Number Sense

Reflection 6

"It is a part of children’s daily mathematical lives and slowly grows and develops over time. In a problem-centered mathematics curriculum, number sense is closely tied to problem solving, as the children described above show. These children have learned, over time, that they are capable of solving problems and that they can play with numbers to make sense of a problem."

WHAT TYPES OF STRATEGIES DO CHILDREN DEVELOP?

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  Partitioning numbers using tens and ones. "First I added the 20 and 10 and got 30. Then I added the 9 and 4 and got 13. Then I added the 10 from 13 to 30 and added 3 more and got 43.

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  Counting on or back from a number. "First I counted on from 29 by tens and went 29, 39. Then I counted on 4 more — 40, 41, 42, 43."

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  Using "nice numbers." Nice numbers are multiples of 10 or other numbers that are easy to work with. "I know that 30 plus 15 is 45, but 29 plus 14 is 2 less than that, so it’s 43."

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  Translating to a new problem. "I took one away from the 14 and gave it to the 29 to make 30. Then I had 30 plus 13, which is 30 plus 10 plus 3, which is 43. 

Taken from: Learn NC - Number Sense Everyday 


I think that this post gives a general overview of Number Sense. It allows us to see that Number Sense is not something that is done in a day but it is an accumulation of experiences one has.

Number and Operations Standard
for Grades Pre-K–2

Expectations

Instructional programs from prekindergarten through grade 12 should enable all students to— In prekindergarten through grade 2 all students should— Understand numbers, ways of representing numbers, relationships among numbers, and number systems • count with understanding and recognize "how many" in sets of objects; • use multiple models to develop initial understandings of place value and the base-ten number system; • develop understanding of the relative position and magnitude of whole numbers and of ordinal and cardinal numbers and their connections; They are always comparing who is first, second, third and so on. • develop a sense of whole numbers and represent and use them in flexible ways, including relating, composing, and decomposing numbers; They love playing games involving addition and subtraction and more than half the class are able to mentally calculate the answers. This can be done with two single digits and they are practicing with three now. • connect number words and numerals to the quantities they represent, using various physical models and representations; • understand and represent commonly used fractions, such as 1/4, 1/3, and 1/2. Amazing what you can do and relate in Mathematical terms when 1 whole muffin is too much for you to finish. You negotiate. Understand meanings of operations and how they relate to one another • understand various meanings of addition and subtraction of whole numbers and the relationship between the two operations; • understand the effects of adding and subtracting whole numbers; • understand situations that entail multiplication and division, such as equal groupings of objects and sharing equally. Compute fluently and make reasonable estimates • develop and use strategies for whole-number computations, with a focus on addition and subtraction; • develop fluency with basic number combinations for addition and subtraction; • use a variety of methods and tools to compute, including objects, mental computation, estimation, paper and pencil, and calculators.

Taken from: NCTM

I believe that the experiences and interactions that the children have everyday is as important as in class discussion. For example, in preparation for their transition into Primary 1, the K2 children have been "buying" their lunch and tea with a specific amount of money given to them at the start of these routine times. Money is not an easy concept to grasp due to the place values each number holds. Starting with small amounts, the children are starting to understand the value behind the numerals in the word fifty cents and 1 dollar. 

It is not always so difficult is it. Sometimes, we just have to keep trying to figure out a way, which will help us understand the concept better.

Resources p.124

Reflection 5

Moving towards the Jetson's Era.

The role of technology in supporting children's learning.

There are actually a lot of sites that are available for references on Mathematics. Perhaps it was not one of my interest to look or find out more about it. However, after all the reflections that I had done, I feel that it was a rather good idea that we are blogging our reflections. This method of communication allows us to be at a platform where we are connected not only to Early Childhood Educators, but also to others who are profound in their given field of expertise.

Math Forum - Problem of The Week

I like this idea of having Problem of The Week. However, it is not free, even though there is a free trial which you could try out and get it if you are really in love with it. I think it is a good resource to find all the cool math problems (if you are like me and are not able to come up with your own) to work with your students on it.

