By Dr. Raymond J. Huntington
If the sight of an algebraic equation or a chalkboard full of fractions makes your children want to run for their lives, they’re not alone. Regardless of how smart or hardworking they are, many students struggle mightily with mathematics. Yet they’re going to have to master a good bit of it once they reach middle school and even more if they want to graduate and go to college. You should also keep in mind that mathematics skills are vital for success in many of today’s most interesting – and lucrative – careers.
One of the first steps on the path to improvement is to understand what’s expected of your child. Most states and school districts have a set standard for the level of mathematics that every public school student should know and be able to do by each grade. You can usually find this information by going to the Web site for your child’s school district or your state department of education.
Because education policies are developed at the local level, there will be differences from state to state. Many states take their cue from The National Council of Teachers of Mathematics (NCTM), which has developed national standards that can be adopted at the state and district level. Here are some highlights of what your child should be learning at each level of K-12 schooling, based on NCTM recommendations.
In pre-kindergarten through 2nd grade, students are developing the foundation for future learning, so it’s important to focus on the basics right away. According to the NCTM, children should understand whole numbers and commonly used fractions such as 1/4, 1/3 and 1/2. They should also be able to recognize, name, build, draw, compare and sort two-and-three dimensional shapes. By the second grade they should also be able to sort and classify objects by size, recognize two and three dimensional shapes and understand the attributes of length, weight, volume, area and time.
From the 3rd to the 5th grade, students should develop a solid understanding of fractions, decimals and percents. They should also be able to represent and compare whole numbers and decimals. They should be assembling the building blocks of algebra by analyzing patterns and functions, and be preparing for advanced geometry studies by being able to classify two-and three-dimensional shapes according to their properties. They should also be exploring numbers less than 0 and be able to carry out conversions, such as from centimeters to meters.
Grades 6-through-8 are important for both psychological and mathematical reasons. During these middle school years, students are developing firm conclusions about their abilities and limitations. Children who adopt the attitude that “I’m just not good at math” will find this to be a self-defeating prophecy while those who make steady progress develop the confidence that’s vital for higher-level work. This means being able to use fundamental algebraic and geometric concepts to solve problems, understanding ratios, proportions, prime numbers, and exponents and – according to the NCTM – being able to “create and critique inductive and deductive arguments concerning congruence, similarity and the Pythagorean relationship.”
During the 9th-through-12th grades, students will face their greatest mathematics challenges. By the 12th grade, a student must be able to solve problems using algebra, geometry, statistics, probability and discrete mathematics. This means being able to understand and use formulas to determine the area and volume of geometric figures, understanding the characteristics of well-designed studies such as those used in surveys and experiments, and understanding how to use Cartesian coordinates and other coordinate systems.
In order to do all of this — and much more as recommended by the NCTM — a typical student will need to have done well in both basic and advanced courses in algebra and geometry. In many states, public school students will also be tested in these courses on exams that they must take to graduate.
If your child is struggling to reach these basic levels, you need to get help right away. Begin by talking with your child’s teachers and ask for an honest assessment of any obstacles that may be getting in the way of success. Does your child pay close attention in class? Are homework assignments being completed satisfactorily? Or is the problem rooted in inadequate preparation in earlier grades?
Dr. Raymond J. Huntington and Eileen Huntington are co-founders of Huntington Learning Center, which has been helping children succeed in school for more than 30 years. For more information about Huntington, call 1 800 CAN LEARN.