Math Misconceptions and Considerations HSA-REI.A.1 & B.3
Look closely at errors in students’ work (formative assessment) to help you reflect and make instructional decisions to suit all students’ needs.
Every equation is solved the same way Students approach the task of solving equations and inequalities mechanically and algorithmically using the same steps over and over again instead of tailoring their work to a specific problem. Misconception: The two equations below will be solved by students utilizing the same steps in the same order:
What to do: Show students many examples, including the same problem being solved different ways.
Not knowing when to switch the inequality symbol Students are unsure of when to reverse the inequality and when to leave it the same. Misconception: Anytime a student encounters a negative sign or a minus sign they automatically reverse the inequality symbol.
What to do: Have students check to see if the properties of equality apply to inequalities in the same manner.
Discuss the last two situations specifically with the students and have them develop a hypothesis as to how they can make the inequalities true. Students will be able to deduce that switching the direction of the inequality symbol creates a true statement. Test this hypothesis on a few more problems.
Voila! – Students have developed the rule on their own instead of you just telling them “here’s the rule and that’s just the way it’s done”. To combine, or not to combine? Students sometime combine like terms when they should be doing the inverse operation and vice versa. Misconception: When a student encounters an equation or inequality that has like terms on the same side, they tend to perform the inverse operation on the same side of the equation.
What to do: Show students examples of problems that involve inverse operations and problems that involve combining like terms. Discuss the differences between the problems. Emphasize that an equation/inequality must be kept in balance by performing the same operation on both sides.