The course has ended and the participants are completing their course assignment. I have enjoyed reading their reflections on their blogs. The blogs, which are listed on the right, give me an insight into their thoughts. Also what they have read and what they have tried out with the kids they teach. It also give me an idea on their ability to synthesize what they get from their reading, the experience during this course and others they attended as part of the prgramme, and their work with children.

In other words, the blogs give me a glimpse into their 'teaching soul'.

## Technology & Readings

## Tuesday, October 12, 2010

## Monday, September 20, 2010

### Lesson 5

There is a reflection to write for todays's lesson. For tomorrow final lesson, please submit your groupwork assignment by copying your files on the desktop of the class computer or giving me a CD.

We did three problems today. The quiz problem was the letter in HAIZI which is the k th letter when counted in a certain way. I am glad students had many ways to do it - the add 8 strategy, the look for multiples of 10 and multiples of 5 strategy, the dividing and using the remainder strategy and so on.

The other problems are based on measurements and geometry. One was on using n pieces of the tangram set to make a square where n = 2, 3, 4, 5, 6 or 7. The class found one solution for n = 2, one solutions for n = 3, three solutions for n = 4, one for n = 5, none for n = 6 and one for n = 7.

The final problem was to find the sum of interior angles in a pentagon.

We discussed Piaget's ideas of assimilation and accomodation. We also spoke about constructivism.

Did the class get the three big ideas in mathematics? Visualization, patterning and number sense.

We did three problems today. The quiz problem was the letter in HAIZI which is the k th letter when counted in a certain way. I am glad students had many ways to do it - the add 8 strategy, the look for multiples of 10 and multiples of 5 strategy, the dividing and using the remainder strategy and so on.

The other problems are based on measurements and geometry. One was on using n pieces of the tangram set to make a square where n = 2, 3, 4, 5, 6 or 7. The class found one solution for n = 2, one solutions for n = 3, three solutions for n = 4, one for n = 5, none for n = 6 and one for n = 7.

The final problem was to find the sum of interior angles in a pentagon.

We discussed Piaget's ideas of assimilation and accomodation. We also spoke about constructivism.

Did the class get the three big ideas in mathematics? Visualization, patterning and number sense.

## Tuesday, September 14, 2010

### Another Blog Entry - Reflect on Practice

Review the chapters on whole numbers in the textbook (and if you have not read them, it is a good time to start, given that we are two thirds way through the course). Write a blog to compare what is suggested about teaching of number sense in the textbook and what is being practised in pre-school teaching. Mention one or two things that the book suggests and are already in practice in pre-schools. Mention one or two things that the book suggests but is not a common practice in pre-school.

Photo Credit: PCF Tanjong Pagar Kindergarten

### Reminder - Blogging

If your blog is not linked to this blog (see right-hand-side of this blog), that mean I have not been able to access it. I think a few of you still have not given me your blog's url. Please check. Let your friends know too.

Please check this blog regularly for updates on what you need to do before we meet next week.

I hope you have your readings up-to-date. Also a chance to work on your story book assignment.

Review the chapters on whole numbers in the textbook (and if you have not read them, it is a good time to start, given that we are two thirds way through the course). Write a blog to compare what is suggested about teaching of number sense in the textbook and what is being practised in pre-school teaching. Mention one or two things that the book suggests and are already in practice in pre-schools. Mention one or two things that the book suggests but is not a common practice in pre-school.

Please check this blog regularly for updates on what you need to do before we meet next week.

I hope you have your readings up-to-date. Also a chance to work on your story book assignment.

Review the chapters on whole numbers in the textbook (and if you have not read them, it is a good time to start, given that we are two thirds way through the course). Write a blog to compare what is suggested about teaching of number sense in the textbook and what is being practised in pre-school teaching. Mention one or two things that the book suggests and are already in practice in pre-schools. Mention one or two things that the book suggests but is not a common practice in pre-school.

## Sunday, September 12, 2010

### Children's Literature & Mathematics

"Select a children’s book. Work in a group of 2 to 3 persons to use the book to teach a mathematical concept. Be creative and choose a suitable format to showcase your group’s work. Your presentation must include the book and the mathematics activity, and allows the audience to understand how the book can be used to help children acquire the mathematical concept. No boundaries – skit, video, poster, slideshow or any other format."

Question - must the activity be to teach a concept?

I have braoden this requirement a bit. Look for a suitable book and explore how it can be used to teach a particular mathematics concept, to practice a mathematical skill or to do problem solving (any one of the three). So if your group prefer, the tasks can be to teach a new concept or to practice a skill / concept or to apply a concept to solve a problem. You decide which of the three you want to do.

