da Carla Weigel mancano 12 anni
510
Math Concepts
Created by Carla Weigel, Hennepin Technical College
da Carla Weigel mancano 12 anni
510
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There are two sides to the concept of time. There is sequence and there is duration. Sequence of time has to do with the order of events. While the child learns to sequence things in patterns, he also learns to sequence events. Duration of time has to do with how long an event takes. A child relates time to three things;
1. Personal experience - the child has her own past, present, and future. The past is often referred to as “When I was a baby.” “Last night” may mean any time before right now. The future may be “After my night nap” or “When I am big.” The young child has a difficult time with the idea that there was a time when mother and dad were little and she was not yet born.
2. Social activity - makes more sense to the child. A change in schedule can be very upsetting. There is a certain routine to follow. There is order throughout the day.
3. Cultural time - is the time fixed by clocks and calendars. The child doesn’t understand this until she is in the concrete operations period. Terms used could be before/after, day/night/, minute/second, now/later, morning/afternoon, yesterday/tomorrow, early/late, spring/summer, fall/winter, and new/old.
Give examples of how you’ve seen your group of children show an understanding of time.
Measurement involves assigning a number to things so they can be compared. Standard units such a pints, quarts, liters, yards, meters, pounds, grams, and degrees tell us exactly how much,(volume); how heavy (weight), how long, wide, or deep (length), and how hot or cold (temperature).
To begin with, a child imitates older children by playing with rulers, measuring cups, etc. She pours sand or water from one container to another. She lifts and moves things as she learns about weight. Her short arms can’t always reach everything she wants - length. Then she begins making comparisons - bigger, smaller, longer, shorter, etc. She begins using anything she can to measure. She will find out how many toothpicks long her foot is. From this she will graduate on to standard units. The sand and water table offer many opportunities to explore the concept of volume. Make sure different sizes of containers are available. Cooking and outdoor activities help introduce temperature concepts. To teach these concepts include words such as thermometer, hot, warm, cool, and cold.
Ordering is a higher level of comparing. It involves comparing more than 2 things or more than two sets. It also involves placing things in a sequence. Ordering is called seriation. Patterning is related to ordering in that children need a basic understanding of ordering to do patterning. Patterning involves making or discovering auditory, visual, and motor regularities. Ordering starts to develop in the sensorimotor stage. Before the age of 2, the child likes to work with nesting toys. As the sensorimotor period progresses, toddlers can be observed lining up blocks.
Other than nesting cups, what opportunities do children in your room have to seriate?
A young child learns that wholes have parts, and later on a child learns that parts are fractions of the whole. He learns that things are made up of parts, that sets of things can be divided into parts, and that whole things can be divided into parts. Two year old Pete breaks up his graham crackers into small pieces and announces to Tim, “I have more than you.” Gradually the child is able to see that a whole is made up of parts.
It is through everyday movement activities that the child first learns about space. Children in the sensorimotor and preoperational stages need equipment that let them place their own bodies on, off, under, over, in, out, through, above, below, and so on. They need places to go, they need things they can put things in and take things out of.
Teachers need to sue space words as they fit into daily activities. They can also plan some structured activities through music and movement activities. Have children play Simon Says - hand on top of head giving the children verbal directions.
Each object in the environment has its own shape. Babies learn that some shapes are easier to hold than others. Some things roll. Later, they learn the basic shapes. Basic shapes are circle, square, and triangle. Later they learn rectangle, rhombus (parallelogram), and ellipse (oval). Interview tasks for shape center on;
• Discrimination - whether the child can see that one form has a different shape from another form.
• Labeling - whether the child can find a shape when the name is given and whether he can name a shape when a picture is shown to him.
• Matching - requires a child to find a shape like one shown to him.
• Sorting - child must separate a mixed group of shapes into sets.
Circles are easiest to copy, then squares, rectangles, then triangles. They can’t usually copy until 4 or 5 years of age. Wait until color concepts are
understood before you try to teach shape. Colors are easier to learn because the terms are more often used. It is important to include more shapes than the four basic ones I listed above. Ask children to compare - how is a circle like an oval?
