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Service Learning in Mathematics
For Undergraduate Future Teachers

Amy Strage

Department of Child and Adolescent Development
San Jose State University

Julie Sliva

Department of Mathematics
San Jose State University

• Abstract
• Introduction and Background
• Method
• Results and Discussion
• Conclusions
• Acknowledgment
• References
• Tables 1, 2
• Appendix A
• Appendix B
• Appendix C

Abstract

We report on students’ reflections, expectations, and performance in an assessment, primarily qualitative, of the infusion of a service-learning component into a college mathematics course designed for undergraduates preparing to be K-8 teachers. Our analysis of student self-reports, along with measures of performance in their mathematics course, seems to confirm that a service-learning component assisting in a middle school mathematics classroom helps students to develop a more secure mastery of the mathematics content of their own course; a better appreciation of how to teach that content to middle-school students; and a more realistic picture of teaching in a public school environment, and whether this was a career goal they wanted to pursue.

Introduction and Background

Standardized testing reveals that expectations for K-12 students are disproportionately and dishearteningly low for mathematics. California is willing to consider schools with as low as 13.9% of students scoring proficient in grade-level mathematics to meet acceptable Adequate Yearly Progress thresholds, satisfying minimum standards (California Department of Education, 2005). Researchers and policy architects who have traced the roots of this problem to teachers’ lack of confidence and competence with respect to mathematics content and pedagogy call for more rigorous coursework in mathematics at the K-12 and college level (e.g., No Child Left Behind). The California Commission on Teacher Credentialing has upped the ante for undergraduates planning to be teachers in its Standards of Program Quality and Effectiveness for the Subject Matter Requirement for the Multiple Subject Teaching Credential (2001). New standards require future teachers to demonstrate firm grounding in the subject matter they will teach, and they call for field experiences that are “early, frequent, and discipline-based.” As a result, an increasing number of college courses are incorporating K-12 classroom components.

Current research indicates that service learning is a powerful and inclusive pedagogy (Billig & Furco, 2002; Eyler, 2002). It helps students to achieve the curricular goals of the courses in which it is embedded (Astin & Sax, 1998; Cohen & Kinsey, 1994; Eyler & Giles, 1996; Gray et al., 1996; Kendrick, 1996; Markus, Howard & King, 1993; Strage, 2000), provides them with a reality check on the challenges and rewards of teaching, and helps them define career objectives (e.g., Gomez, Garcia-Nevarez & Judd, 2003). Two case studies suggest that such hands-on experience significantly enhances teachers’ professional preparation (Ebby, 2000; Vithal, 2003). Still, researchers call for systematic studies to align the experience with specific learning or professional goals (Denton, 1986; Huling, 1998; LeMaster, 2001; Maxie, 2001; Silverman, 1998).

The present study sought to address three questions about the impact of infusing a service-learning experience into math content coursework: (How much) does the service-learning experience help students to develop

• a more secure mastery of the course content?
• a better appreciation of how to teach that content?
• a more realistic picture of teaching in a public school environment, and to confirm their career goals?

The focus of our investigation is the second in a series of three required courses for future teachers. It covers functional representations of algebra, probability and statistical concepts. Modeled after the National Council of Teachers of Mathematics’ guidelines for teaching mathematics, both the course content itself and the pedagogy implemented to teach it are appropriate for K-8 students. Despite the purportedly modest skills required, students find the course very challenging, and as many as one-third regularly receive Ds or Fs. Our expectation, grounded in constructivist theory (for example Vygotsky, 1978), was that the opportunity to help teach concepts that make up the content of the course to younger learners would assist the university students in mastering the material. It would also give them a more concrete and realistic picture of classroom teaching than they would be able to derive from a university-campus-only experience with the course.

Method

Participants

All 55 students enrolled in two sections of the course were invited to participate in an extra-credit service-learning assignment. The assignment entailed assisting in a middle school mathematics class for a minimum of 20 hours, and maintaining a weekly journal of weekly structured reflections. It was worth 50 out of 500 points, tantamount to two-thirds of a course grade (e.g., enough to move a student from a B- to a B+). Ultimately, 24 students signed up for the assignment. Students in both the service-learning (SL) and non-service-learning (NSL) groups were predominantly female (22 of 24 SL students and 27 of 31 NSL students). All were juniors or seniors who declared majors designed for future teachers. All but one of the SL students had previous experience with children in a classroom setting, and all reported having worked with children in some non-classroom capacity, for example, in an after-school program.

