When Should Children First Learn About...?
David L. Haury
Algebra and geometry constitute the conceptual foundation for advanced topics in mathematics.
Chemistry and physics provide the foundation for advanced study in science. As science and
math reform movements continue in states and schools, parents and teachers wonder when
children should first learn some of the key topics in these fields.
The following guidelines extracted from the national standards in science and math--developed
by the National Research Council and the National Council of Teachers of Mathematics,
respectively--summarize when children should be learning certain fundamental concepts. Parents
can use this information to determine whether their children's schools are introducing key topics
in accordance with the national standards. (For more information on standards, see
"National Math and Science Standards: A Primer for Parents")
Algebra
Algebra can be thought of as a specific course in the math program, or it can be perceived as an
array of concepts, skills, and procedures for representing and exploring mathematical ideas. It is
strongly recommended that all children have introductory algebra by the eighth grade, pre-ceded
by algebraic thinking embedded throughout the elementary school math program. Benchmarks to
gauge progress in algebraic thinking include the following:
By second grade, children should be. . .
 | Sorting, classifying, and ordering objects by different properties, as well as recognizing
patterns. |
| Using pictures, words, and various forms of notation to illustrate mathematical ideas. |
| Using numbers and words to make comparisons and describe change. |
By fifth grade, children should be. . .
|
Using tables and graphs to represent numeric patterns. |
|
Identifying and describing relationships between values that co-vary systematically, such
as the length of the side of a square and its area. |
|
Learning about variables and using algebraic notation (x, y, other symbols) and
operations to describe general rules and solve problems. |
|
Investigating varying rates of change and relationships between and among variables. |
By eighth grade, children should be in an algebra class in which they. . .
|
Use patterns to solve mathematical and applied problems. |
|
Represent relationships and functions with tables, graphs, verbal rules, and symbolic
rules. |
|
Solve linear equations and inequalities, identify variables, and learn to interpret graphs
mathematically (intercepts, intersections, and slopes of lines). |
|
Study rate of change and its graphical representation. |
Geometry
Geometry is the mathematics of shape, position, and direction. Studies in geometry bring
numerical precision to the concepts of place and movement.
By second grade, children should be. . .
|
Constructing, drawing, and describing two- and three-dimensional shapes. |
|
Recognizing congruent and similar shapes, as well as relating geometric ideas to numbers
and measurements. |
|
Interpreting and applying the ideas of direction, distance, and relative position in space, as
well as using coordinate systems. |
|
Transforming shapes through simple procedures and recognizing symmetry. |
|
Imagining geometric shapes and representing them from different points of view. |
By fifth grade, children should be. . .
|
Classifying and defining two- and three-dimensional shapes according to their
characteristics, investigating their mathematical properties, and thinking about the relationships
among shapes. |
|
Using geometric vocabulary, graphs, and coordinate systems to describe the location and
movement of objects. |
|
Exploring symmetry and congruence in two- and three-dimensional shapes and objects. |
|
Visualizing and sketching three-dimensional shapes in two dimensions. |
By eighth grade, children should be. . .
|
Precisely describing, classifying, and comparing types of plane and solid figures
according to their main features, as well as recognizing the application of geometry in art,
science, and daily life. |
|
Using coordinate geometry to represent geometric relationships between related
quantities. |
|
Examining the properties of geometric figures and using the Pythagorean theorem to
solve problems. |
|
Using the concepts of congruence, similarity, and rotational symmetry to explore,
describe, and classify polygons and polyhedra and their transformations. |
|
Proficiently using two-dimensional representations of three-dimensional objects, as well
as using geometric models to represent and explain numeric and algebraic relationships and
solving problems by composing or decomposing two- and three-dimensional figures. |
Chemistry
Chemistry is the study of matter, the states of matter, and the nature of interactions among
different substances.
By fourth grade, children should. . .
|
Know that objects are made of one or more materials with characteristic properties that
can be observed and measured using a variety of tools, such as rulers, balances, and
thermometers. |
|
Understand that materials can exist in different states--solid, liquid, gas--and that some
common materials can be changed from one state to another by heating or cooling. |
By eighth grade, children should. . .
|
Know that each substance has characteristic properties, such as density, boiling point, and
solubility, and that often a mixture of substances can be separated into its original components. |
|
Realize that substances react chemically in characteristic ways to form compounds with
different characteristic properties. |
|
Know that chemicals do not break down during normal laboratory reactions and that more
than 100 known elements exist and combine to produce compounds. |
Physics
Physics is the study of energy and matter in motion, from the interactions of subatomic particles
to the natural choreography of star clusters.
By fourth grade, children should. . .
|
Know that an object's motion can be described by tracing and measuring its position over
time. |
|
Realize that an object's position and motion can be changed by pushing or pulling and
that the size of the change is related to the strength of the push or pull. |
|
Discover that light travels in a straight line until reflected, refracted, or absorbed. |
|
Know that heat can be produced in a variety of ways and that it can move from one object
to another through conduction. |
|
Know that electricity flows in circuits to produce light, heat, sound, and magnetic effects. |
|
Understand that magnets attract and repel each other. |
By eighth grade, children should. . .
|
Be able to describe the motion of an object on a graph in terms of its position, direction,
and speed. |
|
Understand that an object will continue to move at a constant speed in a straight line
unless subjected to an outside force. |
|
Know that multiple forces on an object will reinforce or cancel each other, depending on
their direction and magnitude. |
|
Understand that energy is a property of many substances and is associated with heat, light,
electricity, mechanical motion, sound, nuclei, and the chemical nature of a substance. |
|
Understand that heat travels in predictable ways, flowing from warmer objects to cooler
ones until both reach the same temperature. |
|
Know that light interacts with matter by transmission, absorption, or scattering and that
one sees an object when light emitted or scattered from the object enters the eye. |
|
Know that electrical circuits can be a means of transferring electrical energy when heat,
light, sound, and chemical changes are produced. |
|
Know that most chemical and nuclear reactions involve energy transfer into or out of a
system. |
|
Understand that the sun is a major means of energy that drives changes on the Earth's
surface and that it loses energy by emitting light with a broad range of wavelengths, from
infrared and visible light to ultraviolet radiation. |
| A Message From Donna Shirley
Math was my worst subject in school. However, I knew I had to learn it to be an engineer, so I
sweated it out. I was always kidded in high school for taking mechanical drawing instead of
home economics. When I went to college, I walked into my advisor's office and he said, "What
are you doing here?" I said, "I'm enrolling in aeronautical engineering." He responded, "Girls
can't be engineers!" I told him I could, and I did! |
-NASA Quest Project. Reprinted with permission.
Donna Shirley is the former manager of the National Aeronautics and Space Administration
(NASA) Mars Exploration Program at the Jet Propulsion Laboratory, the lead U.S. center for
robotic exploration of the solar system. Ms. Shirley is the original leader of the team that built the
Sojourner Rover.
To participate in NASA's interactive education projects, visit the NASA Quest Project Web site
at http://quest.arc.nasa.gov. To learn more about other NASA education
programs, curricula, and services, go to http://education.nasa.gov.
| David L. Haury is Director of the ERIC Clearinghouse for Science, Mathematics, and
Environmental Education and Associate Professor of Mathematics, Science, and Technology
Education at The Ohio State University in Columbus, Ohio. |
 The New Three R's
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 How Can I Help My Child Become More Interested in Science?
This page was updated on Fri Nov 2 19:14:45 GMT 2001
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