Thursday, April 17, 2014

Lowering Standards or increasing classes?

I think it is time to go back to traditional assessments.  Why? I am tired of large class sizes.... See, larger class sizes are the result of changing assessment.  

First, I abolished grades in my class, then instead of standardizing assessments, I actually personalized my assessment after some time I removed deadlines for assignments.  Why did I do all this?

I did this because my failure/drop rate in my calculus classes was extremely high.  The first 2 years, of teaching Calculus, I had a failure/drop rate of 40-50% of the class.  I would start with classes around 38 and end with classes around 18.  In one class, students had bets on what would be the final number of students.  This had to stop!  

Over the course of 2 years, I realized that my teaching was not the problem; it was how I assessed students.  I made all students know the material by Friday, assessed with a Multiple Choice, Written Response exam, and never let a child have a chance to be reassessed. In addition I would assign over an hour of homework each day.

Below is the result.  If there is one line you look at, it should be the orange one.  The orange line is the percentage of students who have failed/dropped my calculus class in each year.  The time is over 4 years.

I currently have a drop/failure rate of 4-5%.  I do believe I can get this to 0!  Was I joking about going back to traditional assessment? Yes!! Was I joking about classes being larger? No!  However, this is not a bad thing!  Here are what the other lines are

Light blue-The percentage of "traditional assessments" I use in my class.
Green-The class average on my Final Exam (This has been the constant over the 4 years)
Purple- The final class average.


  • The number of traditional assessment is directly related to my drop/failure rate. 

What is also pretty cool is you can see, by the green and blue lines, that the "standard" or "average" of my class has not dropped significantly!!  In fact, my class average has increased.  More kids completing the course and even a higher average....Remember these kids are not doing homework, prepping for exams, or completing worksheets.

There was one year, in which the Final Exam marked dropped, as it was due to the fact that I was perfecting my open ended projects.

Conclusion: If you want small class sizes, please use traditional assessments.  If you want a low drop/failure rate, please click on the links at the top and learn more.

Tuesday, April 15, 2014

Dealing with Change

The following is from

When something is changing you need to realize the following occurs.

Innovators: The adoption process begins with a tiny number of visionary, imaginative innovators. They often lavish great time, energy and creativity on developing new ideas and gadgets. And they love to talk about them. Right now, they’re the ones busily building stills to convert cooking oil into diesel fuel and making websites to tell the world about it. Unfortunately their oneeyed fixation on a new behaviour or gadget can make them seem dangerously idealistic to the pragmatic majority. Yet no change program can thrive without their energy and commitment.

How to work with innovators:
• Track them down and become their “first followers”, providing support and publicity for their ideas.
• Invite keen innovators to be partners in designing your project.

Early adopters: Once the benefits start to become apparent, early adopters leap in. They are on the lookout for a strategic leap forward in their lives or businesses and are quick to make connections between clever innovations and their personal needs.

How to work with early adopters:
• Offer strong face-to-face support for a limited number of early adopters to trial the new idea.
• Study the trials carefully to discover how to make the idea more convenient, low cost and marketable.
• Reward their egos e.g. with media coverage.
• Promote them as fashion leaders (beginning with the cultish end of the media market).
• Recruit and train some as peer educators.
• Maintain relationships with regular feedback.

Early majority: Assuming the product or behaviour leaps the chasm, it may eventually reach majority audiences. Early majorities are pragmatists, comfortable with moderately progressive ideas, but won’t act without solid proof of benefits. They are followers who are influenced by mainstream fashions and
wary of fads. They want to hear “industry standard” and “endorsed by normal, respectable folks”.

How to work with the early majority:
• Offer give-aways or competitions to stimulate buzz.
• Use mainstream advertising and media stories featuring endorsements from credible, respected, similar folks.
• Lower the entry cost and guarantee performance.
• Redesign to maximise ease and simplicity.
• Cut the red tape: simplify application forms and instructions.
• Provide strong customer service and support.

Late majority: They are conservative pragmatists who hate risk and are uncomfortable your new idea. Practically their only driver is the fear of not fitting in, hence they will follow mainstream fashions
and established standards. They are often influenced by the fears and opinions of laggards.

