Secondary Mathematics Classrooms Research Articles

Teacher Code Switching Consistency and Precision in a Multilingual Mathematics Classroom

This paper reports on a study that investigated teacher code switching consistency and precision in multilingual secondary school mathematics classrooms in South Africa. Data was obtained through interviewing and observing five lessons of each of three mathematics teachers purposively selected from three township schools in the Eastern Cape Province. Elements of Gumperz and Mercer’s work on lesson categories and Dowling’s Domains of Mathematical Practice were used to analyse data. Results showed that code switching frequency in general was inconsistent across different lessons for the same teacher. Code switching frequency by all teachers was, however, consistently highest during questioning and explaining when teaching. All participating teachers used code switching strategies most consistently in the public domain and least consistently in the esoteric domain. Some formal isiXhosa translations of mathematical terms were consistently and precisely used and some were not. Two major forms of code switching emerged, namely borrowing code switching and transparent code switching. Very little transparent code switching, which is critical for supporting students’ understanding and thinking in mathematics, was evident in teacher language. Teachers were consistent in the use of borrowed terms. We conclude that consensual understanding of best practices for code switching is required to promote code switching that is precise, consistent, transparent and thus supportive of teaching for conceptual understanding of mathematics in secondary schools.

Analysing Mathematics Teachers’ TPACK Through Observation of Practice

Technological pedagogical content knowledge (TPACK) has been well accepted as a framework to understand and describe types of knowledge required by teachers to teach specific content with technology effectively. However, limited studies have used the framework in analysing the complexity of technology integration in mathematics classrooms. This study investigates, through examining critical instructional events, the most influential TPACK constructs in understanding and shaping teachers’ pedagogical practices using digital technology. This case study was conducted in an early secondary mathematics classroom in Indonesia that used a web-based resource to support students’ understanding of fractions. The finding suggests that the qualitative examination of the four intersected TPACK constructs assists in understanding the challenges and the opportunities to teachers when utilising an exploratory-based technology. It demonstrates that the combination of pedagogical stances and choice of technology significantly influence the visibility of other TPACK constructs. Implications of this study include the need of thoughtful planning prior to using web-based resources and the importance to utilise critical events in developing and assessing teachers’ TPACK.

IMPLEMENTING MATHEMATICS TEACHING REFORM

This study describes the implementation of teaching reform in secondary mathematics classrooms in a rural poverty school in southwest China where a school-wide teaching experiment took place. Classroom teaching and learning practices are primarily concerned with classroom organizations, interactions and social norms. The results indicate that a collective learning approach was taken in the classroom reform, in which mathematical communications, understanding and engagement of students in learning were promoted. However, there was a lack of diversity of thinking and arguments on solving problems among different level students, which implies the mathematical teaching still focuses on acquiring knowledge over generating knowledge.

A Framework for Teacher Verbal Feedback: Lessons from Chinese Mathematics Classrooms

Background:Teachers’ verbal feedback plays an important role in classroom teaching. Different types of feedback can have different effect on students’ learning. Praise and blame feedback could provide positive and negative result for learners. The gap was left in considering teachers’ attitudes in providing verbal feedback to students.Material and methods:Due to feedback which may culture dependently, the types of teachers’ verbal feedback were studies based on analysis of 24 teachers from 4 regions (Shenyang, Beijing, Hangzhou and Chongqing) in junior secondary mathematics classrooms of China.Results:A coding scheme on the attitudes of teacher verbal feedback was developed which included three categories: “Negative”, “Neutral” and “Positive (Encourage in gesture & Encourage in action)”.Feedback frequency and duration were documented and showed that teachers hold neutral attitudes mostly.Conclusions:Teaching method (student-centered or teacher-centered) and school policy were the most apparent factors presented by this study which can have effect on teacher’s verbal feedback.

Retracted: Development and Validation of the Mathematics Teachers' Beliefs About English Language Learners Survey (MTBELL)

Given the increasing number of English Language Learners (ELLs) in secondary mathematics classrooms, it is imperative that mathematics teacher educators develop measures for determining how and why secondary mathematics teachers (SMTs) understand and respond instructionally to these students. This paper reports on the initial development and validation of the Mathematics Teachers' Beliefs about English Language Learners survey, an instrument that measures SMTs beliefs, attitudes, knowledge base, and instructional practices in relation to meeting the academic and language needs of ELLs. Through piloting processes, the instrument was refined for a research study through which reliability and validity were established. The five constructs identified from exploratory factor analysis illustrate perceived opportunities and barriers in meeting ELLs' academic and language needs among SMTs.This article features a Research to Practice Companion Article. Please click on the supporting information link below to access.