The textbook has many suggestions and resources - read the relevant sections.

Question - must we present it?

You can use Powerpoint to present your work - scan the book you use as well as the mathematical tasks you are giving the kids to do. If that is all you have you can submit you work as a soft copy (CD). If there are other things that you need to submit that are not suitable to be submitted as soft copies, hand in the hard copy.

If you have other creative way to present your work please go ahead. If you are doing a skit etc, you may video record it and submit a video file.

But we are not going to have time to have presentations in class. We will share all presentations using our e-learning platform.

Question - must the activity be to teach a concept?

I have braoden this requirement a bit. Look for a suitable book and explore how it can be used to teach a particular mathematics concept, to practice a mathematical skill or to do problem solving (any one of the three). So if your group prefer, the tasks can be to teach a new concept or to practice a skill / concept or to apply a concept to solve a problem. You decide which of the three you want to do.

The textbook has many suggestions and resources - read the relevant sections.

Question - must we present it?

You can use Powerpoint to present your work - scan the book you use as well as the mathematical tasks you are giving the kids to do. If that is all you have you can submit you work as a soft copy (CD). If there are other things that you need to submit that are not suitable to be submitted as soft copies, hand in the hard copy.

If you have other creative way to present your work please go ahead. If you are doing a skit etc, you may video record it and submit a video file.

But we are not going to have time to have presentations in class. We will share all presentations using our e-learning platform.

## Thursday, September 9, 2010

### Another Blog Entry - Technology

This is to be done before we next meet. Read Chapter 7 on Using Technology to Teach Mathematics. Blog about one thing that stikes you as you read the chapter.

Explore Teacher Resources on Page 124. I have put up a few of these links on top of the page. Mention one particular activities / tool that you found on the websites suggested that you like very much.

Explore Teacher Resources on Page 124. I have put up a few of these links on top of the page. Mention one particular activities / tool that you found on the websites suggested that you like very much.

### Review

We have completed 4 sessions. It is time to take stock of our learning.

The textbook is both a resource as well as a stimulant for reflection.

The first session focuses on Chapters 1 and 2 - what is meant to be doing mathematics. The second session focuses on Chapters 3 and 4 - problem solving. The third and fourth session deals with number sense - Chapters 8 through 13. Along the way we touched on some ideas of fractions and algebra (patterns) - Chapters 14, 15 and 16.

The last two sessions will focus on Measurement and Geometry (Chapters 19 and 20) with some discussion on Data Analysis.

In completing the Major Assignment, you should read thoroughly the concept you have selected for your case.

The textbook is both a resource as well as a stimulant for reflection.

The first session focuses on Chapters 1 and 2 - what is meant to be doing mathematics. The second session focuses on Chapters 3 and 4 - problem solving. The third and fourth session deals with number sense - Chapters 8 through 13. Along the way we touched on some ideas of fractions and algebra (patterns) - Chapters 14, 15 and 16.

The last two sessions will focus on Measurement and Geometry (Chapters 19 and 20) with some discussion on Data Analysis.

In completing the Major Assignment, you should read thoroughly the concept you have selected for your case.

## Wednesday, September 8, 2010

### Blogging Activities

As part of elementary mathematics where early childhood students are required to learn mathematics pedagogical content knowledge of primary-level mathematics, students are required to read (at least the basic text) and reflect. The blogging activities are designed for this purpose.

Some students have gone ahead and blog their thoughts even when it is not a course requirement.

The blogs are assessed on the following criteria:

1. how insightful they are - such blogs tend to go beyond what is in the textbook / lessons. the writer tends to blend what they read / hear / experience with their own experience as a learner / teacher of young children.

2. how much pleasure is derived from reading them - such blogs are well-written and presented, sometimes illustrated with quotes, photos, links and so on.

The blogs will be assessed on 25th September 2010. If your blog is not ready to be assessed by 25th September, please alert me by saying something on your latest blog entry. Feel free to edit and improve on your entries. But of course I want to read your first blog soon! There is an earlier deadline for the first blog, remember?

The following are the required blogs:

A. Pre-Course Reading Chapters 1 & 2 - reflect on what you have read.

B. Reflect on your learning in the first session.

C. Read about problem solving in the textbook - reflect on one aspect of problem solving in relation to the environment-based tasks that you did with your group members at the start of the third session.

D. We started a discussion on sequencing learning tasks for place value (the example used was 34) - give your views on how the five tasks on the textbook page should be sequenced.

We now have some time to reflect on what we have learnt in the first four sessions. We have two weeks to read and reflect. During this period, I will nudge you to read and request you to complete three blogs.

