Case Study 1: Omar- Secondary Mathematics 2015 Graduate
Omar graduated from York College in June 2015 with a degree in Mathematics Education 7-12. While at York College, Omar participated in York’s Mathematics and Science Teacher (MaST) Scholars Program, funded through a grant from the National Science Foundation (NSF). As a MaST Scholar, Omar participated in internships, fieldwork, and student teaching in the Peer Enabled Restructured Classroom (PERC) Program. This NSF-funded program, developed through a collaboration among CUNY faculty and NYCDOE teachers, implements a research-based, student-centered instructional model to improve STEM performance and college-readiness. In interviews, Omar credited these experiences at York with developing his teaching philosophy and instructional practices.
Omar is completing his New York State initial certification in Secondary Mathematics and is working on his Masters Degree in Secondary Mathematics, which he will complete in June 2018. In interviews, Omar claimed that he had already learned at York what he was now expected to learn in his Masters Degree.
Omar is in his third year of teaching but his first year at his current school. He spent his first two years teaching at a private school and was offered the position of mathematics department chair at that school. Instead, Omar accepted an offer to teach mathematics and chair the mathematics department at a New York City charter high school that targets students who have challenging home situations and/or are from low performing middle schools. According to Omar, students must have failed their 8th grade exams in order to be admitted. All the students in the class are African American or Hispanic.
The subject of the current case study is a Learning Segment on Factoring from Omar’s Algebra II class. There are 16 students registered for this class, with 14 students attending regularly. The class meets in a conference room where students site around a large conference table. There are windows on two sides of the rooms, a whiteboard on one side, and a broken SmartBoard on the 4th side. The students have access to graphing calculators throughout the lessons.
Assessment D: Effective Teaching Work Sample (ETWS)
TASK1: Context Analysis
Component / Faculty AssessmentHighly Effective (4)
Effective (3)
Developing (2)
Ineffective (1) / Alum Assessment
Highly Effective (4)
Effective (3)
Developing (2)
Ineffective (1)
Knowledge of Teaching Context -Community / 3 / 2
Knowledge of Teaching Context -School / 4 / 2
Knowledge of Teaching Context -Classroom / 4 / 3
Knowledge of Students / 3 / 3
Implications for Instructional Planning and Assessment / 3 / 2
Discussion:
Omar effectively applied professional knowledge, skills, and dispositions concerning learners and learning across multiple measures of his classroom practice. During the Lesson Segment planning discussion, Omar shared insights about his students and school. He discussed the challenges the students faced in their home lives, their prior lack of success in school, and the school’s initiatives to support the academic and socio-emotional growth of the students. As department chair, he shared observations about his own classes and those of his colleagues in the math department. He discussed school priorities and the recent changes in administration.
During the Lesson Segment reflection discussion, Omar rated himself using the ETSW: Task 1 rubric. He repeatedly referenced that this is his first year at his current school. His explanations for his self-evaluation centered on his desire to develop deeper understandings about the students and school. His ratings appeared to have more to do with the gap between what he thinks he know and what he would like to know than an objective application of the rubric. This suggests that Omar has a profound appreciation for the importance of understanding learners in order to implement effective instruction.
TASK 2: Standards & Research-based Learning Outcomes
Component / Faculty AssessmentHighly Effective (4)
Effective (3)
Developing (2)
Ineffective (1) / Alum Assessment
Highly Effective (4)
Effective (3)
Developing (2)
Ineffective (1)
Learning segment articulates a central focus / 3 / 3
Learning objectives align with the central focus / 3 / 3
Learning objectives align with NYSCC Learning Standards and other disciplinary standards* / 3 / 3
Learning objectives connect with knowledge of students’ prior knowledge, interests, and cultural/community assets / 3 / 2
Learning objectives connect with knowledge of students’ prior learning and development and therefore predict misunderstandings / 4 / 2
Discussion:
In the Lesson Segment reflection, Omar discussed the differences between his current students and the students at his previous school. He had developed insights about student misconceptions in his previous context, where students had much stronger academic backgrounds. He discussed his need to develop deeper understanding of his current students’ prior knowledge in order to make appropriate plans. For example, he expressed surprise at many students’ poor performance on the pre-assessment. His subsequent Lesson Segment plans addressed the outcomes of this pre-assessment, establishing appropriate learning objectives for his students. As with Task 1, Omar’s self-assessment seemed to identify gaps between where he was and where he wanted to be, not taking into consideration that he was new to this school.
