If you were asked to teach children on place value, how would you sequence the five learning tasks and WHY?:
-Place value chart -Expanded Notation -Number in Numerals
-Number in Words -Tens and Ones notation
Below will be my suggestion 1. Number in Numerals First of all, I would introduce the number in numerals. My reason is that recognizing numbers in numeric form is one of the fundamental math concept that children are most familiar with. Children will be invited to perform one to one counting using manipulatives such as wooden chopsticks or ice cream sticks. Moving on, they will show cardinality understanding by writing down the total number of sticks counted.
2. Tens and Ones Notion Next, I would introduce numbers on tens and ones. To illustrate using concrete materials, sticks will be bundled in tens using a rubber band. Each time the child counted ten, the sticks will be bundled as one. Teachers will reinforce idea that the sticks can be categorized into tens and ones.
3. Place Value Chart The third step would be showing the place value chart to the students, after they understand the tens and ones notion. Besides tens and ones, there are higher values such as hundreds, thousands and greater. Teacher may draw the students attention to the progressive increased of the number of digits as the value increases.
4. Expanded Notation The more technical step is the introducing expanded notion, where student will see the relation between these numbers. Students will see by adding hundreds, tens or ones would results in a final number (e.g. 345: children will see that 3 hundreds is equivalent to 300 and 4 tens will be 4o)
5. Number in words Finally, students will be introduce to numbers in word form. This step involves a larger role of language and literacy, which might be more difficult for children to fully master, especially two digits numerals such as eleven, twelve etc.
Speaking of problem solving, I'll not be the very first people who can come up with a solution whenever there is a problem. Relating it to Math, problem solving reminds me of those problem sums that would appear at the last section of the exam paper during my primary school days. A short paragraph of sometimes misleading or confusing sentences that demanded us poor students to come up with a solution. Haha. I sound bitter, but being able to solve those problems gained me a sense of accomplishment back then. As Algebra was not introduced till secondary one, those problem sums were taught to be solved by drawing blocks/ boxes to represent units.
Basically, students back then solved math problems by following a standard procedures; problem solve by selecting the correct formula or steps. However, i feel that young children should experience solving problems through authentic situation rather than what is depicted on paper. The four of us, Seow Wei, Sola, Joanne and I met up at Plaza Singapura after work to discuss about how and where we could conduct an interesting Math activity for a group of kindergartners. We were walking towards Ajisen for dinner, and as i stared at the tiles on the floor, an idea popped up from my mind. I was thinking of conducting an estimation and counting activity, where children predict how many of them could stand/sit/lie down on a particular number of tiles on the floor, or how many of them are needed to reach the other end of the entrance of a shop while holding hands. We also shared many other ideas as we proceeded. When we reached Ajisen, our stomach conquered our mind to think as we ate heartily and side tracked for a little while. Finally, we decided on the activity by inviting children to work in pairs, to create presents for Children's Day by purchasing needed materials from Daiso given a budget of $10 each. We thought that it would be easier as everything is selling at $2 (not trying to advertise). This activity integrated a number of skills, from team cooperation and planning, to math concepts such as counting money, and operations including addition and subtraction. The activity provided an opportunity to problem solve using a fixed amount to obtain the necessary items needed for making the presents, as children will have to keep in mind not to overspent and to prioritize which is more important.
Having taken a similar module when i was studying for my diploma in early childhood, it turned out to be a whole new experience, as the first session kicked off with many brain-wrecking activities that got me intrigued. The Math module that I has during my diploma course was more theory-based, while the one conducted by Dr Yeap was much more hands-on.
“Preschool parents, in particular, often ask for pencil-and-paper activities with numbers for their children long before the children are ready for such abstract work.”(Copley, 1999, p.212) I like seeing many manipulatives and materials used during the class, and the games and activities that come with it. It further reminded me that Math should be taught in a fun way so that preschoolers could learn and at the same time, enjoy learning Math. I always believe that the foundation of Math concepts should be build through hands on experience, especially for preschoolers.
I've also learned a number of cool math tricks! The addition of the numbers on 2 dice and the poker card tricks by spelling the numbers. Not forgetting the 'take one or two" game, it was something I played when I was in primary school! Today's session gave me some ideas of the activities i can include in the math learning centers in my class! Before I end, I found this really cool clock trick! somehow, it always ends at 6... hmmm...
