Academic Exchange Quarterly Fall
2002 ISSN 1096-1453 Volume 6, Issue 3
African
American Male Students’ Perception of a Mathematics Learning Environment
Joy Moore,
Dr. Moore has an Interdisciplinary Ph.D. in Mathematical
Sciences and Education from the
Findings from interview data support National Council of Teachers of Mathematics recommendations for student discourse and classroom learning environment. In particular, results indicate that for these African American male students, student involvement and class participation, group work, and student discourse in the classroom are significant contributing factors to their understanding of school mathematics. These perceptions inform pedagogical considerations when seeking to improve the school mathematics achievement of all students.
Gaining Perspective
One of the most prominent problems
in urban education in the
Part of the problem stems from an insufficient and incomplete knowledge base about African American male students’ development and socialization within the mathematics classroom (Murrell, 1994). Though the majority of research has addressed the mathematics achievement of African American learners from a pedagogical perspective, two areas of investigation are conspicuously lacking in the literature, research on mathematics achievement among African American male learners in secondary schools and research that includes the perspectives of the African American male learners themselves. Murrell posits that teachers cannot fully interpret the developmental learning of these students without an analysis and synthesis of the students’ experiences with the curriculum and knowledge of how they position themselves in the culture of the classroom. As an educator, a crucial element of the educational process is what teachers can learn about their students from the students themselves.
Pedagogy that is intended to improve students’ academic achievement needs to be informed by the students. Insight into the perceptions of the learners with regard to their mathematical experiences can prove beneficial in developing effective pedagogy for improved mathematics achievement. African American male students, in particular, are in need of effective pedagogy that will improve their school mathematics performance. The purpose of this article is to provide insights into the perceptions of five African American male high school students with respect to the learning environment and student discourse in their mathematics classrooms. Implications of these perceptions will be discussed in addressing how they inform pedagogical considerations in improving the mathematics achievement of African American male students.
A major aspect of the constructivist response to improving students’ mathematics understanding is the increase of their opportunity and ability to participate in mathematical discourse. Social interaction constitutes a crucial source of opportunities to learn mathematics in that the process of constructing mathematical knowledge involves cognitive conflict, reflection, and active cognitive reorganization (Piaget, 1970). Building upon Vygotsky’s (1978, 1986) emphasis of the importance of social interaction in learning, Cobb and Yackel (1996) proposed a perspective called social constructivism that puts great emphasis on the processes of communicating and negotiating in communities. Their social constructivist perspective incorporates the constructivist and the sociocultural points of view. This emergent framework is used to study mathematical learning as it occurs within the social contexts of the classroom. The development of individual meaning and the development of social meaning are taken as being reflexively related in that neither can exist independently of the other. Thus social constructivists view mathematical learning as an interactive as well as constructive activity (Cobb, 1988). Classroom discourse plays a significant role in this interactive activity. Vygotsky (1978) posited group interaction as one source in the development of mental operations. He suggested that students gradually internalize the talk that occurs in groups. They begin to challenge themselves, ask for reasons, and in general monitor their own mental work as others do their public speech. This view of group work and communication parallels the vision for student discourse outlined in the Standards for Teaching Mathematics (National Council of Teachers of Mathematics [NCTM], 1991) and the Principles and Standards for School Mathematics (NCTM, 2000).
The Standards (NCTM, 1991) address both the student’s role in discourse and the learning environment of mathematics classrooms. Standard 3 states that “teachers should promote classroom discourse in which students listen to, respond to, and question the teacher and one another; initiate problems and questions; make conjectures and present solutions; try to convince themselves and one another of the validity of particular representations, solutions, conjectures, and answers; and rely on mathematical evidence and argument to determine validity” (p. 45). Classroom discourse enables teachers to identify, diagnose and address problems and misconceptions that students possess (Orr, 1997). Discourse is not only vital in developing communication and reasoning skills in the students, but enhances the teacher’s ability to evaluate their students’ progress and to analyze their own effectiveness in the classroom. In addition, classroom discourse allows students to experience the processes of attaining mathematical understanding; thus increasing their mathematical empowerment.
Standard 5 states that “teachers should create a learning environment that fosters the development of each student’s mathematical power by respecting and valuing students’ ideas, ways of thinking, and mathematical dispositions; and encouraging students to work independently or collaboratively to make sense of mathematics” (NCTM, 1991, p. 57). Collaborative group work is an essential component of constructivist theory (Brooks & Brooks, 1993) and the theory of culturally relevant instruction (Baugh, 1994; Haynes, 1993; Ladson-Billings, 1994; Treisman, 1992). Mutual respect for both colleagues and the teacher should be a prime directive in the classroom. The free, open exchange of ideas and debate cannot take place in an environment void of respect for everyone’s contribution. Equal participation by all students in the classroom community should be assured and supported.
