BEDMAS last along with Lottery Winners.

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?

System changers first, followers second.

I had some responses to my “what is right” blog, so I decided to write more about it.  My ideas were inspired by Barry Schwartz: Using our practical wisdom.   Many times in my life, I have had to make the decision “Do I do what is right or I do I do what is expected of me”.  I remember the poster in school that stated, “What is right is not always popular, and what is popular is not always right”.  Still, at the age of 28, I am still finding this relates to me.

Many times I have witnessed “things” not going as planned in a workplace.  The first response is usually “Make Rules”.  This saddens me greatly as usually only a small percentage of the workers are causing things to go amiss, however every worker must suffer under these new rules.

According to Barry, when education is not going correctly “[we] give teachers scripts to follow in the classroom; so even if they don’t know what they are doing and don’t care about the welfare of our kids, if at least they follow the scripts our kids will get educated.”

Of course rules don’t always cause the small percentage to change so the second response is to “create incentives.”  Now, for those who don’t want to follow the rules, it is actually in their interest to follow the interest of the leaders.

When we use incentives, we will start to create people who become addicted to incentives.  For more on extrinsic motivation click here.

“Rules and Incentives or Sticks and Carrots”

Teachers are now trying these responses in their classroom.  When learning is going amiss, some will create stricter rules, such as daily homework, or more quizzes.  If this fails, then incentives are created in the form of bonus marks for completing it on time.  Teachers, however, need to understand that

“There are no set rules, no matter how detailed, no matter how specific, no matter how carefully monitored, and enforced; there are no set of rules that will get us what we need.”

How do we solve this problem? Teachers need to stop creating incentives and rules, and start bringing in virtues which create better character in the classroom.  Educators need to start doing the right thing, and not what is expected.  The most influential quality a teacher can bring, in the words of Aristotle, is “Practical Wisdom”.

A case study:

“Miss B, a teacher in Texas, was listening to a consultant on how to raise test scores on a standardized exam.  The consultant came up with strategies.  First, don’t focus on the students who are going to pass the exam no matter what you do.  Second, don’t waste your time on kids who can’t pass the test no matter what you do.  Third, don’t worry about kids who moved into the district too late for their scores to be counted.  Focus all your time and attention to the kids who are on the bubble. While most teachers were nodding in approval, Miss B shook her head in despair.” 

Practical wisdom is not just doing the right thing, but also realizing what the right thing is.  The most important idea to remember is we are teaching people.  When dealing with people, we need to understand that certain flexibility is needed that no set of rules can encompass.   People, who have practical wisdom, can ascertain when we should bend rules, improvise, and manage a set of rules.  Also, these people bend and are flexible for the right intentions.

I am not naïve in thinking that you do not need rules and incentives.  I am not claiming that anarchy and chaos need to be brought into education.  I am, however, saying that certain rules and incentives are demoralizing the professionalism that has brought me into education in the first place.  Many times, not just in education, I have heard the question from my colleagues, “If we are professionals, why are we not treated as such?”.

What can be done?  People need to start to become “system changers”.  These people are not people who find the loops holes in the rules or systems but actually transform the system and improve it.