Teaching Mathematics in Early Childhood

ACTIVITY 2.2

Doghouse Game

Materials

The following materials are needed for this game:

• Game board for each player, made from poster or tag board (8 x 8 inches)
• Sixteen doghouse pictures for each board, attached to the board in 4 rows, with 4 doghouses per row
• Sixteen small toy dogs for each player
• Deck of cards, made from 3 x 5 inch file cards, with one to four 1-inch circle stickers per card

Description

This game appeals to many children because they are interested in dogs or other pets. It accommodates children from a wide range of developmental levels. Young, preschool children who are not yet ready to draw cards and create matching sets may be interested in just placing a dog on each doghouse picture. This reinforces the important concept of one-to-one correspondence. If children place the dogs randomly on the board, the teacher can direct their attention to a one-to-one relationship by asking whether the children can find one dog for each house. Many children will take turns drawing the cards to determine how many dogs to place on their boards. Children at the one-to-one correspondence level of quantification may actually set the dogs on the dots on the cards before moving them to the doghouses. Children who can count will use that strategy to determine how many dogs to take.

Grid games can be played by an individual child, and they make excellent small-group games as well. In preschool classrooms, a grid game can be used as a special activity or placed on a math game table. Kindergarten teachers might decide to divide the class into small groups to play the game. As with other grid games, the doghouse game can be modified for children who are more advanced. They might be asked to put two or more dogs in each doghouse. The quantities of dots used on the cards can be increased as well. Teachers often have to spend their own money for classroom materials, so cost is an important consideration.

Math Discussions

Questions similar to those used for math manipulative games are also appropriate for grid games. In addition, teachers can draw attention to the number of spaces covered, the number of empty spaces, or the relationship between the two. Note that all of the sample questions and comments listed next relate directly to the game; therefore, although they are excellent math questions, they fit naturally into the flow of the play.

Developing Number Sense

• Do you have more occupied doghouses or more empty doghouses in this row?

Path Games

Path games are more difficult for young children than grid games; however, they are valuable teaching tools because they simulate a number line. Mathematics curricular materials that may be used in kindergarten and first grade often create a physical number line, with numerals listed in order, for children to use when answering questions about the magnitude of numbers or when solving arithmetic problems.

Difficulties occur when children have not yet constructed a mental number line. They may model use of a physical number line without any understanding of what they are actually doing mathematically. When children play path games and move an object along a series of marked spaces to reach their destination, these games model continuous movement along a number line.

With repeated experience, children realize that as they move forward, they take an increasing number of steps along this line, and the spaces which they cover can be quantified. Path games are more difficult for young children than grid and counter games because they are more abstract. Children do not have a tangible object to represent each quantity; instead, they must quantify steps taken toward a goal.

As in Hansel and Gretel’s journey through the forest, however, the steps they have taken seem to vanish as they move forward. Assume that a child has moved three spaces on his first turn, and then moves two more spaces on his second turn. His place on the path does not look like two; instead, it looks like five—or just “a lot.” At first, some children move their marker back to the starting point for their next turn. They realize that it has already been counted because they are standing on it.

Many children stop making this re-counting error on board games after they have had experience with gross motor path games. Games with short, straight paths help children make the transition from concrete manipulative and grid games to more abstract path games. For these initial path games, children should have their own paths to move along so that they are not confused by the markers of other players.

Ten spaces is a good length for initial paths. This relatively short length seems to help children envision their movement along the path. If they have moved five spaces, they can see that they have five more to go. Once children have constructed the concept of moving along a path on consecutive turns, they can tackle games with longer paths that have curves or angles, additional directions, and bonus or trap spaces. Children can now share the same path, which allows them to account for the position of their mover in relationship to those of the other players.

ACTIVITY 5.1

The Magnificent Shape Quilt

Materials

The following materials are needed for this activity:

• Felt squares, 6 x 6 inches, cut from felt in bright colors
• Small geometric shapes, in standard and nonstandard configurations, cut from bright colors of felt with a self-adhering backing
• Puffy paint, to use to write each child’s name on the finished quilt squares

Description

Each child can experiment with positioning shapes to create an individual collage. Older preschool and kindergarten children should be encouraged to arrange and rearrange their shapes until they are satisfied with the result. At this point, the backing can be removed and the shapes mounted to the felt squares. (Younger children may be more interested in the process of mounting the shapes to the backing than in creating a specific piece of artwork.)

As children engage in the process of creating their quilt squares, they may observe the ways in which shapes fit together to create larger shapes. Children may also create symmetrical or linear patterns, form representational images, or simply design a random shape collage. From a mathematics perspective, the conversation that accompanies the activity is a critical component; therefore, teachers should plan for an adult to be seated with the children as they work on their designs.

