Lesson 1 - Learning Mathematics in the Early Years PDF

Learning mathematics in the early years Preliminary Questions: 1. Describe the importance of teaching mathematics in the Early Childhood Education Program. 2. Why is important for children to develop a positive disposition in learning mathematics? Introduction The first few years of...

Learning mathematics in the early years Preliminary Questions: 1. Describe the importance of teaching mathematics in the Early Childhood Education Program. 2. Why is important for children to develop a positive disposition in learning mathematics? Introduction The first few years of a child’s life are especially important for mathematics development. For many education experts, no other group represents a greater opportunity to improve mathematical standards than children in the early years. The more grounded in mathematical concepts young children become, the better their later outcomes. Conversely, research shows that children who start behind in mathematics tend to stay behind throughout their educational journey. What are the early learning goals for mathematics? 1. Number Children at the expected level of development will:  Have a deep understanding of number to 10, including the composition of each number  Subitize (recognize quantities without counting) up to five  Automatically recall (without reference to rhymes, counting or other aids) number bonds up to five (including subtraction facts) and some number bonds to 10, including double facts 2. Numerical patterns Children at the expected level of development will:  Verbally count beyond 20, recognizing the pattern of the counting system  Compare quantities up to 10 in different contexts, recognizing when one quantity is greater than, less than or the same as the other quantity  Explore and represent patterns within numbers up to 10, including evens and odds, double facts and how quantities can be distributed equally 3. Reception  In Reception, children start to work with numbers in a range of different ways. They will be encouraged to be curious and explore numbers by playing number games, singing counting songs, making models as well as being introduced to the ideas of addition and subtraction. How Do children learn MATHEMATICS IN THE The first few years of a child’s life are especially important for EARLY YEARS? mathematics development (National Center for Excellence in the Teaching of Mathematics). Research shows that early mathematical knowledge predicts later reading ability and general education and social progress. As young as eight months old, children are developing an awareness of number names, and include these in their speech, as soon as they begin to talk. As children listen to the talk around them, they are introduced to numbers through opportunities that occur in everyday life, and experience a variety of number rhymes. This supports their growing knowledge of number names. How to teach MATHEMATICS IN THE EARLY YEARS?  Discover and create.  Use number concepts and skills to explore.  Develop confidence in their ability to think things through.  Solve meaningful problems.  Create connections to help discover relationships (e.g. characteristics). Note: Teaching math skills in the early years is an entire subject in its own right, but the key is to make it hands-on, cross-domain, and above all, meaningful.  What are the key areas of mathematical learning? 1. Cardinality and counting  When children understand the cardinality of numbers, they know what the numbers mean in terms of knowing how many things they refer to. 2. Comparison  Comparing numbers involves knowing which numbers are worth more or less than each other. 3. Composition  Learning to ‘see’ a whole number and its parts at the same time is a key development in children’s number understanding. 4. Pattern  Developing an awareness of pattern helps young children to notice and understand mathematical relationships. 5. Shape and space  Mathematically, the areas of shape and space are about developing visualizing skills and understanding relationships, such as the effects of movement and combining shapes. 6. Measures  Measuring in mathematics is based on the idea of using numbers of units in order to compare attributes, such as length or capacity.  What is numeracy?  Numeracy is the capacity, confidence and disposition to use mathematics in daily life.  What are the Principles in counting? 1. The one-to-one principle: children must name each object they count and understand there are two groups: the one that has been counted and the one that hasn’t yet been counted 2. The stable order principle: children must know how to count in the right order 3. The cardinal principle: children need to understand the last number in the set is the total amount 4. Counting anything: children need to realize that anything can be counted, not just objects that can be touched, but also things like claps and jumps 5. Order of counting doesn’t matter: children need to understand that the order of counting in the set is irrelevant and will still lead to the same amount  Activities to boost number sense in reception year 1. Crowd control Display the number of children allowed in each area using pictorial representations of cubes on a 10 frame. Once the children begin to realize how many are allowed in the area, they start to discuss the meaning of more and less. For example, “no more children are allowed in,” or “you can come in because one more than three is four.” 2. Bunny ears Encourage children to show numbers using their fingers above their head. “Bunny ears six” means they place their fingers above their head to show six. They may decide to use three fingers on each hand. As they become more confident, you could introduce swapping, where they show the same number but with a different configuration of fingers, in this case two and four, or five and one. 3. Grouping straws Each morning, drop different amounts of art straws all over the carpet. Say something like, “oh no class, I can’t believe it. I’ve dropped all my straws again. They were all in 10s. Can you help me?” This activity helps children consolidate counting objects and gets them to think about stopping after they have made 10. Providing elastic bands helps them to keep track of their groups of 10. 4. Fastest 10 frames This game can help distinguish between those who have developed a good understanding of number sense and those who need further support. Give each child their own frame and cubes. Tell them a number and observe how they place the cubes on the frame. If the children are working with the number eight, do they say each number name as they place the cube on the frame, or do they realize eight is two less than 10? If so, they should be able to place the cubes down faster than other children. What do they do when you say the next number? For example, for the number five, do they automatically remove three cubes, or do they remove all of the cubes and start over counting from one to five?  Everyday questions to boost number sense 1. When prepping lunch or a snack, count out the different types of food with your child, and as you lay the table, count out the different items. Ask your child questions like:  How many grapes are there?  How many tomatoes are there?  How many plates are there? 2. Practice using the terms more than, fewer than and as many as by asking:  Are there more grapes than tomatoes?  