Description This observation is of an eighth grade mathematics class, in which algebra was being taught. The objectives of the math lesson included to “appreciate the usefulness, power and beauty of mathematics,” and to “recognize that mathematics permeates the world around us,” which are core objectives of the middle grade math curriculum (“The Middle Years Programme – MYP,” 2008). This specific lesson on the day of observation was linear equations, with an introduction to word problems at the end of the lesson. The ages of the students were around thirteen years old; the teacher was in her early 20s and was African American. The classroom was small, only containing twelve students of various ethnic backgrounds. Also, the classroom was specifically arranged and designed as a math class because the posters on the wall, the props, and the computers were all set up for math lessons. This is a middle school that comprises grades seven through nine. Overall, the teacher observed Exceeds Expectations in meeting the objectives of the lessons and of the grade-appropriate and age-appropriate learning.

1. Connection of Field Experience to Course Objectives

Candidate’s performance and response to field experience is clearly connected to course objectives and makes connections between theory and practice. When it comes to mathematical theories and pedagogical practices for instructing eighth graders, this teacher did an excellent job. Linking theory to practice, the teacher fulfilled the main course objectives including bridging the gap between abstract mathematical principles and the real world application of math (Van de Walle, 2014). It is interesting to note how the teacher being observed integrated culturally competent models of instruction. As An, Kulm & Wu (2004) found, instructional methods and lessons used in China differ considerably from those used in the United States, with tremendous implications for pedagogical practice. In the United States, teachers use different approaches to stimulating a creative approach to math, which is conducive to the overall learning and course objectives. However, the Chinese...

145). The teacher was observed using blended methods to appeal to a wide range of learning styles. When asked about her mixed methods, the teacher responded that she had indeed reflected on the literature on mathematics learning. She said that she understands that some students in the class respond better to more authoritarian styles of teaching, but that not all students benefit from that approach. The teacher also said that she liked to link abstract concepts with real life examples of how to apply the linear equations. Technology was used liberally throughout the lesson, helping all students have a hands-on learning experience and engaging with the material. As one of the course objectives was to mix different methods and make adaptations for students with special needs, this teacher met all expectations with aplomb. For example, the teacher used collaborative and cooperative learning strategies as well as the authoritarian and rigid methods. Research by Webb & Farivar (1994) clearly shows that depending on cultural backgrounds and individual differences, collaborative learning can be tremendously effective in the mathematics classroom.
2. Furtherance of Professional Knowledge, Skills, and Dispositions

Candidate’s performance and response to field experience clearly demonstrates ongoing and self-aware development in professional knowledge, skills, and dispositions. The furtherance of professional knowledge, skills, and dispositions depends on familarity with the material and with best practices. This teacher was adept at integrating what she was learning with specific skills development and the cultivation of classroom-appropriate dispositions. When asked about her performance later, the teacher said that she had been a substitute teacher for many years and that her mother was also a teacher. She said that she had developed her professional knowledge, skills, and dispositions in a supportive home and school environment.

This teacher demonstrates a clear understanding of the big picture issues in classroom design…