Tag Archives: statistics

The Election Pollsters Still Got It Right

election-forecastThere has been a great deal of Monday morning quarterbacking about how the 2016 Presidential election polls “got it all wrong.” Radio pundits like KFI’s John and Ken have been claiming that pollsters obviously don’t know what they are doing. There are three points to consider here.

1) Did the polls get it wrong?
2) Did the pollsters do something wrong?
3) What good math activity can we generate from all this fuss?

Here are some direct answers with, hopefully, simple, clarifying mathematical (not political) explanations.

The Polls Got It Right
The poll results were within the expected margin of error. In fact, four days before the election, Harry Enten of FiveThirtyEight wrote “Clinton’s lead is small enough that it wouldn’t take more than a normal amount of polling error to wipe the lead out and leave Trump the winner of the national popular vote.” In the end, Clinton still won the popular vote, by approximately 1.5% compared to the 3.3% predicated the day before the election, well within the normal margin of error. Gallup shows that, historically, the polls have been within 2%, on average, of the actual results, and within 1% half of the time, with the victories of Reagan in 1980 and Truman in 1948 being the most notable anomalies.

In fact, Nate Silver of FiveThirtyEight noted the day after the election that a 1% swing in Clinton’s favor across all states would have flipped the Electoral College tally.

Further support that the polls got it right comes from the understanding of probability. Clinton was given a 71% chance of winning on the eve of the election. That means that Trump had a slighter better chance of winning the election than he had of flipping heads on two consecutive tosses of a coin. When heads occurs twice when tossing a coin, should we all protest that statistics and polling are unreliable? This is why Nate Silver claims that the polls missed, but he did not say that they failed.

The Pollsters Did It Right
People have been willing to give more grace to the mathematics than to the mathematicians. Pollsters (those creating the polls, not the folks on the phone) have taken a great deal of heat for poor sampling, but these pollsters have been vindicated voter turnout numbers, because the pollsters surveyed registered voters, not guaranteed voters.

PBS‘s Michael Reagan writes that the data on actual casted votes reveals that Clinton had 2 million fewer voters than Obama did in 2012, while Trump had a slight uptick over Mitt Romney. Had voter participation been similar to the 2012 election, America would have had a different 2016 result.

Liberal filmmaker Michael Moore was extremely concerned just before the election about the lack of enthusiasm for Clinton versus the overwhelming passionate support for Trump. His concern turned out to be warranted.

A Good Math Activity: Secretary Clinton Attempts A Field Goal Kick
Given the information below from FiveThirtyEight, at what distance (in yards) would a field goal kicker in 2014 have the same chance of success as Secretary Clinton in the election of 2016.

election-percentage

Election Kickers.png

Spoiler alert: Approximately 48 yards.

Fortunately, if an NFL kicker misses a field goal attempt from just inside the 50 yard line, I still have faith in statistics and statisticians… and America.

Recap: CA Mathematics Network Forum, 2015

Logo CAMNThe 2015 California Mathematics Network is a community of math education leaders from twelve regions in the State. This Conference focused on the NCTM publication Principles to Actions. The book is an amazing resource that discusses what needs to be done in math classes, and what actions need to be taken by teachers and administrators alike to make that happen. It should be read by anyone who has an investment in math education. A good primer is p 5, 10, & 109-116, or check out the Executive Summary. Following are some terrific ideas from the conference speakers on how to implement these Principles.


The Best of the Common Core Closes the Achievement Gap — Dr. Lee Stiff, former NCTM President

  • Lee StiffThe Achievement Gap can best be narrowed through Effective Teaching of the CCSSM Practices.
  • Where do these effective teachers come from? … “from our good work!” (as instructional leaders)
  • The primary purpose of Principles to Actions is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards.
  • NCTM Guiding Principles
    (from Principles to Action)
    Teaching and Learning
    Access and Equity
    Curriculum
    Tools and Technology
    Assessment
    Professionalism
  • NCTM Teaching Practices
    (from Principles to Action)
    1. Establish mathematics goals to focus learning.
    2. Implement tasks that promote reasoning and problem solving.
    3. Use and connect mathematical representations.
    4. Facilitate meaningful mathematical discourse.
    5. Pose purposeful questions.
    6. Build procedural fluency from conceptual understanding.