Fostering a Culture of Discourse in Secondary Mathematics Classrooms: Equity Approaches in Teaching and Teacher Education for Emergent Bilingual Students

The continued proliferation of linguistic diversity in US mainstream classrooms, coupled with the language demands of the Common Core State Standards for mathematics instruction (CCSSM), and the National Council of Teachers of Mathematics’ Principles to Actions (PtA), has prompted educational researchers to identify effective, linguistically relevant practices for preparing secondary mathematics educators adept at meeting the needs of emergent bilingual students. In this article we argue for implementation of teacher education courses in mathematics that infuse “pedagogical language knowledge” as a tool for providing future teachers the skills and dispositions to foster a “classroom culture of discourse.” This call come in light of the discipline-specific language demands of the above-mentioned standards and secondary students’ use of variable linguistic repertoires across and within languages to learn and display mathematical thinking and ideas.

Individual teaching methods: Work plans as a tool for promoting self-regulated learning in lower secondary classrooms?

To stimulate individualised learning and give students some autonomy and responsibility in relation to their own schoolwork, Norwegian teachers often use work plans as an instructional tool. A work plan is a document that describes different tasks students are supposed to complete within a certain time period, normally two to three weeks. This article explores whether the use of work plans can be used as a tool for promoting self-regulated learning (SRL). The analyses draw on data from the PISA+ video study. The data include video observations from five lower secondary mathematics classrooms (15-year-olds). Our analyses suggest the teachers rarely provided explicit instructions, cognitive feedback or autonomy-supportive learning strategies.

In-Class Purposes of Flipped Mathematics Educators

This paper provides empirical findings from a study that examined how three grade 7-12 flipped mathematics educators utilized class time when implementing a flipped learning model. Additionally, the researchers investigated the educators' purposes for various in-class tasks as well as their general use of class time. The data revealed flipped mathematics educators engaged students in multiple mathematical activities throughout each class period so as to provide the opportunity for students to develop their (1) introductory content knowledge and procedural fluency, (2) conceptual understanding of mathematical topics, and (3) mathematical problem-solving abilities. Implications from this study contribute to the literature on secondary mathematics classroom teachers’ purposes and provide insights into the classroom practices of flipped mathematics educators.

Development and Validation of an Instrument for Assessing Junior Secondary School Mathematics Classroom Environment in Enugu State of Nigeria

The purpose of this study was to develop and validate an instrument for assessing junior secondary school Mathematics classroom environment as it affects teaching and learning of Mathematics in Enugu State. Instrumentation research design was adopted for the study. The sample of the study consisted of 1710 students drawn from the population of 43,540 Junior Secondary 1, 2 and 3 students for 2010/2011 academic session in the 75 public junior secondary schools in Enugu State. The instrument used for data collection was the Mathematics Classroom Environment Assessment Scale (MCEAS) developed and validated by the researcher. The instrument covered nine dimensions as follows: Involvement, Affiliation, Teacher Support, Task- Orientation, Cooperation, Competition, Order and organization, Teacher Control and innovation. The instrument has two sections: students’ actual and students’ preferred forms. These items will enable students to provide information about the learning environment that is present in their classroom (the actual environment) as well as information about the learning environment that they would like to be present (preferred environment). Three research questions and two hypotheses guided the study. The statistical techniques used in analyzing the data were factor analysis, Cronbach’s alpha and analysis of variance. A test of reliability showed that the instrument was reliable at 0.82 and 0. 97. This result made the researcher to recommend that the instrument MCEAS be used in junior secondary schools in Enugu State to ascertain effective Mathematics classroom learning environment. The findings showed that students preferred more favorable Mathematics classroom environment than was perceived as being actually present.Keywords: Development and Validation, Mathematics, Classroom and Environment

Univocal and dialogic discourse in secondary mathematics classrooms: the case of attending to precision

