Introduction

Teaching mathematics to secondary education students presents numerous challenges within any classroom environment. For English Language Learners (ELLs) these challenges are compounded as they face learning mathematical concepts while attempting to negotiate the nuances of a language in which they are not particularly fluent. Typically, effective instructional strategies for teaching mathematics to ELLs are not formally presented in mathematics education courses for pre-service teachers. Furthermore, if pre-service teachers are not placed in multilingual mathematics classrooms during their field experiences, they may have limited opportunities to consider and practice instructional strategies to enhance mathematical understanding for ELLs.

Early field experiences during pre-service teacher education have the potential to be a positive influence on beginning teachers’ views of themselves and the ways they intend to teach (Mewborn 2000). Typically, early field experiences provide pre-service teachers their first opportunity to practice and begin to develop instructional practices. Providing meaningful early field experiences often encourages and affirms their decision to pursue a career in the teaching profession (Smalley and Retallick 2011) and the type of learning that occurs during the field experience is more important than the duration of this experience (McIntyre et al. 1996). Moore (1995) believes that early field experiences tend to focus on time management, grading papers, and classroom management and recommends placing more attention on the content taught, how it is taught, and what is learned from it. As important, Greeno et al. (1996) suggest that the situation in which a person first teaches plays a fundamental role in shaping what is learned. Pre-service teachers need opportunities to develop and construct new knowledge in situ, which, as Richardson (1996) suggests, “is the only way to develop the practical knowledge that eventually makes routine at least some aspects of classroom practice and provides alternative approaches when faced with dilemmas” (p. 113). This new knowledge can stem from early field experiences in which beginning teachers are provided with opportunities to face dilemmas or tensions as they consider and enact productive instructional decisions in order to effectively teach ELLs.

This qualitative study examines the tensions, planning, and instructional decisions and practices pre-service teachers use as they teach ELLs mathematics during their first whole-class teaching field experience in Arusha, Tanzania. This setting provides a rich context to study the opportunities of learning to learn to teach. Specifically highlighted are the tensions that pre-service teachers face and the instructional approaches and revisions they make in order to accommodate the learning needs of the Tanzanian students studying mathematics taught in English, which is not their native tongue. These approaches are relevant not only to teaching mathematics in Tanzania, but to all classrooms across the globe where students are expected to learn and understand content taught in a language other than their first language.

Theoretical framework

Cultural-historical activity theory (CHAT) provides the theoretical framework that situates both the activity and analysis of this study investigating the pre-service teachers’ cycles of tensions, instructional planning, lesson enactment, and reflection on their teaching relative to their work in English-medium mathematics classrooms. The three fundamental concepts of cultural-historical activity theory are the activity system, the contradictions, and expansive learning (Engeström 1999). As Meyers (2007) explains:

Learning is not an isolated act; rather it is situated in time and space and influenced by the surrounding actors, resources and behavioural constraints. One should also recognize that agents in the learning process, through their activities, influence the contexts in which such learning takes place. Cultural-historical activity theory, then, as a dynamic model, is particularly appropriate for the study of educational practice.

The activity system is comprised of “the individual practitioner, the colleagues and co-workers of the workplace community, the conceptual and practical tools and the shared objects as a unified dynamic whole” (Engeström 1999, p. 267). One of the defining features of this framework is the notion of contradictions. These contradictions (tensions) and how they are resolved form the impetus of new practices (Meyers 2007). Engeström (1999) describes expansive learning as using contradictions (tensions) as a catalyst for changing activity systems. Contradictions (tensions) should serve as a change agent for innovation and improvement of practice. Figure 1 depicts this expansive learning cycle in terms of the pre-service teachers’ field experience in this study.

