Dealing with Change

The following is from http://www.enablingchange.com.au/Summary_Diffusion_Theory.pdf

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: http://www.ted.com/talks/simon_sinek_how_great_leaders_inspire_action

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.


http://realteachingmeansreallearning.blogspot.ca/2014/01/math-in-new-setting.html

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.  

Why multiples strategies makes sense.

I received this story from a teacher who prefers not to be named:

I have been a teacher for the past five years. Although I am not a math teacher now, I did have the opportunity to teach math when I completed my APT a few years ago.

Now before I proceed, I should inform you that I struggled with math when I went to school. I barely passed Math 30 Pure and quite frankly, despised the class. So when I found out that my placement was teaching primarily grades 4 and 5 math I was concerned.

I was given the task of teaching addition to the students. Simple right? Wrong! The new math had me very confused as there were multiple ways to teach students how to add. Growing up, I had learned one way: start on the right and work your way to the left, carry the one, and so on. The math that I was required to teach had me doing things that I had never learned to do. It took time for me to understand this new way of thinking.

Now, at this point you're probably thinking that I'm bashing the new math curriculum. However, I am doing quite the opposite. When I actually sat down with the material and tried to teach myself how I would teach these youngsters this different way of adding, I began to understand! All of the sudden the old algorithmic way that I had learned didn't matter anymore. This was a new way that

I could understand because it was teaching to how I learned! Teaching my students was also a success! My struggling students were able to see different ways of learning, and although they still had their challenges at times, I was able to explain to them why we add this way.

Many times people have shown me that other current math teachers have signed a petition around bringing back the old curriculum and this experience has shown me why.  I assume that these teachers simply don't "get it".  They are trying to show our current students the poor strategies they were shown.  Do this and you will get the right answer, without any explanation.

I hated how math was taught to me because I was forced to solve one very specific way and now that I have learned multiple ways, math has become more enjoyable.

Petition around Math

I am fearful that people who have signed the recent "Back to Basics" Math petition truly don't understand the devil they are asking for.  In our current math curriculum you will see objectives such as

Demonstrate an understanding of addition of numbers with answers to 10 000 and their corresponding subtractions (limited to 3- and 4-digit numerals) by:
• using personal strategies for adding and
subtracting
• estimating sums and differences
• solving problems involving addition and
subtraction.

Also similar objectives around multiplication and division.  The petition, and other critics, are upset that "memorization" is not needed and "discovery learning" is forced.  This is completely, and utterly, incorrect.  I have searched the Alberta's Math Curriculum for the word "discovery" and not one incident of the word exists.  What does exist is: Personal strategies.  Meaning the strategy of one child could be vastly different than the next child.  This curriculum is simply not forcing discovery in the classroom.

The curriculum simply tells all Alberta Educators what they must teach, but it does not, and hopefully never will, tell teachers how to teach these outcomes.  The petition, on the other hand, wants to do just that.  It wants to invade our classrooms and mandate to the professional teacher that every child must memorize.

Imagine if we did this for all outcomes.  Students cannot move a grade forward until they memorize the following facts.....  We would have most graduates who are simply "Siri" clones, and also students who truly hate the idea of learning.  Of course some, the ones who strive on memorization tasks, would get a great education.

I am not claiming that no student should memorize basic math facts at a young age, nor should every child be forced to discover the facts.  All I want is to keep the autonomy to the professional; the teacher.  I trust our Alberta teachers to know which students should use manipulatives, flash cards, centers, collaborative, or independent learning tasks.  I trust that some students will memorize, some will discover, and some will complete activities which are a hybrid of both.

What I do not want is to force all students to memorize.  Are there some people who loved mad minutes?  Sure.  Are there some students who learn best through discovery? Also yes.  To force every student to learn the same way is alienating some.

This is why the petition is causing alarm to me.  They want a culture where the individuality of the student, the teacher, and the lesson is abolished.

There are lots of pictures out there around how horrible the new math worksheets are, or how horrible the lessons are, but I want to remind you that the "how" part is up to the teacher not the government. Also, we should be aware that the context, in which the photo is taken, most likely is lost in the photo.

