Math concepts first, tricks second.

Math tricks do not teach students how to complete questions, the tricks are actually cheating the students of the real learning that could occur.  In one of my classes, students needed to square (x - 2) to complete the question.  When a group of students progressed to this step they were struggling on how to advance.  One student, Timmy, wrote (a - b) squared is equal to  "a squared, minus 2 times ab, plus b squared".  As I was inhaling to ask him "why", one of his group members beat me to the question.  Timmy was questioned, by a peer, "Why does that trick work?".  Immediately, I saw confusion across Timmy's face.  After looking at me for an answer and I informed Timmy, "For you to be able to use a trick in my class, you must be able to explain the reasoning behind it".


"Well Mr. Martin, FOIL, mean First, Outside, Inside, Last, and that will work for any multiplication we need."

As if right on cue, Timmy's peer asked, "Always?".  For the second time, Timmy's face was showing confusion, when he replied "I think so, oh wait, not for a bracket with three things".  Now I did not want to stop the thinking process and correct Timmy with the word "terms", as I saw Timmy was trying to logically work out this trick he had pulled from his brain. 

I could provide more and more anecdotes of the same events.  When students learn formulas, shortcuts, or tricks, and cannot explain why, we are essentially leading them down a path into an abyss.  I have been guilty of this many times in the past, but I am now forcing students to construct their own shortcuts, tricks, and formulas based on inductive reasoning that they complete themselves.  I am then often asked by students, "Does this shortcut work?", for which I will usually respond with "You tell me."

As educators, we need to stop giving tricks and allow the students to complete the process the "long way".  This idea will allow for students to start creating a stronger foundation of learning, and which will then allow for higher level thinking to occur.  Students need to discover these math concepts first and then allowed to create their own shortcuts, however when they create the tricks they are no longer magical to them.

Speak freely first, improvements second.

For true educational reform to occur, we must be able to speak and discuss openly.  On Friday, I was in my staff room and something truly magical happened.  An amazing discussion occurred about current issues in education.  The topics ranged from assessment to cell phone use in a school.  I use the word "magical", because here are educators that are on their lunch break and they want to discuss possible techniques they can implement in their class, to further advance the amount of learning that is occurring.

This is the true demonstration of passion for their jobs.  Even though there were disagreements occurring over certain topics, there was still a sense of congeniality towards each other.  At my school, the staff room is not the only place this happens.  I have had discussions with staff members walking through the halls, in the photocopy room, in my class, and in the parking lot.  I could only hope that other schools demonstrate this constant passion for increasing the quality of teaching and learning inside their walls.

This idea, that I am free to speak my mind, also caries over to my administration.  Many times, I have talked to my principal and have walked away feeling that my opinion matters.  The open door policy is one that I value greatly as a teacher and helps me express my ideas in a safe and respectful environment.  Schools, like any occupation, should have their leaders open to new ideas, views and styles, and I can truly say that my school falls in this category.  Once we are able to speak our mind freely and respectfully, true educational improvement can happen.

Response to the removal of the written response on the diploma

I wanted to blog about my response to the removal of the written response part of the diploma exam. I was asked to speak on behalf of the math council on a panel to debate about the written part of the exam. I currently am the Math counil co-director and sit on the executive as "Director at Large". Below is the question and my response.

What is the value of the mathematics diploma exams for Alberta Students? ~In particular, what is the value of the written response section of the mathematics diploma exam?The primary purposes of student assessment are to facilitate students’ learning, identify certain strengths and weaknesses and to create a decision making process for a student’s progress. According to Alberta Education, the diploma has three main purposes, to certify the level of achievement, to ensure the province-wide standards are maintained and to report individual and group results. The values of assessment and the purposes of the diploma do not seem to coincide at all. Large scale assessment of groups of students is completed to “field test” new ideas, create accountability, and determine curriculum effectiveness. However, these inferences formed and reported are in reference to the performance of the group, not the individual student.

MCATA (Math council of the Alberta Teachers Association) is opposed to all standardized exams, when the exam is not appropriate to the educational needs of the student and when the results are misused. The math diploma has become a high stake exam for all students, as 50% of their mark comes from this test. Valuable classroom instructional time may be spent on teaching students on how to read and answer multiple-choice and numerical response questions. This time is intruding on the instructional process.

MCATA supports the new math curriculum because we believe it has benefits for students. These include “Greater opportunity for conceptual understanding” and “Course sequences are designed to prepare students for their future goals”. The first benefit allows students to go deeper in the ideas and concepts of mathematics and thus allow for intensive understanding of math. Communication is the key to determining if conceptual understanding and learning has taken place. Written response questions, therefore, play an enormous role when determining whether or not students have achieved the second benefit, and are prepared for their future goals. Written response questions allow for students to demonstrate critical and creative thinking to mathematical problems.

Outcomes first, perfection second.

To achieve a 100% in a class, the student will have to be perfect. In my school, our grades are based on a 100 point scale, most commonly called percentage based. I recently marked some exams and a student in my class received a 97% due to the fact he answered one multiple choice question wrong.

