on, counting by twos or threes and improving their oral counting or pattern identification (Van De Walle, 2009, p. 113).

I remembered vividly that one of the example that I was shown  a video in which calculator was used as a tool to teach the concept of place value and counting on. Kindergarten children were asked to observe the patterns in the number as they add 1 number to a value continuously. Many children stopped at the value of a thousand. when the teacher asked what they had noticed, many of them replied that they notice that the place of tens would only change when the numeral in ones reaches 10. The same goes for the thousands and hunderds. Also, they were able to identify the number of numerals makes hundreds, tens and thousands. For instance, one children explained that if there are three numbers, it means that the place value is hundreds.

Thus, I definately agree that using calculator and technology should be integrated into mathematics for young children as we are in the 21st century and technology will always be part of our lives just like the use of a calculator.

one particular activities / tool that I found on the websites that I  like very much:

I like the video that showed place value centers:

 http://www.learner.org/vod/vod_window.html?pid=873

This is because I feel that the activities shown in the video is creative, fun and engaging at the same time. The concept of place value is constantly reinforce and the children were able to grasp the concept completely. I especially like the measurement of their friends and items in the classroom with an inventory sheet for them to write down the answer. This is because the children not only learn the concept, they also make use of team work and problem solving skills to complete their task on hand. This is something that I will like to have in my classroom whereby children foster independent learning.

The tool that I very much like is called concentration :

http://illuminations.nctm.org/ActivityDetail.aspx?ID=73

I like this game as it allows children to use their prior knowledge and concentration to play the game. Also, it reinforces concepts and allows children to play in pairs or alone. This game allow children to match numbers according to their spelling, or items representations or depending on the children. They may even select other concepts such as shapes and fraction to play with. Thus, I have chosen this game as I feel that it is engaging and encourages children to facilitate their thinking skills as they play.

Therefore, technology enhances the extent of content and concepts that student can learn and provides opportunities for children to attempt a variety of  challenging problems (Ball & Stacey, 2005; NCTM Position Statement, 2008; Van De Walle, 2009, p.111).

Sequencing the 5 steps

After using concrete materials, I would sequence 5 steps according to:


Step 1: Numeral

This is because I would first start with a concept that the children are familiar with. Which in this case, would be counting the sticks to find the total number of sticks. Also, 34 is a number that the children of this age group should be able to rote count and recognise.


Step 2: Number in tens and ones

The second step that I have chosen is number in tens and ones as I would like to relate counting with ones with counting with tens. For example, using the sticks that is bundled up in tens, I would like to make use of it to show the children that they can count in tens by just looking at it instead of recounting the sticks one by one before deriving the answer that there are 10 sticks bundled together.

Step 3:  Place Value Chart

I have selected place value chart as the third step as to me place value chart is like a metacognition step that the children undertakes to understand the concept of tens and ones better and also to understand the place value of a numeral. Thus, it is like a chart that allows children to better able to see the numbers in tens and ones in a different format.

Step 4: Expanded notation

The fourth step that I have selected is expanded notation. This is because  The children would have understood the place value of 34 well after step three. Thus, they would be able to understand more easily if I introduce that 3 tens is acutally equivalent to 30. If they are unable to do so, I would ask them to count only the sticks that are in tens and find out how many sticks are there altogether. From there I would try to relate to them that 3 tens and 4 ones is made of 30+4 which gives you 34.

Step 5: Number in words               

                                                         thirty-four

I have chosen this to be the last step as children are just learning to recognise and spell the number in words. Thus, I feel that the rest of the steps allow children to make connections more easily as it links with the notion of counting and understanding the concept of tens and ones unlike this step.

Reflection on environment task

According to Van de Walle (2009), "Rather than building on prior knowledge, teaching for problem solving often starts with learning the abstract concept and then moving to solving problems as a way to apply the learned skills."

Thus, from the activtiy we have created, we have made used of the children's prior knowledge of the concept addition with the incorporation of the concept of counting money.

In my group's activity, we have decided to use  the supermarket to allow children to carry out their tasks as it is an environmet that allows children to experience hands on and relates to their everyday life. The task for the children would be to purchase a particular brand of loaf of bread that cost $1.75. They are given $2 in coins of 50cents, 20 cents, 10 cents and 5 cents. They would be asked to use the coins that they have to purchase the bread by giving the exact amount to the count.

Using the features of a problem for learning mathematics, I have broken down the environment task that my group has planned accordingly to these features.

• It must begin where the students are.

           My group has chosen the supermarket as it is a place that most children would visit almost once a week with their family members. In addition, most centres would have a dramatic corner that allows children to dramatise grocery shopping. Also, for kindergarten 2 children, they are learning the concept of money. Thus, it would be fun and interesting for them to take charge of paying at the cashier and experience it in real-life situation instead of just acting out in their dramatic corner.  

• The problematic or engaging aspect of the problem must be due to the mathematics that students are to learn.