In an effort to gain insight into the mathematical learning experiences of African American male high school students, this qualitative research study was conducted at Davis High School, a magnet school located in an urban setting. The racial composition of the 1800 students was 88% African American, 10% White, and 2% Asian and Hispanic combined.
Participants were five African American male students between sixteen and eighteen years of age. Sean, Dion, and Jay were enrolled in Algebra II and Carleon and Divine were enrolled in precalculus. Four of the participants were selected according to a criterion-based selection (LeCompte & Preissle, 1993). The primary criterion was participation in classroom discourse. Among the male population of each classroom, these students were the most involved in classroom discourse as evidenced by the frequency of their verbal communication during classroom observations. One participant, however, was selected according to a combined opportunistic and maximum variation sampling (Patton, 1990). During classroom observations, it was noted that Jay engaged in very limited discourse. Hence, he was included in the study to understand variations in experiences while also investigating core elements and shared outcomes (Patton, 1990).
Participants were classified as above average students and below average students in school mathematics achievement for the purposes of this study. Classification for achievement was based upon the state proficiency test performance, mathematics course grades for the current school year, and participant performance on a written assessment tool. The below average students were classified as such due to failing school mathematics performance; however, all of the participants had passed the state proficiency test in mathematics by their ninth grade year. Thus, these classifications do not reflect the participants’ potential for success, but serve only as categories for distinguishing mathematics achievement based upon traditional written evaluation and assessment. Carleon, Divine, and Jay were classified as above average students. Sean and Dion were classified as below average students.
Data were collected from interviews with each of the five participants. Interview questions were organized into five categories: experience, opinion and value, feeling, knowledge, and background concerning the students’ mathematical achievement (Patton, 1990). The data reflect students’ insights on the classroom environment, the curriculum, and the external factors of influence that students bring to the classroom from outside the school context. The scope of this article is limited to the participants’ perceptions of the classroom learning environment. Questions pertaining to the classroom environment included: What characteristics of the classroom help or hinder your mathematics learning experience? How do your classmates effect your mathematics learning? Who do you ask, or where do you go, when you need help with mathematics? If you were in charge of a mathematics class, what would your ideal class be like?
The participants’ perceptions of the classroom environment included categories of student participation, group work, and student discourse. This section presents data from these three categories.
Carleon related that his understanding was enhanced when he was allowed to be involved in classroom activity. He stated,
By being able to be more involved instead of just watching the teacher do it all the time. Instead of just watching them be up at the board and they showing the whole class how to do it I like to be able to actually come up to the board and do the problem.
Carleon’s preference for student involvement was not limited to his own, but included the involvement of the entire class. He claimed,
Stuff that helps me is when everybody is in competition. Like when everybody, like they wanna learn, like everybody is like fighting over who’s gonna get up to the board and do the problem cause everybody’s eager. It’s like the more people that’s involved, you become more involved in it and it makes you more happy about returning to math class…Just get everybody involved. And even if it’s a person in the classroom that doesn’t act like they want to get involved, the teacher needs to try to get him involved and his friends need to try to get that person involved…. I figure if it was more, better attitudes in the class and everybody wanted to be more involved than everybody’s grades could be just as good as mine.
Dion preferred an instructional approach that made learning fun. If he were in charge of a class, “It’d be fun. It won’t be all strictly work you know what I’m saying. We’d have fun while we doing work. Long as um the students is gettin’ what I’m teachin’, it’s alright with me.” He claimed that games not only kept mathematics from being “kind of boring,” but they also enhanced his understanding. “When I was like in elementary and like middle school it was fun, like we played games and stuff, like to help us understand.” Hence, when designing his own mathematics class, he suggested the need for “games just to help ‘em understand.”
Carleon also placed great emphasis on making mathematics interesting. He purported that:
When you walk in, it should be exciting…make learning fun. Try to make it interesting because you’re not going to be interested in it if you don’t like it. That’s why they have to make all these different approaches about math. Cause a lot of times, people look at math problems and they see all the functions and all that stuff and it looks kind of hard. But if you just make something more interesting to the mind and more, you just gotta make it more exciting for people to wanna keep doing it… it makes you more happy about returning to math class instead of returning and it being boring.
Though Divine viewed mathematics as
“a subject you can’t make fun”, he did believe it important to keep students
interested. He viewed group work as a means to that end. “Group work keeps the
students’ interest and also keeps them awake in class…so if you interact it
becomes more interesting to the student.” He described an instructional method
called “Ask Three Before You
All of the participants perceived group work as beneficial to promoting communication and thereby increasing understanding. Carleon hypothesized that “if you bring more people together than you might find out better ways of how to do it.” He also expressed the importance of appropriate attitudes for the process to be effective when he commented,
In this class I only like to collaborate with one person…because I know they are as serious about it as me. You can’t talk with somebody that’s never serious and then you’re the only one that’s serious and try to talk about math. It’s not gonna happen.
