Here is my response:

Coming together to create a real learning environment for students

## Saturday, December 18, 2010

### Real teaching first, real learning second

## Friday, December 17, 2010

### Meaning first, videos second.

Usually on the last day before Christmas, a christmas movie or activity is completed or "busywork." This year I decided, instead of watching a movie, why not let the students create one? Today, I tried an activity that I read about on a blog. My students were put in groups of 3-4 and given 11 questions of review. They were then given the following instructions with a flipcam (mini video camera).

Directions

Figure out the solution to three different problems on paper and check to make sure it is correct. Check your solution with the answer key.

Plan out a 2 minute or less presentation. See Presentation below.

Write out the section/problem number(s) on your whiteboard or desk.

Write out the question with any key information on your whiteboard or desk.

Write out part of the problem’s solution on your whiteboard or desk.

Remember each person will do some explaining in the video.

Make sure that your writing is big enough to see through the video.

Get a “FLIP” and read the instructions about “The FLIP”. See below.

Once you are finished with your presentation, return the “FLIP” and begin working on the rest of the homework assignment. Make sure you put a note-card with your names and section/problem into the black bag of the FLIP.

Presentation: 2 minutes or less (redo your video if it is over 2 minutes)

VIDEO

1. Introduce yourselves: first names only.

2. Read the section/problem number(s) from the writing on your whiteboard or desk.

3. Read the question and any key information from the writing on your whiteboard or desk.

4. Explain the solution that you have written out on your whiteboard or desk so far.

5. Finish the problem by actually writing in front of the “flip” while explaining the solution.

6. Thank the audience for their time and to have a good day.

The students started to collaborate and solve the questions. Surprisingly, on the last day before Christmas, students were engaged on meaningful tasks. Below are some of the videos that were created. I published one of them from my ESL student explaining in English how to do math.

ESL Student talking math

Another student discussion elimination.

I cannot find the original blog were this activity was created, if you do know the author please comment so I can give him/her the recognition he/she deserves.

## Thursday, December 16, 2010

### Support first, learned helplessness second

Few years ago when a student had a question in my class, I would tell them the answer. Telling answers, providing solutions, and informing students was the way I would teach. Recently I have realized, as a true educator, I should not be telling, providing, or informing, but in fact facilitating learners in my class. I no longer want to be an instructor of information, but in fact a facilitator of education.

When we, as teachers, grab the pencil/pen from the students’ hands, or complete a task for a student we are perpetuating a single idea; “Learned helplessness”. Learned helplessness is defined as:

*a condition wherein a person believes that no matter how hard he or she tries, failure will result.*

This condition is being enhanced by environments were tasks are completed for students. Some educators will say “finishing the questions for the students need to be done, due to time constraints”. However, constantly “finishing questions” is creating a condition in the students’ mind that they are incapable of thinking on their own. They will start to actually believe that there are inadequate to achieve success in certain areas.

This, unfortunately, will result with students becoming reluctant or even scared to complete challenging tasks. To some, learned helplessness will appear as being lazy, or bored, but I truly believe that students crave reasonable expectations from others, and want to live up to these expectations. Saying that, if we have great expectations from students we will witness great things, but if our expectations are low then consequently little learning will result.

Here are several tips for combating learned helplessness:

· set high expectations for your students

· let your students know that you see them as capable individuals

· encourage your students to try it on their own

· provide multiple opportunities for student trials

· positively reinforce the student's efforts

· if completing the entire task is not a possibility, encourage the student to complete the parts that he or she can do

· encourage the student to try a bit more with each success

· if you must complete a task due to time constraints, let the student know that he or she will be expected to do the task when time is not an issue

· allow your students to see you struggle with a difficult task

Students need to be challenged, empowered, and congratulated, but not told, informed, or provided with answers. Once students have the support, learned helplessness will be abolished.

## Wednesday, December 15, 2010

### Learning first, achievement second, homework still dead last.

I have received many responses to my "no homework" policy, so I decided to blog more about it. In my classes, I do not assign daily required work. I have, however, given my students assignments to complete out of class time, but these are not the traditional math assignments.

