Quantitative
Academic gains are the ultimate door opener – they are the foundation of a truly transformational teacher. Students make dramatic levels of academic growth (that is measurable and rigorous). Families know the level of rigor necessary for college and career readiness in the 21st century.
Introduction
My students took a diagnostic ACT at the beginning of the school year. A benchmark was administered at the end of each quarter to track progress and growth. The ACT breaks down questions into three categories: Preparing for Higher Math, Integrating Essential Skills, and Modeling. A more detailed breakdown of students’ knowledge beyond these categories is not readily available, but the questions students can and cannot answer provide insight into their mastery of core mathematical concepts. Students receive immediate feedback on their ACT scores, and I push students to reflect on their own growth regularly. The same topics appear on the ACT in different ways, and my teaching focused on helping students identify gaps in their content knowledge themselves.
The math section of the ACT is used for state and federal accountability in the Commonwealth of Kentucky. My school has underperformed expectations each year and has yet to meet the goals laid out in the school improvement plan. Last year, juniors at the school scored an average of 16.1 on the math portion. My district's goal is for this average to improve to 17.5 by March of this year, but I don't feel like that goal is ambitious enough. I believe that my students can improve their average to 21 in that time and have organized my curriculum to push students to achieve dramatic academic growth.
ACT OVerview
The ACT is a nationally recognized college entrance exam. There are four tests included: English, Math, Reading, and Science. The math portion of the test is used for state accountability in Kentucky, and it consists of 60 increasingly difficult multiple choice problems. The number of questions students answer correctly is converted to a scale score ranging from 0 to 36. In the Commonwealth of Kentucky, scores are delineated as Novice (0-15), Apprentice (16-18), Proficient (19-26), or Distinguished (27-36). While it varies from year to year, students must correctly answer between 25 and 27 questions of 60 to achieve proficiency.
Students take the full test in March of their junior year, but they were assessed multiple times throughout the year in preparation. Students took released exams, providing tangible progress toward ACT mastery. Students were made aware of their scores and set goals for themselves for the next assessment period. The ACT lacks tools for analyzing student data in instructionally beneficial ways, so I relied on student-led reflections to monitor less visible indicators of growth. Students reflected on and identified gaps in their knowledge in order to develop actionable plans for preparing for the final test.
More information can be found on the ACT website, found at https://www.act.org/content/act/en.html
Sample ACT Math Questions
The ACT releases full exams along with keys and score charts from past years. The exam above is taken from the 2014-2015 test. This is the sample released test that students took in December.
The math topics tested on the ACT are relatively simple as high school math standards included don't have much depth. As a result, the questions focus on testing these concepts in unique and challenging ways. The underlying mathematical principles are not what students struggle with: operations and substitution are not complex topics for high school students, but the ACT obfuscates them by asking questions in bizarre ways. Question #2 above is an example of how these relatively simple concepts are made into a challenge. The first section of the test consists mostly of 8th grade and pre-algebra content. When students miss a question in the first twenty problems, the issue is usually not in the calculation. They misunderstand the problems, and their responses give me the insight necessary to plan a curriculum that addresses my students’ significant literacy needs.
ACT preparation in my classroom focuses on meeting these literacy needs. I spent a great deal of attention on the standards the ACT have identified as essential for the bands of scores I am pushing my students to. Students generally work on at least one of these standards every day. This helps my students grow more familiar with the way questions are asked on the ACT as well as practice skills foundational to mathematical understanding. Incorporating these standards and regularly practicing ACT questions helps students understand the rigor necessary for college and career readiness.
ACT Scores breakdown
The number of questions students get correct is converted to a scale score using the table below. Scale score requirements are adjusted year to year depending on the test, but the raw scores required for benchmark scores are fairly consistent. The ACT sets the benchmark for college readiness at 22, claiming that students who score 22 have a 50% likelihood of earning a B or better in a college algebra class. In the Commonwealth of Kentucky, the benchmark score is 19. My district’s goal is for juniors to average 17.5 on the math portion in order to close the gap with the statewide average of 18.5.
The ACT does not subtract points for incorrect answers, so students can guess on a significant number of problems. The scale scores themselves do not provide insight into which concepts students have mastered or are struggling with. It is a higher level benchmark of college readiness and not meant to be used to as formative assessment.
This is the score conversion chart included with the 2014-2015 test. The raw scores on the math exam and corresponding scale scores are highlighted.
Data and Analysis
Student score breakdown based on Kentucky benchmark scores.
