Joe Sipper, Durham K-12, Examiner

In the spirit of making algebra more concrete and accessible to students, Dr. Henry Borenson invented a method of teaching variables in a concrete method. Hand-on Equations® is actually targeted toward a 4th-grade audience, with some classes using it as early as 3rd grade.

### Elementary School Student Solving Algebra Problems

The system uses a structure (or a drawing) that resembles a double pan balance. An algebraic equation is given. The students “set up” the equation on the balance using game pieces and cubes with number values written on them. The numbered cubes literally represent the number written on them. The game pieces are “x”. The center of the balance is the equal sign.

Students begin by taking away equal amounts from each side until the equation is simplified. Then they do the simple arithmetic needed to solve for “x”. Maybe the best part is that students then have a way of checking their solution by seeing if both sides of the balance have an equal value.

Some video demos of elementary students using the device can be seen here.

Concerning the ideas that sparked his invention, Dr. Borenson allows:

*“Even before the National Research Council issued a report in 1998 that included the statement, ‘We know from experience that the current school approach to algebra is too abstract and an unmitigated disaster for most students,’ I was already aware of this phenomenon. I wanted to find a way to make the abstract concepts of algebra visual, hands-on, and accessible to students of all ability levels– and at much younger age. It turns out that the symbols and concepts of algebra related to solving equations such as 4x + 3 = 3x + 9 can be expressed perfectly via objects and actions. Using the Hands-On Equations approach that I developed, even 3rd and 4th graders can solve equations that many 9th graders find difficult when presented abstractly.”*

The main idea behind the product is to take the fear out of algebra and allow students to strengthen applicable skills before actually enrolling in the class. Users and researchers swear by the results and hail it as a method for teaching *how to think* mathematically.

**About Joe Sipper**

*A former science teacher and coach, Joe Sipper also has experience as a content and assessment developer, project director, program manager, strategic planner, presenter, and director of staff of large educational publishing companies. Joe Sipper has experience on more than 20 testing programs across the United States, Puerto Rico, and Chile. Joe Sipper is the owner of his own educational consulting company, iJS Education Services . His client list includes Pearson Educational Measurement, Educational Testing Service, the Educational Records Bureau, Education 2020, and several large school districts.*