Are there fewer tomatoes than grapes?  Are there as many plates as people eating? 3. Remember to practice each sentence:  There are more grapes than tomatoes  There are fewer tomatoes than grapes  There are as many plates as family members eating Note: When counting, make sure that you count one number for one item to strengthen your child’s sense of one-to-one correspondence.  Other Helpful Number sense activities 1. Number Rhymes Carefully select number rhymes to include those that children are familiar with from home. Make sure the rhymes include:  Counting back and counting forward  “No” or “none” (Five little ducks went swimming one day)  Counting in pairs (two, four, six, eight, Mary at the cottage gate)  Counting to five, 10 and beyond 2. Problem solving, reasoning and numeracy Children must be provided with opportunities to practice these skills and gain confidence through play. For their learning to be effective, they need sensitive and informed support from adults. All children can be successful with mathematics, provided they have opportunities to explore ideas in ways that make personal sense to them and opportunities to develop concepts and understanding. Children need to know that practitioners are interested in their thinking and respect their ideas. 3. Mark making Young children use their own marks and representations to explore and communicate their mathematical thinking. These graphics include scribble-marks, Drawings, Writing, Tally-type marks, and Invented and standard symbols including numerals. Young children’s graphical exploration builds on what they already know about marks and symbols and lays the foundations for understanding mathematical symbols and later use of standard forms of written mathematics. 4. Developing understanding with careful questioning When children play and interact with other children, there are always opportunities for math talk to help them develop a deep understanding. For instance: I have made a pattern. What’s your pattern? How many blocks taller is my model compared to yours? How do we know this area is full? I have three cars, how many do you have? Do you have more? How do you know? Give learners long enough to think about their answer and give their response, but not so long that it disrupts the flow of play. 5. Sorting and grouping objects as a class Sorting and grouping objects as a class helps children learn to reason and look for patterns. Give them a variety of buttons each day and ask open-ended questions like, “how can we sort the buttons?” They can use critical-thinking skills to come up with a range of ideas like sorting by size, color, pattern, and shape. 6. Vote for a story First, ask a child to pick two books. Everyone in the class gets to vote (using a piece of lego, for instance) on which of the books should be read. Tally the votes at the end of the day to determine the winner. This can lead to questions such as:  Why?  How do you know?  How many more votes did one book have than the other? Note: The key to introducing mastery in the early years is to keep activities fun and part of your daily routine. The more learners explore math through play, the more engaged they become. What is mathematical pattern awareness?  Pattern awareness has been described as early algebraic thinking, which involves: noticing mathematical features. identifying the relationship between elements and observing regularities. Three kinds of mathematical patterns: 1. Shapes with regular features, such as a square or triangles with equal sides and angles, and shapes made with some equally spaced dots 2. A repeated sequence: the most common examples are AB sequences, like a red, blue, red blue pattern with cubes. More challenging are ABC or ABB patterns with repeating units like red, green, blue or red, blue, blue 3. A growing pattern, such as a staircase with equal steps Children who are highly pattern aware can spot this kind of regularity: they can reproduce patterns and predict how they will continue. Why is pattern awareness important?  It is important for identifying many different kinds of mathematical relationships.  It underpins memorization of the counting sequence and understanding number operations.  Pattern awareness has been described as early algebraic thinking, which involves:  Noticing mathematical features  Identifying the relationship between elements  Observing regularities Math play examples   This category includes ordering and comparing objects to figure out time, weight and length.  For example, Kyle held up his block tower and said, “this is taller than me.” James looked towards Kyle and Measurem pointed towards the block tower. “Me too, it’s taller than ent me,” he said as he looked up towards the top of the block tower. Kyle and James demonstrated how they could compare how tall the block tower is to each of their heights.   Also known as number sense, this category includes saying number words, writing numbers, counting, and recognizing a number of objects.  For example, “1, 2, 3, 4, 5, 6, 7, 8, 9, 10,” counted Devon Numeracy as he pointed towards the cars lined up on the table. “I have more than you,” he said as he pointed towards Melissa’s cars lined up. “1, 2, 3, 4, 5, 6…oh yeah,” she said as she pointed towards her cars lined up next to Devon’s cars. Devon and Melissa demonstrated counting and recognizing the number of cars they each had to compare each other’s quantities.   This category includes identifying or creating patterns and shapes.  For example, Jeremy and Mira sat on the carpet next to Patterns one another in the block area. Jeremy placed a magnetic block together. “I’m making a house,” he said as he placed and more magnetic blocks together. He took a magnetic block Shapes apart and said, “this needs to be over here,” and pointed at his magnetic blocks on the floor. Mira looked towards Jeremy’s magnetic blocks and pointed down toward her magnetic blocks. “I’m making a pizza,” she said. Jeremy and Mira created patterns and shapes with 2D magnetic blocks to build symmetrical structures.   This category includes grouping or sorting objects by characteristics.  For example, Casey placed a red horse into the red bowl. Classificati She picked up a blue pig and placed the blue pig into the on blue bowl. “The blue pig goes in the blue pig pen,” she said. Casey was classifying by sorting the blue and red animals into the corresponding same colored bowls.   This category includes using symbols or tokens to refer to quantities and operations.  For example, Sarah takes four crackers from the plate. Represent “Four because I am four,” she said. Preetish points to his ation plate: “I have four grapes because I’m four, too.” Sarah and Preetish are representing their age using snacks.   This category includes the ability to approximate values, i.e., make an educated guess about size or quantity.  For example, Jack is shown a jar filled with jellybeans and Estimation asked to guess how many are inside. “There must be a hundred jellybeans there!” he said. “I bet there’s a thousand jellybeans,” Sheena guessed. Jack and Sheena are estimating by trying to guess how many jellybeans are in the jar. QUESTI ONS? 1. Describe the importance of teaching mathematics in the Early Childhood Education Program. 2. Why is important for children to develop a positive disposition in learning mathematics? Thank you!