Early Experiences Presented by Frank H. Osborne, Ph. D. © 2015 EMSE 3123 Math and Science in Education 1

What to Teach and When Educational research shows that: Children learn mathematics best when they construct their own knowledge via a child-centered learning environment emphasizing cooperative work and hands-on experiences. NCTM suggests that K-4 children concentrate on whole-number concepts. 2

What to Teach and When Children are developmentally ready to learn the numbers at ages 5-7. This is in the pre-operational stage. Children at this age concentrate on only one aspect of a problem. Here they center on size and cannot see that there are two differences, namely number and size. 3

Pre-Number Concepts Classifying and sorting Children need practice in working with a variety of manipulatives together. The manipulatives are sorted according to a particular attribute. Attributes can be size, color, shape, thickness, length, etc. 4

Example Use colored attribute blocks or shapes. Pick out all with a given shape. Later activities can concentrate on two attributes (e.g. red with four corners) 5

Example Use attribute blocks or shapes to construct the shape below. Have the students duplicate the shape. 6

Example Given the pattern on the left, complete the pattern on the right. Activities like these are most important for Kindergarten and First Grade but can be modified for use in higher grades. Children should also be able to sort things and also place them in sequence. 7

Seriation Seriation refers to the ability to place objects in correct sequence. Piaget says that seriation is vital to understanding the concepts of numbers. An example would be placing various objects in sequence according to length. Related would be their ability to place the children in the class in order according to height. 8

Examples for Seriation Children classify pictures of animals. –Animals with no visible legs (worms, snakes) vs. animals with legs (cats, dogs) –Animals that can live in water vs. animals that cannot. Group rocks according to color Group things according to living vs. non- living Group matter into solid or liquid 9

Relationships between Sets A set is a collection of specifically designed items. Each item in a set is a member or element of the set. Examples include a set of golf clubs, a deck of playing cards, etc. Children need to develop the ability to decide if two sets can be matched exactly. This is called one-to-one correspondence. 10

Relationships between Sets In this example, there is a one-to-one correspondence. In this example, there is NOT a one-to-one correspondence. 11

Relationships between Sets When two sets cannot be matched, then one of the sets has more elements than the other. This introduces the concepts of greater than and less than. Have children make sets of objects where the numbers in each set are the same, then change one of the sets so that the numbers are different. 12

Learning the Numbers 1-10 Once children have experience with sets of objects, both equal and unequal, the next step is to arrange them in order from smallest to highest. These concepts need to be reinforced frequently so that the children internalize them. 13

Learning the Numbers 1-10 Make a set of cards with different numbers of objects. Have the children shuffle the cards and then sort them in order. 14

Learning the Numbers 1-10 Prepare containers with one to nine pencils in each. Have the students sort them in order. Try the same idea with paper cups with one to nine marbles in each. 15

Learning the Numbers 1-10 Add numerals to the Bear Cards. Have the students sort the cards and recite the numerals as they do the sorting. 16

Learning the Numbers 1-10 Use two sets, one with numerals only and the other with pictures only. Have the children match them up by numbers. 17

The Concept of Zero (0) Zero is associated with any set that has no elements in it. They can count different objects in the room. Point out that there are no giraffes in the room therefore the number in the set is 0. 18

The Concept of Ten (10) Ten is what happens when a set of 9 elements has one more added to it. Children at this point are not ready to understand that the numerals in 10 have place values. So we use it to represent the next set after 9. 19

Example How many elements in Set A? With two slid to the right, how many elements in Set B? Take away the ones on the right. How many in the set now (Set C)? 20

Counting Activities like this should be repeated frequently enough so that children learn to count the sets in their head. They practice with sets of different sizes counting the number of elements. –Some elements are added and recounted. –Some elements are subtracted and recounted. 21

Example How many more elements in Set A than in Set B? How many objects should be added to Set B to make it equal to Set A? How many objects should be subtracted from Set A to make it equal to set B? 22

Science in the Early Grades Children come to school with a tremendous amount of curiosity about the world around them. Teachers need to build on this interest. What passes for science in most schools only succeeds in killing this curiosity. 23

Science in the Early Grades Children need to learn by doing things and practice science as a way of learning about the world. Reading information and memorizing facts only serve to dull their interest in science and the natural world. Children should be engaged in activities they do themselves under teacher supervision. 24

Science and other Subjects Science is related to other subjects. Students should keep a science journal. –The best kind begins life as a blank spiral or composition notebook. –Students write in their science journal about the things they did and what they learned. –Teachers use the opportunity to improve vocabulary development, spelling and writing skills. 25

Examples of Science Activities Collect leaves from different trees. Students research the type of trees the leaves came from and make displays indicating how to tell the trees apart by their leaves. Students draw pictures of their leaves in their science journals. 26

Examples of Science Activities Collect seeds from trees in the spring. Students drop them from a certain height to determine how long it takes seeds to fall from the tree to the ground. Students write results in their science journals. 27

Examples of Science Activities Give each student or group of students a magnet. Students make a list of objects in the room that are magnetic and another list of objects that are not magnetic. They write these two lists in their Science Journals. 28

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