Omar had no ELLs in his class.
TASK 3: Planning for Assessment
Component / Faculty AssessmentHighly Effective (4)
Effective (3)
Developing (2)
Ineffective (1) / Alum Assessment
Highly Effective (4)
Effective (3)
Developing (2)
Ineffective (1)
Assessments align with the central focus, standards, and learning objectives / 3 / 3
The plan includes aligned pre- and post-assessments / 3 / 3
The plan includes several opportunities for the teacher to conduct formative assessments / 3 / 3
Plans include adaptations/ modifications of assessments / 3 / 3
Plans include quality assessment instruments including assessments adapted for ELLs / 3 / 3
Plans include a variety of assessment instrument(s) / 3 / 3
Assessment Plan Commentary. Include commentary on research /theory for ELLs / 3 / 3
Discussion:
Omar began his Learning Segment with a pre-assessment to determine whether his students had the prior knowledge about factoring that was necessary to succeed in his planned quadratic equations unit. Omar explained his planning for his pre-assessment during the Learning Segment planning session. Omar knew that most of his Algebra II students had passed the Algebra I Regents exam, but not at the college ready level. He also knew that most of his students were in 11th grade and had not studied Algebra since 9th grade. He described his analysis of the results and plans based upon those outcome during the first post-lesson reflection session. Since only 3 students attained an 80 or above on the pre-assessment, Omar decided to teach a 3 day Learning Segment focused on developing these essential skills before moving on to more complex aspects of working with quadratic equations. Thus, he designed a pre-assessment and made instructional decisions based upon the outcomes of that assessment. Fieldnotes record that Omar explained this instructional decision based upon the pre-assessment to the students.
Omar imbedded multiple formative assessments into his Learning Segment lessons. Fieldnotes and lesson plans indicate that these included ‘Warm Up’ problems, observations of students as they worked during the lesson, student presentations of problems on the board, and exit problems at the conclusion of the lesson. Each lesson plan included questions to ask to formatively assess student progress. Omar explained his formative assessment decisions during post-lesson reflection sessions and in the reflection session after the Learning Segment. For example, aware that his students needed to be motivated in order to persist on challenging problems, Omar turned one of his formative assessments into a puzzle, requiring students to solve multiple problems in order to decode a message. He wanted their student to expend maximum effort so that he could assess their best work.
Fieldnotes document that, throughout all of the lessons in the Learning Segment, Omar circulated as students worked on their assigned tasks, observing the students and posing questions. He spent the majority of his time at the end of the table where students who struggled on the pre-assessment were seated, believing that these students needed the most support and that he would learn the most from observing and questioning them. During the reflection sessions, Omar acknowledged that he paid minimal attention to the students who scored the highest on the pre-assessment and may have missed some of their misconceptions.
Omar was deliberate in his selection of students to put problems on the board, as he explained during post-lesson reflections. Three students regularly volunteered for this responsibility, but Omar requested that specific students share their work after he saw what each had to contribute. Fieldnotes record that during the students’ work at the board, Omar questioned both the presenter and the other students. He encouraged students to give feedback to each other about their work on the board and articulate their thinking using mathematics language.
Omar designed and implemented a post-assessment that measured his students’ factoring skills, but also included problems that were substantially more challenging than on the pre-assessment. Omar explained this assessment decision in his reflection session after the Learning Segment, Based upon his formative assessments, Omar believed that his students had mastered the basics he had included on the pre-assessment. He wanted to see if his students could apply their learning to more complex tasks. Students stayed into their lunch period working on the post-assessment because they were so engaged with these complex problems.
