Data, Data, Everywhere…

Continuing in my series of posts reflecting upon this past semester’s courses, I’ve decided to take a much less verbose approach for algebra 1.  More precisely, I’m following the popular maxim “a picture is worth a thousand words.”  With that, here are a set of pictures that capture aspects of my algebra 1 course this past semester as compared with outcomes achieved by students from last year taking the same course.  While there was a different approach used this year, following aspects of the common core, especially on the mathematical practices side, the content covered was essentially the same.

2011 versus 2012: Readiness Test and Final Exam

As the following table illustrates, my 2012 algebra 1 cohort’s performance lagged the 2011 cohort by six to eight-percentage points, on average.  As any teacher wonders, to what extent do these scores reflect my effort and ability as well as the effort and ability of my students?  I frankly do not know.  I do know I gave it my all both semesters.

AY11 v AY 12 RT & FE Descriptive Stats

Taking a more graphical view of the two cohorts performance on the final exam, it becomes clear that the 2011 cohort outperformed the 2012 cohort when comparing how each cohort fared on their final as compared to a readiness test given at the outset of the course.  The readiness test consisted of fifty multiple choice questions touching on many of the first semester of an algebra 1 course with a large dollop of pre-algebra / arithmetic concepts tossed in for good measure.  The final exam spanned the major concepts of a first semester of algebra 1.  An overview of my final is included at the end of this post.

Alg1 Fall Final Comparison

When comparing the two cohorts scores using ten-percent bins, both follow a somewhat normal distribution, with the 2012 cohort appearing to be shifted to the left by one bin.  In other words, if you shifted the columns for the 2012 cohort to the right one bin (e.g. 10% points), the two cohorts’ distributions would align quite nicely.  The average difference of 6-8% points between the two cohorts explains the shift.

Final Scores Using Traditional Cut Scores

Incoming Students CA Algebra 1 CST Scores

When examining outcomes between two different cohorts, it may be useful to consider the relative performance of each cohort for within cohort as well as between cohort comparisons.  As the following histogram reveals, the 2012 cohort’s incoming performance, as determined by their achievement on the Algebra 1 California Standardized Test (CST), is more highly concentrated in the far below basic range.

Granular CST Score Distribution 2

Comparing Final Exam and CA CST Distributions

Another cut at comparing outcomes between cohorts, as well as with the overall population of California students who took the algebra 1 CST in 2010, follows where the cut scores for the 2010 CST are used for the California student data, while the cut scores I use in all of my courses are used for my two cohorts.  The general shape of each distribution is similar, albeit when viewed with a high degree of tolerance.

Final Scores Using CA CST and My Cut Scores


What does all of this data tell me?  It tells me more than I likely need to know and less of what I do need to know.  However, that is the essence of data.  It is like another popular maxim “water, water, everywhere but not a drop to drink.”

Final Exam Overview

Final Exam Overview 1 Final Exam Overview 2

About Dave aka Mr. Math Teacher

Independent consultant and junior college adjunct instructor. Former secondary math teacher who taught math intervention, algebra 1, geometry, accelerated algebra 2, precalculus, honors precalculus, AP Calculus AB, and AP Statistics. Prior to teaching, I spent 25 years in high tech in engineering, marketing, sales and business development roles in the satellite communications, GPS, semiconductor, and wireless industries. I am awed by the potential in our nation's youth and I hope to instill in them the passion to improve our world at local, state, national, and global levels.
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2 Responses to Data, Data, Everywhere…

  1. Dave says:

    I have taught this for over ten years. Sections 9 and 10 should be deferred, maybe even section 8. Ratio and proportions should be emphasized in term one instead; maybe even mean, median, and mode. If I know I will have same group for full year I adjust order and depth of topics to class level.


  2. Pingback: Earning One’s Stripes As a Teacher | Reflections of a Second-career Math Teacher

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