Thursday, November 20, 2014

Why not PEMDAS?

I know this is ahead of the game however it is coming up and I was hoping to get a jump start on rethinking the process.

A teacher asked me if it was OK to teach order of operations using PEMDAS.  My very cautious and then ask yourself why...

PEMDAS is inherently wrong.  It actually teaches students the wrong order of operations.  The correct order is:

1.  Parentheses
2.  Exponents & Radicals
3.  Multiplication & Division
4.  Addition & Subtraction

This may seem similar but acknowledging that multiplication and division are inverse operations as are addition and subtraction are vital to true understanding later on.  We want them to understand what they are doing - not just follow a "rule."  

I could go on but I would rather you hear it from others.  

Here are some great Teaching Videos - they will help improve instruction!

Tuesday, November 18, 2014

How are you enhancing instruction with Math Practice #1?

Comment below on how you are encouraging students to:
  • Explain the problem
  • Organize information
  • Persevere while working through rigorous situations
  • Monitor their work - are they on the right track
  • Change their plan if things are not working out
  • Ask themselves, "does this make sense?"
  • Check their work for correctness
  • Evaluate what worked - what could we have done better?

Below are some questions that teachers can prompt students with to encourage Math Practice #1.
  • How would you describe the problem in your own words?
  • What information do you have? 
  • What do you need to find out?
  • What strategies are you going to use?
  • Can you think of another method that might have worked?
  • Can you explain what you have done so far?  
  • What else is there to do?

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.  


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?