E. Blog about techonolgy - read the related blog about this task

F. Review chapters on whole numbers / numeracy and reflect on common practices in pre-school teaching - read the related blog about this task.

G. Read the chapter on geometric thinking and blog something relating what you read to the problem of finding the (interior) angles in a pentagon.

The final blog should be done within a couple of days of the end of the course.

H. Write about the most significant impact this course has on your work as an early childhood educator - its relevance, if it changes your mindset, blah blah blah exceot that I hope it is more succint than blah blah blah.

Some students have gone ahead and blog their thoughts even when it is not a course requirement.

The blogs are assessed on the following criteria:

1. how insightful they are - such blogs tend to go beyond what is in the textbook / lessons. the writer tends to blend what they read / hear / experience with their own experience as a learner / teacher of young children.

2. how much pleasure is derived from reading them - such blogs are well-written and presented, sometimes illustrated with quotes, photos, links and so on.

The blogs will be assessed on 25th September 2010. If your blog is not ready to be assessed by 25th September, please alert me by saying something on your latest blog entry. Feel free to edit and improve on your entries. But of course I want to read your first blog soon! There is an earlier deadline for the first blog, remember?

The following are the required blogs:

A. Pre-Course Reading Chapters 1 & 2 - reflect on what you have read.

B. Reflect on your learning in the first session.

C. Read about problem solving in the textbook - reflect on one aspect of problem solving in relation to the environment-based tasks that you did with your group members at the start of the third session.

D. We started a discussion on sequencing learning tasks for place value (the example used was 34) - give your views on how the five tasks on the textbook page should be sequenced.

**EDU330 Variations**

View more presentations from jimmykeng.

We now have some time to reflect on what we have learnt in the first four sessions. We have two weeks to read and reflect. During this period, I will nudge you to read and request you to complete three blogs.

E. Blog about techonolgy - read the related blog about this task

F. Review chapters on whole numbers / numeracy and reflect on common practices in pre-school teaching - read the related blog about this task.

G. Read the chapter on geometric thinking and blog something relating what you read to the problem of finding the (interior) angles in a pentagon.

The final blog should be done within a couple of days of the end of the course.

H. Write about the most significant impact this course has on your work as an early childhood educator - its relevance, if it changes your mindset, blah blah blah exceot that I hope it is more succint than blah blah blah.

### Lesson 4

We started with Quiz 2 on meaning of division of fractions - followed by a discussion of the meanings of operations.

Addition & Subtraction

1. Part-Whole Model

2. Change Model

3. Comparison Model

Division

1. Sharing

2. Grouping

How about multiplication?

We focus on some early number concepts - place value, for example. We played some games and I demonstrated some maths tricks. For example, try to goggle fido dido puzzle. We played that today.

We discussed Zoltan Dienes' idea of variation.

We ended the class with a children's literature session where I read a book to teach measurements - How Big Is A Foot?

The class were asked to blog about their views on how to sequence the teaching of place value. I am writing a separate blog for this.

Addition & Subtraction

1. Part-Whole Model

2. Change Model

3. Comparison Model

Division

1. Sharing

2. Grouping

How about multiplication?

We focus on some early number concepts - place value, for example. We played some games and I demonstrated some maths tricks. For example, try to goggle fido dido puzzle. We played that today.

We discussed Zoltan Dienes' idea of variation.

We ended the class with a children's literature session where I read a book to teach measurements - How Big Is A Foot?

The class were asked to blog about their views on how to sequence the teaching of place value. I am writing a separate blog for this.

## Monday, September 6, 2010

### Lesson 3

The students worked in groups to come up with tasks based on the environment.

Let's discuss this group's task. It seems like this task is set in a supermarket and students are asked to hunt for a set of items that has a total value of 5. A variation is to do the lesson in class and give students cards representing each item. But what is the value of bringing the kids to the supermarket?

First, let's be clear what the content is. It is about the fact that an item has a value, usually denoted in cents and dollars (money). Students are then expected to selected a combination of items that come up to a given total value (addition).

Questions: Is there a reason why the group has decided not to denote the value of items in the conventional way (using money)? What role does the venue (supermarket) play in this activity?

Today we begin to look at the four operations of whole numbers and ended the lesson learning two meaning of division - as sharing and as grouping.

Sharing: Three boys share all 12 cookies equally. How many does each boy get?

Grouping: All 12 cookies are put in groups of threes. How groups of cookies are there?

Students are asked to read about problem solving from the textbook and write a blog entry about problem solving in relation to the environment task they designed in the first part of this lesson.

