# EDU330 Elementary Math

## Thursday, September 30, 2010

### I have 10 cookies ^_^

## Wednesday, September 29, 2010

### Reflection on Elementary Math

**"Students must learn mathematics with understanding, actively building new knowledge from experience and prior knowledge. (NCTM, 2000, p.20)**The learning principle summarizes the six lessons that I had in class. In my years of learning, Mathematics was my favourite subject because it was easy to get good grades with lots of practices; not because I understood the concepts behind it.

I looked forward to attend every class; as I have learned and understood Mathematics in a different light. This time, I know why I am learning Mathematics, as I was

*LEARNING BY DOING*! The practical knowledge in class, coupled with the knowledge acquired from the textbook, prompted me to reflect on my teaching practices.

*suggests that the "generalization of a mathematical concept is enhanced when variablesw irrelevant to that concept are systematically varied while keeping the relevant variables constant" (Post, 1988).*

**Mathematical Variability Principle**The activities in the class all geared toward getting us to understand number sense, visualisation and patterning! Through the activities, I am more careful with details; trying to find a relationship or pattern among numbers.

My school will be celebrating Children's Day tomorrow, and I will be performing magic using "spelling number" and "dice trick" learned in lesson 1. I want to excite the children and arouse their curiosity minds, in all my future Mathematics classes!

And yes... we must be meticulous in the Mathematical terms that we used in class.

*Similar*is

**DEFINITELY**not the same as

*identical*!

Reference:

Post, T. (1988). Some notes on the nature of mathematics learning. In T. Post (Ed.), Teaching Mathematics in Grades K-8: Research Based Methods (pp. 1-19). Boston: Allyn & Bacon. Retrieved September 29, 2010, from http://www.cehd.umn.edu/rationalnumberproject/88_9.html

### Geometry

### Teaching of Number Sense

The framework of the Mathematics curriculum by Ministry of Education (MOE, 2006) states the learning of mathematics involves more than learning of concepts; it involves the understanding of underlying mathematical thinking, the strategies to problem solve, the positive attitudes, and the appreciation of mathematics as an important and powerful tool in everyday life. This is congruent to the big ideas by Van de Walle (2010, p.125) when he states that the "number concepts are intimately tied to the world around us" and by applying number relationships to the real world settings, it marks the "beginning of making sense of the world".

In the preschool, the number concepts that we introduced are:

1)

**the relationships of more, less, and same**

This is one concept that we can introduce to the preschool children. Children as young as 3 year olds are able to tell that a tray with five bear counters is

*more*than a tray that contains 1 bear counter.

2)

**Problem structures**

Be it join problems, separate problems, part-part-whole problems or compare problems, our school curriculum only covers the simplier problem structures that require less than 3 steps to solve the questions given.

In the preschool years, children learn from concrete to pictorial to abstract (CPA approach by Jerome Bruner). When doing the problem sums, we use concrete materials (e.g. unifix cubes or counters) to help children understand and reinforce learning through the introduction of models. We did not use the number line concept to solve story problems. I believe, both methods work equally well, as long as we introduce the appropriate tools to the appropriate age group to help them understand what is happening in the story problem.

Other mathematical concepts that we taught in the preschool are:

1) Numeral writing and recognition

2) Counting on and counting back

3) Patterned set recognition

4) Part-part-whole relationships (based on single number)

5) Addition and subtraction

6) Estimation and Measurement

7) Data Collection and Analysis

In my school, we did not teach the following concepts:

a) **Doubles and near-doubles**

This is an interesting concept and I would like to try this out. When children understand part-part-whole concept, the doubles and near-doubles strategies strengthen children's understanding of basic addition facts. However, this can be challenging, even for the K2 children.

b) **Anchoring numbers to 5 and 10**

Though teaching the anchoring numbers to 5 and 10 is an useful way to help develop thinking about various combinations of numbers, it is not an easy task for the 6 year olds children. The five-frame or ten-frame provide opportunities to train children to "see" the relationships among numbers, and when the children are familiar with the relationships among numbers, we have also trained them in terms of mental computation skills.

The development of number concepts and number sense cannot be underestimated, and children need to have a good foundational ideas in order to extend their learning to larger numbers and computation.

### Using Technology to Teach Mathematics

*Mathematics Syllabus Primary*. Retrieved September 29, 2010, from http://www.moe.gov.sg/education/syllabuses/sciences/files/maths-primary-2007.pdf

Van de Walle, J. (2010).

*Elementary and middle school mathematics: Teaching developmentally*(7th ed.). New York: Longman.

## Friday, September 24, 2010

### Sequencing Learning Tasks for Place Value

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.

## Friday, September 17, 2010

### Problem Solving in relation to Environment-based Task

**.**

*TEACH THROUGH PROBLEM SOLVING*"Good problems will integrate multiple topics and will involve significant mathematics" (Van De Walle, Karp, & Bay-Williams, 2009, p.32). That set me thinking of the challenges to plan a meaningful lesson for my children. Am I not doing the right thing so far?

I found my answer from the phrase, "

**children are learning mathematics by doing mathematics!**" (Van De Walle et al, 2009, p.33). When we plan our lessons, we always plan according to the children's level of development, and most importantly, what they are interested to learn.

I agree that teachers require a paradigm shift when we want to teach through problem solving. In fact, I have to learn more ways on how to engage the children to learn content eagerly. On the other hand, it is imperative to prepare learning materials and select appropriate manipulatives if I want the children "to learn content by figuring out their own strategies and solutions" (Van De Walle et al, 2009, p.34).

I am teaching the Nursery 2 children this year; a fantastic group of children! Each of them has a different learning style and different level of development (and they should be!). Now, it is time to rethink and redesign my teaching methods. A major shakeup time for me!

I had a good understanding of chapter 3 and 4 contents when we were carrying out the environment-based task. It is not just trying to find learning contents to teach from our environment or find any environment and try to fit it to our learning contents that we deemed fit.

After reading the textbook, I realised the Three-Phase lesson format is also applicable to our environment-based task.

Firstly, the BEFORE phrase of a lesson must be clearly established. From our daily experiences with the children, we need to understand what interests them, what are their prior knowledge and experiences, and are they ready to problem solve with me?

During the DURING phrase, we are just like the students, excited and ready to

*and tried to find the environment suitable for our learning contents. In the AFTER phase, we*

**GO****ideas and reflected on what we have created for the children.**

*SHARED*The age group that we are targeting for our environment-based task was the Kindergarten 2; as the content initially planned for was

*- to learn addition and subtraction. The objective of using the nine "squares" on the metal gate was to get children to fill up the spaces using either addition or subtraction of whole numbers. In fact, we had fun trying to outwit each other to complete the nine squares.*

**numbers and operations**During the AFTER phase, we reflected and realised that the contents can be

**to "make the task accessible to all students" (Van De Walle, 2009, p.65). In this case, if we want to teach the Nursery 2 class, we can ask the children to complete the nine squares by filling unrepeated numbers from 1 to 9. In fact, we can scaffold their learning by increasing the number of squares, as long as the children are having fun learning.**

*modified*During our reflection stage, we realised that the metal gate is a fantastic learning tool for charts and graphs learning too. Thus, learning is multi-leveled and we can integrate multiple topics for this simple learning material.