Share Cognitive Science Implications for Teaching Mathematics

The Zero Factor Property is a property of the Real Numbers and should be taught as such. We do our students a great disservice when we lead them astray into believing that The Zero Factor Property is simply a technique for solving certain quadratic equations. To teach The Zero Factor Property properly as a property of The Real Numbers requires conscious effort o0n the part of teachers. It should be presented and used long before quadratic equations are introduced. A few examples of how this might be done are:

**Example 1:** Solve equations like (3x + 2)x = 0 during a discussion of solving linear equations in one variable.

**Example 2:** Solve equations like (2x + 7)(9x – 4)(x + 3) = 0 during a discussion of linear equations in one variable.

**Example 3:** During a discussion of linear equations in one variable, use the Distributive Property and The Zero Factor Property to solve equations like x(2x + 5) + 7(2x + 5) = 0.

**Example 4:** During a discussion of linear equations in one variable use the Distributive Property and The Zero Factor Property to solve equations like 3x^{3}(x – 8) = 0.

**Example 5:** During a discussion of linear equations in one variable find some solutions of equations like (7x – 8)(7x^{3} + 5x – 11)= 0.

**Example 6:** During a discussion of linear equations in one variable solve equations like (4x + 8)(9x + 1) = 0.

**Example 7:** Solve equations like (x^{4} + 5)(x^{3} – 8) = 0

**Example 8:** When discussing factoring, long before introduction of the exponential or logarithm functions, you should teach students how to factor expressions like e^{2x} – 2e^{x} -15. During that discussion, point out that consideration of an equation like e^{2x} – 2e^{x} -15 = 0 is equivalent to the equation (e^{x} – 5)(e^{x} + 3) = 0 and the Zero Factor Property informs us that is equivalent to the **two** equations e^{x} – 5 = 0 or e^{x} + 3 = 0. So although we might not know (at this point in time) how to solve exponential equations we know what will be required to solve that original equation.

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