Mathematics and Teaching

Michele D. Crockett

• Publisher: Routledge
• Year: 2008
• Print ISBN: 9781138453050
• eBook ISBN: 9781135705121
• Topic: Education
• Subtopic: Education General

Mathematics and Teaching uses case studies to explore complex and pervasive issues that arise in teaching. In this volume, school mathematics is the context in which to consider race, equity, political contexts and the broader social and cultural circumstances in which schooling occurs. This book does not provide immediate or definitive resolutions. Rather, its goal is to provoke and facilitate thoughtful discussion about critical issues for professional decision-making in mathematics teaching.

This is the 7th volume in Reflective Teaching and the Social Conditions of Schooling: A Series for Prospective and Practicing Teachers, edited by Daniel P. Liston and Kenneth M. Zeichner. It follows the same format as previous volumes in the series.

• Part I includes four case studies of classroom experiences: "Race and Teacher Expectations"; "Mathematics for All?"; "Culture and School Mathematics"; and "Politics and School Mathematics." Each case is followed by a space for readers' own reactions and reflections, school stakeholders' reactions, and a summary with additional questions for further discussion.
• Part II presents three public arguments representing different views about the issues that arise in mathematics teaching: conservative, liberal and radical multiculturalist.
• Part III offers the authors' reflections on the centrality of culture in teaching mathematics, resources and exercises for further reflection, and a bibliography for further reading.

Mathematics and Teaching is pertinent for all prospective and practicing teachers at any stage in their teaching careers. It is appropriate for any undergraduate and graduate course addressing mathematics teaching issues.

I
CASES AND REACTIONS

INTRODUCTION TO CASE 1

In the United States, The Education for All Handicapped Children Act (Public Law 94-142) was passed in 1975, requiring states to provide “a free, appropriate public education for every child between the ages of 3 and 21 regardless of how, or how seriously, he may be handicapped.” In 1990 the Individuals with Disabilities Education Act (IDEA) was passed as an amendment to Public Law 94-142. The amendment extended services for students with disabilities. For example, it provided services for students with ADHD; and it replaced the word “handicapped” with “disabled.” These laws were intended to address the educational rights of children long neglected by our public school system. However, these federal guidelines have unintended consequences. Minority students are over-represented in special education programs throughout the United States. Misdiagnosis is a widespread practice (Harry & Anderson, 1994). Policymakers assume that “clinical” decisions that label children for special education services come about in some rational way. In fact, the decision-making processes are far less clinical than many of us care to acknowledge. Case 1 is about Benjamin, an African American boy in the 3rd grade. It illustrates how his teacher’s beliefs about race, class, and gender interact in ways that produce labels that may not operate in Benjamin’s best educational interests.

CASE 1: “RACE AND TEACHER EXPECTATIONS”

As soon as the dismissal bell rang, Benjamin Sykes, an energetic African American boy, darted for the door, backpack in tow, nearly taking out Maisha who sat in the desk near the exit. Mrs. Carlton sighed. She knew Benjamin’s action warranted a reprimand, but it was Friday. She was exhausted and ready to go home. From the moment he walked into her 3rd-grade classroom, Mrs. Carlton knew he was trouble. It seemed he couldn’t sit still for more than two minutes and she often placed him on “time out” for being out of his seat. It bothered Mrs. Carlton that his 2nd-grade teacher had not referred him for special education services. Now, she was stuck with another low achieving student. This was particularly annoying, since considerable district pressure was being placed on the teachers to raise test scores. Thank God for Anna, Mrs. Carlton muttered to herself as the last of the bunch noisily vacated the classroom. Anna seemed to have a calming effect on Benjamin and four other little Black boys in her classroom.