    7. Support productive struggle in learning mathematics.
    8. Elicit and use evidence of student thinking.
  • Student placement and support should be based on DATA not DEMOGRAPHICS.
  • We create the gap!!
    Screen Shot 2015-05-21 at 10.50.39 PM

Teaching Practices that Support Student Learning of Mathematics — Peg Smith, University of Pittsburgh

Peg Smith PicDr. Smith had us read through a well-known task, the Hexagon Train, and then analyzed it through the lens of each of the Teaching & Learning Principles in Principles to Actions (Summarized Below):

Hexgon Train

 

 

1. goals
2. tasks
3. representations
4. discourse
5. purposeful questions
6. procedural fluency

7. productive struggle
8. evidence of student thinking

  • It’s all about the task. Choosing the task really matters.
  • “What you put in front of the students frames their opportunity to learn the mathematics.”
  • Have your questions “locked and loaded,” and your responses “in your back pocket.”
  • It’s time to break out of the “postage stamp” lesson plan, (the homework, & examples fit in a little box), and write analytical, anticipatory lesson plans. (This one needs a cute name, too)
  • It’s difficult for teachers to use a high level task. It’s even more difficult for them to use it well.
  • Decrease the complexity of language without decreasing the cognitive demand of the task.
  • “Never Say Anything That a Kid Can Say.” (Article)
  • Writing “SWBT” objectives limit what students learn. Is the goal really to be able to find the length of the hypotenuse or to understand the relationship of the areas of the squares formed by the three sides of a right triangle?
  • Dr. Smith is the co-author of 5 Practices for Orchestrating Productive Discourse in Mathematics Class.
  • Dr. Smith shared this Principles to Action Tool Kit:

Dr. Smith then asked us to restructure a standard series of textbook questions into a more robust task. The conversation at my table was very rich. It was a briefer version of a lesson makeover, and would be an awesome PD activity.


Smarter Balance Update — Mary Tribbey & Jane Liang

This slide makes two BIG statements:

  1. The Red Dot () is along a timeline from the start of the assessment initiative to full implementation. We are still in the early stages of perfecting it.
  2. There do exist Interim Assessments that few schools (including mine) are using to check for student readiness.

Screen Shot 2015-05-19 at 9.52.34 AM

This day was the first I heard of the scaled score for the reporting of the test. It appears that there will now be some reporting on the standards as well as the claims, after all.

Screen Shot 2015-05-19 at 9.53.08 AM

 


Equity-Based Teaching Practices — Karen Mayfield-Ingram, EQUALS Program, UC Berkeley

  1. Mayfield PicGoing Deep with Mathematics
  2. Leveraging Multiple Mathematical Competencies
  3. Affirming Mathematics Learner’s Identity (multiple access points)
  4. Challenging Spaces of Marginality (diminish status within class)
  5. Drawing on Multiple Resources of Knowledge (including culture and experience)

Lesson: “He Was Suspended for Being Mexican” (excerpt from The Impact of Identify in K-8 mathematics Learning and Teaching) This was an anecdote of a teacher who took a students statement, “He was suspended for being Mexican,” and turned into a statistics lesson in which the students had to analyze data to determine if the school policies truly were racist or not. While we can’t tie every topic into a student-oriented context, I think it is a powerful idea that should be done more often.