Most of the students had transferred from community college, and more than half had taken the prerequisite mathematics course elsewhere. Given the great range in academic extent, focus and rigor of their college experience prior to the course, we felt that cumulative GPA or grade earned in the prerequisite would not have served as valid indices for the purpose of comparing the academic standing of students in the two groups. We used instead performance on examinations within the course, the first one taken two weeks into the course, prior to any service-learning experience.

Students were given a list of interested host teachers, and roughly half (eleven) found placements with these teachers. The remainder (thirteen) secured placements elsewhere. In no case did students have children or siblings at their school sites, and in no case had they been students there themselves. In one case, the student had previously volunteered at the same school site, but with a different teacher.

Data and Data Collection

Students in the SL group completed a variety of written reflections, including

• starting points narrative completed prior to the first classroom visit, where they articulated their expectations and goals relating to their classroom participation;
• student reflections, consisting of structured weekly log entries completed within two days of each classroom visit;
• final field experience reflection completed after their final classroom visit, where they wrote about their experience over the course of the semester; and
• field experience pre- and post-surveys, consisting of Likert-type and open-ended items focusing on their goals and expectations, were completed before their first and after their final classroom visits, respectively. This instrument, developed by the first author and her colleagues, has been administered to some 600 other future teachers at four campuses.

Additionally, scores earned by students in the SL and NSL groups on course assignments were compared; see Appendices. For coding of narrative data, categories were derived through analyses of the corpus and reciprocal reliability checks performed by the two authors. In general, there was excellent agreement between coders (>90%), and anomalies were resolved through discussion.

Results and Discussion

We begin with a snapshot of students’ starting points, and we then present evidence from our data as it speaks to our specific questions about the impact of the service-learning experience.

Starting Points

Before their participation in the middle school classroom, students were asked to reflect on their expectations and goals for the semester.

Evidence from the Starting Points Reflections

Three themes emerged in response to the initial prompt to “list and elaborate upon three or four adjectives or phrases that describe how you feel about your upcoming experience.” Of 21 respondents, 18 said they were excited and eager to participate in a “real classroom”; 14 reported some apprehension; and 13 reported looking forward to the information this experience would provide them about career choices.

When asked what they thought would be easiest, the most common answer (12 of 21) was that they looked forward to this opportunity to observe in a real classroom.

When asked what they thought would be most difficult, about half (10 of 21) were concerned that their own mathematics skills might not be strong enough. This finding is consistent with earlier researchers’ reports that many future teachers were “math-anxious” or “math-avoidant” (Kelly & Tomhave, 1985; Rech, Hartzell & Stephens, 1993). The next most commonly cited challenge concerned the more content-neutral question of “connecting” and communicating with the middle school students, although expectations were mixed: seven students expressed concern that they would have trouble in this area, while five thought it would be easy.

Evidence from the Field-Experience Pre-Survey

One of the pre-survey narrative items asked students what they expected to learn from their service-learning experience. Protocols from 19 students were available for analysis. Nearly everyone (17) indicated that they expected to learn about teaching. Four students said that they expected to learn about the realities of the job, and two said they looked forward to confirming their interest in teaching.

(How Much) Does the Service-learning Experience Help Students to Develop a More Secure Mastery of the Course Content?

Five sources of information were examined to address this question.

Evidence from students’ exams and projects

A series of one-way ANOVAs was performed to compare the performance of the SL and NSL students overall, on the four course exams, and on the course project. The second author, as the course instructor, knew which students were participating in the service-learning experience. However, all grading entailed applying an objective rubric, minimizing the possibility of scoring bias. In terms of final course outcome, students in the SL and NSL groups performed comparably (a .05% difference in total points earned in the course). But examination of the scores on the four course exams suggests that the SL students may have started at something of a deficit and then caught up. Their scores on the first exam were 7.4% lower than those of the NSL students, but their scores on the rest were nearly identical (1.6%, .49%, and .95% lower, respectively). The SL students’ scores on the course project, completed near the end of the semester, were 5.8% higher than those of the NSL students. This project entailed applying course constructs to a real-world situation of the students’ choosing.