The problem is that not everyone completes addition, subtraction, multiplication, and division the same.  There are algorithmic ways, and many mental strategies.  It is ludicrous that a child should be told "Don't do it the way you understand, you must memorize another way".  People can solve "82-19" multiple ways. Does this mean that one way should be norm? How you solved that problem should be the exact way the next person does?

At the root of the new math curriculum is simply "Differentiated Instruction".  Each student is taught using more than just pencil and paper, but also tying into their passions and interests.  Which do you want for your child?  To be formed into a clone, or to be allowed to blossom into their own character?

Lastly, here is a link to what the new math curriculum looks like in my class.  Let me know if you have a problem with me allowing students to solve the same problems, in different fashions.

http://realteachingmeansreallearning.blogspot.ca/2014/01/math-in-new-setting.html

Larger shoes makes your child smarter!

Yes that is right, the larger the shoe of the student the better the child is at math.

Of course you are asking, where is your proof?

Well, I tested students in a K-12 School on basic math skills.  I then ranked them according to shoe size, and I noticed that the larger the shoe, the better the score...on average of course.


If you buy this research, then I have to inform you it is bogus, however if you knew right away there were some critical flaws then I invite you to read on.




See there are more variables at play then simply shoe size.  Age, years in school, gender, socio-economic status, language, etc are just some of the other variables.  However critics of new math are using this same logic above to make claims that the new curriculum is making our students less smart.

See, PISA is a test administered every 4 years and since the last test marks have dropped by 6%.  First, there is a problem with using PISA  and next a lot has changed in our Country, schools, and communities then simply math instruction.

Should we ignore every other variable and pick one out of a hat and attribute this change to it?  If so, then we can also prove that shoe size is linked to math scores.  However we need to realize that in the last 4 years,

• Class sizes have increased
• Immigration population has increased
• English Language learners population has increased
• Education Funding has been reduced.
• Special education projects, such as AISI in Alberta, has gone to 0
• Our culture has changed

This is to name a few.  Lastly, if they want to blame the new math curriculum, because it doesn't "teach the basics", you might want to know that the students who wrote the last PISA test.......were taught the basics under the old math curriculum.

Case for the new math curriculum

I have seen many pictures, articles, and petitions on why the new math needs to leave our schools.  Here is a quick explanation, and "Myths around the new math curriculum".

First, I want to ask you to determine what is

82-19


Take a moment and complete it.  Don't worry there is no test, just please don't use a calculator.


The answer is 63.  Now did you:

1) Borrow one from the 8 to get 7(12)-19, then say the ones are 3 and then 7-1 is 6, so the answer is 63?

2) Did you add 1 to 19 to get 20, then added 60 to get 80, then added 2.  Finally, added 1+60+2 to get 63?

3) Did subtract 20 from 82 to get 62, then added 1 to get 63?

4)Did you do it a different way?

Finally, which way is the best way?  Which way should your child learn?

If you answered "NUMBER 1 MUST BE THE WAY TO DO IT" you are in favor of the old math curriculum.

If you answered "Number 1,2,3, or 4 is a way to do it" then you are in favor of the new math curriculum.

Myth: Discovery Math is a mandatory strategy to be used in K-12 curriculum.
Fact: "Discovery" or any synonym, cannot be found anywhere in the curriculum at all.  The government tells the teachers WHAT to teach, but not HOW to teach.

Myth: The teachers are simply no longer teaching children.
Fact: The teachers are not teaching each child the same.  Differentiated instruction is now part of the classroom. Students A, and B may be taught differently; one with manipulatives, one with without, based on the needs of the child.

Myth:Children don't need basic math facts.
Fact: Basic math facts are part of the curriculum.

Myth: Students are becoming dumber.
Fact: While the PISA score has dropped 2%, the students who wrote the last PISA test were taught in the old curriculum.  Therefore, if you think this is a problem you should be advocating for the new math.

Myth: Teachers hate the new math.
Fact: Teachers have the choice and autonomy to teach however they want, and therefore some extremely creative and innovative things are occurring in classrooms.

Lastly, if your child comes home with a different way of completing math than you were taught, then ask them to explain how they are solving the problem.  Lets not forget that there is not only ONE way to solve a problem.