Technology & Computation — Joe Fielder, Cal State Bakersfield

  • Pic FeidlerAll computation outside the classroom is done by a machine.
  • Machine computation is mostly done with spreadsheets.
  • Hand calculations are only done in math classes. (referenced TED talk by Conrad Wolfram)
  • If we are going to teach students mathematics that is relevant beyond the college entrance exam, we need to give explicit instruction on the tools of computation.
  • TI InspireDr. Fiedler is currently working with the college board to change the SAT to reflect computations done by hand-held graphing calculators.
  • The introduction of the first scientific calculator 1972 was controversial, because teachers were worried that students would no longer be able to use tables.
  • “Students are idle, indifferent, irresponsible in response to absurd work. This is a rational response!”
  • There is no change without a loss. If there is no loss, there is no change. Similarly, literacy diminished the need for memory, but we still teach students to read and write.
  • Yes, part of education’s job is to pass on old knowledge, but it’s not the entire job. It’s time to get with the times.

BREAKOUT: Exploring the Common Core Statistics & Probability Standards — Jim Short, Ventura County Office of Ed

  • Pic Jim Short“Statistics means never having to say your certain.” The irony is that this is what makes math teachers uncomfortable with stats.
  • Teachers are avoiding the teaching of statistics, but the ponderous of the Performance Tasks on State Tests are based on Statistics and Data Analysis.
  • Statistics is more important than Calculus. (referenced TED talk by Benjamin Arnold)
  • From the GAISE Report,
    4 Components of Statistical Problem Solving
    I.   Formulate Questions
    II.  Collect Data
    III. Analyze Data
    IV. Interpret Results
  • You aren’t teaching statistics unless you are teaching modeling.Here are some great tools that we used in the session to generate statistical displays in a spreadsheet:
    g(math) {Google Sheets add-ons}
    Geogebra {box-n-whisker}

    Core Math Tools {NCTM}
    =norminv(rand(), means.d.)” {Excel Macro for generating a set of normalized data}
    Stats vs Prob

BREAKOUT: The Right Answer is Not Enough — Ivan Cheng, Cal State Northridge

  • PIc Ivan ChengWhat the teacher assesses is what the students think that the teacher values.
  • How is “doing math” defined differently under Common Core versus NCLB? How you answer that questions, determines how you teach and assess under the new standards.
  • After a test, if the teacher can’t state what the student misconceptions are, then the teacher needs to do some more digging.
  • Teachers should use assessment questions that intentionally reveal misconceptions.
  • Why “a” student missed a question is as important as which question they missed.
  • Clicking Smarter Balanced ASSESSMENTS (in SBAC navigation bar) will take you to documents that map targets to standards.
  • “Think about getting through to the kids instead of getting through the textbook.”
  • This sample question demonstrated why the students have issues with the new assessments. The students instantly think that the answer is “20,” because x = 20. Since 20 is not a given situation, they often choose “D: Neither.”

Inequality Sample


My Big Take-Aways

  • The achievement gap can be closed by the effective teaching of the Math Practices.
  • It’s all about the task!!
  • Two Big Words kept coming up: Meaningful & Equity. Equity is achieved by giving all students access to meaningful, high-level mathematics.
  • Get with the times, and start using technology in order to move from computation to deeper, higher mathematics.
  • There are some amazing tools available for Statistics tasks. This is a pervasive topic that needs serious attention and support.
  • Our assessments communicate what we value. The assessments are changing, because our goals are changing. Therefore, we teachers must change our values and practices.
  • We should all read Principles to Action.
  • The Region 10 Team is an amazing group of intelligent, passionate people. I look forward to seeing how we will put all these principles into action.

Region 10

Stats Are Like A Fist Full Of Worms

wormsAlgebra is like an ox. It does a lot of work for us, obeys our commands and remains very predictable.

Geometry is like a puppy. It’s fun to play with, doesn’t ask for anything other than your attention, and doesn’t promise anything other than that in return.

Calculus is like a horse. It is gorgeous to watch when it runs, exhilarating to ride and takes us places we have never been before.

Statistics are like a fist full of worms. They wiggle around and are hard to get a hold of. They live underground, so you always have to dig deep to find them. Once you get one, you don’t know what to do with it other than stick it on a hook and cast it out into the ocean in hopes that it brings you back something useful.