STANDARD 5 - TOOLS AND TECHNOLOGY
Standard 5 - Tools and Technology - Grades 3-4
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 grades 3 and 4, manipulatives have traditionally not been used as much as they have been in the primary grades. It is fairly common for teachers at this level to think that once initial notions of number and shape have been established with concrete materials in the lower grades, the materials are no longer necessary and a more symbolic approach is preferable. Research shows, however, that concrete materials and the modeling of mathematical operations and concepts is just as useful at these grade levels as it is for younger students. The content being modeled is, of course, different and so the models are different - but no less important.
Third- and fourth-graders can use square tiles to model one-digit multiplication arrays in a manner that makes the operation very meaningful for them, and later use base-ten blocks to model two-digit multiplication arrays. The added advantage to this kind of a model is the degree to which students who have used it can visualize what's happening with the factors in the problem and so can develop much better estimation and mental math skills than students who have simply learned the standard paper-and-pencil algorithms. The relationship between multi-digit multiplication and division is also clearly shown by such models.
Geometry models, both two- and three-dimensional, are an important part of learning about geometry and development of spatial sense in students of this age. Students should use geoboards to explore area and perimeter and to begin to develop procedures for finding the areas of irregular shapes. They can also use construction materials like pipe cleaners and straws to make three-dimensional geometric shapes like cubes and pyramids so that they can study them directly. Such models make it much easier to determine the number of faces or edges in a figure than two-dimensional drawings.
Third- and fourth-graders should also be in the habit of using a variety of materials to help them model problem situations in other areas of the mathematics curriculum. They might use different colored unifix cubes to represent all of the different double-decker ice cream cones that can be made with three different flavors of ice cream. They should be able to use a variety of measurement tools to measure and record the data in a science experiment. They might use coin tosses or dice throws to simulate real-world events that have a one-in-two chance or a one-in-six chance of happening.
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 construct mathematics that is meaningful to them.
There are several appropriate uses for calculators at these grade levels. It is never too early for students to be introduced to the tool that most of the adults around them will use whenever they deal with mathematics.
The use of calculators at this level does not imply that students don't need to develop 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 which can be continued in grade three is the use of the constant feature of most calculators to count, forward or backward, or to skip count. This process allows children to anticipate what number will come next and then get confirmation of their guess when they see it come up in the display. Students can greatly enhance their estimation ability through calculator use. Range-finding games ask students, for instance, to add a number to 342 that will give them an answer between 800 and 830. After the estimate is made, it is punched into the calculator to see whether or not it did the job.
Calculators will also prompt students to be curious about mathematical topics to which they are about to be introduced. For example, while routinely using calculators in problem solving activities, some students may notice that whenever they add, subtract, or multiply two whole numbers, they get a whole number for an answer. Sometimes that happens for division, too, but sometimes when they divide they get an answer like 3.5. What does that mean? These kinds of questions offer a great opportunity for some further exploration and investigation; for example, Which problems give you answers like those? What happens when you solve those problems using pencil-and-paper?
Computers are a valuable tool for students in third and fourth grade. As more and more computers find their way into these classrooms, the software available for them will dramatically improve; however, there are already many good programs that can be used with students of this age. MathKeys links on-screen manipulative materials to standard symbolic representations and to a writing tool for children. Logo can be used by students to explore computer programming and geometry concepts at the same time. Tesselmania! and other programs offer an opportunity to play with geometric transformations on the screen and produce striking designs. The King's Rule is a program that asks students to determine the rules that distinguish one set of numbers from another, fostering creative and inductive thinking. The World Wide Web can be an exciting and eye-opening tool for third-and fourth-graders as they retrieve and share information. Specifically, in these grades, they might look for state populations, meteorological data, and updates on current events.
Standard 5-Tools and Technology-Grades 3-4
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 grades 3 and 4.
Building upon knowledge and skills gained in the preceding grades, experiences in grades 3-4 will be such that all students:
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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