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Do you think algebra concepts should be taught in such a way that they challenge and reinforce the student's arithmetic skills, or should only...

The way algebra is taught should be geared to the students in the class. This is the basic tenet of differentiated instruction, which the Association for Supervision and Curriculum Development describes in practice as "offering several different learning experiences in response to students' varied needs" (see the link below for more information).


Some students need to reinforce the basic skills involved in algebra. If, for example, they are solving a one-step equation, they will struggle to understand how to set up the problem. They need to work on isolating and solving for the variable before integrating other skills (such as working with fractions and decimals). Once they master this skill, they can move on to solving one-step equations with fractions or decimals, for example. Students who are more skilled in solving one-step equations can integrate the use of fractions or other forms of numbers that aren't "nice" right away, but students who are on shakier ground may be overwhelmed by the concepts involved in solving the problem if they also have to attend to numbers that aren't "nice." Students can be presented with a range of problems depending on their abilities so that they are offered truly differentiated teaching, leading each student to advance his or her skills. 

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