Fig. 1
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Expansive learning cycle (adapted from Engeström 1999 and Meyers 2007)

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This expansive learning cycle aligns with the Hiebert et al. (2003) “experiment” model for teaching and teacher preparation in mathematics. As Hiebert et al. suggest, it is important to consider the kinds of environments pre-service teachers are provided in order to influence their own learning. Furthermore, they contend that pre-service teachers may not develop adequate competencies in their preparation programs and must learn to teach by taking advantage of new knowledge gained by themselves and others (Hiebert et al. 2003): “Teachers who are equipped with tools for learning from their experiences are in a strong position to learn more effective methods . . .” (p. 205). Providing pre-service teachers opportunities to study their teaching affords them the chance to develop tools for monitoring and examining their own practice and the impact of their instructional practices, which enables them to learn from their experiences.

Hiebert et al. (2003) further suggest, “Prospective teachers should be inclined and able to treat the lessons they teach as experiments” (p. 206). That is, pre-service teachers must be able to design lessons with well-articulated goals, monitor their implementation and instructional practice, gather feedback, and reflect on their practice with the intention of revising, changing, and improving on future practice. Thus, the cultural-historical activity theory, and this learning to learn to teach “experiment model,” share many of the features of design experiments – a teaching-learning cycle in which pre-service teachers plan, enact, analyse, and revise their work. When pre-service teachers approach their teaching as an experiment, the emphasis then becomes the open and public process needed to grow from a shared knowledge for effective teaching (Hiebert et al. 2003). Figure 2 displays the expansive learning cycle embedded within this teaching-learning cycle.

Fig. 2
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Expansive learning cycle within the teaching-learning cycle

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Cultural-historical activity theory is suitable as a lens in qualitative research, as it provides a framework for understanding and analysing phenomena in an educational setting. Engeström (1999) confirms that cultural-historical activity theory is a developmental theory that seeks to explain and influence qualitative changes in human practices over time. Referring to cultural-historical activity theory, Stillman and Anderson (2011) concur that a collective, mediated, and contradiction-rife context provides an especially useful theoretical lens. With this in mind, this study sought to understand the revisions in instructional practices pre-service teachers were able to make as a result of their contradictions (tensions) teaching ELLs in secondary mathematics classrooms situated in Arusha, Tanzania.

Background

Most Tanzanian students are fluent in at least two languages: their tribal language and Kiswahili, a uniting trade language that approximately 120 different tribes in Tanzania use to communicate with each other. Kiswahili is spoken in Tanzanian parliament, lower judicial courts, and primary schools (Brock-Utne 2003); however, English-medium secondary schools are commonplace in Tanzania due in part to the recognition that English has become the lingua franca for communication in international business, international education, and international research (Paltridge and Starfield 2011). Although English is not the native language of the students or teachers, these schools utilise English as the primary means of instruction. The ability to speak English is often regarded as a status symbol, and as a reflection of a respected education. Many Tanzanians believe that the command of English provides a path to power and prestige as well as success in accessing desirable vocations.

In 1995, the Education and Training Policy (Ministry of Education and Culture 1995) set forth goals for students and teachers in Tanzanian secondary schools. One goal for both Tanzanian students and teachers is the development of linguistic ability and effective use of communication skills in Kiswahili and at least one other foreign language (Qorro 2006). To meet this goal, most students are taught in Kiswahili in primary school, yet are expected to be prepared for English instruction in secondary schools. Basic communication skills in a new language typically requires 2–3 years of study, while gaining grade-level competence takes 4–10 years (Lucas and Katz 1994). These language limitations suggest that most Tanzanian students who matriculate from primary school will not be adequately proficient or prepared to learn in English.

Okwonko (1983) emphasises the important link between language and learning:

There is little doubt that the systematic but frequently ignored differences between the language and culture of the school and the language and culture of the learner’s community have often resulted in educational programmes with only marginal success at teaching anything except self-depreciation. (p. 377)