The apparent modest advantage enjoyed by the SL students may have stemmed from their experience working with the middle school students. While the differences on the first exam and the course project did not achieve statistical significance, they do suggest a marginally beneficial effect of the service-learning experience. (See Table 1.)

Table 1.
Service-learning (N = 24) and non-service-learning (N = 31) students’ course performance. (Scores reported as percentages.)

Evidence from the Field Experience Post-Survey. All 24 students in the SL group agreed or strongly agreed with the statement, “This field experience has helped me learn the material in this course.”

Evidence from the Weekly Student Reflection Logs

Every student noted at least one mathematics concept which they found easier to grasp as a result of their having the chance to watch the middle school teacher present it, or to teach it themselves. The following two comments illustrate this outcome: “This activity really reinforced my understanding of the ideas we have been learning in class about box arrays and theoretical results versus experimental results.” and “The more methods I see to explain the difficult quadratic formula and equations, the more it secures my understanding of quadratic equations.”

Evidence from Students’ Final Field Experience Reflections

In response to the prompt “How has participating in a middle school mathematics class affected your understanding of the content we covered in Math 105 this semester?” two thirds of students (16 of 24) identified particular constructs from their mathematics course that they felt they had “learned better” or “finally understood.” The following comment, drawn from a student’s final reflections, illustrates this outcome of the service-learning experience:

Participating in a middle school math class has dramatically increased my understanding of the content in Math 105. … As my confidence level increased, so did my test scores. Observing in Laura’s class helped me to better understand the math content as well as how to teach it to children.

Two students indicated explicitly that the middle school classroom experience had not helped them learn the college course content. One said it was too simple, and the other was generally very critical of the host teacher with whom she had been placed.

(How Much) Does the Service-learning Experience Help Students to Develop a Better Appreciation of How to Teach the Content?

Throughout the weekly logs, the final reflection and the post-survey, students shared their insights into the importance of being skilled in classroom management techniques, of being patient, of understanding middle school students, and of having a broad repertoire of teaching strategies, in order to reach every child in the classroom.

Evidence from the Field Experience Post-Survey

All 24 respondents either agreed or strongly agreed with the post-experience survey item, “This field experience has helped me develop skills such as teaching strategies and classroom management techniques, and leadership and teamwork skills.”

Several themes emerged from students’ responses to the post-survey prompt, “What did you learn from your field experience this semester?” Nearly half of the respondents wrote about how many teaching strategies and techniques they saw their teacher use on any day (eleven), as well as about how many classroom management techniques teachers had, and how important they were in creating and maintaining effective learning environments (ten). Seven commented on how diverse students were in their abilities and in their learning styles. Five reflected on insights they had gleaned about how to motivate students and keep them interested, and four commented on how important it is for the teacher to be patient. Evidence from Students’ Weekly Reflection Logs. Students’ comments about insights they had could be divided into three categories: accommodating the wide diversity of learners by approaching teaching in many ways; seeking feedback from students in order to appreciate what they were learning and where they were struggling; and the having command of a full repertoire of effective classroom management techniques. (See Table 2.)

Table 2.
Students’ insights about effective teaching methods reported in reflection logs (N = 24)

(How much) Does the Service-learning Experience Help Students to Develop a More Realistic Picture of Teaching in a Public School Environment, and to Confirm Their Career Goals?

This section reports on the evidence that the hours spent assisting in middle school classrooms provided valuable opportunities for students to glean a more realistic picture of the everyday lives of teachers, and to revisit the question of whether this was a good fit for them.

Evidence from the Field Experience Post-Survey

All 24 respondents either agreed or strongly agreed with the post-experience Likert item, “I have a good understanding of the challenges and resources in the school community where I completed my field experience.”

Of 23 respondents, 16 agreed or strongly agreed with the Likert item, “This field experience has helped me decide what career to pursue.” Of the seven who disagreed, three had already been confident of their career objective prior to the field experience and four students indicated that they were still exploring. Additionally, while none of the participants had mentioned middle level teaching as a career objective on their pre-surveys, seven did on their post surveys, six of whom had initially declared they wanted to be elementary teachers, and one who was still undecided.

When asked, “What, if anything, surprised you about your field experience?” students cited a variety of things. Nearly half (11 of 24) commented on characteristics of the middle school students themselves, seven in more positive terms, citing their energy and enthusiasm as well as their responsiveness to intellectual challenge; but four others responded in more negative terms, citing their insubordination, lack of attentiveness, and disengagement from school matters. Six students commented on the magnitude and variety of job demands. Three commented on how pleasantly surprised they were to find themselves well suited to the job, and three gave other responses.