How to work with the late majority:
• Focus on promoting social norms rather than just product benefits: they’ll want to hear that plenty of other conservative folks like themselves think it’s normal or indispensable.
• Keep refining the product to increase convenience and reduce costs.
• Emphasise the risks of being left behind.
• Respond to criticisms from laggards.

Laggards: Meanwhile laggards hold out to the bitter end. They are people who see a high risk in adopting a particular product or behaviour. Some of them are so worried they stay awake all night, tossing and turning,
thinking up arguments against it. And don’t forget they might be right! It’s possible they are not really not laggards at all, but innovators of ideas that are so new they challenge your paradigms! In the early stages,
where you are focusing on early adopters, you can probably ignore the views of laggards, but when you come to work with late majorities you’ll need to address their criticisms, because late majorities share many of their fears.

A great video to follow this up:

Monday, April 14, 2014

Curriculum Redesign in Alberta

Before you read on, I ask that you stop and think for a couple of minutes about "What should school look like?"

WHY do we need to change?

My reason comes from "WHY do I teach?":  I teach because I believe in a classroom that is structured different for each student in the class.  My "perfect class" would be focused on meeting the needs of the students not the system.  Students in my class should be thinking critically, not only learning what to learn but also how to learn.  Innovation and creativity will be at the core of all my lessons, as the focus will be creating opportunities for my students for the future and for the world outside the walls of my classroom.  Students can work at different paces, and implement various learning strategies to achieve the goals of my class.  I believe in a classroom that allows me to dig deep in various interests of students without worrying about losing time.  Personalized learning will be allowed to flourish in my classroom as the passion and interests of my students will be just as important as pencils and paper.

I don't believe that any teacher or any educational stakeholder, in Alberta, is 100% content around the current education system.  If this is true, then isn't it about time we change?

Our education system needs to prepare students to be successful in a future world that will be defined by global interaction, competition, engagement and networks. It needs to ensure Alberta’s young people will have the knowledge, skills and attitudes to be prepared for jobs that do not exist yet and in industries that are emerging or evolving.

HOW will curriculum change?

Inspiring Education involved parents, teachers, students, business, and many other educational stakeholders and listened to them around "What should change in Education?".  The comments called for more student centred, personalized, authentic learning experiences that will result in youth becoming engaged thinkers and ethical citizens, with an entrepreneurial spirit.  The vision was for an education system which is significantly different from that of yesterday and today.

The Alberta Government listened and is creating a curriculum with a different focus.  We need to invest in our students and empower them to bring out their potential.  We are emphasizing the development of key competencies in our students, cultivating engaged thinkers, ethical citizens and entrepreneurial spirits.  We’re recognizing that not all students learn the same way, and that textbooks and classrooms are just one way for them to experience education.

Lastly, so WHAT will change?

All classes will focus on core competencies, which will be integrated into the curricular outcomes.  The competencies are:
  • Know how to learn
  • Think Critically
  • Identify and solve complex problems
  • Manage information
  • Innovate
  • Create opportunities
  • Apply multiple literacies
  • Demonstrate good communication skills and the ability to work cooperatively with others
  • Demonstrate global and cultural understanding
  • Identify and apply career and life skills

This change will allow any classroom to become the teacher's "dream classroom".  An example of how my class has changed.


Friday, April 11, 2014

11 Reasons why we need the new math

Answer to Top 11 Reasons against New Math.  Recently, I have read an article titled "Top 11 Reasons to Return to old math".   Below is each point, and my rebuttal.  

1) Johnson has failed to admit any mistakes and adequately correct them
There are approved textbooks, but no Mandated textbooks.  Teachers have the choice and freedom to determine what is best for their own classes.  Some teachers follow textbooks closely (the book they choose) and others don't even use textbooks at all.

2. Twice the number of math illiterate kids
Has other things in Alberta changed over the last 4 years? If you they have then how can we ignore everything that has changed and point the blame entirely on the math curriculum?