Anna had been placed in Mrs. Carlton’s 3rd-grade class three weeks ago. It was the first trimester of her student teaching practicum. For two hours each morning, she observed the teacher’s instruction, management strategies, and assisted students with their work. With each passing week, her observations became more astute as her university professors posed questions about the experiences. Before leaving campus, she spent about thirty minutes writing down her thoughts and trying to address questions raised by her professors. The assignment she liked best was developing a case study focused on the math experiences of one student. The case study involved gathering information about the student’s math achievement in school, as well as the mathematics the student encounters in the lunch-room, on the playground, and at home. The professor suggested that the prospective teachers spend one or two evenings at the student’s home interviewing parents, siblings, and shadowing the student. Initially, Anna worried about getting permission to go into a child’s home. However, this proved easier than she thought possible. The child she decided to study was Benjamin. Benjamin’s mom was especially agreeable once she found out that Anna was the “new teacher” at school, the one who had been tutoring her son.

Anna had become accustomed to the complaints Mrs. Carlton aired during the morning recess. At first, Mrs. Carlton’s complaints seemed reasonable. Anna could see that some of the children were often off-task, not following directions, and not completing assignments. Some were even rude, yelling out answers and talking out of turn. Yes, Anna agreed that this was inappropriate behavior. How could one teach under such circumstances? Little by little, however, Anna began to recognize that Mrs. Carlton’s management skills left something to be desired. She contributed to the bad behavior that left her so exasperated. Anna observed a math lesson on multi-digit addition with regrouping. As Mrs. Carlton explained step-by-step how to add the digits, few of the students seemed to pay attention. Two students were poking each other with pencils, another secretly, so she thought, played with her Barbie doll, while several others stared out the window as a custodial crew painted white lines on the playground’s black top. Mrs. Carlton continued as though unaware of the students’ lack of attentiveness. It wasn’t until she assigned them problems from the textbook that chaos ensued. Some students didn’t have their books and many complained that they didn’t understand the word problems. “Weren’t any of you listening?” she shouted. “This stuff is easy. Just go step-by-step starting in the ones place. You can do the word problems if you just read them!” Mrs. Carlton was more than agitated.

Mrs. Carlton frequently complained about parents. “These parents aren’t like the ones we used to have. If they would discipline their children and see to it that their children did their homework every evening, my job would be a lot easier. These parents don’t care. I’m not trying to be insensitive, but if the parents are low quality then their children are low quality.” Anna guessed that the “low quality” parents were Black parents. It was likely that Mrs. Carlton and other teachers in the school weren’t used to having Black children in their classrooms. In recent years, professional and working-class parents fleeing the pressures of urban life moved to the fast-growing suburban community where housing was more affordable. For the first time, the community saw an increase in its Black residents. Nevertheless, Anna was growing weary of Mrs. Carlton’s constant indictments of the children and their parents. Many of them flew in the face of her classroom experiences and knowledge of the children’s backgrounds. Because of the case study she was developing about Benjamin, Anna wondered if Mrs. Carlton knew anything about the lives of the students she taught.

For example, Mrs. Carlton insisted that Benjamin was a low achiever. She seemed to think he didn’t know his basic facts. When Anna examined his cumulative file, his test scores from 2nd grade indicated that he was at grade level. In fact, the grade equivalent score was 6.2 and 4.8 for mathematics basic skills and problem solving respectively. This information was consistent with her tutoring experiences with Benjamin. He resisted doing the daily math assignments, but with her urgings, he always successfully completed them. He knew his basic facts like the back of his hand. His resistance, Anna speculated, was because he found it boring to do 20 computation problems a day. On two occasions, Anna observed Benjamin on the playground. Basketball seemed to be his game. When Anna talked to him about it, she marveled at the numerical data he kept in his head. He knew the scores of each team for every day that week, how many points each team member made, how many fouls were committed and by whom. He talked about who was the best free throw shooter and who could make the best lay ups. Anna spent her first evening with Benjamin’s family several days ago. It was laundry night. Anna followed Benjamin and his mom into the basement of their apartment building. She watched Benjamin count out 12 quarters for three loads of laundry. As his mother loaded the clothes into the washers, Benjamin carefully poured liquid detergent into a measuring cup. Anna asked, “How much are you pouring in?” “One fourth cup,” he replied, putting the cup close to her face before pouring it over the clothes in the washer.

