research and hypothesis
Students often have misconceptions about solving problems involving order of operations. Sometimes students think they should do all the operations left to right because that is what they do when they read. This misconception is solidified when they use a calculator, because when they type in a problem exactly as it is typed on their worksheet, they get the correct answer. Students incorrectly believe that the calculator is solving the problem from beginning to end, when in reality, calculators are programed to complete the problem using the order of operations rules.
Many students learn a mnemonic device to remember what order to solve questions with multiple operations. PEMDAS (Parentheses, Exponents, Multiply, Divide, Add, Subtract) is often used in the United States. Several mnemonic devices are used in Europe and Asia including BEDMAS (Brackets, Exponents, Divide, Multiply, Add, Subtract), BIDMAS (Brackets, Index, Divide, Multiply, Add, Subtract) and BODMAS (Bracket, Of Order, Divide, Multiply, Add, Subtract). Mnemonic devices are great to help students remember material, but usually each letter means something separate. So students think they are supposed to complete the process in the parentheses, then solve the exponents, then multiply, then divide, then add, then subtract. Multiplying and Dividing are actually performed at the same time and they should be solved left to right. The same thing applies to adding and subtracting. The most common misconceptions seem to be that students think each letter is performed separately. There are some teachers that go to great lengths to emphasize that M and D are performed together left to right, but students get caught up in the fact that most other mnemonic devices they have used have been applied one letter at a time. Sometimes teachers actually teach order of operation incorrectly because they remember PEMDAS and apply it in the wrong way. Kyungsoon Jeon is a professor that works with preservice teachers and notice that many of them have misconceptions about Order of Operations and are therefore most likely teaching it incorrectly. (Jeon, 2012)
Many students learn a mnemonic device to remember what order to solve questions with multiple operations. PEMDAS (Parentheses, Exponents, Multiply, Divide, Add, Subtract) is often used in the United States. Several mnemonic devices are used in Europe and Asia including BEDMAS (Brackets, Exponents, Divide, Multiply, Add, Subtract), BIDMAS (Brackets, Index, Divide, Multiply, Add, Subtract) and BODMAS (Bracket, Of Order, Divide, Multiply, Add, Subtract). Mnemonic devices are great to help students remember material, but usually each letter means something separate. So students think they are supposed to complete the process in the parentheses, then solve the exponents, then multiply, then divide, then add, then subtract. Multiplying and Dividing are actually performed at the same time and they should be solved left to right. The same thing applies to adding and subtracting. The most common misconceptions seem to be that students think each letter is performed separately. There are some teachers that go to great lengths to emphasize that M and D are performed together left to right, but students get caught up in the fact that most other mnemonic devices they have used have been applied one letter at a time. Sometimes teachers actually teach order of operation incorrectly because they remember PEMDAS and apply it in the wrong way. Kyungsoon Jeon is a professor that works with preservice teachers and notice that many of them have misconceptions about Order of Operations and are therefore most likely teaching it incorrectly. (Jeon, 2012)