Once the squares are completed, each child’s name can be added with puffy paint. The quilt squares can be whip-stitched together or mounted to a backing to create a class quilt. Quilts provide a fascinating array of geometric representations for children to study. It is helpful if children have the opportunity to examine quilt designs, either on actual quilts or in photographs, before they work on this project.

Math Discussions

Many excellent topics of conversation should emerge during this project. Children who are just learning the names of shapes should have this vocabulary reinforced by the teacher. During the activity, children should be encouraged to experiment with placing some shapes so that they touch other shapes, although the final design should, of course, be the child’s choice.

When children combine shapes, this should be discussed. The teacher might say, “What happened when you put a square and a triangle together?” The child may reply that she created a house, and the teacher can agree while adding that in geometry that shape is called a “pentagon.” Teachers should also look for symmetrical relationships that children may create. Some children may begin with a central shape and then branch out, in a symmetrical fashion, from that starting point.

Other topics of conversation might be items that are the same shape, but a different size; how shapes look when they are turned (rotated), or flipped; and the types of lines that form the edges of the shapes.

ACTIVITY 5.2

Quilt Bingo

Materials

The following materials are needed for this activity:

• Quilt-square game board for each child, created by tracing quilt designs that feature geometric shapes onto paper and mounting them to poster or tag-board
• Shapes that match all those used on the game boards, made by cutting the shapes from heavy-weight, colored paper and laminating (scrapbook paper is a good source)
• Grab bag, to hold the shapes

Description

This activity coordinates with the previous quilt activity and may serve as a precursor to it. Children take turns passing the grab bag and drawing shapes to match those on their game boards. The matching process encourages children to focus on the attributes of the shapes, especially when they are searching for a particular shape to complete their boards.

Math Discussions

Once again, the discussions that occur during this activity are a critical component of the learning. Without the accompanying math talk, children may match shapes, but not learn their names or notice the patterns that they create. A main focus of the conversation should be on the attributes of the various shapes. For example, if a child is looking for a triangle, the teacher might ask whether it will have straight or curved sides, and how many points it will have. After several teacher-led clues, children may begin on their own to look for particular attributes.

This activity also provides an excellent opportunity to talk about transformations. As children draw shapes from the grab bag, at first they may not be able to visualize where the shape can fit on their game boards. The teacher may need to scaffold, such as suggesting that the child turn the shape and look at it again. Other children can be brought into the conversation.

ACTIVITY 6.5

Container "Brainer"

Materials

The following materials are needed for this activity:

• Sensory table, or several plastic dishpans
• Assorted clear containers, in various sizes and shapes
• Several small scoops
• Several funnels
• Recording chart (optional)

Description

This activity is designed to help children visualize the various parameters that affect volume. Preschool and kindergarten children typically believe that tall containers automatically hold more than shorter, wider containers. Therefore, for this activity, teachers should select containers that confound that notion. Some taller containers should be included that have less capacity than shorter containers.

At first, children will need time to randomly experiment with the materials, particularly in preschool. The teacher can then introduce the challenge of finding the containers that hold the most water. The idea of using the funnels and scoops to measure how much water goes into each container can be modeled, perhaps during group time.

For recording purposes, a chart with a list of the children’s names and a digital photo of each container can be placed near the activity. Children can add comments, such as “a lot,” or measurement numbers, to the chart. To facilitate later discussion, the bottles can be labeled with letters; however, numbered labeling should be avoided because children may confuse the numbers with a volume hierarchy or think that the numbers refer to the measurements.

Math Discussions

This activity should be repeated, perhaps during the following week, using a dry material, such as sand or rice. Some children believe that the filler material affects the capacity of the containers.

Snake Adventure

Materials

The following materials are needed for this activity:

• Small container of play dough for each child
• Measurement tools, such as string, linking cubes, or standard measures (e.g., ruler, yard stick)
• Recording sheet (optional)

Discussion

Children who do not yet conserve mass, which includes most children in preschool and many in kindergarten, typically believe that the mass of an object changes when it is spread out or compressed. Therefore, they think that a lump of play dough that has been spread out now has more mass.

In this activity, children experiment with stretching out play dough and then returning it to its original container. Children frequently experiment with coiling by rolling play dough or clay back and forth across a flat surface with their hands. As they do this, the dough becomes longer and thinner. Children often announce that they have made a snake.

This activity extends this natural focus of children by encouraging them to measure their snakes, speculate as to whether the play dough will still fit into its original container, and then see for themselves. There are various ways that children can measure their snakes. They can cut a piece of string that is as long as the snake, use interlocking cubes or other manipulative materials, or compare the snake to a standard measure.