Sunday, March 30, 2008

A COMMENT ON THE NATIONAL MATH PANEL REPORT

The Final Report of the National Advisory Math Panel noted that many students "have difficulty grasping the syntax or structure of algebraic equations and do not understand the procedures for transforming equations or why transformations are done the way they are." It is indeed true that for many students algebra is a foreign language. Many students simply do not understand the meaning of the symbols used in algebra. Some students succeed by memorizing rules or procedures for solving equations.

All students, however, would benefit from instruction in algebra that made the concepts visual and hands-on. This is where Hands-On Equations comes in. A study recently completed, "The Effect of Hands-On Equations on the Learning of Algebra by 4th and 5th Graders of the Broward County Public Schools, shows that such instruction can be provided as early as the 4th and 5th grade. Of the 195 students from the regular classrooms which participated in this study, more than 80% of the students experienced success in solving equation such as 3x = x+12 and 4x+3=3x+9 after seven lessons of instruction. On a retention test administered three weeks later with no Hands-On Equations instruction in the interim, the students did equally well.

The students learning via Hands-On Equations develop an intuitive and indeed a kinesthetic sense of important algebraic principles, such as the subtraction property of equality, by physically removing three blue pawns, representing the x's, from both sides of the balance scale.

If students beginning an Algebra 1 course have not been fortunate enough to have had this hands-on experience earlier in their educational career, it is still important for the regular high school algebra teacher to provide this experience to the students. Even a few short lessons can demystify basic algebraic equations and how to solve them.

Ideally, though, it is best to provide this hands-on experience earlier on, say in grades 4 to 6. Indeed, the ability to solve such equations should be a prerequisite, in the view of this educator and publisher, for a student to enter an Algebra 1 or even a pre-algebra class. If the students have had Hands-On Equations they will have no trouble at all solving these types of equations with the game pieces, and then pictorially using only paper and pencil. (The retention test noted above was administered without the game pieces.)

The Task Group on Conceptual Knowledge and Skills noted, "Without any doubt, the foundational skill of algebra is fluency in the use of symbols." Students working with Hands-On Equations develop a high level of comfort in working with algebraic linear equations of increasing complexity with unknowns on both sides of the equation. If, in addition, the students develop strong computations skills, as advocated by the Panel, the success level of such students in Algebra 1 should be significantly higher than has been the case in the past. Borenson and Associates, Inc. hopes to conduct research in this area in the 2008-2009 academic year with algebra 1 students.

If your district has a large number of students failing algebra 1, and you would like to participate in a research study to determine if Hands-On Equations instruction can make a difference in student success when they repeat the course, please send a note of inquiry to info@borenson.com.

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