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Comparing solution methods in math to develop higher-order thinking skills

Tuesday, January 17, 2017

When walking into a second grade classroom you might hear the Spanish teacher, Maria Luisa (Malu) Offermann ask "is there a different way of solving this problem?", "what is your way?", or "how is your method the same or different to your friend's method?". By asking these questions the teacher encourages students to explain, model, compare, and contrast their different problem solving methods. Educators implement this practice in their classroom as it is supported by cognitive science theory, that states that comparing and contrasting methods allow students to build and transfer knowledge to real-life situations, as well as reach higher mathematical thinking by analyzing methods. Additionally, a recent study led by Professor of Education Jon Star, from the Harvard Graduate School of Education demonstrated that "comparing and contrasting alternative solution methods led to greater gains in procedural knowledge and flexibility, and comparable gains in conceptual knowledge, as opposed to studying multiple methods sequentially" (Star, 2007). With this theoretical understanding, Malu develops experiences where second graders will model, explain, and discuss their methods. Additionally, she will lead them to the end goal of evaluating the efficiency or accuracy of each one of these methods. For example, when adding 23 + 20, would it be more efficient to count by ones or by tens? Developing different methods; seeing them side by side to compare, and evaluating the most efficient way is an important component to reach the highest levels of mathematical thinking.