Third Time is the Charm…Or is it?

In my three algebra 1 classes this past month, students learned about parallel lines, perpendicular lines, and solving systems of equations using graphing, substitution, and elimination.  Of the sixteen school days available to cover these topics, we spent thirteen days on instruction, practice, and re-learning and three days taking assessments.  Six other weekdays were not available due to a teacher in-service day, Veteran’s Day, Thanksgiving, and two days of district mandated testing.

Over this period, students took the same assessment three times, with the structure, focus, wording, and sequence of the assessment the same each time and only the specific values of coefficients and constants changing in the problems.  Students took the first assessment after six days of instruction, the second assessment one week later after two more days of review, and the third two weeks after the second, with Thanksgiving and district-wide testing in between.  Students’ scores improved each time, on average, and  very much so by the third attempt, as the following figure shows.

Figure 1: Overall Student Performance Improvement Over Time

Each line in the graph represents the scores of 96 different students on successive attempts of the assessment.  While a few students scored well on the first assessment, most did not fair as well with a mean score of 36%.  This pattern repeated itself on the second attempt, as shown in the following table.  Fortunately, by the third attempt, the mean scored jumped to 62%, which while below what one might idealize, or mandate, is as much as this electrical engineer with two masters degrees and a quarter century of high-tech work experience could achieve. (see note 1)

Table 1: Performance Statistics over Three Assessments

As figure 1 shows, some students raised their scores by nearly thirty percentage points from the second to the third attempt.  Some went from receiving failing scores on the first to scores that correspond to an A on the third; one particular student, classified at an English language development level of two (ELD 2), scored a 22% initially, followed by a 66%, and finally an 86%, a phenomenal achievement, and testament to his perseverance.  Sadly, half of the class remained below a failing grade level if a score below 60% equated to an F.  In my class, however, individual assessments are graded on a modified scale as shown in the adjacent table, where an F equates to a score below 30%; students are able to retake assessments to improve their grades, if desired.  With this lower threshold, about one-quarter of my students still failed the third assessment.

Looking at the data as successive scores, one can see how each student improved in their learning over time, with more than a few improving considerably in the month.

Figure 2: Individual Student Performance Improvement Over Time

In fact, histograms of the first assessment and the third assessment clearly show a reversal in scores.

Even with this improvement, however, I still wonder what I could do better next time so even more students attain a high degree of skill.  I still continue to reflect on this data, and other data collected, and planned, to see what might be inferred to help my students improve.  If only the educational system were in the 21st century, or even the end of the 20th regarding processes, tools, and systems.  A judicious degree of process re-engineering, and ideally re-architecting education, is required immediately so teachers can focus on their students’ learning, and associated challenges in the classroom, instead of spending inordinate hours planning, designing, and creating curriculum, lessons, activities, and assessments then manually collecting, assessing, grading, entering, manipulating, and analyzing the resultant data just so they have a modicum of insight into the macro and micro trends in their classroom.

Overall, the effort to analyze this data, and write about it here, took more than several hours of my time each day this weekend; this should not be the case.  Education is in such dire need of improvement, and so few citizens understand the necessity.  One of my larger goals is to inform my community, city, state, and nation about the necessity to invest in, and revamp, public education so it succeeds in its mission to provide society with future leaders, followers, and doers of all stripes.  We have failed this great country of ours these past three to four decades, I am afraid.  For as we bicker over the latest edufad, we find ourselves stagnated in many socioeconomic strata, failing our youth by rigidly adhering to beliefs that do not yield increases in graduation rates, or national preparedness.  Instead, we churn out large percentages of students unprepared to serve in careers of nearly any sort, other than minimum wage occupations.  This corrosion erodes our national infrastructure both tangibly and intangibly.  The ways of craftwork and other trade skills needed for societies to thrive are sacrificed on the altars of redemption for past transgressions, in hopes that all might attend and graduate college.  However, in the rush to open the doors to higher education, with its commensurate high levels of personal debt à la student loans, which enrich the top 1% even more, little is done to make sure students have the most basic of academic skills mastered so they may succeed when they arrive at college.  High school teachers are too busy shepherding already ill-prepared students through the throes of adolescence, helping them to develop a glimmer of self-sufficiency, so they may continue with their studies, and yet also juggling unrealistic expectations to raise achievement levels in mandated courses where prerequisite skills are much diminished to non-existent for up to half of the students in our classrooms.  The irony is these are exactly the students I want to help most, yet with all the inefficiencies latent in an outdated education system, I am lucky to impact but a fraction of these students, as the data above show.

God help me as I continue as a first year teacher so that the pressure of this job does not crush my spirit or dampen the passion which drove me to this profession in the first place.  Like a gristmill, education can turn the most dedicated of people into so much dust to be scattered into the winds, ne’er to be seen standing tall above our eager to learn students again.  But, that is not my fate; I will triumph through this keeping the motto from my West Point class, “Courage Never Quits,” in mind.  Our country requires it.  And I will serve it dutifully until the day I breathe my last.


Note 1:  I am a member of three college honor societies to include Eta Kappa Nu (electrical engineering), Alpha Chi (top 10% of class, general academic), and Beta Gamma Sigma (business).  I mention these to highlight aspects of my bona fides as a highly educated teacher, yet one that can only achieve so much regardless of mandates, accountability measures, or other beliefs that imposing more on teachers will somehow boost student achievement.


About Dave aka Mr. Math Teacher

Secondary math teacher teaching math intervention, algebra 1, honors precalculus, and AP Calculus AB. 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 Third Time is the Charm…Or is it?

  1. Jack says:

    I enjoyed reading your post. You bring a very pragmatic and studied approach to your teaching. By posting your data and sharing your analysis, you invite good discussion about the nature of evidence in improving teaching.

    I read the data in two ways: a) the more you review the format of an assessment, the better students appear to do. b) while keeping the format of the test constant helps make for a cleaner analysis, it also limits what you can say about what students might be actually “learning: because the degreee of transfer is so close. I know you are aware of these, but I am stating these as shared assumptions. Forgive me if I am a “master of the obvious.”

    What I wonder about is what is how you interpreted the data each time you gave the asseessment. What did you do differently when you after you saw the first scores? the second scores? Any mid-course corrections? Any items or groups of items that you saw needed more bolstering? I realize that you have already done so much analysis as it is, so it would be completely understandable if time did not allow for formative analyses. I guess i am speaking to the larger issue of data management and usage in teaching; that it points us to where the problems might be, but not necessarily what to do about them instructionally. I am not sure either. But you are right, no teacher should have to be doing this from scratch!

    Keep going, Dave!


    • Thanks for your comments, Jack. Glad you highlighted the distinction in the data, which results in a double-edged sword effect. As I graded the assessments, I could not help but wonder how students would do if I varied the structure, format, and wording of the questions. My instinct is scores would suffer in a statistically significant way. What portion of the drop is due to reduced conceptual understanding versus language challenges versus general familiarity (test anxiety) is not clear, although I believe these effects could be measured with more forethought and time planning the assessments.

      Re: your questions, I retaught everything after each assessment, initially reviewing each question from the assessment, then expanding to alternate representations such as tree diagrams and process flow charts to connect topics together as well as highlight differing dimensions of a concept. Those topics where student scores were lower, on average, received greater emphasis and time. I have data that shows average performance per question over the three assessments, which I will analyze at some point.

      And your comment on data management and usage is spot on. I have the seed of a post planned titled “Data, data, everywhere…” Just need some more time, like 24 more hours per day!



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