Qualitative Growth

QUALITATIVE GROWTH OVERVIEW
While Algebra II is a highly quantitative subject, I regularly assess student understanding through qualitative writing assignments. Analytical writing place an emphasis on higher order thinking, as students are challenged to write with clarity and precision. I assign qualitative writing assignments because through writing, students internalize and communicate their learning. Through their writing, students define what they have learned, draw connections between mathematical concepts, and propose various applications. By writing about Algebra II, students increase their retention and mastery of Algebra II topics, and also practice the college-level skill of explanatory writing. 

Please scroll down or click on the table of contents below to learn more about how my students achieved quantitative, dramatic academic growth on the statistics and probability unit of our Algebra II Curriculum.
​
TABLE OF CONTENTS
Beginning-of-Unit Writing Assignment
End-of-Unit Writing Assessment
Teacher Reflection

Student Writing Samples: Beginning-of-Unit
BEGINNING-OF-UNIT WRITING ASSIGNMENT OVERVIEW
​Beginning-of-unit writing assignments are particularly important in Algebra II, as Algebra II topics build off of Algebra I, so I need to gain a deeper understanding of my students' prior learning. As I review the diagnostic writing assessments, I categorize each unit's concepts into skills my students have already mastered, skills my students have misconceptions about, and concepts my students have no exposure to. In my curricular plans, I do a spiral review of mastered concepts to explicitly address common misconceptions, and explicitly teach new concepts.

Below please find the diagnostic writing assignment give at the start of our unit on probability and statistics. I provided simple directions to this writing assignment, as I only posed two requirements. First, that students write in complete sentences, thereby practicing proper writing skills. Second, that students write "I don't know" if they know nothing about the concept, so that I can distinguish lucky guesses from actual knowledge.
BEGINNING-OF-UNIT WRITING ASSIGNMENT: STUDENT WORK
Below please find examples of student work from the beginning-of-unit writing assignment on probability and statistics. I selected writing samples from three students, who have varying levels of Algebra II mastery. Student #1 has a 96% mastery of all past Algebra II units, while Student #2 has a 71% mastery average, and Student #3 has an 87% mastery average. At the end of each writing sample is the rubric I used to rate each students' prior understanding of probability and statistics. Since this is a diagnostic assessment, I used the rubric for instructional planning purposes only, and students were not graded for the accuracy of their answers.

End-of-Unit Writing Assessment
END-OF-UNIT WRITING ASSESSMENT OVERVIEW
At the end of our fourth week in the probability and statistics unit, my students completed an end-of-unit writing assessment. Students had 20 minutes to write informatively and analytically about the significance of statistics and probability, counting principles, single event probability, multiple event probability, and conditional probability. I used the same prompts for the beginning and end-of-unit writing assessments, so that I could measure qualitative growth on the same topics. In addition, this writing assessment was paired with a traditional multiple-choice and short answer summative assessment, in order to assess student understanding through multiple opportunities and formats. Below please find the writing prompt and rubric given to all students. Before students began writing, we first discussed the prompt and rubric, so that the assessment expectations were clear. Students were expected to provide a definition and example for each question, and compare terms where prompted to do so.
END-OF-UNIT WRITING ASSESSMENT: STUDENT WORK
Below please find examples of student work from the end-of-unit writing assessment on probability and statistics. I selected writing samples from the same three students showcased for the beginning-of-unit writing assignment to showcase individual student growth. At the end of each writing sample is the rubric I used to rate each students' prior understanding of probability and statistics. I used the same rubric as I did on the beginning-of-unit assessment, so that I could directly compare the two scores and evaluate qualitative growth. However, unlike the beginning-of-unit assignment which was graded only for completion, the end-of-unit writing assessment was graded for accuracy, as students were explicitly taught the concepts covered on the assessment.

Teacher Reflection
My students' qualitative growth reflects the depth of their learning. Therefore it is important for me to analyze their qualitative growth, strategically adjust curricular planning according to their growth, and explicitly teach my students how to gain a qualitative understanding of mathematics. At the beginning of each unit, my students take a diagnostic assessment in which they write what they know, and what they think they know, about various concepts in the upcoming unit. At the end of each unit, my students take a summative assessment in which they write about what they have learned during the unit. A comparison of my students' diagnostic and summative writing assessments showcases their qualitative growth over the course of a unit.