### Lesson 2

Today we focused on problem solving. The class solved the five-digit problem as a quiz and did the extension in class. Afterwards they also solved a couple of PSLE problems.

Do we know what defines a problem? What makes a task a problem? What distinguishes a problem from an exercise? In problem solving we cannot not know about George Polya. What did he suggest as the stages in prblem solving? What are some examples of looking back? How does Polya's stages compare to Newman's stages?

Are we able to name heuristics children use?

We ended the session with Bruner's Theory.

There is a task that groups have to complete for the first half of Lesson 3. The focus is on the use of the environment to elarn mathematics and we will begin our investigation on whole numbers and the four basic operations.

## Wednesday, September 1, 2010

### Lesson 1

In class today, the participants wrote a letter to their own student to say why they are studying for this degree. It will be interesting to read what they wrote.

We solve three problems, and looked at the Singapore mathematics curriculum framework. The class ended with a reflective activity.

Participants were asked to write a blog entry to say what they learnt I the first lesson.

There are some announcements about educations in general today. I wonder what are the implications for pre-school teachers?

## Monday, August 30, 2010

### Question About Blogging Task

This is from the course information sheet:

Pre-course reading: Students are expected to read Chapter 1 and Chapter 2 and make a blog entry to show that they have understood the readings and have an opinion on the readings. The blog entry should not be excessively long and, hopefully, is creative and interesting to read. Photographs, videos and so on may be use to make a point.

These are the questions raised by some participants of the course:

Q1. Do I need to have my own blog?

A1. Yes. Please create your own blog such as this one on blogspot or other blogging platforms and send me your blog's url. I will link everyone's blog to mine so that you can visit each others' blogs regularly. Hopefully, reading each others' views and opinions will set us thinking about teaching mathematics to children.

Q2. How long must it be?

A2. According to the requirements, it should "not be excessively long". In order to show your understanding, you need to synthesize what you read. So, it cannot be very long. Best entries are a joy to read. Try to make your entries a joy to read.

Q3. Is it compulsory to use photographs and videos?

A3. According to the requirements, it is not compulsory. But sometimes it is easier to make a point using tools other than language.

Pre-course reading: Students are expected to read Chapter 1 and Chapter 2 and make a blog entry to show that they have understood the readings and have an opinion on the readings. The blog entry should not be excessively long and, hopefully, is creative and interesting to read. Photographs, videos and so on may be use to make a point.

These are the questions raised by some participants of the course:

Q1. Do I need to have my own blog?

A1. Yes. Please create your own blog such as this one on blogspot or other blogging platforms and send me your blog's url. I will link everyone's blog to mine so that you can visit each others' blogs regularly. Hopefully, reading each others' views and opinions will set us thinking about teaching mathematics to children.

Q2. How long must it be?

A2. According to the requirements, it should "not be excessively long". In order to show your understanding, you need to synthesize what you read. So, it cannot be very long. Best entries are a joy to read. Try to make your entries a joy to read.

Q3. Is it compulsory to use photographs and videos?

A3. According to the requirements, it is not compulsory. But sometimes it is easier to make a point using tools other than language.

## Monday, July 19, 2010

### Other References

Bibliography

Asklock, R. (2005). Error patterns in computation (9th ed.). New Jersey: Prentice Hall.

Borko, H., Eisenhart, M., Brown, C., Underhill, R., Jones, D. & Asgard, P. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up to easily? Journal for Research in Mathematics, 23, 1994-222.

Bove, S. (1995). Place value: A vertical perspective. Teaching Children Mathematics, 1(9), 542-546.

Cobb, P., Yackel, E., Wood, T., Wheatley, G. & Markel, G. (1989). Creating a problem solving atmosphere. Arithmetic Teacher, 39, 46-47.

Empson, S. (1995). Using sharing situations to help children learn fractions. Teaching Children Mathematics, 2.

Friedlander, A. (1997). Young children investigate number cubes. Teaching Children Mathematics, 4, 6-11.

Giganti, P. & Cittadino, M. (1990). The art of tessellation. Arithmetic Teacher, 38(3), 6-16.

Henningsen, M. & Stein, M. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematical Education, 28, 524-549.

Jensen, R. (1993). Research ideas for the classroom: Early childhood mathematics. Gale Group.

Kamii, C. & Dominicl, A. (1997). To teach or not to teach algorithms. Journal of Mathematical Behavior, 16, 51-61.

Kazemi, E. (1998). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 4, 410-414.

Ladson B. G. (1993). Making mathematics meaningful in multicultural contexts. In New Directions for Equity in Mathematics Education. Cambridge University Press.