Though Jay preferred working alone on mathematics problems, he acknowledged the benefits of group work. Jay commented that if he were in charge of a mathematics class, he would “do group work. Sometimes people have their own ideas that might help somebody else.”
All of the participants perceived inquiries for understanding as the most appropriate form of student discourse in class. These inquiries included teacher-student discourse and student-student discourse. With regards to teacher-student discourse, Divine expressed his belief about the role of communication in the classroom:
I see that a lot of students they don’t understand it, they’re kind of embarrassed so they don’t ask questions and the teacher is always talking. Then we have to say be quiet and let me tell you that I don’t understand this or let me tell you that I’m having problems with this…they got to communicate back and forth, and I think if we do more of that, then more of the students would be successful.
Carleon also believed most talking should be for acquiring understanding:
Most of the talking should just be can you do this problem? If you can’t do it then tell me why you can’t do it and I will show you how. It should be dialogue of that nature. Like, well I can’t do this. Okay, tell me what your problem is, tell me where it’s a gap in the road where you’re not able to go on a straight path. Just tell me. And that’s the way it should be, like you approach the teacher with the problem and they give you feedback on how to do it or how to finish it.
In reference to student-student discourse, Carleon related that talking with a friend about math helped him “figure out how to do the problem.”
Jay believed an ideal mathematics classroom required that “the students be quiet with their books out learning.” He did allow for talking within the confines of “helping each other. If somebody needs help and the teacher can’t give it to them then they can ask somebody who already knows how to do it. Students can help each other understand.”
Dion reported, “If we both like stuck on one problem we could like put our minds together and figure out the problem.”
Sean expressed that talking was essential to helping other students understand, “Like most of the times if I understand something I won’t really discuss it more, unless it’s like somebody who don’t understand something. And then that’s when I might give them my opinion about something I understand… Well, sometimes I learn from the students and the students learn from me sometime. So basically we be helping each other out when we can.”
Participants’ perceptions of classroom discourse included issues of student involvement, group work, and students helping each other. Carleon implied a direct correlation between student involvement and academic achievement, “I figure if it was more, better attitudes in the class and everybody wanted to be more involved than everybody’s grades could be just as good as mine.” He believed it was the mutual responsibility of the teacher and the students to get everyone involved in classroom discourse. His vision for a high-achieving environment (total student involvement and participation in classroom discourse) is a vital component of constructivist theory. During whole-class discussion, students are expected to give coherent explanations of their problems, interpretations, and solutions and to respond to questions and challenges posed by their peers (Yackel et al., 1990). This interaction maintains students’ interests while empowering them with the ability to communicate mathematically and increase their understanding of mathematics concepts. Hence, according to these research findings, teachers need to design activities and select worthwhile mathematical tasks (NCTM, 1991, 2000) that maximize student involvement.
Participants related that they gleaned from each other an increased understanding of the lesson when working in groups. They expressed an ability to focus better and felt they had more opportunity to have their questions answered within small groups. They reported that when trying to help someone else, they gained insight into their own mastery of mathematics concepts. Participants also reported learning from others’ contributions to whole-class discussions. Ladson-Billings (1995) reported that successful teachers of African American students encourage students to learn collaboratively, teach each other, and be responsible for each other’s learning. Creating a community of learners is a major paradigm shift identified in the Standards (NCTM, 1991, 2000). Within this community, students are afforded the opportunity to participate in meaningful discourse as they construct their own understandings of mathematics concepts. Hence, pedagogy that is responsive to the findings of this study requires opportunity for students to work individually, in pairs, and small groups, and to participate in whole-group discussions in order to provide a full breadth of learning experiences.
The findings of this study inform pedagogical considerations with respect to active student participation in the learning process, opportunity for collaborative group work, and student discourse in the classroom. The five African American male high school student participants viewed student engagement important to the learning process in that interest is maintained for acquiring the requisite knowledge. They found collaborative group work to be helpful in gaining mathematical understanding. They also valued opportunities to participate in classroom discourse, gleaning understanding and meaning from the contribution of others. These students’ perceptions of a mathematics learning environment that promotes their academic achievement are closely aligned with the Standards (NCTM, 1991, 2000) and contain the elements of environment supported by culturally relevant instruction. In seeking to improve the mathematics achievement of all students, these students’ perceptions merit pedagogical consideration and incorporation.
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