The myth about daily repetitive work is that this actually increases student mastery of a concept. Many people believe the saying “Practice makes perfect”. This saying, recently, has evolved to “perfect practice makes perfect”. I would agree to the second statement when referring to a physical skill, such as shooting a basketball. To master a physical skill, our body needs to mimic the correct actions multiple times. The question that homework in a classroom does not address is “How does one practice understanding?”

Psychologist, Nate Kornell, completed a study that showed that intensive immersion is not the best way to master a particular concept. Nate found that college students and adults of retirement age were better able to distinguish the painting styles of 12 unfamiliar artists after viewing mixed collections (assortments, including works from all 12) than after viewing a dozen works from one artist, all together, then moving on to the next painter. Nate then deduced:

*“What seems to be happening in this case is that the brain is picking up deeper patterns when seeing assortments of paintings; it’s picking up what’s similar and what’s different about them,”*

Unfortunately, most classes immerse students into one concept; assign them multiple questions of the same concept, then move on to the next concept. The research states that this is not the most effective way if we want students to retain mastery.

According to Cooper, homework increases student achievement (Even a formula has been created, 10 min per grad level) This is a self-fulfilling prophecy. First, educators need to realize that student achievement and student learning are not the same idea. When looking at Cooper'sstudies, he shows that test scores increase due to the homework assigned. Unfortunately, assigning repetitive work for students, or giving them loads of questions before an exam is the equivalent of cramming for an exam.

Cognitive scientists do not deny that cramming will lead to a better grade on an exam (thus increase student achievement), however this knowledge is quickly forgotten (student learning has decreased). We, as educators, need to realize we are here to increase student learning first and student achievement second.

## Tuesday, December 14, 2010

### Makeover first, passion second

Today I thought I would blog about something that can relate to not just educators; Passion. Most people would put their top three priorities as their family, job, and religion (or belief system about life). Looking back a couple years ago, I would have put socializing as number one. Recently I have changed.

I can truly say I love my job and have passion for doing the best I can do. After reading many educational research papers and blogs, my pedagogy has started to change. No longer do I have classes which spectate, but are actively involved in their own learning. This new way of teaching, however, has not been the easiest change.

My time spent on work has increased drastically since this change; however I do not see this as a drawback. Sometimes in life you must do something, or change, because that is what you are drawn to do and not because that is the logical decision.

My students, overall, are now learning more and actually understanding math. This result has inspired even more desire to grow as an educator. This is why I started blogging in the beginning. Everyone, educators alike, need to be aware of their passion and enthusiasm for their environment and if things are lacking, a change will most likely need to be made. The change for me was a “teaching makeover”, but in the end it has created more passion than I have ever felt before.

## Monday, December 13, 2010

### Educators first, entertainers second.

"If students are having fun then they will learn more." This was a comment I heard and decided to look more into this idea. Most people understand the meaning of the words "engagement", "entertainment", and "meaning", but do people understand that engagement and meaning does not imply entertainment?

When I look back to a couple of years ago, I would start my class with a funny YouTube video or a funny website. I believed that these videos and sites convinced students that what I was about to teach was worth learning. Unfortunatly, I was being decieved by this notion.

Students want and need to have fun, however not at the expense of learning. I believe true student engagement can be fun, but it doesn't have to be. Recently, I have asked some of my students which of the two enviornments would they prefer:

Option 1: A class where you laugh and joke, watch funny videos, but do not understand the concepts being presented

Option 2: A class that is very structured where no jokes are allowed, but you can completely apply the knowledge and concepts you have learned.

When I look back to a couple of years ago, I would start my class with a funny YouTube video or a funny website. I believed that these videos and sites convinced students that what I was about to teach was worth learning. Unfortunatly, I was being decieved by this notion.

Students want and need to have fun, however not at the expense of learning. I believe true student engagement can be fun, but it doesn't have to be. Recently, I have asked some of my students which of the two enviornments would they prefer:

Option 1: A class where you laugh and joke, watch funny videos, but do not understand the concepts being presented

Option 2: A class that is very structured where no jokes are allowed, but you can completely apply the knowledge and concepts you have learned.

Most either said option 2 or a mix between the two classes. Not one student picked option 1. As educators we need to realize we are not doing our students or ourselves a favour by showing non-relevant material in class. The question then is “How do we engage students on learning and allow them to also have fun?” The answer is simple; create activities that relate to the outcomes not to entertainment.

