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

Madden 14 and Calculus

Recently I was playing Madden 14 with a friend on my XBOX 360 when he asked me

Dave, does the wind make that much of a difference when I punt the ball?  If so, should I change my angle a lot, or a little?

I replied with "It would change your angle, but by how much I don't know".  This question also sparked my most recent calculus optimization problem.

I asked the students in my class

If a football punter is kicking into the wind, should he/she worry about the angle they kick at?

Also showed this video

What came of this was a great 10 minute  discussion around questions such as

• How windy is it?
• How much should the angle change by before we worry about it?
• How fast does the ball move?

After doing some "googling" we decided to work on the following problem

If a punter can kick a ball at  40 kph, and there is a head wind of 20kph, what angle should the punter kick it at so the ball travels the farthest distance?

Here is a possible solution: (Yes I do realize we ignored air resistance, as I said I assumed Madden 14 did the same)

When you kick a ball there are vertical and horizontal components and we determined the following, starting at acceleration and integrating, with respect to time.(Using h=horizontal, v=vertical)

We then discussed physics, that if I kick a ball with velocity 40 at an angle of theta, then the vertical velocity is 40sin(theta), and horizontal velocity is 40cos(theta), as well as initial distances were 0, and subtracting 20 off the horizontal velocity due to the wind, and so the formulas become

Now, we realized we have two variables in the equation we are optimizing (d_h(t)) and so we needed a way to relate the angle and time.  Knowing at the top of the kick the vertical velocity would be 0, and that the total time in the air would simply be double this value we get the total time to be: (setting v_h(t)=0, then multiplying by 2)

Now we substituted this into the horizontal distance equation, and took derivative (knowing that the derivative equals 0 at a max), and solved for theta

I allowed my students to solve this last equation graphically to determine when it equaled 0.  

We got an angle of 32 degrees.

We then discussed how easy it would be to simply make the wind speed a letter, the kicker speed another letter and ultimately create a program which could do this for any experience.

I am in the process of making an app and selling it to all football teams and retiring in the next year..jokes!!

Feel free to use, tweak, comment, etc.

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.