I would like to address a convention in mathematics that needs to change; BEDMAS. For those who are unfamiliar with this it stands for: Brackets, Exponents, Division, Multiplication, Addition, Subtraction. This is how I was taught order of operations. However, division and multiplication actually are completed from left to right, and the same goes for addition and subtraction. Therefore, we really need students to memorize also BEDMAS, BEMDAS, BEDMSA, depending on the order of the operations.
Also there could be operations inside brackets, so in actuality all that must be memorized is B(BEDMAS)EDMAS, B(BEMDAS)EDMAS, B(BEDMSA)EDMAS, …
I hope we are all confused as I am.
I have had a conversation recently where I was told, “If we don’t focus on order of operations then 3 + 2 * 10 could be 23 or 50, and there can only be one right answer”. Now without a context 3+2*10 is 23. However, students need to know WHY to put brackets, and when to add sometimes before we multiply. As for 2 examples:
If you are taking a cab which has a base charge of $3, and $2/km, then it would cost you $23 to take the cab 10 km.
If you are planning a party for 10 people and want to supply cookies, which costs $2/person, and cake, which costs $3/person, the total cost would be $50.
I understand that we need a procedure to solve questions that have no meaning, but for students who are just learning a new concept there should always be meaning in their learning.
This idea of memorization through acronyms can been in many subjects:
HOMES – Great Lakes
Mrs. Vasquez Eats Many Juniper Seeds Until Nurished – Planets.
I could go on and on. I am not saying knowing the order of things is unimportant but should not be more important than the meaning and application of the knowledge memorized. For my own students, I would rather they understand why the order of the planets are important for the equilibrium of our solar system than just the order of the planets.The sad truth is that the only time students are going to see a question, as 3+2*10, is when they need to answer a skill testing question for a prize. Are we teaching critical thinkers, or lottery winners?