Learning Mathematics at Elementary level
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This document discusses the importance of learning mathematics at the elementary level. It covers Piaget's stages of development, the development of key mathematical concepts like numbers, measurement, and spatial thinking. It also discusses how children best learn mathematics through manipulation, representation, problem solving, and avoiding mathematics phobia. The document emphasizes making mathematics learning pleasurable through games, activities, discussions and relating it to other subjects.
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Learning Mathematics at Elementary level
- 1. Course -504 Learning Mathematics at Elementary level Block -1 Importance of Learning Mathematics at the Elementary Stage of schooling( U-1,2,3,4) Block -2 Enriching Contents and Methodology (U-5,6,7,8,9) Block -3 Learner Assessment in Mathematics (U-10,11,12)
- 2. NIOS 504 Block -1 UNIT- 1 HOW CHILDREN LEARN MATHEMATICS
- 3. Piaget’s stage of development 1) Sensory motor period ( birth to 2 yrs) 2) Pre-operational period (2 yrs - 7 yrs ) 3) Concrete operational period ( 7yrs – 11 yrs ) 4) Formal operational period ( 11 - 12 yrs to 14-15 yrs)
- 4. Development of Mathematical concept Three groups of mathematical concepts require in elementary stages A. Number and Operational numbers B. Spatial thinking C. Measurement
- 5. Development of Number concept Pre number concepts (develop attaining 7 yrs) a) Matching b) Sorting c) Comparing d) Ordering e) Subitizing
- 6. Number concepts a) Counting ( Ordinal aspect and cardinal aspect) b) Use numerals c) Operation on numbers
- 7. Development of Measurement concepts It depends upon conservation and transtivity process
- 8. Development of Spatial thinging It is genarally develop in formal operation period
- 9. Ways of Learning Mathematics a) Manipulation of objects b) Placing tasks in meaningful concepts c) Representation in multiple ways d) Developing alternative strategy e) Problem solving and Problem posing
- 10. Common causes of Mathematics Phobia 1) Prenegative experiences with mathematics a) unfavourable school climate b) lack of encouragement from teachers/ parents c)lack of positive role model d) math problem being used as a punishment in school
- 11. 2) Pressure of taking timed tests 3)The fear of looking in front of others 4) Lack of preparedness
- 12. Making Mathematics Learning Pleasure Number race Place value Addition game Guessing game Tangrams Rangoli Quiz,Debate,Seminar,Discussion Local play ,song ,story etc
- 13. NIOS 504 Block -1 UNIT -2 Mathematics and Mathematics Education – Importance ,Scope and Relevance
- 14. Nature of Mathematics 1. Logical 2. Symbolical 3. Precise Expression 4. Abstraction 5. Exactness 6. Order and Sequence 7. Pattern
- 15. Corelation of Mathematics with other Subjects Mathematics and Literature Mathematics and EVS Mathematics and Science Mathematics and Geography Mathematics and History Mathematics and Other Subjects A. Work Experience B. Art Education C. Health and Physical Education
- 16. Ability to think Mathematically Problem Solving in Math
Editor's Notes
- S-M=The child is beginning to think with,some purpose or an end and then a search for appropriate means to that end. Further, towards the end of this period, the child begins to talk using mono-syllables of the language used at home. This is indicative of onset of symbolic action, a component of intelligence. P-O=2-4 YR rapid language learn.4-7yr able to classify but not in many way.If we change shape then fails to classify.Bottle waterexpt. C-O =important for us. With exposure of concrete object he can establish relation like small,big,…starts reversible operation.multiple way of classification possible. F-O=Able to think logically.solve logically. The child now in the post-primary grades, reasons hypothetically using symbols or ideas and no more is in need of physical objects as a basis for his/her thinking. The child has attained new mental structures. These new structures include the propositional combinations of symbolic logic like implications (if…then), disjunction (either-or, or both), exclusion (either – or), reciprocal
- Subitizing: Instant recognition of a number pattern without counting is subitizing. The pattern can be reconstructed without knowing the amount. Subitizing helps the children see small collections as one unit. This provides an early perceptual basis for number, but it is not yet “number knowledge. 10*2=20 10*3=30 Ordering: Ordering is foundational to our number system. Children have to be able to put items in an order so they are counted once and only once. Putting items in order is a prerequisite to ordering numbers. Seriation is ordering objects by size, length, or height. When giving a child directions use ordinal words (first, next, last)
- Ordinal-first,second Cardinal-1,2,3
- Initially, the young child in the preschool i.e. below 6 years of age displays no grasp of conservation of length. His judgments are based primarily on a single perceptual feature. At this age a child judges the two lines (Fig.1.2) to be unequal because their end points are not aligned. Fig. 1.2 Area and volume judgments are usually based on the longest linear dimension (it is bigger because it is longer) as visually perceived by the child. Around 6 to 7 years of age, the child uses non-standard unit of measuring length like his hand span or his own height to measure the length The child begins to understand the conservation of volume of liquid at about 7 to 8 years of age when he/she realizes that the liquid poured from a wider vessel from a tall thin vessel is of same amount. 11 How Children Learn Mathematics Block 1 : Importance of Learning Mathematics at the Elementary Stage of Schooling Notes It is not until roughly around 8 to 10 years of age the average child can appreciate measurement in terms of covering whatever is to be measured, with smaller units of measure. Up to this stage, development of the measurement has been characterised by a trial and error approach. Now the child is able to proceed by means of a more calculated approach. However, the measurements of area and volume in terms of space occupied by a particular object lags behind. The child reaches the final stage of development to measure area and volume by calculation of linear dimensions (length, breadth, and height/thickness) by the age of 10 and 11 or a few years later.
- Development of Spatial Thinking: The child’s first impression of space or world in which that lives is a very disorganized one. Neither can she/he discriminate the figures nor can he hold the image of the figure for long time. When the child has passed the scribbling stage, around three and half years of age, he/she can distinguish between the closed and open figures. But all simple closed figures such as squares, circles or triangles are all the same for him/her and are drawn the same way. Around 7 to 8 years of age the child becomes able to differentiate between similar shapes such as squares, rectangles and rhombus correctly. But it is not until the child reaches 10 years old, he/she is able to name the figures correctly and it is not until a year or two older than this that he/she could distinguish the presentation of 3D objects from those of the 2D figures. There are more intricate aspects of development of spatial thinking which mostly unfold during the later years of the concrete operation period and mostly during the formal operation period.
- Manipulation of objects: As you have observed, it is through the manipulation of concrete objects that the children acquire the mathematical skills at the early stage. Acquisition of any mathematical skill at the early stage like comparison, categorization, counting, fundamental four operations,cannot be possible without manipulation of concrete objects. Provision of a variety of objects both familiar and novel, should be made available to children in the classroom for their free handling, so that it would be easier for you to facilitate their learning of desired mathematical
- Sometimes a student in higher class or a family member with exceptional mathematics abilities inspires the childrenin lower grades in their mathematics learning. Such a role model is rare to find and the child does not find adequate inspiration towards an abstract subject like mathematics
- 3-express owns feeling in min language and precisely . use of time properly 5-right or wrong
- Relation Between HCF and LCM Whether LCM > HCF HCF < each number ………………… …………………. ……………………..