I have included the score breakdown for the tests students took in the fall semester above. Students were tested at the beginning of the year (September) and the end of the semester (December). In September, only 23% of my students scored Proficient. By December, 56% of my students scored proficient or higher in comparison to the statewide proficiency rate of 36.2%. The number of students in the lowest category shrank from 38% to 7% while the number of students in the highest category grew to 5%. As a class, my students have shown a full year of typical growth in the first semester of the school year. I expect 15% of students to score Distinguished and 65% of students to score Proficient by March. This would mean that 80% of students score at or above grade level, and I anticipate that the 20% who don't will score Apprentice rather than Novice.
September data compared to December
These data represent only the first half of the school year, but they still demonstrate dramatic academic growth for a full year. An ambitious growth goal over a year on the ACT is 4 points, and this is generally what ACT tutors aim for when they work with individual students. The class average for my students grew 4.44 points from 15.35 in September to 19.79 in December. For context, the ACT says that 15 is the average score for a freshman nationwide. The average Scale Score for juniors in Kentucky is an 18.5. My classes' average was just about what would be expected for freshman in September and outpaces the average score for juniors by over a full point. My students' growth far surpasses the district’s yearlong goal of 17.5 and does so three months in advance. I expect the growth trend to continue through the official ACT in March. By the end of the year, I expect the class average to be 22, for an overall growth of 6.65 points. With this growth, I expect over 80% of students to score Proficient or higher compared to just 23% of students in September.
This table is the ACT scale scores for September and December for my students. Novice scores are highlighted red, Apprentice scores are highlighted yellow, and Proficient/Distinguished scores are highlighted in green. The table is sorted by December scores to make it easier to identify trends.
Several layers of analysis stemming from the data above support my students' dramatic academic growth at every level. Students in each cluster are showing significant growth halfway through the year. Only 6 students scored in the Novice category in December, but 5 of these students have previously scored Apprentice. The first semester focused on getting students to achieve consistent scores. Most growth was seen in the middle of the range, where many Apprentice and Novice students improved their scores to the benchmark score of 19. Of those who scored Novice or Apprentice, 25 moved to Proficient, and 16 students moved from Novice to Apprentice. At the higher end of the range, 4 students broke into Distinguished by scoring 27 or 28.
Student 45 showed exceptional growth in every aspect of the ACT and moved from a scale score of 16 in September to 28 in December. This 12-point gain was hard fought through many hours of 1-1 tutoring and additional support throughout the semester.
Student 30 made a 5 point gain from 15 to 20 in one semester, thereby scoring Proficient. This growth will continue into the spring semester, and I expect this student to score at the higher end of Proficient in March.
Students 11 and 28 represent the the average growth in my classroom. Both of these students struggled on the September ACT test, but, through my teaching and support, are approaching proficiency with scores of 18.
The way these students, and my students as a group, grew is significant. The growth in my classroom came largely from the approach taken to prepare students for the ACT. The first 20 questions of the test include simple topics asked in challenging ways, and the literacy work students did in my classroom prepared them to better understand these problems. Focusing on these problems allows me to tailor my instruction to my students’ needs. They have the underlying skills necessary to answer them, but they struggled to understand what the problems were asking in September. Their improvement on the December exam marks the impact my literacy focus has had on my students. The tables below show that far fewer students are missing these early easy questions. Average accuracy improved from 54% to 68% in just one semester.
September
December
Individual Samples of Growth
One of my frustrations with the ACT is the lack of detail the scores provide. Looking at the data in aggregate is useful for identifying trends, but it does little to explain where students are growing or not growing. To address this, I look into how students score on the first twenty questions of the test. My first semester focused on teaching students the content and the strategies they can use to answer these problems specifically. Students’ scale scores could stay the same while still showing growth where I focus my teaching. Analyzing where their scores came from provided me the insight necessary to differentiate my instruction for each students’ needs.
The slides below highlight three students at different levels of proficiency. While they each showed dramatic growth in their scores, I focus on the aspects of my teaching that prepared them for the test. Their question-by-question performance is used to provide additional understanding for how each student can be best supported, and the impact is borne out in the December exam.
The ACT serves a litmus test for students’ college readiness. I can use this assessment to open doors and broaden outcomes for my students. To maximize the impact on my student’s academic growth, I use the data I gather from these assessments to shape the instruction I deliver. Students are demonstrating dramatic levels of growth as a result. By December, 56% of my students demonstrated mastery of the topics covered on the ACT according to Kentucky’s standards. This more than quadruples my school’s prior performances on the March ACT. Only 36% of students in the Commonwealth of Kentucky score Proficient, and my students have beaten that mark by 20%. This growth is due to utilizing the data I gather in the classroom to provide rigorous and individualized work for my students. I will continue to analyze the data to reinforce the trend of immense student growth.