Tech Matrix

Out of all of the sites, I love this the most. They layout and outlook is not to die for nor is it interesting, however, the content is amazing. The best part is that they do not only focus on Mathematics but also other subject areas. The other good thing about it is that you don't really have to pay for the articles!

It is like moving into the 21st century for dummies who requires help in being technologically savy. You just need to know and click away, many information awaits you. 

Incorporating technology is also a very "hot" topic in the education sector as it is in our daily lives. It is ever changing and it would be good that we are up to date. Can you imagine if you are in the world of The Jetsons and you are not technologically savvy? Do you think you would survive? Time to move with the changes and keep up.

Geometry

Reflection 4

Who would have thought you could find all the angles in this diagram even if you are not given any of the angles to help you out?

The 4 content goals for geometry, p.400:

1. Shapes and Properties
2. Transformation
3. Location
4. Visualization

As I was reflecting on this topic through my experiences with preschoolers, I realized that most of the time spent is focused on the first content - Shapes and Properties. Getting to know shapes, exploring with shapes, looking at shapes in the environment.

Are we able to push the children further or further up van Hiele's level of Geometric Thought? To analyze, to deduce? The more curiosity we invoke in the children, the more likely we will be able to engage and interest them in this area. This definitely will not be done in a technical "Me Teacher, I Teach and You Student, You Listen" kind of manner. It has to be a learning journey for both parties where there are new pieces of information that are being explored. 

However, I think that to do this, we as educators need to have more understanding of the subject through more research done on this topic.

Scholastic - Ready for Math

Teach Math Vocabulary

Number place values

Reflection 3

"To Thales the primary question was not what do we know, but how do we know it."

- Aristotle-

How does this apply to the preschoolers?

Bruner's CONCRETE-PICTORIAL-ABSTRACT approach is the basis for all Early Childhood educator. The notion of using concrete materials and giving concrete experiences is a long standing method of working with children.

To "teach" or present a concept to a child, we must first present a basis for the child. 

Before we can even introduce number placement, the child has to first and for all make meaning of the symbols that represents numbers. These representations will then have to have concrete representations that relates to their daily lives (perhaps that is why we use counters and the environment to help children make sense) and meaning of these symbols in their lives.

When these experiences are built on a strong number foundation, children will be able to make connections based on logical thinking, driven by their natural curiosity to question and find out about the world around them.

As an educator, we would have to be aware of the end goal and work backwards to see the gradual steps that each child have to tale before attaining these goals.

Problem Solving

Reflection 2

We went out on with a task at hand.

Exploring the environment around us to teach Mathematics to young children.

In some ways, it brought back memories of Math Challenges that you had to pay for in Primary and Secondary school.

 I could never phantom any question, thus not being able to answer any of the questions leading to frustrations and irritation, increasing angst feelings towards this subject.

We decided on The Cathay next to SOTA and because of the distance, we explored both areas.

We thought the lights in front of The Cathay were an interesting start to this task.

They were in groups of fives and Sharifah made connections to her Kindergarten Ones who were working on skip counting. With that in mind, when we looked around the environment the focus was to look for structures or materials which could be used to skip count in fives.

Floor under the lamps.

Tiles in different shapes and sizes.

Bars.

Pebbles.

Plants.

All we need are pieces of chalk enough for the children in the classroom to work on various areas.

This could also be continued on a multitude of stairs in front of SOTA.

Count till you drop!

Of course relating it to our text book, to find quality task and problem-based lessons, we need to "determine if an activity is a good fit for the content you are teaching" 

(Walle, Karp, & Bay-Williams, 2010)

Activity Evaluation and Selection Guide

Elementary & middle school mathematics, Figure 3.2, p.39 

Step1: How is the activity done?

Actively doing the activity, to get an understanding of:

 what we may need, 

what has to be recorded and

 what are the misconceptions the children may have. 

Doing the activity will allow us to perceive how the children will be involved and engaged in the activity as they are attempting to solve the problem.

Step 2: What is the purpose of the activity?