TASK 4: Lesson Plans
Component / Faculty AssessmentHighly Effective (4)
Effective (3)
Developing (2)
Ineffective (1) / Alum Assessment
Highly Effective (4)
Effective (3)
Developing (2)
Ineffective (1)
The plan is clearly articulated / 3 / 3
The plan reflects pedagogical content knowledge / 3 / 3
The plan reflects content knowledge / 3 / 3
The plan follows an organized progression of activities - a logical flow / 3 / 2
The plan includes a variety of instructional strategies / 3 / 3
The plan includes the deliberate grouping of students when appropriate / 2 / 3
The plan includes differentiation for students based on an understanding of the different needs of the students in the classroom / 3 / 2
The plan includes academic language / 4 / 3
The plan includes the implementation of digital technology / 4 / 3
The plan cites research/theory / 3 / 3
TASK 5: Impact on Student Learning
Component / Faculty AssessmentHighly Effective (4)
Effective (3)
Developing (2)
Ineffective (1) / Alum Assessment
Highly Effective (4)
Effective (3)
Developing (2)
Ineffective (1)
Graphic Presentation of Data / 3 / 3
Interpretation of Data for Whole Class / 4 / 3
Interpretation of Data for Three Students / 4 / 3
Data Demonstrate Positive Effect of Instruction / 4 / 3
Implications for Future Teaching “Next Steps” / 4 / 2
Accuracy and Completeness of Data Collection / 3 / 3
Assessment I: Lesson Evaluation Part B: Observation Evaluation
Component / Faculty AssessmentMultiple lessons
Highly Effective (4)
Effective (3)
Developing (2)
Ineffective (1) / Trained Observer Assessment
Single lesson
Highly Effective (4)
Effective (3)
Developing (2)
Ineffective (1)
The Learner and Learning
1. Establishes a positive learning environment. Respect and rapport are evident. / 4 / 3
2. Demonstrates flexibility and responsiveness to students’ diverse needs. / 4 / 4
Content Knowledge
3. Demonstrates pedagogical content knowledge. / 3 / 3
4. Demonstrates content knowledge. / 3 / 4
Instructional Practices
5. Effectively models and/or uses demonstration or representation (chart/picture/poster) to support learning a strategy or skill. / 4 / 3
6. Presents learning tasks in a manner that engages students. / 3 / 4
7. Engages students in learning tasks to support the mastery of academic language. / 3 / 3
8. Uses a variety of questions to elicit and build on student responses to deepen content understanding. / 4 / 3
9. Uses questioning to monitor student learning. / 4 / 4
10. Appropriately responds to formative assessment data with instructional decisions and feedback to students. / 3 / 3
11. Connects new content to prior learning as well as cultural and personal assets. / 3 / 3
12. Engages students in challenging work and conveys his/her high expectations for the students. / 3 / 3
13. Demonstrates an ability to manage time (closure). / 3 / 3
14. Demonstrates an ability to manage classroom rules, routines, and materials / 3 / 3
15. Demonstrates an ability to manage classroom space. / 3 / 3
16. Demonstrates an ability to use technology effectively. / 4 / NA
17. Makes a positive impact on student learning. / 4 / 3
Assessment C
Dispositions Assessment
Component / Faculty AssessmentHighly Effective (4)
Effective (3)
Developing (2)
Ineffective (1)
1. Addressing Individual Student Needs / 3
2. Cultural and Linguistic Awareness / 3
3. Openness to Technology / 4
4. Support All Students / 4
5. Student-centered Classroom Management / 3
6. Collaboration / 3
7. Professional Interactions / 4
8. Problem Solving / 4
9. Professional Ethics / 4
10. Timeliness / 3
11. Responsible for student learning / 4
12. Lifelong Learner / 4
13. Openness Feedback / 4
14. Reflective Practice / 4
Student Performance Data:
Pre-Test / Post-Test / Unit Exam / Pre-Test to Post-Test Change / Pre-Test to Unit Exam Change26 / 69 / 72 / 43 / 46
29 / 44 / 55 / 15 / 26
51 / 67 / 68 / 16 / 17
58 / 79 / 82 / 21 / 24
60 / 69 / 65 / 9 / 5
65 / 79 / 70 / 14 / 5
67 / 75 / 80 / 8 / 13
67 / 77 / 86 / 10 / 19
73 / 61 / 75 / -12 / 2
73 / 75 / 78 / 2 / 5
78 / 79 / 82 / 1 / 4
80 / 73 / 88 / -7 / 8
90 / 93 / 90 / 3 / 0
100 / 96 / 95 / -4 / -5
Mean / 65.50 / 74.00 / 77.57 / 8.50 / 12.07
Discussion
As Omar summarized in an email, “Overall, we can clearly see that there is growth in the students’ understanding of the topic and learning.” During the reflection session after the Learning Segment, Omar discussed the impacts that he had demonstrated on his students learning.