When I was in primary school, I would often look forward to computer class. A typical Math class I had everyday would include learning tools such as the whiteboard that the teacher would used (not forgetting the unbearable smell of the markers), workbook, worksheets, ruler and the never-seemed-to-end rote practice of Math sums. Computer class opened up a new way of practicing Math as it incorporates more fun into learning. The school offered a number of computer software that helps students to learn and practice Math skills such as operations, geometry, patterning, estimation and many more. There were many fun games in the program that somehow made students enjoyed learning math subconsciously. I can vividly remember controlling the character named Coco in the game, to help him reached the top of the building by planting seeds for him to climb. The game involved math concept like simple operations, counting and problem solving. Using technology like computer software, Math had been a very enjoyable learning experience for me.
There are various emerging technology such as electronic gadgets like iphone and ipad. The children in my center as young as 4 years old know how to use their parents' iphone to play and download games. Just last week, a child in my class came to me excitedly and said, "Teacher Xinli! I have ipad you know. My daddy buy for me." I notice, or most of us should have realized, that technology has taken over most of the current generation's play experiences, from watching cartoons to playing Wii games, PSP etc. There was a 5 year old boy who told me that he likes staying at home because he can play video game with his brother all day. Children now spent lesser time critically thinking to construct materials to play, instead, they can just hold on to an iphone, shake it, and the dice in the screen will roll by itself. Even though I strongly feels that children need authentic materials to learn, the virtual element of technology has overshadowed what I advocate- first hand, real, and hands on learning. I've heard of this joke, about how human of the future generation will have a much bigger head with small and limp body since they will only use their brain to create more advance technology and then rely on those inventions. Some technological tools to learn Math: However, I cannot underestimate the power of technology as it has greatly influenced how children acquire knowledge nowadays. As I have previously mentioned, I did find learning Math enjoyable through the technology approach too. More importantly, it is how adults educating children weigh the importance of both technology and hands on approaches to strike a balance in children's learning and their attitude to learn. Thinking through my teaching experience for the past one and a half year, I have never really include technology into children's learning. I find that it is a time to start after reading the chapter, as I have a clearer idea of the impact of teaching Math to children using technology, as well as the appropriate tools to teach Math.
The first thought that crossed my mind when i flipped open the textbook was, "Wow, it's colourful." It didn't strike me as a book that will have colours, so i was pretty surprise. It kind of reminded me of my Biology textbook during secondary school. Frankly speaking, i had this stereotypical attitude towards math since young. I've scored amazing high marks, but also outrageous bottom line marks during my years of study with math. That is probably one of the reason that made me mad, it wasn't consistent. The 6 principles mentioned in chapter one has become a guideline that i will reflect on each time i conduct a math activity in class. I always conduct hands on math activities to my class of children. I believe that children need to learn mathematics with understanding, and that should be build through authentic experience rather than memorizing formula. There was once i did estimation and measurement, where the children estimate how many of them could stand on a chair, squat under the table, stand on the table etc. They had a lot of fun! And then I came across this video:
I am talking about preschool's math, I wouldn't be able to designed a hands on activity to teach "Differentiation" (I dreaded this topic so much during secondary school).
Chapter 1 also addressed positive attitude as one of the factors in becoming an efficient educator to teach math to young children. Eventhough math is never my favourite subject, I do find teaching math to preschooler and kindergarten fun. Many of us should be familiar with Albert Cullum (A Touch of Greatness). He is one of the very inspirational educator that I really look up to, as he was a teacher that would go beyond textbook in making learning a joyful experience. Below is a blog entry by Albert Cullum's ex student:
"Al Cullum changed all that. He taught me that there was a world of greatness, creativity, and beauty just waiting to be experienced. Every thing Al touched was magical, be it history, math, poetry, or art. His classroom hummed with joy and excitement. Every subject was treated with contagious creativity. We solved math problems in King Tut's tomb, raced around the room solving geography problems, read great poety to our peers, guessed the names of masterpieces of art and I'm not even scratching the surface." Ken Ramirez. I've had children who are unable to differentiate 12 and 21, 13 and 31 and so on. One of the child in my class would ask me how to write the number 9. It worries me sometimes that situation like this happened. I would go home and cracked my brain to think of interesting ways to help them recognize numbers. One of it was "all then 'teens' begins with 1". My other challenges would be parents, because they are more keen to see worksheets and results, while I always always focus the process. Chapter 2 highlights many familiar child development theories that connect to how children learn math. I agree that visual aid is a very important tool in teaching math. Children need to see and touch to internalize the fundamental of a particular math concept. Providing physical model, pictures, manipulatives or real objects is definitely going to make math learning fun and effective for young children. The coordination of teachers and the classroom environment plays a crucial role in providing optimal math learning experience for children. It would be nice to have us sharing about some of our interesting teaching experience on Mathematics =) With that, i shall sign off now~