When asked, “How has this field experience affected your thoughts about your career goals?” all 24 respondents expressed enthusiasm about teaching. Twelve indicated that the experience had allowed them to confirm a desire to teach; seven indicated that they had confirmed desire to teach at the elementary level; a five said they were thinking about switching to teaching at the middle or secondary level; and two, who had expressed some doubt about teaching earlier in the semester, indicated that they were now more enthusiastic about working in the classroom.

Evidence from Students’ Weekly Reflection Logs

Four main themes relating to the realities of the job emerged in students’ weekly writings. Over three-quarters of the students (20 of 24) commented on the vital role of patience. An equal number commented on how different middle school students were, cognitively, socially and emotionally, from younger learners, and how this created different kinds of demands on elementary and middle school teachers. Half of the students wrote extensively about the impact of standards and high stakes assessment on daily life. And finally, five commented on the special challenges of working with children who were not fully English language proficient. They wrote thoughtfully about how this obstacle made it harder for students to learn, but also harder for teachers to appreciate how much mathematics the students actually understood. Notably, four of these five students were not native speakers of English themselves, and they drew on their own experiences.

Evidence from Students’ Final Field Experience Reflections

The final reflections were replete with descriptions of student insights about what teaching, teaching mathematics, and teaching middle school students were really like. The apprehensions students had expressed in their starting points reflections apparently were ill-founded. They did, in fact, feel that they connected with the students and were able to make a difference. One student comments were representative:

I learned a lot about what it’s like to be a teacher in a seventh or eighth grade classroom. … I observed many different approaches to classroom management and motivation techniques to get the students interested and focused on the task at hand. This experience made me really think about teaching this particular age group, the potential lessons I could teach and how I might teach them. The field experience gave me a real life look into what it is like to be a middle school math teacher as well as what its like to be an adolescent growing up in this time, which I think gave me more insight as to how I might motivate the students in my future classrooms.

Conclusions

To be sure, this study is preliminary, and lacks the methodological rigor envisioned by Furco & Billig (2002), and the limitations are admittedly numerous. Our sample size is modest. Participants were not randomly assigned to service-learning or non-service-learning groups, but were volunteers for an extra-credit assignment. Little quality control was exercised in the selection of teachers. Students spent only twenty hours in the middle school classroom. Their contributions were not tabulated directly in terms of hours spent on specific work. Measurement of their understanding of mathematics concepts was confined to scores on tests within the course. Further, the present investigation did not seek to assess the impact of the students’ presence in the classroom on the middle school students or their teachers. These limitations notwithstanding, some preliminary conclusions can be drawn from the confluence of evidence collected.

These data provide support for the CCTC recommendation that future teachers participate in “early, frequent, and discipline-based” field experiences (2001). Future teachers who participated in this experience gained skill in mathematics; they appear to have developed a more textured appreciation of how to approach teaching those concepts, as well as a more realistic picture of teaching in contemporary schools; and they appear to have gleaned valuable insights about how well suited they felt to a career as an educator.

These findings extend other researchers’ assertions that service-learning experiences can enhance mastery of course content (see Kendrick, 1996; Knutson Miller, Yen & Merino, 2002; Markus, Howard & King, 1993). They are also consistent with the literature regarding the utility of service-learning as a pedagogical vehicle for enabling future teachers to better understand the subtle aspects of the role of the teacher in contemporary public schools (Hamm, Dowell & Houck, 2000; Service Learning 2000, 1999; and Strage, Meyers & Norris, 2002).

Our current work involves comparing outcomes for students enrolled in service-learning-required course sections vs. sections where other, non-field-based assignments are required. We are collecting data regarding a broader array of dependent variables (including content knowledge, pedagogical skills and teaching efficacy). We are also collecting information from host teachers to identify effects of the college students’ classroom contributions on them and on their students.

Acknowledgment

The authors wish to express their appreciation to San Jose State University for its support of the research reported in this paper through a Learning Productivity Grant.

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Posted April 5, 2006.

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Publication in this journal in no way indicates the endorsement of the content by the California State University, the Institute for Teaching and Learning, or the Exchanges Editorial Board.
©2006 by Amy Strage and Julie Sliva.

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