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 answer...be 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?

Wednesday, February 19, 2014

RTI Help - Struggling student - lots of interventions given

I am hoping you can help me brainstorm some things for a student.

Even though we do not need to give the winter MComp and MCap, I did it for this student.  Her computation has gotten better, but is still in the below average range.  She is practicing math flash cards (the intervention ones targeting certain strategies) and has a set for home.  She is on Xtramath.  

But her math applications and understanding is in the critical range.  I have her working with a parent helper 3 times a week one-on-one.  She is very unfocused unless she works with someone to keep  her on task, and doesn't pay attention to lessons...hence the lack of understanding.  I check in with her for each lesson, and use the reteaching pages or modify her work.

Do you have any other intervention strategies I can try?  There is not one area I would say is a strength or weakness for her (i.e. geometry, patterns, computation, etc.).  She is just LOW!!!

--------

Additional information:  

She is/has not been identified as special education and she might get the strategies for the day, if you are sitting there, but doesn't retain well.

This is one of your colleagues looking for help.  Anything you can provide would be beneficial.



Sunday, February 16, 2014

Highest Effect Sizes in the Math Classroom

As teachers we always believe we know what is right for students in the classroom.  We work hard, practice our skill, and care about kids.  However, if you take the time to look from classroom it is apparent we go about our skill in different ways.  This is fine for the most part but as more studies are done, and the results repeat themselves it becomes obvious there is a science to our art called education.  The studies have been done irregardless of grade level and there is some background to understand the numbers.

     - An effect size greater than 0.4 has a positive effect.
     - An effect size between 0.5 - 0.6..."your crazy not to do it."
     - and an effect size of 0.7 needs to beg the question "why are you not doing this already."

As it turns out, the teacher staple that smaller class sizes help instruction holds no merit.  Good teachers succeed in any class size.  The statistical effect for class sizeis 0.27.  This correlates to showing no positive effect at all.  Sorry...

On the contrary, if you would like to start off simple get your kids up and around.  The simple act of physical movement shows an effect size of 0.54 (your crazy not to do it).  The trick is, how can we structure the time with our students that gets them up and moving?

The three highest effect sizes should come as little to no surprise if you have been engaging in professional development.  

  1. Spaced vs. Mass Practice (0.71)  -  Mass practice is all students do 1 - ???.  Spaced is differentiated.  Some students do #1, ...  Other students do a different set or an entirely different practice depending on their level of understanding or areas of interest.  By doing this practice it opens the door to knowing your students well enough to differentiate.  
  2. Assessment as a Process of Formative Feedback (0.75) - Everyone knows what formative assessment is.  However, lots of teachers (math in particular) are still stuck on the summative assessment being the be all end all of student learning.  Challenge yourself to consider when learning is completed and what our job is as teachers?  If my sole job is to rate/rank my students then I am drastically selling short my abilities.  We are hired to inspire learning and engage students in a manner that causes them to dig deeper and do things they don't always feel comfortable doing.  Something called learning.  Formative assessment gives me the information necessary to know exactly where my students are at and determine the instruction necessary to get them to where we need them to be.
  3. Classroom Discourse (0.82) - Getting a discussion going in your classroom about the topic you are working on has an effect size higher than the category labeled "why are you not doing this already."  To often as math teachers we feel teaching is us talking.  In reality, the more we talk the less they learn.  Clearly there are those topics we need to describe.  The challenge is how you can get a deep discussion going about the topic.  These discussions, if done properly by letting the students do the talking will greatly increase the depth of your topic while also performing a large degree of the formative assessment needed to understand where your students are at.
The basic gist that everyone needs to hear is simple.  Do not "try" these classroom strategies.  DO THEM.  The better we do them the higher the effect.
 

Monday, February 3, 2014

Thoughts on the SMARTER Balanced Practice Questions...

What did you think?  Are your students going to be well prepared?  Are there things we are doing well?  Things we need to improve upon?

This is a great forum to make suggestions, comments or compliments to what we are currently doing since it is only known within the school district.  Click on the comment link below.  You may need to register (bottom right of the page).  

Monday, January 27, 2014

Call for quality intervention ideas:

Your colleagues need your help.  There are no great researched based interventions except for good quality instruction.  However, we have students who need assistance.  

During the March PD, for those in grades 3-5 one option of PD is help with the blue box for intervention within EnVision.  This is a step in the right direction but will not solve all ills and in reality...is just more practice problems.  It does not fix the problem...only good instruction does.  

Below are the scoring subsets for the AIMSweb math assessments.  If you have suggestions on how to intervene through quality instructional ideas please comment on this blog post.

Kindergarten
Number Identification
Oral Counting - measure requires students to orally count starting from 1 as high as they can 

Missing Number - what is the missing number in a set of numbers
Quantity Discrimination - identify the bigger number from a pair of numbers


1st Grade

Number Identification
Oral Counting
Missing Number
Quantity Discrimination
M-COMP - math computation - see already setup process at M-COMP Interventions

2nd - 5th Grade
M-COMP - math computation - see already setup process at M-COMP Interventions
M-CAP - hardest to intervene on.  This is all about applying the math.  Students need thinking skills.  See the Mathematical Thinking pieces and/or Writing to Learn for some help.