Observing a Mathematics Classroom Assignment

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 approach is more “rigid” and have “value for teaching mathematics content,” (An, Kulm & Wu, 2004, p. 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 and lesson planning. Her level of cultural competency was admirable, and will prove helpful in a number of different educational and professional environments. She empowered the students, and reached out to those who seemed like they were struggling. Even when she was using the more rigid methods that An, Kulm & Wu (2004) recommend, she did not isolate any students in the classroom. During the more creative parts of the lesson, and during the collaborative learning exercises, all the students were actively engaged because the candidate had been applying what she had learned outside of the classroom and through her knowledge of evidence-based practice. In terms of dispositions, this teacher is calm, cool, and collected. Middle school students can be challenging and some present behavioral problems but the teacher never lost her composure during class. Her classroom management skills were exceptional, as she seemed to empathize and tap into what the student was experiencing rather than reacting to the behavior. This resulted in a lot of respect given to the teacher, as she showed respect to the students. I was particularly impressed that during the observation, the teacher used cooperative learning methods that were difficult to design in an algebra lesson. Yet she overcame the challenges and did have the student pair off to solve linear equations while using the fun math teaching game loaded on their iPads. In their research on collaborative learning, Webb & Farivar (1994) found that students often benefitted from the integration of collabortative learning, especially non-white students who may be used to collaborative learning at home: “Results showed that Latino and African-American students gave and received more elaborated help, and showed higher achievement (p. 369). I was impressed that this teacher candidate was applying evidence-based practice in the algebra classroom.
3. Overall Quality
Candidate’s performance and response to field experience exceeds expectations of time and accomplishment of objectives. It is difficult to exceed expectations this early in a person’s career, but clearly this is a person who was born to teach. The teacher demonstrated command of pedagogical practices related to algebra, and to linear equations specifically. Being able to show how linear equations have a real-world and real-life application is not easy, but this teacher achieved that goal through varied word problems. The word problems were culturally sensitive and diverse, allowing different students to grasp the concept quickly. Also, the teacher did not pressure the students in any way. There were no pop quizzes or burdensome homework assignments. All the exercises were fun, especially the ones that used the iPads. The students were also able to practice what they had learned on their own time at home, using the “math is fun” games the teacher provided. When asked about her strategies for classroom management, the teacher said that she is the eldest child with five siblings, and that she has always been in that disciplinary role. Having mastered these skills on a personal level, the teacher was able to deftly balance the need for culturally appropriate classroom management with the need for order.
The teacher said that she meets with parents monthly to discuss student progress. She said that every once in a while one of the students with behavioral problems gets sent home. She does not like to take the student out of the classroom, but does so only when he causes a serious disturbance to the other kids in the class. I was amazed to see that the teacher knew how to manage the classroom without using authoritarian styles. Finally, the teacher said that she plans her lessons well in advance and has a software application that allows for her to make quick adaptations for students with special needs. There is a student in this class with special needs but dyslexia, which does not require any specific adaptations in this mathematics classroom. Overall, the candidate performed exceptionally well, surpassing all expectations.



References

An, S., Kulm, G. & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the US. Journal of Mathematics Teacher Education 7(2): 145-172.
“The Middle Years Programme – MYP,” (2008). OIS. http://yayoi.senri.ed.jp/ois/curriculum/maths_aims_objs.htm
Van De Walle, J.A. (2014). Elementary and middle school mathematics teaching development. Fourth Edition. http://floridastateseminary.com/wp-content/uploads/2014/10/Math-Quest.pdf
Webb, N.M. & Farivar, S. (1994). Promoting Helping Behavior in Cooperative Small Groups in Middle School Mathematics. American Educational Research Journal 31(2): 369-395.