Don’t forget that cleanup is an obvious example of a sorting activity.
These concepts could be considered a beginning math concept because they help children learn to discriminate among objects. They can pattern and sequence. This also helps in language development. Children generally learn colors first, but may confuse colors and shapes. By age 2 many can match a color to a sample. If a 3-5 year old has problems, they may be color blind. If you think a child is, report it to the director and then one of you should discuss it with the parents.
List ways you teach about color.
The child finds a relationship between two things or sets of things on the basis of some specific characteristic.
Children have many contacts with comparisons in their daily life. Parents and teachers are constantly using these words to describe things. In addition, children notice things for themselves. They can’t lift some objects because they are too heavy, or they can’t go behind a couch because the space is too narrow. Children want to be bigger, taller, faster, and older. They want to be sure they have the same, not less, and if possible, more of things that the other child has. Most children learn the idea of comparison through naturalistic and informal activities.
Sets refer to things that are put together in a group based on some common criteria (color, shapes, size, use) A set can contain from 0 (empty set) to and endless number of things (or members). Most sets that children work with have an observable limit. A car has a set of 4 tires plus a spare. To add is to put together or join sets. To subtract is to separate a set into smaller sets. A car has a flat tire. The flat is taken off and subtracted from the set of five. There are now 2 sets, four good tires and one flat tire being repaired.
Children must practice sorting and grouping before doing any formal adding and subtracting. Things may belong together because they are the same color, shapes, do the same work, same size, the material they are made of, the pattern of the objects, the texture of the objects, association between the two objects, class name, common features, numbers of objects, and so on.
Young children spend much of their playtime in classification activities.
Note is children playing with a pegboard put each color peg in its own row, etc. As long as the adults provides the free time, the materials, (junk is fine as long as it is safe), and the space, the child does the rest.
Matching is a form of classification - putting like objects together. The child’s first classroom experiences should involve only one concept - color, size, or shape.
What ways of classification do you have around your classroom?
Number sense makes the connection between quantities and counting. It underlies the understanding of more and less, amounts, the relationship between space and quantity, and parts and wholes. Quantities from one to four or five are the first to be recognized. Rote counting involves reciting the names of numerals in order from memory. A child counts from 1-10. Rational counting involves attaching each numeral name in order to a series of objects in a group. A child has some pennies in her hand. She takes them out of her hand one at a time and places them on the table. Each time she places one on the tables she ways the next number name in sequence- one; places first penny, two; places another penny. It is a higher level of one-to-one correspondence. It serve as a basis for developing the concept of number conservation. Children need repeated and frequent practice to develop counting skills, but this practice should be of short duration and center on informal instruction. Rote counting develops ahead of rational counting. Counting things is much more complicated than reciting number names in order from memory. The child must coordinate eyes, hands, speech and memory to correctly do rational counting. By the age of 4 or 5, rational counting skills should begin to catch up with rote counting skills. When doing structured counting activities, try to give children the opportunity to work together so they can discuss and compare ideas.
Children count frequently in everyday activities. They hear 1,2,3 on the television and repeat it. They may run up to a teacher and say, “I can count - 1, 2, 3.” Listen carefully to see if the child gets the names in the right order.
Teachers can find many ways to take advantage of opportunities for informal instruction. Counting while waiting, asking how many shoes the child has, counting the number of children in the group, setting the table. Check their understanding by asking them to go get 3 blocks, etc.
There are also short structured activities than can be used to help children learn the number names in the right order. This Old Man, One Two, Buckle your Shoe, other counting fingerplays, clapping and counting at the same time teach number order and give practice in rhythm and coordination. Groups of four or less are easier to work with. It helps if the child is able to touch the objects as he counts.
Older children may have a Hundred Days Celebration. Starting the first day of school, using concrete materials, the class records how many days of school have gone by. Each day, count the number of days of school. Whenever 10 days are collected, gather 10 straws or tongue depressors and bundle them with a rubber band. Explain that when there are 10 bundles, it will be the 100th day. On the 100th day, each child brings a plastic zip-loc bag containing 100 items. It could be macaroni, beans, pennies, candy, hairpins. Working in pairs, they can check their collections by counting groups of 10 and counting the groups they have.