Omar highlighted the improvements in most students’ performance from before to after instruction. The mean score for the pre-assessment was 65.5 and the median was 67, while the post-assessment mean was 74 and the median was 77. On average, student scores were 8.5 higher on the post-assessment than on the pre-assessment. Students who started off with lower scores on the pre-assessment demonstrated dramatic gains on the post-assessment. Students who failed the pre-assessment (below 60) had an average improvement of almost 24 points on the post-assessment. Students whose pre-assessment score was in between 60 and 70 had an average improvement of 10.3 points. However, students who scored above 70 had an average decrease of almost 3 points from pre- to post-assessment. Three of these students showed small positive gains and three had lower scores on the post-assessment than the pre-assessment.
In addition to the post-assessment at the end of the Learning Segment, Omar gave his students a unit exam that incorporated assessment of learning objectives from the Learning Segment. On average, students improved by 12 points from the pre-assessment to the unit exam. The mean on the unit exam, which was considerably more challenging than the pre-test, was 77.6 compared to the pre-assessment mean of 65.5. Similarly, the median increased from 67 on the pre-assessment to 82 on the post-assessment. Students who failed the pre-assessment had an average improvement of 23.6 points on the unit exam, with students initially in the 60s increasing by an average of 10.5 points, and students initially scoring over 70 increasing by an average of 2.3 points.
As mathematics department chair, Omar’s positive impacts on student learning extend beyond his own classroom. In a meeting to obtain permission for the case study, Omar’s principal lauded his contributions to the department as a whole, citing his leadership as the foundation for significant changes in teacher practice and student performance. Omar described one example of this leadership in the planning session for his Learning Segment. He is a peer-tutoring program that Omar is piloting based upon internship and student teaching experiences while at York College. While at York, Omar worked in classrooms that were part of the National Science Foundation-funded Peer Enabled Restructured Classroom program. In his modified implementation, Omar is working with students from his Algebra II class to teach them how to be peer instructors for student taking an Algebra I class. Omar describes positive impacts for both the Algebra I and Algebra II students in terms of both academic achievement and self-concept. He is writing his Masters thesis based upon this project.
Component / Alumni SurveyStrongly Agree (5)
Agree (4)
Somewhat Agree (3)
Disagree (2)
Strongly Disagree (1) / Employer Survey
Strongly Agree (5)
Agree (4)
Somewhat Agree (3)
Disagree (2)
Strongly Disagree (1)
Overall York College prepared this graduate to be an Effective Educator. / 4 / 5
Content
1. Content knowledge / 4 / 5
2. Pedagogical content knowledge / 4 / 5
3. Access prior
knowledge / 4 / 5
Learners
4. Establish a learning environment / 4 / 5
5. Establish expectations
. / 4 / 5
6. Responsiveness to students / 4 / 5
Instruction
7. Use technology / 4 / 5
8. Critical thinking / 4 / 5
9. Assessment / 4 / 5
Instructional Resource Management
10. Manage time / 4 / 5
11. Manage behavior / 5 / 5
Professionalism
12. Collaborate / 4 / 5
13. Problem solve / 4 / 5
14. Exhibit professional ethics / 5 / 5
15. Open to feedback / 4 / 5
16. Engage in reflective practice / 4 / 5
17. Impact student learning / 4 / 5
Several questions on the Alumni and Employer Surveys measure program completers’ application of professional knowledge, skills and dispositions connected to Learners and Learning, specifically those in the Learners section of the survey. Omar ‘Agreed’ that York College prepared him in the areas of ‘Establishing a learning environment, ‘Establish expectations,’ and ‘Responsiveness to Students.’ His principal ‘Strongly Agreed’ that York prepared him well on for these job responsibilities. This demonstrates both the program completer’s and the employer’s confidence in his mastery of Learner Development, Learner Differences, and Learning Environment.
Case Study 2:
Julia is a 2015-2016 graduate of York College’s program in Bilingual Education. She has been a teacher in the current school for 3 years. While at York, Julia participated in the Bilingual Pupil Services (BPS) program, a program for students pursuing a New York State certification in bilingual education. BPS is a Title I, Tax Levy program that operates within the New York City Department of Education, Division of Human Resources, Office of School Based Support Services. Its purpose is to prepare and train bilingual paraprofessionals in pursuit of a teaching career to support and serve English Language Learners (ELLs) in Title I public elementary schools. The goal is to promote linguistic and academic progress of these students, whose primary language is Spanish and several languages other then English. York ‘s EPP actively partners with the BPS program to recruit qualified candidates and sustain them in this program.