Students learning mathematics in a language other than their native tongue often struggle to comprehend the concepts. The lack of vocabulary and expressions needed to comprehend mathematics along with the often-abstract content are obstacles that ELLs need to overcome in order to learn. Mathematical terms do not always translate well and students often fail to understand key mathematical vocabulary. Nation and Webb (2011), however, advocate for content-based instruction to help promote vocabulary learning: “Content-based instruction involves the learning of the language while studying content matters . . .” (p. 631). These two issues contribute to the difficulties students face when learning new mathematical content in a second language. Studies have demonstrated that the lack of proficiency in the language of instruction results in poor performance in the subjects taught (Krashen 1985). Warren et al. (2007) further suggest that when there is a mismatch between the language of instruction and the language spoken at home, students are disadvantaged in terms of long-term literacy and numeracy proficiencies. These are significant issues with respect to teaching mathematics to ELLs, and pre-service teachers have not often accumulated the background knowledge from their university training to effectively tackle these problems. How pre-service teachers were able to tackle these issues in terms of an expansive learning cycle is described below.

Data

This qualitative study was designed to encompass a variety of sources in order to triangulate the data and enhance the validity of the research findings (Denzin 2006; Lincoln and Guba 2000). The corpus of data included classroom observations, informal conversations, on-site interviews, lesson plans, oral and written reflections of enacted lessons, blog-posts, and concluding interviews. The data was analysed using Spradley’s (1980) method of data analysis which involves “systematic examination of something to determine its parts, the relationships among parts, and their relationship to the whole” (p. 85) to guide the search for patterns and domains within the data. Specifically, analysis of data included documenting specific instances of the pre-service teachers’ contradictions (tensions), the revisions and subsequent implementation of the instructional strategies that appeared to assist ELLs in understanding the mathematical content, seeking clarification and affirmation of the motivation behind the evidenced strategy, and finally reflections on their modified instructional practices. In addition, once the pre-service teachers verified instructional strategies, common instructional practices were grouped together to form categories. Table 1 summarises the data sources and purposes. The focus of this paper will highlight the enactment of new models of implementation (instructional practices) based on the contradictions (tensions) the pre-service teachers experienced.

Table 1 Data sources and purpose
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The study

This study provides preliminary insight into the capacities of pre-service teachers relative to instructional decisions in teaching mathematics to ELLs with respect to planning, enacting, analysing, and revising their work based on their instructional practices within English-medium mathematics classrooms.

Participants and setting

Fifteen pre-service teachers (mathematics education majors) supervised by two university professors spent 1 month (May 2011) teaching mathematics to secondary students (Form I–Form IV; this is akin to Years 9–Year 12 in Australia, Grades 9–12 in the United States), during an ongoing Study Abroad program situated in Arusha, Tanzania. This program is administered through a university in the Midwestern United States in conjunction with three secondary schools in Arusha. Pre-service teachers were selected to participate in this program through an application and interview process.

Specifically, this study highlights four pre-service teachers who were placed at School A. These students are a representative subset of the students in the Study Abroad program and epitomize the typical mathematics education majors at the university. That is, the pre-service teachers are white middle-class seniors who have completed their mathematics course requirements (Calculus I, II, and III, Euclidean Geometry, Communicating in Mathematics, Linear Algebra I, Modern Algebra, Discrete Mathematics, Mathematical Activities for Secondary Teachers, and Teaching Middle Grades Mathematics) and many of their education courses. They begin their student teaching within a year after returning from Tanzania.

Teaching and learning mathematics in English-medium schools

Learning mathematics for many students can be a complex endeavour, and learning mathematics in an unfamiliar language often compounds the complexity. Language is the source of difficulties for students in learning mathematics, as it plays a significant role in learning (Zevenbergen 2000a). Zevenbergen (2000b) further explains that the nuances of the language of mathematics can be the source of difficulties when the first language is not English. In addition, Zevenbergen states

. . . where there are extreme differences between the language of instruction and background, there is a greater chance for error not due to some innate ability but due to differences between the formal language of school and the language of home. (p. 18)

In the pre-service teachers’ experiences teaching mathematics to secondary students in Tanzania, it was all too apparent to them the difficulties students faced in trying to learn mathematical concepts that were taught in English when the language of home was their tribal language or Kiswahili.

