Lesson 3: Fundamental Mathematics Concepts & Experiences PDF

CLE4103 MATHEMATICS FOR YOUNG CHILDREN LESSON 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 corr...

CLE4103 MATHEMATICS FOR YOUNG CHILDREN LESSON 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 Number Sense & Summary Counting of Today Lesson Other Mathematical Concepts Developing Number One to one may no Sense correspondence come in Number Concepts & exam Comparing Numeration Counting Principles & Ordering Skills Counting: Number Set Classification Number Symbol Reversibility Awareness of Number symbols Number Symbol Skills Writing Numbers  One to one Number corresponde Comparison Ordering Mathematical concepts sense nce Classificatio Conservatio Reversibility Estimation n n Spatial Geometry Shape Patterning Sense  Number Sense & Counting Number sense Referred to the concept of number or understanding number. Counting Counting a set of objects that can be moved as they are counted is easier than counting objects that cannot be moved or touched. Makes the connection between quantities and counting. Counting a set that is ordered in some way is easier than counting a randomly arranged set. Number Sense & Summary Counting of Today Lesson Other Mathematical Concepts Developing Number One to one Sense correspondence Number Concepts & Comparing Numeration Counting Principles & Ordering Skills Counting: Number Set Classification Number Symbol Reversibility Awareness of Number symbols Number Symbol Skills Writing Numbers  Developing Visualizing Number Exploring numbers Sense numbers in a Number variety of contexts sense is a “good intuition Relating numbers about numbers and their relationships.” in ways not Using common sense based on the limited by way numbers and tools of traditional rules measurement work within a given culture. and procedures It develops gradually as a result of: Number Sense & Summary Counting of Today Lesson Other Mathematical Concepts Developing Number One to one Sense correspondence Number Concepts & Comparing Numeration Counting Principles & Ordering Skills Counting: Number Set Classification Number Symbol Reversibility Awareness of Number symbols Number Symbol Skills Writing Numbers Do they mean the same thing? I have 3 apples. (Cardina l) My house number is 3. (Numerical)  All the 3 boys were not at school today. (Numercia l) Samy is at the 3rd position in his class. (Ordinal )  nu Numerical Number Sense: Number Concepts & 3 g. e. r, be m Numeration na Nominal e re th g. e. e, m or Ordinal nk ra r, de ho Cardinal e ar e er th ng hi et m so of y an m w Number Sense & Summary Counting of Today Lesson Other Mathematical Concepts Developing Number One to one Sense correspondence Number Concepts & Comparing Numeration Counting Principles & Ordering Skills Counting: Number Set Classification Number Symbol Reversibility Awareness of Number symbols Number Symbol Skills Writing Numbers  Counting Principles & Skills One-to-one Stable-order Counting Principles 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=1 EzGw-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=ie RYzlFWWUg 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=6WbYP sr9lgc 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  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 Number Sense & Summary Counting of Today Lesson Other Mathematical Concepts Developing Number One to one Sense correspondence Number Concepts & Comparing Numeration Counting Principles & Ordering Skills Counting: Number Classification Set Number Symbol Reversibility Awareness of Number symbols Number Symbol Skills Writing Numbers   Is a type of classification Concreteness- hands-on activity, manipulative  Instead of criteria such as size or colour, the grouping is based on number of items Number of items- easy, 3 or 4 or 5 items  Experiences in forming number sets Broad groupings (a lot, a are considered in terms of the levels Counting: few/more/less) Perceptual features: below: Matching up Number games (dot Set domino) Number Sense & Summary Counting of Today Lesson Other Mathematical Concepts Developing Number One to one Sense correspondence Number Concepts & Comparing Numeration Counting Principles & Ordering Skills Counting: Number Classification Set Number Symbol Reversibility Awareness of Number symbols Number Symbol Skills Writing Numbers  Number Symbol Developing concepts of classification, quantity and ordering (number set) + Awareness of symbols (numerals) Connecting symbol to set (number-numeral association) Symbolic level (using numerals)  Awareness of Number symbols  Children gradually become aware of number symbols, and the connection between number symbols and language.  Number symbols are called numerals.  Examples of numerals available in the environment: A clock or calendar on the wall Weighing scales or height charts Attendance book where you record number of children present Measuring containers with numeral graduations  The role of adults is to help children notice these number symbols and draw their attention to the meaning of these numbers.  Invented symbols or pretend numerals, Awareness of Symbols a stage children go through before using real numerals.  