Mathematical ideas?

Concepts

Procedural skills

Possibilities of making connections to other concepts or ideas?

Step 3: Can the activity accomplish your learning goals?

The problem? Relation to identified Mathematical content?

Reflection involved? How?

Step 4: What must you do?

Planning for:

Connection to past knowledge

End goal / objectives

Questions to engage and provoke reflective thinking

Areas to discuss after lessons

Reflective Thought, 

Critical Thinking

A can of worms?

Reflection 1:

Is Mathematics a can of worms?

I had a conversation with a colleague of mine, and I asked, why is it we do not place a lot of focus on Mathematics when we are working with the children?

The answer was plain and simple. None of us had any interest or positive experience relating to numbers and logical circumstances. 

Perhaps, because of our lack of positive experience, we choose to stay away from this area.

After the first lesson, I thought that Mathematics was actually like 

Kinder Surprise.

A delicious problem (If you are persistent enough to follow through!).

It may take some to figure out faster than others, but it is how you choose to perceive the "problem" and solve it to achieve your end goal. 

At the end of the process, you have gained more than solving the problem and achieving the answer.

This was even clearer when I saw the Mathematics curriculum. 

There is so much more than just computation to Mathematics and I think it would help if we could refer to it more often when we are planning for our activities and lessons.

MOE Mathematics Primary School Syllabus

Addition and Subtraction

I was with the Kindergarten 2 children on Friday and they were in the midst of playing games on the computer. I was curious to find out what had enthralled them and enticed them to be shouting out numbers to each other. 

They were trying to help the man wash the windows by subtracting the numbers shown. 

Was I amazed at the speed they were able to mentally calculate 2 single digit numbers!

A boy said, "Why don't we give the wrong answer!" His friends did not understand why he wanted to do such a thing because their main objective was to reach the top floor as fast as they could.

He was more interested in finding out the cause of getting the answer wrong and the effect it would have on the man cleaning the window. Rather interesting perspective don't you think?

Of course there are many many more games that can be played on the site. It is extremely easy to navigate and your children will have fun picking out the games that excites them most.

fun4thebrain.com

Reflections: Chapter 1 and 2

Becoming a Teacher of Mathematics, 

consists of understanding what it means to know and do Mathematics.

We need to have a strong understanding of the Mathematical content, however, just like it is for the children, we also need these dispositions as well as habits of mind.

We need to be:

Persistent

Positive

Adaptable

Reflective

Imagine a student who armed with content skills but no understanding why they are applying the steps to resolve mathematical problems...

Melissagordon

Developing understanding is key to resolve problems from many different view points. 

Why do we do if we do not understand?

Then is the basis of math only to be able to obtain the right answers to the questions?

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Language of Doing Mathematics: Authentic Mathematics

Textbook pg.14

Explore. Investigate. Conjecture. Solve. Justify. Represent. Formulate. Discover. Construct. Verify. Explain. Predict. Develop. Describe. Use.

These are the exact same principles that we as early childhood educators hold. 

Then what is the difference between preschool and primary school?

What is the basis of the "education' that we are providing for the children?

Funny Times

Is this how we would like the children in our class to be?

OR

Principalstein

Do you want a class where the students are empowered and encouraged to try in partnership with the educator as well as their peers?

It is up to the educators to decide the direction they want to take with the knowledge of theories they have acquired. 

How the children learn depends on how we choose to pass the knowledge on to them. 

What they choose to learn and take away from that, is entirely up to them. 

Plan. Do. Reflect.

It is is a cycle which helps us to understand the children and to our best ability support them as a group and an individual.

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Math Collage : Helping the children to see Mathematics in their everyday lives

Orrillas

Beginning

Finally started the blog for our Mathematics module. An interesting concept which is new and innovative. Making full use of the technological aspects of our time.There are two tasks at had for this class right now.

1. Review of chapters 1 and 2
2. 3 reflections from each class attended

Will have to finish it in a while before the Hari Raya celebrations tomorrow.
Due date 12 September, which is this Sunday by the way.