Number Sense

What is number sense?

The term "number sense" is a relatively new one in mathematics education. It is difficult to define precisely, but broadly speaking, it refers to "a well organised conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms" (Bobis, 1996). The National Council of Teachers (USA, 1989) identified five components that characterise number sense: number meaning, number relationships, number magnitude, operations involving numbers and referents for numbers and quantities. These skills are considered important because they contribute to general intuitions about numbers and lay the foundation for more advanced skills.

Researchers have linked good number sense with skills observed in students proficient in the following mathematical activities:
 

• mental calculation (Hope & Sherrill, 1987; Trafton, 1992);
• computational estimation (for example; Bobis, 1991; Case & Sowder, 1990);
• judging the relative magnitude of numbers (Sowder, 1988);
• recognising part-whole relationships and place value concepts (Fischer, 1990; Ross, 1989) and;
• problem solving (Cobb et.al., 1991).

Activities to promote number sense

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Ten frame

Ten frames and dot cards can be used to develop students’ subitizing skills, the ability to “instantly see how many”. This skill plays a fundamental role in the development of students’ understanding of number.

Two types of subitizing exist. Perceptual subitizing is closest to the original definition of subitizing: recognizing a number without using other mathematical processes. For example, a child as young as two might “see 3” without using any learned mathematical knowledge. Conceptual subitizing is being used when a person sees an eight dot domino and “just knows” the total number. The number pattern is recognized as a composite of parts and as a whole. The domino is seen as being composed of two groups of four and as “one eight”. 

Go to Ten Frame Cards if you need resources.

Teaching equal groups

Hula Hoops and Equal Groups

Calling all different kinds of learning modalities!! I found  an exciting way to teach equal groups and would like to share with all of you.

In this activity children practiced how to make equal groups together. 

Get children to stand up, and then said something like "make equal groups of 2"...they had to quickly get into pairs scattered around the room. Then "make equal groups of 4"..."5"..."6"..etc.

For example: 4x2

Make four hula hoops for the four groups on the floor. 

 Put 2 students in each group. 

Count the number of students "in all"...4x2=8

Next try on 5x2= 10

3x3=9

Three hoops with 3 students in each group.

We can bring this activity into our classrooms too. :)

About Numbers

Cardinal, Ordinal, and Nominal Numbers

A cardinal number tells "how many." Cardinal numbers are also known as "counting numbers," because they show quantity.
Here are some examples using cardinal numbers:

• 8 puppies
• 14 friends

Ordinal numbers tell the order of things in a set—first, second, third, etc. Ordinal numbers do not show quantity. They only show rank or position.
Here are some examples using ordinal numbers:

• 3rd fastest
• 6th in line

A nominal number names something—a telephone number, a player on a team. Nominal numbers do not show quantity or rank. They are used only to identify something.
Here are some examples using nominal numbers:

• jersey number 4
• zip code 02116

Word problems

The purpose of word problems

One purpose of word problems is to prepare children for real life. This is true for example of shopping problems.
Another, very important purpose of story problems is to simply develop children's logical and abstract thinking and mental discipline. Note: one-step word problems surely will not do that! 

We can also bring it in to their everyday life by:

Practice problem solving daily by simply asking more questions. For example:

• How many students brought their homework today?
• How many more children brought their homework yesterday?
• We had 8 markers on the board, but now we only have 3. How many did we take away?
• How many animals are there in this magazine? How many are mammals? How many are birds? (introduction to fractions and percentages)

This will encourage children and ignite their interests in math too!

Not only that, it allows children to practice problem solving skills. http://nzmaths.co.nz/why-teach-problem-solving

Enrichment or acceleration learning??

This is something that I have been thinking over the last few days, enrichment or acceleration learning for students. 

Enrichment - teaching the same topic but increase the difficulty of the topic 

Acceleration- increasing the level

Which do you think is more important???

I didn't know about these 2 terms before the start of this module. After knowing, I realized that preschool educators should do more of enrichment teaching for preschool children rather then acceleration teaching to prevent over teaching and over whelming the children. 

Enrichment is essential to challenge the children's thinking and hence help build a strong foundation as they move on to primary school. If preschools are more focus on acceleration thinking, I feel we are mainly doing it to meet the parents demand. This is why I feel is it so important for all early childhood educators to have a stand on what to teach and what skills children have to possess by the end of their preschool years. 

Pre Course Reading

Being a teacher who teaches mathematics, I will need to have a profound, flexible and adaptive knowledge of mathematics content to ensure that I am prepared to pass on the knowledge to the students. And definitely being a teacher is not an easy job, we will have to be persistence, positive attitude, readiness for change and reflective disposition. Among all the qualities listed, I believed that all those qualities work hand in hand to make a good teacher and being reflective is the most important attribute of all. This is because we should always examine oneself for areas that need improvement or reflect on successes and challenges is critical for our growth and development. 

Having a good teacher is not enough for a student to strive, having the right environment is equally important to support children in learning and doing mathematics. In the right classroom environment, children will be given opportunities to talk about mathematics with one another and therefore creating chances to engage in reflective thinking and internalize concepts. In addition, children should be exposed to multiple approaches, learning to develop new ideas with mathematical skills and treating errors as learning opportunities. 

In all, I feel learning mathematics should be an enjoyable moment for every child and can be taught outside of the classrooms as well. As teachers, we could help children understand the concepts of mathematics better by providing them with concrete materials and used things that are of interest to them to let enjoy learning process.