Reading through the 2007 GAISE report, I’ve found some very cool teaching ideas and knowledge I didn’t know. My first observation was that the report was bland and teaching elementary concepts, but as I progressed through the report I picked up on ideas to help incorporate in my own middle school and college classroom. The report used some methods that I have used in my classes with the MAD to help students understand variation, but later used a Quadrant Count Ratio(QCR) to help students understand strength of a relationship. This quadrant count directly relates to the covariance between two data sets, which is of course used in Pearson’s R. I like the idea of using this to help students understand how Pearson’s R is either positive or negative relative to the relationship of the trend line. I don’t see a page devoted to the QCR on wiki, but it does have some statistical usefulness (Holmes 2001). If you have not heard of this method for relationship, it relates to what you see in many textbooks for an explation of the covariance between two random variables. The scatter plot is divided into 4 quadrants based off of the mean for both variables. The number of data points in quadrants that represent values that are both above the mean and both below the mean are added together and subtracted by the number of points in the 1st and 3rd quadrnants, then divided by the total observations to produce a number between 1 and 1. The larger the number, the strong the relationship is positively. It’s seem to be a mix between a parametric and nonparametric estimate on strength of a relationship. It’s weakness lies in the fact that the values may lie anywhere within a quadrant and not particularly related to the linear relationship of the pairs of points. It would be interesting to see how this relationship holds in extreme cases and any effectiveness of using the median instead of the mean to create quadrants.

Search It!

Recent Entries
 2014 AP Stat Reading: Best Practices Presentation
 Principles to Actions: Ensuring Mathematical Success for All
 Qualitative and Quantitative Research Validity
 Change of Angle… Slightly
 Evolving Methods or Emergent Design
 Pilot Test
 Trying on a Ethonograpy and Grounded Theory Lense
 Formative Assessment
 Trying on a Phenomenology and Narrative Lens
 The Beginning of a New Research Era (Qualitative Research)

Links
 AMSTAT Community
 Dataists
 Gelman's Statistical Blog (Columbia University)
 Junk Charts
 mathblog.com
 Messy Matters
 OddHead Blog
 Q/A Statistics
 Rational Math Education Blog
 Scientific Blog
 Sports Statistics Blog
 Statistical Q/A
 Statistics and Probability Blog
 The Log Cabin
 UK Data Blog
 Unapologetic Mathematician