3. Kids need direct teaching and practice to attain mastery
 Direct Instruction is in the new math curriculum. The curriculum tells us WHAT to teach not how to teach.  If you feel that there is a teacher which only does discovery then I advise you to phone the teacher.  If it is a problem that with what the teacher is teaching then you call the government.

4. Major support for conventional math, little for discovery/inquiry math
If you support that some students should be taught with memorization and some students learn best through inquiry then you support the new math, if you believe that we should ignore individual student differences and force memorization on all then you support the old.  Which do you want?

5. Johnson not open to input
Johnson has offered many symposiums and sessions, which are open to parents and community, to attend and ask questions.   Johnson has gone to many school boards and discussed concerns, and has shown how most just don't "get" the new math as it allows students to learn under conditions which are best for the individual student not the best for the group.

6. New math is harming kids, making them hate math
People enjoyed math before the change? Really?  When I tell people I am a math teacher, with a masters in mathematics, I get looks of disgust and often asked "WHY?".  Forcing students to all memorize caused many to hate math.

7. New math has created inequitable, two-tier education in Alberta
This is more opinion than fact.  I teach in a school with various income levels and all of these kids are representative in my calculus class, and all are doing quite well.

8. Educators say we need to get back to conventional math teaching
Many educators are wanting the ability and autonomy to teach how they want. The irony is that going back is actually putting more restrictions on the teacher, while keeping this way is actually providing options for teachers.

9. New math was brought in without any credible classroom studies showing it’s better or even effective
Lots of research was done.  Again, the words "discovery, inquiry, 21st Century" are not found ANYWHERE is the curriculum.  The curriculum dictates to the teacher WHAT to teach, and what you will find are the words "personal strategies".  Meaning that a student can determine how to answer a question based on what makes the most sense for them.

10. Direct instruction and memorization can lead to creativity, deeper understanding, critical thinking
This might be true...for some, while for others inquiry can lead to creativity.  Both strategies are embraced in today's math classrooms, while only one group can be "creative" in the old style.

11. Conventional math advocates are open to discovery-inquiry techniques
 All strategies can be used in Today's Classrooms.

Lastly, if you aren't convinced here is what an actual "new math classroom" looks like.

Thursday, April 3, 2014

Zombies meet Mathematics

Below is how I brought in "28 days later", "World War Z", or "The walking dead" into my calculus class to introduce points of inflection.  At this point my students have been taught derivative rules, relative maximums and minimums, but not yet application of second derivatives.

First ask the class
What would the graph of "Zombie population" vs "time" look like?
Have them explain their answers and why.  Instead of telling them, play the following game.
1) Number the students from 1- X
2) Put a table on the board with Days, and Number of Zombies as the headings.
3) Draw a random number (I used a simple random number generator)-The number becomes the Zombie.
4) Each following day draw N numbers where N= the number of zombies on the previous days.  If the number of a student is drawn they become a zombie and will attack the next day.

Your chart should probably start like:

On Day 2 you would have drawn 1 number, on day 3 you would have drawn 2 numbers, etc.
Of course, it will slowly stop doubling due to some numbers being drawn more than once.  For example if number "10" was drawn on day 2, and again on day 3, then it represents a case where a zombie attacked another zombie (stupid zombies!).

You can then graph the data and it should look like a horizontally stretched out "S". 

Now lets integrate calculus. I used the following equation, (however if you find, or create, a better equation please let me know) Also you could also use base 2, as it looks very similar.  My world ends roughly after 28 days (since I love the show 28 days later).
Where Z(t) is the population of zombies, in billions, at year t.  The graph should be

From here you can answer the following questions:

Now you want them to lead you towards points of inflections, so here is how I suggest you do it:
At this point we have discussed relative maximums and minimums are there any of these on the graph? No.  Alright, is there anything "special" going on?
Then let them talk, explain, discuss.  You want them pointing towards the middle, and determining that the derivative here is a maximum.  You can then relate how you determine relative maximums of functions to determine that you simply make the second derivative equal 0.  This is what we call a Point of Inflection!

Please change, tweak, use, etc as you see fit.