In an attempt to prepare for the experience in Tanzanian schools, pre-service teachers were instructed in basic conversational Kiswahili, (eight one-hour lessons) and learned about the Tanzanian school culture prior to their departure from the United States. In addition, onsite the Tanzanian teachers and students were willing to assist the pre-service teachers in acquiring foundational Kiswahili speaking skills. In spite of consistent efforts, the pre-service teachers’ Kiswahili speaking skills were somewhat limited, and they were cognizant of the fact that this multilingual teaching and learning environment would present challenges for both the students and themselves.

The pre-service teachers were responsible for teaching three or four mathematics classes daily. On their first day at school, the pre-service teachers observed the Tanzanian teachers teaching and then began their field experience work the following day. From the first day of their field experience, the pre-service teachers taught in the classrooms with little or no direct teacher supervision. On occasion, the pre-service teachers and classroom teachers met to discuss content. Table 2 describes the mathematical content the pre-service teachers taught during their experience.

Table 2 Mathematics concepts taught by pre-service teachers across Forms I-IV
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In all cases, the pre-service teachers were responsible for developing the lessons, teaching the lessons, and designing assessments, often without materials or resources. The teaching day concluded with each pre-service teacher individually conferencing with the university faculty members. During this conference they analysed and reflected on the mathematics lessons they taught and how their students engaged in the lessons. It should be noted that the university faculty assisted the pre-service teachers with mathematical content and classroom management recommendations when needed, but did not offer suggestions pertaining to negotiating teaching mathematics to ELLs. As described below, the pre-service teachers navigated these issues on their own or with one another.

The secondary schools where the pre-service teachers taught are private institutions (rather than government-run schools) where English is mandated as the language of instruction. Private schools in Tanzania are non-profit entities and are primarily administered by churches (Samoff 2002). These schools must follow the same curriculum as the government-run schools and are registered with the Ministry of Education. At the conclusion of each academic year, students participate in the Tanzanian National Examinations, which are written in English. Students attending private schools are expected to speak English at all times during the school day. Signs posted throughout the school grounds remind students and teachers of this requirement, although Kiswahili is often overheard when students congregate outside of the classroom and teachers gather in faculty rooms.

According to Puja (2001), students in Tanzania feel uncomfortable speaking English in a classroom as it poses an artificial situation, in that it is not how they typically communicate outside of the classroom. We found similar results while observing the Tanzanian teachers instructing their students. When teachers posed questions in English, students would either not respond or respond with very few simple words in English. The responses, however, were typically inaudible.

Discussion between students and teacher in the mathematics classroom is considered an important aspect of learning (Bailey and Taylor 2010; Walshaw and Anthony 2008) in Western classrooms. Yet, the Tanzanian mathematics teachers observed seldom posed questions requiring students to respond with an explanation or justification of their own reasoning, which could have provided impetus for a discussion. It may be the case that the classroom teachers are not comfortable facilitating a discussion in English. The teachers’ own proficiency level with English is somewhat limited, and it is difficult to orchestrate a productive discussion when language presents a barrier. This dynamic is often counter-productive to social theory, which characterises student learning as active and interactive participation in which meaning is constructed through this active participation (Wenger 1998). Another possibility is that students’ apprehension to respond to questions in English may be a result of the fear of making a language-related mistake in front of their peers. According to Osaki (1991):

Students either talk very little in class and copy textual information from the chalkboard or attempt discussion in a mixed language (i.e., English and Kiswahili) and then copy notes on the chalkboard in English . . . teachers who insist on using English only end up talking to themselves with very little student input. (p. 377)

The language of mathematics is both unique and foundational to learning. Mathematics utilises three types of vocabulary: (1) specialised vocabulary (e.g., collinear, congruent); (2) academic vocabulary, defined as procedural terms that are used across academic areas (e.g., describe, graph, next, pattern); and (3) vocabulary with multiple meanings (e.g., foot, odd, plane, yard), which often leads to confusion when non-native students understand only one meaning. At the onset of the pre-service teachers’ teaching experience in Tanzanian mathematics classrooms, they became aware that most students did not understand many key mathematical terms being taught (e.g., variable, equation, proportion), possibly because of the different types of vocabulary, or because these were words they had not used previously.

