Week 3 - Fundamental Mathematics Concepts & Experiences PDF

CLE4103 MATHEMATICS FOR YOUNG CHILDREN WEEK 3: Fundamental Mathematics Concepts & Experiences Learning Outcome(s) Upon completion of this lesson, students will be able to: Describe the number sense and counting concept. discuss the fundamental mathematical concepts:...

CLE4103 MATHEMATICS FOR YOUNG CHILDREN WEEK 3: Fundamental Mathematics Concepts & Experiences Learning Outcome(s) Upon completion of this lesson, students will be able to: Describe the number sense and counting concept. discuss the fundamental mathematical concepts: one-to- one correspondence, comparing, ordering or seriation, and reversibility Identify the mathematical learning experiences of children. Mathematical Concepts  Summary of Today Lesson Number Sense & Counting Other Mathematical Concepts Developing Number Sense One to one correspondence Number Concepts & Comparing Numeration Counting Principles & Skills Ordering Counting: Number Set Classification Number Symbol Reversibility Awareness of Number symbols Number Symbol Skills Writing Numbers Mathematical concepts One to one Number sense Comparison Ordering correspondence Classification Reversibility Conservation Estimation Geometry Shape Patterning Spatial Sense Number Sense & Counting Number sense Counting Referred to the concept of number or Counting a set of objects that can be moved as understanding number. they are counted is easier than counting objects Makes the connection between quantities and that cannot be moved or touched. counting. Counting a set that is ordered in some way is easier than counting a randomly arranged set.  Developing Number Sense ✓Number sense is a “good intuition about numbers and their relationships.” ✓Using common sense based on the way numbers and tools of measurement work within a given culture. ✓It develops gradually because of: Visualizing Relating numbers Exploring numbers in in ways not limited numbers a variety of by traditional rules contexts and procedures Number Sense Activities Does the number “three” mean the same thing? I have 3 apples. (Cardinal) My house number is 3. (Numerical) All the 3 boys were not at school today. (Cardinal) Samy is at the 3rd position in his class. (Ordinal) Please turn to page 3 of the book. (Numerical) Number Sense: Number Concepts & Numeration Numerical number, e.g. 3 Nominal name, e.g. three Ordinal order, rank Cardinal how many of something there are  Counting Skills ◼ rote - memorises number sequence without thinking of the meaning ◼ rational - counts with understanding ◼ counting on - continues counting sequence where he has left off ◼ skip counting - counts in groups of twos, fives, tens, etc ◼ counting back - counts back in sequence ◼ sight counting - gives correct answer without counting, just a look Play this game: https://www.ilibrarian.net/games/guess-how-many/index.html  Counting Principles & Skills Counting Principles One-to-one Stable-order Cardinality Abstraction Order irrelevance One to one Principle ▪ Child uses only one number word for each object. ❑Tendency for children to skip objects or to say two number words for the same object Watch this video: https://www.youtube.com/watch?v=dvyLUpE6o7A  Stable Order Principle ▪ The number words are used in fixed order - memorized correct sequence in counting ▪ This principle is only meaningful if applied with one-to-one correspondence Watch this video: https://www.youtube.com/watch?v=1EzGw- JxSmA  Cardinality Principle ▪ Child realizes that the last number word used is the number of objects in the set. Watch this video: https://www.youtube.com/watch?v=ieRYzlFW WUg Abstraction Principle ▪ Counting can be applied to all kinds of things (tangible or non –tangible) and even to groups. Watch this video: https://www.youtube.com/watch?v=6WbYPsr9lgc Order Irrelevance Principle ▪ It does not matter which object is assigned a number first, but that all objects have to be counted. 