Everyday, there are many opportunities for children to practice counting. Without prompting, my N2 children will "report" to me the number of children that are present and absent for the day. With half-day programme children leaving the school after lunch, the children will count again and tell me the number of mattresses that I have to prepare for them during nap time.
All of them know how to count beyond fifty; some even beyond hundred. However, after reading Chapter 11 and attending the class on place value; it made me wonder if my N2 children comprehend the whole-number place-value concept.
Few days ago, I did an experiment with the N2 children. I placed fifteen unifix cubes on the table and delibrately connect ten unifix cubes in a row, followed by placing the balance five unifix cubes loosely on the other end. When I asked the children to tell me the number of unifix cubes I had, more than 90% of the children counted every single one of the unifix cubes. One girl, who was observing her friends, started counting at 10, then 11, 12... till she reached 15. I was surprised with her strategy and asked her why she started counting from 10. Her answer? She said many friends counted "10" for the row of unifix cubes, so it must be 10 and there is no need for her to count again. What a smart observation!
"Children count out the tiles one at a time and put them into the pile with no use of any type of grouping" (Van de Walle, 2010, p. 188). "Counting plays an important role to scaffold children's construction of base-ten ideas" (Van de Walle, 2010, p. 189). The N2 children are great at counting, one at a time, and the simple activity enabled me to understand their present level of development.
I agree with Jerome Bruner's instructional approach to learning mathematics, where teaching of concepts should be based on Concrete-Pictorial-Abstract (CPA) approach.
With the CPA approach in mind, I hope the sequencing of learning tasks for place value put forward will scaffold the children's understanding of the tens and ones concepts better.
My sequence of learning tasks for Place Value is as follows:
1) Place Value Chart
From the earlier lessons on three bundles of ten and four sticks, 3 groups of ten unifix cubes and four unifix cubes, and the introduction of dime and cents, the children will have a good understanding of 3 tens and 4 ones. Thus, to place the number 3 in the 'tens' pocket and 4 in the 'ones' pocket is congruent to what they have seen in the earlier lesson.
2) Tens and Ones notation
From the Place Value Chart, children will have a good idea that the 3 is in the tens place and 4 is in the ones place. As such, to introduce the 3 tens 4 ones at this junction is an extension to the earlier concept.
3) Number in Numerals
Next, I will introduce the number "34" to the class. This is simply a transfer of concepts learnt from the Place Value Chart and "tens and ones notation" to the numeral "34".
4) Expanded Notation
By now, the children will have a good understanding that 34 is make up of 3 tens and 4 ones. To reinforce children's learning, I can further expand 3 tens to 30 and 4 ones as 4. This acts as a check on whether the children have fully comprehend the place value concept.
5) Number in Words
From part 4, children know that 34 is make up of 30 and 4. To teach thirty-four at this junction is appropriate as children literally say thirty-four from the expanded notation of 30 - 4.
The objective of the whole-number place-value concept is to get the children to understand the base-ten ideas. With learning activities that integrate the "grouping-by-tens", the ultimate aim is to get the children to learn "through reflective thought" (Van de Walle, 2010, p. 189).
Reference :
Van de Walle, J. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.). New York: Longman.
All of them know how to count beyond fifty; some even beyond hundred. However, after reading Chapter 11 and attending the class on place value; it made me wonder if my N2 children comprehend the whole-number place-value concept.
Few days ago, I did an experiment with the N2 children. I placed fifteen unifix cubes on the table and delibrately connect ten unifix cubes in a row, followed by placing the balance five unifix cubes loosely on the other end. When I asked the children to tell me the number of unifix cubes I had, more than 90% of the children counted every single one of the unifix cubes. One girl, who was observing her friends, started counting at 10, then 11, 12... till she reached 15. I was surprised with her strategy and asked her why she started counting from 10. Her answer? She said many friends counted "10" for the row of unifix cubes, so it must be 10 and there is no need for her to count again. What a smart observation!
"Children count out the tiles one at a time and put them into the pile with no use of any type of grouping" (Van de Walle, 2010, p. 188). "Counting plays an important role to scaffold children's construction of base-ten ideas" (Van de Walle, 2010, p. 189). The N2 children are great at counting, one at a time, and the simple activity enabled me to understand their present level of development.
I agree with Jerome Bruner's instructional approach to learning mathematics, where teaching of concepts should be based on Concrete-Pictorial-Abstract (CPA) approach.
With the CPA approach in mind, I hope the sequencing of learning tasks for place value put forward will scaffold the children's understanding of the tens and ones concepts better.
My sequence of learning tasks for Place Value is as follows:
1) Place Value Chart
From the earlier lessons on three bundles of ten and four sticks, 3 groups of ten unifix cubes and four unifix cubes, and the introduction of dime and cents, the children will have a good understanding of 3 tens and 4 ones. Thus, to place the number 3 in the 'tens' pocket and 4 in the 'ones' pocket is congruent to what they have seen in the earlier lesson.
2) Tens and Ones notation
From the Place Value Chart, children will have a good idea that the 3 is in the tens place and 4 is in the ones place. As such, to introduce the 3 tens 4 ones at this junction is an extension to the earlier concept.
3) Number in Numerals
Next, I will introduce the number "34" to the class. This is simply a transfer of concepts learnt from the Place Value Chart and "tens and ones notation" to the numeral "34".
4) Expanded Notation
By now, the children will have a good understanding that 34 is make up of 3 tens and 4 ones. To reinforce children's learning, I can further expand 3 tens to 30 and 4 ones as 4. This acts as a check on whether the children have fully comprehend the place value concept.
5) Number in Words
From part 4, children know that 34 is make up of 30 and 4. To teach thirty-four at this junction is appropriate as children literally say thirty-four from the expanded notation of 30 - 4.
The objective of the whole-number place-value concept is to get the children to understand the base-ten ideas. With learning activities that integrate the "grouping-by-tens", the ultimate aim is to get the children to learn "through reflective thought" (Van de Walle, 2010, p. 189).
Reference :
Van de Walle, J. (2010). Elementary and middle school mathematics: Teaching developmentally (7th ed.). New York: Longman.
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