Anna was fascinated by Benjamin’s family life. She was pleased when Mrs. Sykes agreed to a second visit. Mrs. Sykes was a single parent, but from what Anna could tell, Benjamin’s home life was reasonably stable. He had an after school routine that included homework and chores. Once a week he helped his mother do laundry. Her growing knowledge about Benjamin and his family caused her considerable concern. Benjamin demonstrated mathematical competence in tutoring sessions, on the playground and at home. Why was he not engaged in Mrs. Carlton’s math lessons? Why did Mrs. Carlton insist that he had limited capacity to learn? She threatened to refer him for special education services. Based on his school records and her observations, she could not see how Mrs. Carlton could justify such a referral. As far as Anna was concerned, what Mrs. Carlton needed was an attitude change. And, to put it mildly, her teaching was uninspired. She wondered if she should say something. Should she share her case study with Mrs. Carlton once it was done? Maybe she’d think better of the students after reading it, or, at least of Benjamin.

READER REACTIONS TO “RACE AND TEACHER EXPECTATIONS”

REACTIONS TO “RACE AND TEACHER EXPECTATIONS”

There were a wide variety of responses to this case. Many respondents grappled with Anna’s dilemma. How and to what degree should she serve as Benjamin’s advocate? For some, it was clear that Anna should share her findings with Mrs. Carlton. Some thought she should proceed cautiously, given her tenuous status as a classroom observer. Other respondents strongly identified with the events in the case as they paralleled their own student teaching experiences. Some respondents pointed to classroom management issues as the reasons for Mrs. Carlton’s difficulties with children like Benjamin. One respondent who identified Mrs. Carlton’s attitudes as racist said it was the result of “teacher burn-out.” Two veteran educators commented on the challenges that Benjamin’s situation presented to the educational system and what might be done.

Anna’s Dilemma

Many respondents thought that Anna should share her case study with Mrs. Carlton, emphasizing an approach that is both professional and cautious. One respondent explains that sharing the case is the right thing to do if Anna has any integrity at all.

I definitely think that Anna should share her findings with Mrs. Carlton. Who knows how many students there are like Benjamin who may simply require extra attention or a more intriguing way of learning in order to succeed in the classroom, but instead are being cast off to the side and given up on? It is certainly a teacher’s job to help her students understand what is going on and make use of constructive approaches to accomplishing a lesson. If a teacher does not care whether her students take anything from the lesson, why should the students bother trying to learn it? Furthermore, if a teacher gives up and reprimands for not understanding a problem the first time around, how is a student supposed to learn anything? These are questions that should be offered to Mrs. Carlton to address.

—Undergraduate, Prospective Teacher

I think that Anna should most certainly show her observation results to Mrs. Carlton. Anna has come across a wonderful discovery that Benjamin is doing well with math at home and outside of school, and it is important that the teacher knows this. Anna should approach the teacher in a professional, non-accusatory manner in order to get this situation cleared up. It could very well be that Mrs. Carlton holds some prejudice against her Black students, or somehow stereotypes them into learning categories without examining the testing information.

—Undergraduate, Prospective Teacher

Although it might be helpful for the student teacher to let the teacher read her paper, she needs to step lightly. If she were to show her the responses, it would contain a substantial amount of proof, as this teacher seems particularly stuck in her old ways. Additionally, it could be problematic during the rest of the semester if the master teacher felt threatened by Anna and her observations. Congratulations are in ord...

Table of contents

• REFLECTIVE TEACHING AND THE SOCIAL CONDITIONS OF SCHOOLING
• CONTENTS
• SERIES PREFACE
• PREFACE
• ACKNOWLEDGMENTS
• INTRODUCTION
• I CASES AND REACTIONS
• II PUBLIC ARGUMENTS
• III CONCLUDING REMARKS, SOME REFLECTIONS, AND RESOURCES FOR FURTHER REFLECTION
• BIBLIOGRAPHY
• INDEX