manipulation and discovery

Jo Ann Brewer

MANIPULATION AND DISCOVERY

MATHEMATICS

What is the definition of Mathematics?

How Mathematics is learned ?How Mathematics is taught ?What are the Mathematical objectives?

QUESTIONS

WHAT IS THE DEFINITION OF MATHEMATICS ?

1ST QUESTIONS

For young children, mathematics is a way of viewing the world and their experiences in it. It is a way of solving real problems. Mathematics is the understanding of numbers, operations on numbers, functions and relations, probability, and measurement. It is much more than the pages of simple equations that you may remember working as a child. The early childhood years, mathematics should continue to be a manipulative activity.

MATHEMATICS

How Mathematics is

learned ?

2ND QUESTION

Piaget (1970) describes three ways that human beings can learn. They can learn from:

1- The physical world- Concept- Ex: hot cold, 2- The social world – Concepts such as “ Language” , religion …3- The construction of mental relationship – concepts such as “ counting ‘ “ seriations” numeration”, conservation and so on

HOW IT IS LEARNED

The learner creates categories and hierarchies of objects without regarding their physical properties.

Example: setting the dinning table for three students.

CONSTRUCTION OR LOGICO-MATHEMATICAL THINKING

If Math concepts are constructed by each learner based on the observations with real-life materials and situation then

what are the responsibilities of the teacher?

1- To supply the language for the concept. The terminology.

2- To ask questions about what the children observe?

3- To provide the materials and the assistance that would enhance making those discoveries

CONSTRUCTION OR LOGICO-MATHEMATICAL THINKING

How Mathematics is taught ?

3RD QUESTIONS

TEACHING MATHEMATICS

According to Schwartz(1995), authentic mathematics occurs in the classroom when children play in learning centers , distribution of snacks or materials and should make sure to be an integral part in the school day. Examples: 1- Use attendance figure to know how many are absent and how many are presents.2-A grocery store 3- A calendar:Today is ------yesterday was ----- and tomorrow will be -------. 4- Cooking activities.

MATHEMATICS STRANDS TO BE TAUGHT

Logical Thinking and

Mathematical Reasoning

Measurement

Statistics and

Probability

Geometry

Patterns and

Functions

Arithmetic

Statistics and

Probability

Examples: 1- putting the sand toys in one container2-Sorting dishes in the housekeeping area into

storage area for plates3-Classifying the unit blocks into diff erent sizes for

storage. 4- Comparing sets and using categories such as more-

less- few – many .

LOGICAL THINKING AND

MATHEMATICAL REASONING

Comparing and Analyzing InformationExample: 1- Observing and comparing the number of sunny days, cloudy days, snowy days or rainy days marked on the calendar.

STATISTICS AND PROBABILITY

MEASUREMENT

Children are always interested in their own heightsWeights, ages , ect.…Examples:1- Using blocks to measure walls.

Encourage the learners to participate in activities that help them develop concepts of space and the relationships of objects in space ---- two triangles can make a square.

PizzaA bar of chocolate

GEOMETRY

Patterns are visual, auditory, spatial, numerical or combination of these.

Promoting recognition of patterns is extremely important in helping young children develop mathematical concepts.

PATTERNS AND FUNCTIONS

PATTERNS AND FUNCTIONS CONT’…

Function: it is the pattern that is created when certain action are performed on objects or numbers. Example: Cutting an apple in the middle.

Arithmetic is a part of every strand in mathematical thinking. It includes:

1- one to one correspondence2- counting3-nunbers4-place value5-operations on whole

numbers 6-fractions.

ARITHMETIC

Go Thru the Slides

again and see the

materials used.

MATERIALS

To GroupTo sortTo classifyTo seriateTo constructTo weightTo measureTo countTo graph

OBJECTIVES

REFLECTION