In order to read and write, children must first recognize written numbers and their symbols. This skill develops as children are exposed to numerals. Calendar time, number walks, and grocery store set-ups with price tags are ways to help children with this skill.
The most fundamental component of the concept of number. It has the understanding that one group has the same number of things as another. It is preliminary to counting and basic to the understanding of equivalence and to the concept of conservation of number.
When observing for this concept, watch to see if the child has each paintbrush in the appropriate color paint. See if the child lays out one napkin for snack for each child.
These activities develop naturally in an infant. The child learns that one thing can be held in each hand. The toddler learns that one person fits on each chair, one shoe on each foot, and so on. Toddlers spend much time with this. They line up small containers and put one small animal in each.
Materials are easier to match if the groups are different. Matching an animal to a cage or a spoon to a bowl is easier than making a match between two groups of blue chips. The more objects in each group, the more difficult it is to match. Groups with fewer than five things are much easier than groups with five or more. If a child is able to place groups of 10 in one-to-one correspondence, he or she has a well developed sense of the concept. The easiest activities use real objects such as small toys and familiar objects. Later on cutout shapes and pictures of real objects and pictures of shapes could be used. It is easier to do if objects are joined than if they are not joined. A shoe on a foot is easier than a ball next to a box.
Give an example of how you’ve seen children practice this.
Ordering events in time such as playing a game and there is only one way to go on the game board to win, reading a book—only one way for story to make sense from beginning to end, sequencing cards showing how to build a snowperson; only one correct way, following a recipe.
Includes use of Ordinal Numbers: 1st, 2nd, 3rd, 4th, etc.
The ordering of items according to one characteristic like size: biggest to smallest, light to dark, tall to short, etc. Can be ordered both ways and still be correct.
: “Where things are in space”. Children discover meanings of words like over, under, behind, in front of, in back of, etc. To gain these skills the use of puzzles , wooden blocks, legos and movement activities are planned.
Ability to group objects together by one or more characteristics like: color, size, shape, fruits vs. vegetables, cars vs. trucks, etc.
Blocks are real life examples of geometric shapes. Children can group by size, shape. They can measure. A teacher can hold up 5 objects and have children put away greater than, or less than that amount. Make sure you have manipulatives that are open ended - that there is no right or wrong and that they can be put together in a variety of ways. There should also be some self correcting table toys where pieces fit together in specific ways, such as puzzles, lotto games, nesting boxes, or pattern blocks. Ideally, a manipulative that you choose for children should teach more than one concept. There are a variety of books that teach math concepts. Don’t forget collectibles, such as bottle caps, buttons, keys, seashells, seeds, rocks, that children can sort, match and compare.
Main goal is for the child to explore Piaget’s concepts and some of the following concepts through activities
Exploration of number concepts like:
Explore pre-math concepts like:
Children think of this in terms of visual, not numbers so a child may measure a car in how many sticks it is long—visual cues and then assign a number to that—not yet able to grasp inches, feet, but should be exposed to these systems to understand they exist and that is how people measure.
Explore pre-math concepts like:
Experiences should stress;
• Observing and describing concrete objects
• measuring time, temperature, space, volume
• recognizing colors and shapes
• comparing objects and using terms to describe quantity - ‘more than’ and ‘less than’
• classifying objects
• copying patterns
• recognizing and writing numerals
• counting
• using logical words - all, none, some
Early childhood teachers face the challenging responsibility of exciting children about math. We can provide creative stimulating and manipulative experiences that can initiate long term positive feelings, or we can provide a boring stream of workbook pages and dittos. Reciting numbers is a key step in learning math concepts. Early experiences should focus on exploration, discovery, and understanding. Math concepts in the early years are taught informally in day to day activities (cooking, games, storytelling).
Think of examples of how children can use math through:
• Cooking (amounts, order - 1st, 2nd, 3rd)
• Games
• Dramatic play
• Fingerplays
