STANDARD 5 - TOOLS AND TECHNOLOGY
Standard 5 - Tools and Technology - Grades K-2
This standard addresses the use of calculators, computers and manipulatives in the teaching and learning of mathematics. These tools of mathematics can and should play a vital role in the development of mathematical thought in students of all ages.
In the primary grades, manipulatives are the most natural of the three types of tools to use. Primary grade teachers have traditionally used many manipulative materials in their teaching of mathematics because they correctly perceived them to be of great value for young children. Typically, concrete materials are used to model mathematical concepts such as number or shape when those concepts are first introduced to the students.
Young children counting with lima beans, colored chips, linking cubes, smooth stones, or their fingers is a familiar sight in many New Jersey classrooms as they begin to master early counting skills and are introduced to addition and subtraction concepts. More sophisticated models should then be used, though, to begin to explore more sophisticated number concepts. Colored rods in graduated lengths give students a different sense of number than a set of discrete objects. Students should be able to see both a yellow rod and five colored chips as representative of the number five - the first being more of a measure model and the second a count model. Ice cream sticks and base ten blocks as well as chip trading activities help students begin to understand the very abstract concepts involved with place value and number base.
Attribute blocks, blocks with different shapes and colors, help students begin to classify and categorize objects and recognize their specific characteristics. Pattern blocks allow them to make patterns and geometric designs as they become familiar with the geometric properties of the shapes themselves. Geoboards allow students to explore the great variety of shapes that can be made and also to deal with issues of properties, attribute, and classification.
A great variety of different materials should be used to explore measurement. Paper clips, shoes, centimeter and decimeter rods, paper cutouts of handspans, and building blocks can all be used as non-standard units of length (even though some of them are really standard). Students place them down one after another to see how many paper clips long the desk is or how many handspans wide the doorway is. The transition can then be made to more standard measures and, following that, to rulers.
This list is, of course, not intended to be exhaustive. Many more suggestions for materials to use and ways to use them are given in the other sections of this Framework. The message in this section is a very simple one - concrete materials help children to construct mathematics that is meaningful to them.
Calculators have not been used traditionally in primary classrooms, but there are several appropriate uses for them. It is never too early for students to be introduced to the tool that most of the adults around them use whenever they deal with mathematics. In fact, many students now come to kindergarten having already played with a calculator at home or somewhere else. To ignore calculators completely at this level is to send the harmful message that the mathematics being done at school is different from the mathematics being done at home or at the grocery store.
The use of calculators at this level does not imply that students don't need to develop the arithmetic skills traditionally introduced at the primary level. They certainly do need to develop these skills. This Standard does not suggest that all traditional learning be replaced by calculator use; rather, it calls for the appropriate and effective use of calculators.
One of the most effective uses of the calculator with young children is the use of the constant feature of most calculators to count, forward or backward, or to skip count, forward or backward, by twos or threes or other numbers. This process allows children to anticipate what number will come next and then get confirmation of their guess when they see it appear in the display. Students can also greatly enhance their estimation ability through calculator use. Range-finding games ask students, for instance, to add a number to 34 that will give them an answer between 80 and 90. After the estimate is made, it is punched into the calculator to see whether or not it did the job. Calculators will prompt young students to be curious about mathematical topics that are not typically taught at their level. For example, when counting back by threes by entering 15 - 3 = = = . . . into the calculator, after the expected sequence of 12, 9, 6, 3, 0, the child will see -3, -6, -9, . . . A curious child will begin to ask questions about what those numbers are, but will also begin to develop an intuitive notion about negative numbers.
Computers are a valuable tool for primary children. As more and more computers find their way into primary classrooms, the software available for them will dramatically improve; however, there are already many good programs that can be used with kindergartners and first and second graders. MathKeys links on-screen manipulative materials to standard symbolic representations and to a writing tool for children to use. A number of different counting programs match objects on the screen to a standard symbolic representation of the number and the number is said aloud so that a young student can count along with the program. Many other new programs focus on money skills and help children recognize different coins and determine the values of sets of coins through simulated purchases.
Standard 5 - Tools and Technology - Grades K-2
Indicators and Activities
The cumulative progress indicators for grade 4 appear below in boldface type. Each indicator is followed by activities which illustrate how it can be addressed in the classroom in kindergarten and grades 1 and 2.
Experiences will be such that all students in grades K-2:
1. Select and use calculators, software, manipulatives, and other tools based on their utility and limitations and on the problem situation.
2. Use physical objects and manipulatives to model problem situations, and to develop and explain mathematical concepts involving number, space, and data.
3. Use a variety of technologies to discover number patterns, demonstrate number sense, and visualize geometric objects and concepts.
4. Use a variety of tools to measure mathematical and physical objects in the world around them.
5. Use technology to gather, analyze, and display mathematical data and information.
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