Findings

In this section, the contradictions (tensions) the pre-service teachers noted, and their revisions to their instructional practice, are described. In order to orchestrate effective mathematics lessons and promote student learning, the pre-service teachers found it necessary to make shifts in instructional practices. For the most part, these shifts were not instructional practices the pre-service teachers had considered or were aware of prior to their work in Tanzania. Rather, these shifts were a result of the contradictions (tensions) the pre-service teachers experienced as they monitored their implementation and instructional practice, gathered feedback, and reflected on their practice with the intention of revising, changing, and improving future practice.

Instructional revisions in response to contradictions (tensions): vocabulary

Each of the four pre-service teachers remarked that “the students didn’t really understand me,” or “I (we) didn’t know what the students were saying.” Upon their group reflections, the pre-service teachers came to understand that attention to the mathematical vocabulary was of critical importance. During the “design a new model for teaching mathematics” or the “revise” stage of the teaching-learning cycle, the pre-service teachers would often attempt to repeat words in Kiswahili to help the students make sense of the mathematical terms they were using and the concepts they were trying to build, even though English is the language of instruction in these schools. For example, when the students were perplexed by the word equation, the pre-service teacher used the Kiswahili word usawazishaji to help the students understand the question posed. Other words have multiple translations in Kiswahili (e.g., the Kiswahili terms for area include uwanja, mahali, eneo, and mahala), and exact translations are difficult. The approach whereby the teachers uses more than one language to explain an idea is approach is code switching. In reflecting upon their practice the pre-service teachers reported that this instructional strategy was valuable in teaching mathematics. They commented that it was important to ensure that the students understood the mathematical vocabulary in order to help facilitate learning, and commented that “this made a big difference,” and “the students seemed to appreciate our willingness to help explain words in Kiswahili.” When preparing their lessons, the pre-service teachers carefully considered each mathematical term they would use while teaching, and then learned the Kiswahili equivalent of the term. The pre-service teachers came to understand that if they were unsuccessful conveying the information speaking in English, they could often depend on the Kiswahili translation. While the pre-service teachers were aware that instruction was to take place in English, they often reported that they felt an enormous amount of tension between this expectation and desire for the students to learn the mathematics.

Instructional revisions in response to contradictions (tensions): mathematical concepts

Even though the pre-service teachers were able to mediate issues pertaining to mathematical vocabulary, they reflected that some students (typically those students who attended Kiswahili primary schools) continued to experience difficulty understanding the mathematical concepts they were attempting to teach. The pre-service teachers resolved this tension by moving students capable of understanding English near students who did not understand as well. While the pre-service teachers were not able to teach the mathematics lessons in Kiswahili, the students could translate to each other what was being taught. According to Brooks and Brooks (1999), students retain 90 % of the information they teach one another. The pre-service teachers believed that this seating arrangement helped to create a classroom environment that encouraged students to interact and work with one another, even though the students were not familiar with working in groups. In terms of teaching mathematical concepts, the pre-service teachers felt this proved to be a valuable adjustment, as the students who struggled with understanding English felt comfortable asking their classmates to translate to Kiswahili. One pre-service teacher remarked, “This was such a simple move, that really paid off.”

Another instructional practice the pre-service teachers utilised was non-linguistic resources to help communicate the meaning of mathematical concepts. The pre-service teachers appeared to focus primarily on pictorial representations and gestures. McNeill (1992) suggests that gestures are “an integral part of language as much as are words, phrases, and sentences” (p. 2). Shein (2012) offers the notion of gesturing as a critical component for English Language Learners (ELLs) to communicate mathematics. Pointing and representational gestures (i.e., an action or a movement that represents an idea – drawing a diagonal line in the air) was an instructional strategy the pre-service teachers reported to be very effective in their teaching of mathematics to the Tanzanian students. For example, in their lessons that focused on proving triangle congruence using theorems of Side Side Side (SSS), Angle Side Angle (ASA), and Side Angle Side (SAS), the pre-service teachers used gestures to denote triangles (drawing a triangle in the air), pointing to the sides and angles of the triangles in the drawings on the board and in the air. The use of gestures and pictures provided all students access to the mathematical ideas, as these non-linguistic representations are easily understood (Shein 2012).