To introduce non-permissible values in math, I showed an example on how 1 could equal 2. I then asked the students to find the mistake.

The mistake is at one step you have to divide by 0 which is breaking the law in the world of math. Was this task as fun as showing a video where a kid runs into a stop sign? Absolutely not, however this task was more meaningful to the students. As teachers, we are not entertainers but educators, and sometimes we need to be reminded of this.

## Friday, December 10, 2010

### Trust first, true assessment second

Saskatchewan has the roughriders, and now they have the “rougheducation” policy. On Tuesday December 7, CBC wrote the article LATE SCHOOL WORK WILL MEAN LOWER MARKS, MINSTER CONFRIMS. The article begins with

“

I truly hope all educators are as disgusted as I am.

“

*The minister of education says she is preparing a province wide grading policy that will require teachers to deduct marks if students don't do their work.”*I truly hope all educators are as disgusted as I am.

Their minister of education, Donna Harpauer, exclaimed,

“

*at least five or six school divisions don't deduct marks for bad behavior*”.
I was wondering, why don’t ALL the divisions not deduct marks for bad behavior?

Her solution is a provincial wide policy that will require teachers to deduct marks if students don’t complete their work on time. I agree that schools should be a place where responsibility is addressed, but where in the mandated outcomes, does it express that schools should be grading such responsibility? In fact, when you start grading on ideas outside of the mandated outcomes, is that not malpractice?

When we start putting grades on tasks it actually decreases the potential learning that is possible. The most insightful piece of research in the field of motivational psychology is that the more people are rewarded for doing something, they more they tend to lose interest in the actual task. Also, by deducting marks for last assignments, the grade is distorting what it actually should represent; what outcomes have the students learned.

As teachers, we need to be trusted that we will assess properly and appropriately. I believe that these “blanket mandates” actually destroy the trusts this trust. In my school, I truly do feel my opinion is valued and true innovation is approved and endorsed. Once a teacher truly feels trusted that he/she is allowed to endeavor on new educational roads, without criticism and reproach, we will start to see assessment practices that are actually validated

## Thursday, December 9, 2010

### Embracing first, imagination second.

Schools are forcing students to leave their digital media tools outside of the classroom; however the students are craving these tools to be used inside the class. We need to change our paradigm from looking at standardized test scores and graduation rates, to start focusing in on allowing students to perform on what they are passionate about.

Education needs to move away from being the same to everyone and towards giving students opportunities and options that were not available when we, the educators, were in school. How do we do this? In my class, I have posted notes we created as a class onto a discussion group through Facebook. Also, I have created a youtube video of a concept for which a student can watch whenever and wherever they are.

Every week-end I give my students a problem that they must solve. This problem must not be solved in the conventional paper and pencil way. The students must either send me a message on facebook, email, or write it out on paper (for those students who have no access to the Internet over the weekend). The student must actually write out how they solved the problem and communicate their answer to me through text. To illustrate this I have attached a student's answer for a problem on how to factor a cubic equation.

*"First, I found the factors of three and substituted each until I found three to be the number that once substituted, equals zero. Using synthetic division, I got x^2-x-1. There are no two numbers that multiply and add to get -1 so I used the quadratic equation. After simplifying, I found x to equal one plus or minus the square root of 5, divided by 2 and x to equal 3".*

As you can observe the student can longer just write out their answers using math, but instead communicate the solution to me. By sending it to me over facebook/email, I have the ability to give them immediate feedback on their solution. To illustrate this one student had the problem of 5f(x+2) and they had to explain in English what this meant.

*Student: substitute x into function f and multiply by 5 and then you add 2*

*Myself: The plus 2 is in the brackets, want to try your answer again?*

*Student: substitute (x+2) in for the f function, then multiply that by 5*

This conversation was done on a Saturday through Facebook.

The sad truth is that students are craving information immediately and at light speed. If educators do not recognize this need, students will tire of our classes and not reach their full engagement.

A comedic representation of this fact is shown by this video “Everything is amazing, and no one is happy”.

If we compared the technology that a 20 year old had available, in school, to what a 28 year old could access in school, you would see such a drastic difference. Sadly, most 5 year olds are more competent with the internet than some 50 year old people. This is due to the fact that children have access to these amazing technology tools.