Mastropieri, M., Scruggs, T., & Shiah, S. (1991). Mathematics research for learning disabled students: A review of research. Learning Disabilities Research and Practice, 6, 89-98.

Musser, G. L, & Burger, W. F., & Peterson, B. E. (2005). Mathematics for elementary teachers: A contemporary approach (7th ed.). Wiley.

National Council of Teachers of Mathematics (2000). Principals and standards for school mathematics. Reston, VA: The Council.

Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2004). Helping children learn mathematics. Boston, MA: Allyn & Bacon.

Russell, S. & Friel, S. (1989). Collecting and analyzing real data in the elementary school classroom. In NCTM Yearbook: New Directions for Elementary School Mathematics. Reston, VA: The Council.

Sharma, M. (1985). Children at risk for disabilities in math: Some remedial perspectives. Exchange, 3, 1-2.

Smith, S. S. (2008). Early childhood mathematics (4th ed.). Boston: Allyn and Bacon.

Wearne, D. & Hiebert, J. (1994). Place value and addition and subtraction. Arithmetic Teacher, 1.

Whitin, P. & Whitin, D. J. (2000). Math is language too: Talking and writing in the mathematics classroom. National Council of Teachers of English.

Asklock, R. (2005). Error patterns in computation (9th ed.). New Jersey: Prentice Hall.

Borko, H., Eisenhart, M., Brown, C., Underhill, R., Jones, D. & Asgard, P. (1992). Learning to teach hard mathematics: Do novice teachers and their instructors give up to easily? Journal for Research in Mathematics, 23, 1994-222.

Bove, S. (1995). Place value: A vertical perspective. Teaching Children Mathematics, 1(9), 542-546.

Cobb, P., Yackel, E., Wood, T., Wheatley, G. & Markel, G. (1989). Creating a problem solving atmosphere. Arithmetic Teacher, 39, 46-47.

Empson, S. (1995). Using sharing situations to help children learn fractions. Teaching Children Mathematics, 2.

Friedlander, A. (1997). Young children investigate number cubes. Teaching Children Mathematics, 4, 6-11.

Giganti, P. & Cittadino, M. (1990). The art of tessellation. Arithmetic Teacher, 38(3), 6-16.

Henningsen, M. & Stein, M. (1997). Mathematical tasks and student cognition: Classroom-based factors that support and inhibit high-level mathematical thinking and reasoning. Journal for Research in Mathematical Education, 28, 524-549.

Jensen, R. (1993). Research ideas for the classroom: Early childhood mathematics. Gale Group.

Kamii, C. & Dominicl, A. (1997). To teach or not to teach algorithms. Journal of Mathematical Behavior, 16, 51-61.

Kazemi, E. (1998). Discourse that promotes conceptual understanding. Teaching Children Mathematics, 4, 410-414.

Ladson B. G. (1993). Making mathematics meaningful in multicultural contexts. In New Directions for Equity in Mathematics Education. Cambridge University Press.

Mastropieri, M., Scruggs, T., & Shiah, S. (1991). Mathematics research for learning disabled students: A review of research. Learning Disabilities Research and Practice, 6, 89-98.

Musser, G. L, & Burger, W. F., & Peterson, B. E. (2005). Mathematics for elementary teachers: A contemporary approach (7th ed.). Wiley.

National Council of Teachers of Mathematics (2000). Principals and standards for school mathematics. Reston, VA: The Council.

Reys, R. E., Lindquist, M. M., Lambdin, D. V., & Smith, N. L. (2004). Helping children learn mathematics. Boston, MA: Allyn & Bacon.

Russell, S. & Friel, S. (1989). Collecting and analyzing real data in the elementary school classroom. In NCTM Yearbook: New Directions for Elementary School Mathematics. Reston, VA: The Council.

Sharma, M. (1985). Children at risk for disabilities in math: Some remedial perspectives. Exchange, 3, 1-2.

Smith, S. S. (2008). Early childhood mathematics (4th ed.). Boston: Allyn and Bacon.

Wearne, D. & Hiebert, J. (1994). Place value and addition and subtraction. Arithmetic Teacher, 1.

Whitin, P. & Whitin, D. J. (2000). Math is language too: Talking and writing in the mathematics classroom. National Council of Teachers of English.

### EDU330

This is the blog for the courses for kindergarten teachers. In particular, as part of their BSc (Early Childhood Education), undergraduates at Wheelock College and SEED Institute, are required to read EDU330 Elementary Mathematics. The students will be blogging their reflection during the course. The course starts on 1 September 2010.

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