According to the report findings if an instructor uses a version of some of these examples, students may be denied a useful frame of reference from the very start of their algebra studies. The last example does relate algebra to arithmetic, a subject which most students will have studied, may know reasonably well and may actually use in their daily lives. But even though algebra and arithmetic both involve signs, equations, numbers and computation, approaching algebra with an arithmetic mindset can cause students major problems.

As the paper declares when introduced to algebra, students must reorient their thinking and recognize that “the expressions on both sides of the equals sign are of the same nature (or structure), and that there are actions which give meaning to the equality of the expressions (for instance, the action of substituting a numerical value for the unknown)”. The process to handle the minus sign before parentheses results in simplifying the expression. Thus, in the above example, 5x – (3 – x) becomes 6x – 3, a more concise and clearer way of restating the original expression without changing its value. In algebra, there is another rule for simplifying expressions, known as combining like terms, which is the third major issue confounding algebra students. Unlike the issues of the equals sign and the minus sign, solving the issue of combining like terms is a matter of following concrete rules rather than grasping concepts. ...Show more