I then asked myself, "Am I not supposed to be assessing outcomes and not perfection?".  Looking at his work, I realized his only mistake on the exam was that he squared a negative number and kept the answer negative. Solving the question this way, led him to a "distractor", and thus a wrong answer.  This test was in my calculus class, and squaring a negative number was not an outcome that was meant to be tested.

The question I ponder is, "doesn't he deserve a 100%?". Looking at the entirety of his exam, he truly demonstrates he understands all of the outcomes tested and all he is showing, in my mind, that he is not perfect.  Should I be grading him based on how he does each question, or should I be looking for mastery of the outcome in a holistic fashion? 

Next term, I am wanting to implement a new way of grading, which will be outcome based. This will allow for students to achieve mastery but still hold true to human nature and not be perfect.  We, as educators,  need to realize that students can truly demonstrate mastery of concepts with imperfections.  Once this idea is understood we can then put outcomes first, and perfection second or even never.

Pedagogy first, instructional tools second.

Some teachers believe that if they use a more engaging tool then students will become more engaged, and hence more learning will occur.  This statement is one that needs to be addressed.  I was talking to a teacher, where her school is using Ipod touches, mini whiteboards, Senteo, and other "engaging" tools, and I was intrigued since my district is doing the same.  She promised to give me an update as to how the tools were working.  After three or four lessons, she explained that the students were becoming more and more off-task during the lesson.

I wanted to dig deeper into this problem.  First off, I don't believe a student is ever "off-task", they are just on-task to something that is more meaningful to them at the time.  I questioned about the tasks students were given with these tools.  She was teaching "solving single-variable equations" and on the fourth lesson, she had posted "4x + 5 = 13" on the board and asked students to solve on their mini-whiteboards, and when finished flash the boards where she can quickly assess the class as to whether or not they are understanding how to solve the problem.  I quickly realized the issue.  Before implementing a new tool, teachers need to realize that if they teach the same way, just with the new tool, nothing will change. I explained that she was just giving the same meaningless problems without any context to the students, and now just asking them to solve it on a whiteboard.  Sadly, over the first three or four lessons the students were learning more about writing on a whiteboard or using the senteo machine, then actually learning the mathematical concept. 

How do we fix this? Students should need the tool to solve the problem! For example, if you are giving students a mini whiteboard, it should be because they are going to need to try to attack the problem in many different ways and will need to erase multiple times before achieving the solution.  Also, we need to start giving the students problems in a meaningful and contextual way.  I asked her to try this question, "Jason drove the store, which cost him $5 in gas.  He then bought 4 items, and the total cost of the trip was $13, what are some possible items he could have bought at the store?".  This question will need you solve the equation above, but students will have to create the equation, and then use their answer in a meaningful way, as to choose what possible items at a store are $2.  Due to the higher level thinking that might occur on this problem, having students collaborate might be a necessity. 

We, as educators, need to stop giving students problems that have no meaning, and no context.  Many believe that teaching in the same fashion but just using a fancy tool will engage the students more.  This should be compared to morphine.  If a person was to sustain a major injury, and was asked "Would you like morphine, or for the doctor to repair the injury", most would rather the latter over the former.  In education, it seems that most are asking for morphine.  This is illustrated by the comment, "I want PD, that I can use on Monday!", and I always rebuttal, "Why not have PD that you can use the entire next semester?". 

When we start doing the same pseudo-context questions, just on a fancy senteo machine, it is the equivalent of giving morphine to the injured patient.  It will work for a day or two and then students lose interest, because they are more engaged in the senteo, then in the actual problem.  We need to be ready to address, or possibly change, our pedagogy before we start changing our instructional tools.

Students first

I had the privilege of attending the ``Alberta Technology Leaders in Education`` conference at the Capri last night.  I truly was inspired.  The keynote talked about ideas of being connected and how the more minds working on the same problem allows for quicker and more effective solutions.  This idea, to most, is obvious however some educators don`t understand the power we truly could attain if we use the Internet and networking sites as our ``connectors``.  During the conference I was on Twitter and Facebook, not to chat with my old friends but connect with educators around the world!  I commented on ideas, tweets, and learning strategies while others commented on my comments.  This connectedness is truly an idea we should be embracing and not criticizing!  How does this look in classroom? We should be allowing students to publish their thoughts, work, and ideas in an international context.  Journals can be changed to blogs, instead of writing about a picture on paper, students could find an intriguing picture on the Internet and post a review on the website.  The ideas are endless.  One question I have been asked is, "Will this increase test scores?".  My thought is, we need to realize that test scores are not the way to judge whether or not true learning has occurred, and a scantron machine is not assessing what a students truly knows.  As an educator, I need to start listening to my students and how they learn effectively.  Worksheets do not increase learning, or even start it, however higher level thinking with actual context to the questions is where the true learning occurs.  I was called a "radical" thinker, and I am glad to be called this.  Radical is Latin for "root", and I believe we need to look back at the root of these problems and start addressing them.   I say this because we should be there for the students first and curriculum second.