What is going to happen with this 5 year old enters school? He/she already has such creativity and imagination. The true potential of this child will be amazing. Schools need to be ready to embrace these tools and allow for the imaginations of children to shine.

## Wednesday, December 8, 2010

### Differentiated instruction first, differentiated assessment second.

I teach my students in many different ways, but I grade all using the same process. There is a major problem occurring here. Every teacher, I would hope, in Alberta knows what differentiated instruction is, but do they know what differentiated assessment is? Educators know that every student learns in a different way, but do we know that every student can demonstrate their learning in a different way?

In our province, students write standardized exams in grades 3, 6, 9, and 12. When our school is evaluated for “students’ achievement”, we are assessed on standardized exam participation, acceptable standard (over 50%), and standard of excellence (over 80%). I find this very contradictory! Our province is forcing every student to demonstrate learning in the same way, on the same exam and on the same questions. Where is the differentiated assessment?

Currently, due to a mandate of my department, I am administering common exams to all my students. Every test day I shake my head as I use differentiated instruction in all my courses, but then grade all my students the same.

Next semester, I will be changing my grading process. I will keep differentiated instruction, but I will be implementing differentiated assessment. Students will inform me when, during the term, they want their outcomes assessed. No longer will I grade based on my progress through the course, but actually grade the students on their own progress through the outcomes. Students will also be allowed to demonstrate any outcome as often as they would like.

To truly be teaching for the students, we need to realize that differentiated instruction is no longer enough, we need to start implementing differentiated assessment as well.

## Tuesday, December 7, 2010

### student learning environment first, teacher's work enviornment second.

Below is a chart from "What to look for in a classroom". After reading this article, I realized that I have some remodelling to do. When I first started my teaching career, I used to organize my classes with the mindset "What is best for me to teach in". Lately, I have came to the conclusion that I must actually be thinking "What is best for students to learn in".

## Monday, December 6, 2010

### Application first, why second

To further show assessment, without the use of worksheets or homework checks, I gave an assignment called "Calculus in the real world". Students were asked to design a real-life context problem where calculus could be used to solve. I gave a week to complete. As the deadline approached, a couple of students were complaining by informing me, "I know how to solve the questions you give us, but I just can't create my own". After some discussion, I alleviated the stress and empowered them with the confidence that they needed; this a task they can complete. One students gave me the following problem,

The student also provided me with the calculus solution:

*Oh no! It’s Christmas Eve and I still haven’t wrapped my sister’s present! There are no boxes left in the house, so I’ll have to improvise. I spot a piece of cardboard that is 12 inches by 12 inches, so I can make my own box. But, after I put my sister’s present in the box, I want to fill the rest with chocolate. What dimensions will maximum the volume of the box that I can make from this piece of cardboard? Also, what will this maximum volume be so that I can optimize the space for chocolate?*

The student also provided me with the calculus solution:

After polling the most important stakeholders, my students, they felt that after creating a question, and solving it, they could further describe the importance of calculus in the real world.

In class, I had students pair up and exchange each other’s problems. At the end of class, I asked for feedback and it was an overwhelming response of “Can we do that again?”

When students are given real applications of the concepts required by a course, they truly grasp the “WHY” part of education. In my class, I no longer hear, “Why do I have to complete this?”, or “What is the point of this?”, however I do hear “I finally understand why we are learning this!”. Give students the application, and they will learn the “why” on their own.

## Sunday, December 5, 2010

### Understanding first, application second.

I have completed another lesson using the discovery method. In Math 20 Pure, students are required to calculate, using two points, the slope, midpoint and distance. Last year, I wrote the formulas on the board and then spent the rest of the class using the formulas on different points. Both my students and I hated this method. There was no engagement.

This year, using a map of Alberta, I had students discover the formulas for themselves. Using two cities in our province, Calgary and Edmonton, students created their own two points. In collaborative groups, students were required to calculate the slope, midpoint (which is our city, Red Deer), and the distance between the two cities.

At first, students didn't know how to start. I heard comments such as "We know the midpoint is Red Deer, but how do we show that?", "Let’s try measuring the line with a ruler", and my favourite "If we measure with a ruler, that won't be the exact distance."

