The Dangers of KISSing and other Mnemonic Devices Presenters: Christy Danko Graybeal and Tricia Strickland.
Mnemonic devices are often used to help students remember certain procedures and are an evidence based practice in special education. However, the presenters urged teachers to be careful of tricks that are used for computation, as students tend to over-generalize or misuse the tricks. A trick that is risky is the “Butterfly Method'' for comparing fractions because it does not address the idea of common denominators. There are some tricks they consider to be acceptable if the conceptual understanding is built first. For example, “Keep it, switch, switch” (KISS) is a strategy for rewriting subtraction problems as addition problems. Students may appear to be getting the “right answer,” but teachers may not know whether they understand the concepts and will often see them apply the trick at inappropriate times. Number chips or number lines can be used first to establish the connection between addition and subtraction. The use of FOIL for multiplying binomials is also questionable because it is not generalizable to other types of polynomials. However, if the box method is taught first, students have a larger range of options to apply to future problems. As their conclusion, the presenters stated that they supported the use of mnemonic devices when teaching problem solving processes, conventions, definitions, or facts. For example, SOH CAH TOA is simply a restatement of the trig ratio definitions to help students with recall, but it is not a “trick” because it is not changing the way that students solve problems.
Moving Beyond Cross Multiply and Divide Presenter: Elizabeth Peyser
In a similar vein, this presenter referred to cross multiplication as an “answer getting” strategy and claims that the use of this strategy in isolation does not help students develop proportional reasoning. She emphasized the use of visual strategies such as bar models, double number lines, tables, and graphs to show how students can reason through the solution to a proportional relationship, rather than relying on cross multiplication on their calculator to automatically give them a solution. A firm understanding of diagrams and ratio tables can either be used instead of or as a precursor to cross multiplication to make sure that students are gaining conceptual knowledge needed for future mathematics topics. This proportional reasoning is taught in 6th and 7th grades, and, if done conceptually, will allow students to extend their understanding to linear functions and slope easily when in 8th grade.
In this example, the presenter recommended the “fair share” strategy for determining how many cups of sugar would be needed for 27 cups of flour. I normally have students extend the diagram until there are enough bars to represent the problem; she recommended using beads or tick marks within the bars to show how much each is representing. For example, 27 cups of flour spread out between the 3 bars means that each bar is worth 9 cups. Students can then extend this to the sugar, never having used cross multiplication.