These contradictions (tensions) the pre-service teachers experienced with respect to vocabulary and mathematical concepts provoked a third modification – their planning process. They were able to determine that not only word choice but sentence structure was crucial because of many students’ limited knowledge of English vocabulary. Even though English is deemed the language of instruction, the pre-service teachers often observed the Tanzanian teachers using Kiswahili in their teaching when students seemed confused. The pre-service teachers purposely considered addressing ways to incorporate simpler sentences and common words in order for the students to better understand what they were attempting to convey. When possible, the pre-service teachers incorporated Kiswahili words and phrases into instruction, introducing a concept using both the English and Kiswahili words when necessary, and asked students to write both in their notes. According to the pre-service teachers, this documentation ensured that all students had a reference throughout the lesson as well as at home. Students were also asked to write in English a summary of what they learned that day. In doing this, students were provided the opportunity not only to practise their English skills, but also to synthesise the mathematical concepts taught during class. Since students typically do not have access to textbooks, these notebooks proved to be a valuable learning tool for instruction.

Instructional revisions in response to contradictions (tensions): context

The pre-service teachers remarked that the initial contexts they presented were meaningless to their Tanzanian students. (“Their faces suggested that the story I made up didn’t register with them.”) The pre-service teachers reflected the importance of purposely integrating relatable contexts into the lesson, infusing common Kiswahili words and contexts such as cattle (e.g., ng'ombe), and money (e.g., shilingi) so students could connect with the ideas. While this is certainly an important instructional practice in any classroom, it became obvious to the pre-service teachers how significant and effective contextualisation in mathematics for ELL students is. The pre-service teachers noted that in these cases the students appeared to be more willing to assist the pre-service teachers with their Kiswahili and engage in the lessons because they realised the pre-service teachers were trying to teach the concepts in a manner that best suited their needs. For example, throughout the lessons on transversals, perpendicular, parallel lines, and angle measures, the pre-service teachers integrated contexts that were very familiar to students. To frame the idea of a transversal they provided the following information:

There are two parallel roads in Arusha, Unuru Road and Sokoine Road. A dalala is traveling down Unuru Road, but several of the passengers want to get to Sokoine Road. What does the dalala driver need to do? [The driver needs to find the road that crosses both Unuru Road and Sokoine Road]. (Student B – lesson plan)

The context of a football field was utilised to communicate the idea of perpendicular and parallel lines. The pre-service teachers remarked that providing these contexts to introduce these concepts was helpful for the students because it enabled them to understand the word, and then build a mental image of real-world applications of transversals, parallel, and perpendicular lines. Whenever possible, the pre-service teachers made an attempt to infuse Kiswahili words and contexts that were both meaningful and relevant for the students. Perso (2003) confirms this instructional practice as she states

the relevance of any mathematical context to a particular group of students, their cultural background, and the subsequent practices of the students and their families are all factors that must be considered by the teacher if meaningful learning is to occur. (p. 15)

Instructional revisions in response to contradictions (tensions): active discussion

Another contraction (tension) the pre-service teachers experienced involved promoting active discussion. The pre-service teachers reflected that the same small number of students volunteered to respond to the questions they posed. This phenomenon was similar to what was observed while the Tanzanian teachers taught. The pre-service teachers noted that the students who did respond seemed more comfortable speaking English. In an effort to engage all of the students and initiate active discussion, the pre-service teachers called upon those students who did not take the initiative to respond to specific questions. While some sheepishly answered the questions, or reluctantly went to the board to solve a problem, many simply stared at the pre-service teachers or attempted to respond in Kiswahili. Since the Tanzanian students often did not fully understand what was being asked or taught, or have the confidence to respond, they typically would not answer the questions or actively participate in the discussion. While the pre-service teachers recognised this was a contradiction (tension), they were unable to mediate an effective resolution in terms of instructional practice. Throughout their field experience in Tanzania, this contradiction (tension) was a source of continued frustration for the pre-service teachers.