Most groups started working on slope first and calculated it correctly; from there they realized a right angle triangle can be drawn. After 10 minutes, all groups had calculated all three parts correctly. I then posted on the board two general points (x1, y1) and (x2, y2). The groups were then instructed to work with general points. They didn't realize this, but they were forming the formulas.

At the end of the lesson, students did not only know what the formulas were, but also the mathematical representation and application of them. In recent years, I have taught students how to memorize mathematical ideas and concepts, and when it came to application, just regurgitate the information down. This year, I believe my students truly understood each formula and how to apply them.

This year, using a map of Alberta, I had students discover the formulas for themselves. Using two cities in our province, Calgary and Edmonton, students created their own two points. In collaborative groups, students were required to calculate the slope, midpoint (which is our city, Red Deer), and the distance between the two cities.

At first, students didn't know how to start. I heard comments such as "We know the midpoint is Red Deer, but how do we show that?", "Let’s try measuring the line with a ruler", and my favourite "If we measure with a ruler, that won't be the exact distance."

Most groups started working on slope first and calculated it correctly; from there they realized a right angle triangle can be drawn. After 10 minutes, all groups had calculated all three parts correctly. I then posted on the board two general points (x1, y1) and (x2, y2). The groups were then instructed to work with general points. They didn't realize this, but they were forming the formulas.

At the end of the lesson, students did not only know what the formulas were, but also the mathematical representation and application of them. In recent years, I have taught students how to memorize mathematical ideas and concepts, and when it came to application, just regurgitate the information down. This year, I believe my students truly understood each formula and how to apply them.

## Friday, December 3, 2010

### Critical thinking first, butt second.

I have blogged quite a bit about the theory behind my pedagogy; today I thought I would illustrate how I actually apply my philosophy to my teaching. Last week, I thought I would assess if my calculus students truly understood the critical thinking involved to solve a problem.

Using the methodology of Dan Meyer and an idea I read about on the AP Calculus discussion board, I gave the students a sheet that is illustrated in the photo above. No numbers, formulas, or guiding questions were given. The students were to collaborate on how to solve the problem.

The problem: The picture is a blue print, to scale, of a main floor of a prison. The circle is the camera that rotates in a full circle. Due to the difference in distances from the walls, when the camera pans over the two Xs, the speed will be different. Jailor Jimmy wants to slow the camera down, such that when it pans over the North X, it will be at the same speed it pans by the South X.

For the non-calculus teachers, I gave my students a question, with context, for which calculus is needed to solve. Acting like Jailor Jimmy, I answered any question the groups might have. Some questions, I would respond with “I don’t know”, or “Can’t remember”. Students were forced to decide what information is needed, and what information they can determine on their own. All groups where provided with ruler, protractors, and any other tool them deemed necessary.

At the beginning, students were frustrated and I heard comments such as “What should we ask?”,

“What do we need to know?”. I realized that these students were accustomed to being provided any and all information needed in the question, and usually in the order they needed it. This problem I have perpetuated by providing this information all semester long.

“What do we need to know?”. I realized that these students were accustomed to being provided any and all information needed in the question, and usually in the order they needed it. This problem I have perpetuated by providing this information all semester long.

After 5 minutes or so of struggling, the critical thinking started. Students started asking certain distances. Jailor Jimmy only remembered one distance. This information allowed for students to determine the scale of the diagram. Also, the current speed of the camera was given. These two pieces of information are all that is needed to solve the problem. I realized that is no longer what I COVER in class that sticks and makes sense, but what the students DISCOVER in class that carries the most meaning.

Students struggled at the beginning, but after 20 minutes, most groups were on their way. Measuring, on their own, the information needed and using formulas they decided were pertinent to solve the problem. At the end of class, I heard some students walking out expressing, “Man my head hurts!”, this made me smile as last semester I had students walking out saying “Man my butt hurts!”.

Video that inspired this:

## Thursday, December 2, 2010

### Meaning first, homework second

I have stopped assigning daily required homework to my students. Over the last 4 years of my teaching career, I assigned daily homework, and at the start of each class I would "check", or assess, the completion of their work. When I started to think about it, what I was doing could be considered malpractice.

The students would open their work booklets to the assigned page and I would walk up and down the rows and either give the students a 100% or a 0%. It is ludicrous to call this true assessment. I was grading their work ethic more than their actual knowledge of math. Almost every student's mark was being either inflated or deflated due to their work ethic.