Print Awareness: children become aware of Understand symbolism. print, and the connection between print and language. Important to respect and accept these early attempts and  Teachers praiseneed the idea. to use informal experiences to help children focus and notice the numerals around them. How? Number Sense & Summary Counting of Today Lesson Other Mathematical Concepts Developing Number One to one Sense correspondence Number Concepts & Comparing Numeration Counting Principles & Ordering Skills Counting: Number Classification Set Number Symbol Reversibility Awareness of Number symbols Number Symbol Skills Writing Numbers 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 Number Sense & Summary Counting of Today Lesson Other Mathematical Concepts Developing Number One to one Sense correspondence Number Concepts & Comparing Numeration Counting Principles & Ordering Skills Counting: Number Classification Set Number Symbol Reversibility Awareness of Number symbols Number Symbol Skills Writing Numbers Recognizing & Writing numbers Activities to facilitate number recognition: Match cards with number symbols Match number symbols to number words Play number Bingo Have number work cards for a child to copy Have simple connect-the-number pictures Look for number words or symbols in books and magazines Make a number collage  Requires Structured A way to skills fine motor literacy and knowledge, math paper ideas on e math communicat format to paper markings on ideas with represent The Writing Numerals purpose 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 Number Sense & Other Mathematical Summary ofConcepts Counting Today Lesson Developing Number Sense One to one correspondence Number Concepts & Numeration Comparing Counting Principles & Skills Ordering Counting: Number Set Classification Number Symbol Awareness of Reversibility Number symbols Number Symbol Skills Writing Numbers 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 one of the Is a pre-requisite earliest skill for the more mathematical difficult task of concept to conservation develop Matching Concept When assessing matching tasks, four dimensions are considered: 1 Are the items identical or different? 2 Are the sets “joined or not joined?” 3 Is there the same number in each set? 4 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. Summary of Today Lesson Number Sense & Other Mathematical Counting Concepts Developing Number Sense One to one correspondence Number Concepts & Numeration Comparing Counting Principles & Skills Ordering Counting: Number Set Classification Number Symbol Awareness of Reversibility Number symbols Number Symbol Skills Writing Numbers  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 Has to do with of readily observable difference feature is easiest. Compare two objects- Learn comparative direct comparison language or (example: long vs. short, opposites. more vs. less) Summary of Today Lesson Number Sense & Other Mathematical Counting Concepts Developing Number Sense One to one correspondence Number Concepts & Numeration Comparing Counting Principles & Skills Ordering Counting: Number Set Classification Number Symbol Awareness of Reversibility Number symbols Number Symbol Skills Writing Numbers 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 of “one More difficult than comparing more” Common ways to order may be by size, length, height, Order or width, and later more sequence of complex dimensions such as numbers color, texture, weight, temperature and sound Ordering Simple seriation Double seriation Summary of Today Lesson Number Sense & Other Mathematical Counting Concepts Developing Number Sense One to one correspondence Number Concepts & Numeration Comparing Counting Principles & Skills Ordering Counting: Number Set Classification Number Symbol Awareness of Reversibility Number symbols Number Symbol Skills Writing Numbers 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 LEVEL 1 Sticks red Classifying using blu only one property or e Household characteristic items io us obv kitche bathroo e an h av c e : n m a ls re n Junk r i e M ate diff scissor plastic  Levels of Classification Activity LEVEL 2 Increase number of objects Increase number of categories LEVEL 3 (3 or 4 attributes) Increase level of abstraction LEVEL 4 (example: happy vs unhappy) LEVEL 5 Overlapping categories (intersection) (all squares and blue blocks…) LEVEL 6 Invent classifications  Classification Square but not Blue but not all blue square All blue and square PowerPoint® Slides By Melanie Bodipalar Summary of Today Lesson Number Sense & Other Mathematical Counting Concepts Developing Number Sense One to one correspondence Number Concepts & Numeration Comparing Counting Principles & Skills Ordering Counting: Number Set Classification Number Symbol Awareness of Reversibility Number symbols Number Symbol Skills Writing Numbers 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 & Other Mathematical Counting Concepts Developing Number Sense One to one correspondence Number Concepts & Numeration Comparing Counting Principles & Skills Ordering Counting: Number Set Classification Number Symbol Awareness of Reversibility 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.  Summarize and conclude on the number sense and counting topic. To help: you may want to Tutorial share your understanding on how children can experience mathematics Mathematical concepts that children need to master to understand mathematics.