1 3 2 1 3 2 Watch this video: https://www.youtube.com/watch?v=xVv-qjhEUgc  ▪ Is a type of classification ▪ Instead of criteria such as size or colour, the grouping is based on number of items ▪ Experiences in forming number sets are considered in terms of the levels below: Counting: Concreteness- hands-on activity, manipulative Number Set Number of items- easy, 3 or 4 or 5 items Broad groupings (a lot, a few/more/less) Perceptual features: Matching up games (dot domino) Number Symbol Skills Number symbol skills developed by children in the pre- operational stage includes: ❑Recognizing and naming numerals (i.e. ‘read’ the numerals) ❑Placing numerals in order ❑Associating sets and numerals (in order) ❑Realizing each numeral means one more than the one before it ❑Writing numerals  Writing Numerals A way to represent ideas with markings on paper Structured format to communicate math ideas on The purpose paper Requires math knowledge, literacy and fine motor skills When the time is right, teachers use a number of mediums to teach children formation of symbols correctly: Tracing a finger over sandpaper numerals Forming the numerals with clay Tracing the numerals using templates Forming the numerals in wet sand or salt Tracing by connecting dots PowerPoint® Slides By Melanie Bodipalar One-to-one Correspondence Uses only one number word for each object It forms the foundation for the development of many kinds of logical Is the concept of thinking matching. Is a pre-requisite skill for Is one of the earliest the more difficult task of mathematical conservation concept to develop Matching Concept When assessing matching tasks, four dimensions are considered: Are the items identical or different? Are the sets “joined or not joined?” Is there the same number in each set? Are there many items to match, or few? Different items are easier to match PowerPoint® Slides By Melanie Bodipalar Similar items but different sizes are harder to match Are there many items to match or few? Easier (lesser items) Harder (more than 5 items) Is there the same number in each set? Easier (even sets) Harder (not enough or too many in one set) Are the sets joined or not? (Joined is easier) Not joined is harder One-to-one Correspondence ✓ The more “real” and familiar the objects being matched are, the easier it is for the child to deal with mentally as they are able to relate to them every day. ✓ Avoid using abstract items such as geometric shapes or dots or numerals.  Comparing The child finds a relationship between two things or groups of things on the basis of some specific characteristic or attribute. Comparing Comparison on the basis of Has to do with difference readily observable feature is easiest. Compare two objects- direct Learn comparative comparison (example: long vs. language or opposites. short, more vs. less) Ordering (Sequencing, Seriation, Grading) Involves putting more than 2 objects, or sets with more than 2 members, into a sequence In terms of amount – the idea More difficult than comparing of “one more” Common ways to order may be by Order or size, length, height, width, and later sequence of more complex dimensions such as numbers color, texture, weight, temperature and sound Ordering Simple seriation Double seriation Classification Grouping or sorting objects into classes or categories according to some systematic scheme or common criteria Grouping may be by color, shape, size, material, pattern, texture, function, etc Helps build logical thinking capabilities Levels of Classification Activity Sticks red Classifying using only one blue property or characteristic Household items kitchen bathroom Junk scissor plastic  Levels of Classification Activity Increase number of objects Increase number of categories (3 or 4 attributes) Increase level of abstraction (example: happy vs unhappy) Overlapping categories (intersection) (all squares and blue blocks…) Invent classifications  Classification Square but not blue Blue but not all square All blue and square PowerPoint® Slides By Melanie Bodipalar Reversibility Recognizing that if a physical process is reversed, there is a return to the original starting point Watch the video: Video 1:https://www.youtube.com/watch?v=gA04ew6Oi9M Video 2:https://www.youtube.com/watch?v=bqlu_ml6F0E  Summary of Today Lesson Number Sense & Counting Other Mathematical Concepts Developing Number Sense One to one correspondence Number Concepts & Numeration Comparing Counting Principles & Skills Ordering Counting: Number Set Classification Number Symbol Reversibility Awareness of Number symbols Number Symbol Skills Writing Numbers Resource Charlesworth, R. (2012), Experiences in math for young children ( 6th ed.). Cengage Learning. Haylock, D. & Cockburn, A. (2012). Understanding Mathematics for Young Children: A Guide for Teachers of Children 3 -8 (4th ed.).SAGE. Smith, S. S., (2013). Early childhood mathematics (5th ed.). Pearson. Tucker, K. (2010), Mathematics through play in the early years (2nd ed.). Sage.