Friday, September 4, 2015

What "this" means for Math Education???

It wasn't that long ago that Math was the subject that never changed.  We had our postulates, theorems, graphs, and our clear steps to solving equations.  The advent of the graphing calculator was about the biggest event in math education since, well, forever.  Sadly, even today some teachers still resist its use.

It seems now math is the subject in schools that doesn't stop changing.

The change may have coincided with the Common Core State Standards but that was not the push.  It started well before that but only is gaining traction in the last few years.  The change is causing educators to rethink how we teach, what we teach, the tools we use to teach and what students have the potential to do.  The change isn't just one thing but an onslaught of instructional opportunities.  An interesting piece of technology that came out a short while ago as improved to the point of being interesting is  Photo Math.
Photo Math     https://youtu.be/WvIoYUr1SWI
"Photo Math reads and solves mathematical problems by using the camera of your mobile device in real time. It makes math easy and simple by educating users how to solve math problems."  Not sure about the educating portion but it truly works.  Typed equations of almost any kind can be solved with all of their steps shown in a blink of an eye.  I tried it on a traditional Algebra 2 textbook.  It solved everything from multi-step equations to logarithms to systems of equations with 3 variables.  It solved it all.  So what does this mean for math education.  Are we to put our slide rulers away and just take a seat on the side?  Is our career in jeopardy?

The answer lies in math.  What is math truly about?  It's not about solving equations and multiplying correctly.  It is about patterns and logical reasoning.  This occurs outside everything everyone thinks is math.  It's about continuing the direction we are heading and making it stick.  Apps like Photo Math won't help solve an applied problem.  They won't help visually show why the best price point for a product is $8.57 according to a set of supply and demand equations.  They won't help analyze data or learn why higher mathematics is important to learn.

The easy solution is to ban the phone from the classroom or lock the iPad to only use a basic calculator upon entering the classroom.  The short sightedness of that is scary.  To ignore the opportunities to truly understand and enhance math through the plethora of available apps is to ignore an entire generation of students who are able to play and learn higher levels of mathematics than we dreamed possible before.  Not the math of algorithms.  The math of applications.

We live in a world where application is now easy.  Video, sound, photo are all made readily available by the same phone that makes a skill and drill problem useless.  We are entering a new playing field. It is time to take our skills-based DOK 1 and 2 style questions out of our summative assessments, place them as learning skills and formative assessments throughout a unit and focus on how to apply those same skills in a setting that means something to students.  People like Dan Meyer began the momentum several years ago and we started to listen.  Then others joined the game like Jo Boaler who decided to not just focus on tasks but on how we instruct and what we expect.  Now programs such as the Discovery Math TechBook change the way we offer instruction using a constructivist style learning with an emphasis on real applications.  We are finally seeing the combination of resources and quality instruction.
Discovery Education Math TechBook
For the first time in history technology and resources are catching up to classroom pedagogy.  It's up to us as teachers to make math instruction be what it was always meant to be.  A search for a better more efficient way to the find the solution to any problem life throws at them.


Thursday, November 6, 2014

Confessions of a constructivist/pragmatic teacher.

I did a major application today.  It is below.  

The goal was to engage the students in the topics we are trying to get them to understand (determining profits - new topic).  Of course, a simple application doesn't cut it.  The plan was small group work for 10 minutes, then every 1-2 minutes a new group would come up and "add to the problem" slowly forming the process and understanding.  Periodically I would interject and ask questions but mostly I just talked group to group 
never saying an answer was correct.  

Here are my results:

  1. The students HATED the large "real" numbers.  (my response was that they were the reality, not fake school numbers - they got past this)
  2. Period 1 did awesome - fully engaged except for 1 child who is making poor choices.  They really liked it.
  3. Period 2 did fine but their struggles indicated a lack of knowledge in the pre-steps (served as a great formative - with things I can address tomorrow)
  4. The discussions in the small groups cannot be understated.  They are the backbone to why we need to do these applications.  Priceless.
  5. I was bombarded with questions after each class - the kids wanted to know the results - To be continued into tomorrow.
  6.  NO TIME WAS LOST because this method replaced a lesson.  In fact, I would estimate time was SAVED giving more time for depth!
  7. My kids stink at problem solving.  If they are not handed the process they quit.  This in unacceptable to me.  MP #1
These applications do not always work in our content.  However, they work more than I feel we say they do simply because we are at times afraid to make that leap of faith that a lesson that is not the norm will work.  Today, was a leap of faith for me.  Not because I have never done this but the task was so rigorous for this clientele.    My class is clearly not advanced (more on the remedial side for a senior - they are not "math" kids).  
By the way:  This problem was not found - it is not in any book - I made it on my own time using Google to find numbers.  Unfortunately, what every study says in regards to quality math instruction is not what textbooks produce.  They produce what the public wants.  We need to challenge the norm and apply our math.  

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Apple Inc. sells its 16GB iPhone 5S for $649.  It costs Apple $335.00 to manufacture the iPhone including packaging, labor, freight, and warranty renewals according to a report published by UBS AG.  Apples fixed cost is in excess of $5 billion dollars.  However, they sell many more products than the iPhone.  Assume for this situation that their fixed costs are $7.4 million dollars.  The iPhone is a highly sought after phone in the SMART phone market.  The demand function is q=-3000p+5628000.
 
Given this information, use your classes know-how to help determine if Apple Inc. has priced its iPhone correctly. What should the price of the iPhone be in order for Apple to maximize its profit?.

Wednesday, July 2, 2014

Enrichment #1 - 3rd - 6th Grade (Taipei-101)

This is the first in what is hopefully a series of enrichment problems at different grade levels.  The goal is to take a problem that has potential and make is something better.  All the problems can be used at different grade levels with different expectations.

Collaboration is the key.  Post how you would edit the problem.  I will edit it as the week goes on.  The initial problem will be up for 1 day without any edits.  Be creative - think outside the box.  What would make this problem a much better problem or task?  Can we differentiate the problem to meet a broader audience?  What would make it more rigorous and meet the needs of the 21st century learner?

Taipei-101

Taipei-101 is the 2nd tallest building it the world.  The building has 101 floors averaging 22 steps per floor.  If you were to walk from the 1st floor to the top of the building, how many steps would you have to climb?

EDITS - let me know what you think...

3rd Grade:  https://drive.google.com/file/d/0B9nQxOSHG8M0Q3JGT29nR29Cdmc/edit?usp=sharing
4th Grade:  https://drive.google.com/file/d/0B9nQxOSHG8M0UW9WM0kxQ1ZUdUE/edit?usp=sharing
5th Grade:  https://drive.google.com/file/d/0B9nQxOSHG8M0cFhHVGZzdFUtQnM/edit?usp=sharing
6th Grade:  https://drive.google.com/file/d/0B9nQxOSHG8M0M0JxSllLYnRfczA/edit?usp=sharing