          The problem in the task for the children would be trying to use the coin to add up to the specific amount given to buy the bread which is $1.75. This is because they are not given the exact amount. Thus, the children need to work out on the number of 50 cent coins, 20 cents coins, 10 cent coins and 5 cents coins needed to form $1.75.

• It must require justifications and explanations for answers and methods.

The children would be able to justify for themselves and with their partners how they derive to the cost of $1.75. This is because the children are free to choose the method that they would use to come to the cost of $1.75. For instance, some children may immediately understand that 3 fifty cents make up $1.50 while there are children who would slowly add up the coins individuly to amount it to $1.75. Also, they need to be confident of their own counting as the teacher would not check the amount of money that they have counted before making payment at the counter.

What did I learn from lesson 1?

What gave me the most impression among all the problems that we have seen during our first lesson was the video and the activity on the paper clips and the poker cards.

The spelling numeral activity was an eye opener to me as it showed me how play-based activity and manipulatives aid in constructing a mathematic lesson. I was really amazed by how the activity works and I totally enjoyed the process of figuring out how to come about with a method in order to carry out the trick. Thus, it has shown me the importance of allowing our children to think and figure a concept on their own instead of explanation by the teacher.

The video provided me with an insight as to how to carry out an activity that facitlitates children's problem solving skills and metacognition. It gave me an opportunity to observe how the teacher questions and facilitates children's answers without spoon-feeding them. From this video, it had taught me that children would be able to figure out concepts on their own, however, as a facilitator, we must use the right approach or instruction to help them. However, I would very much prefer to see how the teacher actually used differentiated instruction to aid in the students who did not understand the concepts so that I am able to observe and learn from him.

Lastly the paper clips has proven to me that mathematics is not just about learning an individual concept that should be taught in a particular method. A concept can be solved by different methodologies based on one's own understanding and deriviation. Thus, from this activity, it has shown that concepts can be linked and connected to one another. Also, the thinking and discussion approach has shown it's effectiveness as everybody plays a part in wanting to solve the problem and learn from one another at the same time. Therefore, my ideal lesson with the older age group would be something like the discussion that we had held in class as it has throughly displayed how interactive and engaging a mathematics lesson should be. 

Reflection: Chapters 1 and 2

After reading chapter one and two, I feel that the author is trying to convey the message that we should encourage children to be actively process thinkers, explorers and investigator in learning mathematical concepts instead of just spoon feeding children with procedures and explanation that might lead to memorisation of concepts.


I definitely agree with this message as I too believe that children need to understand the concept before being able to grasp the concept fully. Therefore, one of the ways that I try to make use of and the authors have mentioned in one of the implications for mathematics would be to build in opportunities for reflective thought. For instance, when I was teaching my children multiplications, the children were initially unable to come up with an explanation for their approach towards a sum during a class activity. However, after modelling and asking these questions a few times, the children soon were more confident and were more willing to attempt explaining their method’s to the class. For example, they were asked to explain how they had the answer 3twos after looking at the pictures in the questions. One of the children explained that there are three groups of two, thus, she derives the answer of 3twos. Another child mentioned that there are altogether 3 rectangles that represents as groups and in each rectangle, there are two birds. The first child based her explanation on her knowledge of equal numbers that she had learned before this topic while the other child tried to explain more explicitly in his own words.

Also, as a teacher, I agree with the authors that we must treat errors as opportunities for learning. I would always try to make it a point to sit with the students who made errors in their work to work with them to see if they could identify their own mistakes or at times, I would notify the child that she has made an error and would ask her to try to resolve or problem solve the error by herself until she needs my help. This implications has indirectly boast the children’s confidence and interest in mathematics as they no longer feel upset about making mistakes but instead, have the drive to want to solve the error.

Lastly, I would use concrete materials and counting manipulative such as cubes, wooden blocks and etc to incorporate it into my teaching to provide a visual image to help them better understand the concepts. After reading the text about ineffective manipulatives, I realise children with difficulties understanding the concept was carrying out mindless procedure as their focus was on trying to get the answer instead of the process. Thus, this would be definately something that I would like to reflect upon and work with these children to focus on their process with them. However, I failed to imply the encouragement of the use of various methodologies to a problem as initially, I thought it would become a foundation to all children to learn the same method so that they would be better able to understand the next concept that I would be teaching. Nevertheless, I am willing to change and imply it into my classroom setting. Also, I agree with the authors that we should inculcate technology-based models into our teaching as it would act as a tool for children to develop their own network of methodologies and understanding of the concepts.

In conclusion, as a learner and a teacher, I believe that helping children develop relational understanding between concepts and making connections is more beneficial than just developing procedural understanding in children as they will be truly able to understand and retain each concept in their mind and assimilate and accommodate new knowledge prior to what they already know.

The boy is trying to count in twos with the aid of the straws.

the child is using the abascus to figure out how many beads makes the numeral 14.

The children are exploring with the balancing scale by selecting different items based on their choice to see which of them are heavy or light.