Instructional revisions in response to contradictions (tensions): a source for pre-service teachers’ learning

While these are significant issues with respect to teaching mathematics to ELLs, pre-service teachers often have not accumulated the background knowledge from their university training to effectively tackle these problems. This raises the question: How were these pre-service teachers able to make shifts in instructional practices to meet the learning needs of their ELLs mathematics students? Kohler et al. (2008) suggest that pre-service teachers are able to execute some instructional decision making, “such as noting a specific difficulty with student learning and making an on-the-spot adjustment in their instruction” (p. 2108). Johnson (1992) found that pre-service teachers’ instructional strategies were influenced by “unexpected student responses and the desire to maintain the flow of instructional activities” (p. 507). She further believes that pre-service teachers genuinely desire that their students understand the content being taught and are “overwhelmingly influenced by the need to ensure student understanding” (p. 507). The pre-service teachers in this study were driven by the desire to promote effective mathematics lessons to ELLs. This desire provoked contradictions (tensions) within the pre-service teachers and as a group and served as an impetus to analyse, revise, and then reflect on the effectiveness of their practice.

Conclusion

It has been determined that initial field experiences can significantly impact the development of pre-service teachers’ instructional practices. Even though these pre-service teachers will not be teaching in Tanzanian classrooms, providing a field experience where they were faced with significant contradictions (tensions) within a culture much different than their own forced an examination of the effectiveness of their practice and then opportunities to revise their instruction. These opportunities to experience contradictions (tensions) enable pre-service teachers to grow and learn. The need to ensure mathematical understanding seemed to be the primary motivation, and the ensuing tension created opportunities for the pre-service teachers to reflect upon and revise their instructional practices. Faced with a majority of their students finding minimal success understanding mathematics through English instruction, it was necessary to make modifications “to maintain the flow of instructional activities.” Making modifications is significant in all teaching situations, and should be precipitated by the contradictions (tensions) teachers face as they analyse the effectiveness of their instructional practices.

The pre-service teachers recognised that revisions to their instructional practices were necessary in order to effectively teach mathematics to students whose primary language was not English. The Tanzanian students seemed to benefit from the modifications such as purposeful seating of students, code switching, using relatable contexts, non-linguistic representations, and simplifying word choices, which seemed to be effective strategies for the students in this secondary mathematics classroom. While these are not strategies the pre-service teachers learned in their university courses, they quickly understood that using a multi-modal approach that is both culturally and linguistically responsive had a positive impact on the students they taught, and on themselves. It is surmised that what the pre-service teachers gained from this experience will transfer to their own classroom teaching, regardless of culture and location.

This ongoing work in Arusha, Tanzania is both informative and rewarding. Each encounter with the Tanzanian secondary mathematics students and teachers provides insight and awareness, as well as new and different ways to confront instructional practices. Not all pre-service teachers, however, have the opportunity to participate in a field experience teaching in English-medium schools. However, all pre-service teachers should be provided opportunities to plan, enact, analyse, and revise their work. Teacher education programs need to ensure that all pre-service teachers have the opportunities to learn important instructional strategies for teaching ELLs through both their university coursework and field experiences in which they are faced with contradictions (tensions) and in which they must then revise their instructional practices.

These instructional strategies are relevant not only to the ELL students in Tanzania, but to all classrooms across the globe where students are expected to learn and understand content that is taught in a language other than their native tongue. As classrooms continue to become more culturally diverse, it is important that pre-service teachers are provided with the necessary tools and opportunities to meet the learning needs of all students in their classrooms, especially those who are learning mathematics in a language they often do not understand.