I have had the discussion that daily homework teaches good work habits and/or develops positive character traits. After reading many articles and research I have yet to find one piece of evidence that supports this claim. Another argument is that homework "gives students more time to master a topic or skill". I have read reports from researcher Richard C. Anderson that claims "the actual learning that is occurring depends strictly on time spent learning the concept". However, when Anderson completed further research he found that this claim also turns out to be false.

A colleague of mine used the example of reading to illustrate the need for daily homework. Anderson found that when children are taught to read by focusing on the meaning of the text (as opposed to strictly memorizing the phonetic sounds of the words), then the learning completed by the reader does not depend on the amount of instructional time. His research also carried over to math, which showed that the more time spent on completing math facts only increased achievement if the achievement was based on low level thinking and strictly recall as opposed to problem solving. The truth is that when creativity and higher level thinking is involved, the more hours spent are least likely to produce better outcomes.

Another colleague used the idea of sports to prove that homework is a necessity. Of course it makes sense that if you practice a certain athletic skill the correct way you will improve in that area. However, using sports to promote homework in class is using

*petition principii,*or more commonly known as “begging the question”. A proposition which requires proof is assumed without proof; we are assuming that an intellectual skill and an athletic skill can be classified in the same category.The majority of people that I have encountered that are supporters of daily required homework fail to look at the tasks from the students’ point of view. Most “drill and practice” assignments actually do the contrary to students’ learning, and actually “drill and kill” any interest in the subject area. Also, when students are struggling with a concept, asking them to complete questions on this concept will become frustrating for them and still no actual learning will occur. I have realized that I need to stop treating my students with the notion that “if I give them more to do, then they will know more”.

In my classes, I challenge students in meaningful contexts and provide them with questions that are similar to the ones in class. I do not require my students to complete these questions, I do not grade these questions, and I do not force my students to do work that is not important to them. The meaning of the math is what I put as a priority in my class, and home work as second.

## Wednesday, December 1, 2010

### Collaboration first, cooperation second.

Just recently, I have understood the true difference between collaboration and cooperation. According to Dictionary.com collaboration and cooperation are defined as:

Collaboration - something created by working jointly with another or others.

Cooperation - an act or instance of working or acting together for a common purpose or benefit; joint action.

I attended an association instructor's training where we dug deeper into these words. If I wrote this blog a year ago, I would have written that these words are synonyms of each other. I would have continued with stories that, in my classes, students are truly collaborating with each other throughout their learning. I would have been lying.

Cooperation was, and still is, present in my teaching. I have my students sit in groups and always allow them to "act together for a common purpose". However, this is different than "creating [something] by working jointly with another". An example that can differentiate the terms would be an assembly line at a car factory. The workers are working together to finish a project (the car), however the workers are not sharing ideas, or working jointly with another to finish the task.

I have taken this point back to my class and now, I have my students truly collaborating with each other. Students must rely on the knowledge of each group member to solve a problem. One strategy I have implemented, to allow for true collaboration to occur, is if a student is not understanding a certain task, or is uncertain of a step, he/she must ask his/her group members for assistance. Once assistance is given, he/she must be able to explain the reasoning he/she was taught, before moving on in the problem. I truly have noticed a change in the dynamics of my classroom.

Before this change occurred, students preferred to work with others that share their same level of knowledge and calibre. If a weaker student was present in the group, they would leave the student behind, to watch from the "sidelines". Now, with true collaboration occurring, students embrace the weaker ones and truly assist them in their learning. No longer are students left behind, but instead picked up and helped along. Two amazing ideas are being created in my classes.

1) Most students are feeling a sense of ownership for their learning. They are not afraid to take chances, and are becoming more responsible for their knowledge.

2) Students are becoming teachers. When a group member is confused on a certain outcome, the group will stop and teach the idea to the other member.

I have now realized that if you have collaboration then you must have cooperation, however the converse may not necessarily be true. Knowing this, I put collaboration first and therefore am guaranteed to have cooperation.

## Tuesday, November 30, 2010

### 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.

## Monday, November 29, 2010

### 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.

## Sunday, November 28, 2010

### 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.

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.

**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.

## Saturday, November 27, 2010

### 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.

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.

## Friday, November 26, 2010

### 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.

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.

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