Univocal discourse, characterized by its function of conveying information from one person to another, is common in mathematics classrooms but dialogic teaching aims at students coming to participate in dialogic discourse, that is, discourse functioning to generate new meaning within a community. Many mathematical practices are directed at the development and refinement of new mathematical ideas, and many mathematics educators call for collaborative sense making, so there is potential for mutual support between dialogic discourse and such practices as attending to precision. Drawing on data from five secondary mathematics classrooms, this study focused on instances of attending to precision in whole-class settings. We coded these instances based on the degree to which the discourse was univocal or dialogic. We found that the instances were predominantly univocal but that these univocal instances varied with regard to whose ideas were being transmitted—the teacher’s or a student’s. Dialogic instances were rare but we share examples in which the co-construction of meaning through discourse involved attending to precision in ways that were qualitatively different than the univocal instances. The study provides illustrations of dialogic interactions and discusses the balance between univocal and dialogic discourse that is sought within dialogic teaching. It also contributes to the field an initial analytic framework for and examples of attending to precision in secondary classrooms. We discuss implications with regard to students’ roles in secondary mathematics classroom discourse.

Cultivating Leadership into Secondary Mathematics Classrooms: Putting Belief into Practice

Effective leadership is critical for the success of an educational organization. Leadership is also one of the key professional responsibilities of teachers. However, leadership often remains an abstract concept even for teachers in leadership positions owing to administrative tasks, day-to-day issues, problems reaching students’ achievement targets, and demanding deadlines. Therefore, this study aims to identify the most common type of leadership possessed by secondary mathematics teachers in Brunei Darussalam. We also investigated whether mathematics teacher-leaders are putting their beliefs into action in their teaching practice. There were three leadership styles identified in the study: Autocratic, Democratic and Laissez-faire. In order to meet the objectives of this small-scale case study, a questionnaire was adapted and distributed to 17 secondary mathematics teachers in two secondary schools in Brunei Darussalam. Pearson's correlation was used to identify the factors affecting teacher's leadership style. One finding from the quantitative analysis indicated that teachers are more likely to adopt the autocratic style of leadership as their teaching experience of mathematics increase. On the other hand, the qualitative part of the study involved two classroom observations and further interviews with two selected teachers from each of the participating schools. The analysis revealed that the two teachers, who practiced democratic and autocratic leadership styles respectively, do put what they believe into their classroom practices.

A professional experience learning community for secondary mathematics: developing pre-service teachers’ reflective practice

This paper reports on the reflective practice of a group of nine secondary mathematics pre-service teachers. The pre-service teachers participated in a year-long, school-based professional experience program which focussed on observing, co-teaching and reflecting on a series of problem-solving lessons in two junior secondary school mathematics classrooms. The study used a mixed methods approach to consider the impact of shared pedagogical conversations on pre-service teachers’ written reflections. It also examined whether there were differences in the focus of reflections depending on whether the lesson was taught by an experienced mathematics teacher, or taught by a pair of their peers, or co-taught by themselves with a peer. Results suggest that after participants have observed lessons taught by an experienced teacher and reflected collaboratively on those lessons, they continue to reflect on lessons taught by their peers and on their own lessons when co-teaching, rather than just describe or evaluate them. However, their written reflections across all contexts continued to focus primarily on teacher actions and classroom management rather than on student learning.

The Status of Proving Among US Secondary Mathematics Teachers

This report examines teachers’ self-espoused attitudes and beliefs on proving in the secondary mathematics classroom. Conclusions were based on a questionnaire of 78 US mathematics teachers who had completed at least 2 years of teaching mathematics at the secondary level. While these teachers placed importance on proving as a general mathematical skill, when they discuss their own classrooms, procedural skill consistently surpasses proof-related activities in importance for a majority of high school teachers. Furthermore, teachers labeling their own past experiences in proving as causing anxiety are predictably more likely to put less value on proving. Interestingly, the quantity of past college mathematics courses is a reverse predictor indicating that further study should consider how students perceptions of proving change as they pass through a mathematics major.

The Effects of the Flipped Model of Instruction on Student Engagement and Performance in the Secondary Mathematics Classroom

In many of the secondary classrooms across the country, students are passively engaged in the mathematics content, and academic performance can be described, at best, as mediocre. This research study sought to bring about improvements in student engagement and performance in the secondary mathematics classroom through the implementation of the flipped model of instruction and compared student interaction in the flipped classroom with a traditional format. The flipped model of instruction is a relatively new teaching strategy attempting to improve student engagement and performance by moving the lecture outside the classroom via technology and moving homework and exercises with concepts inside the classroom via learning activities. Changes in the student participants’ perceptions and attitudes were evidenced and evaluated through the completion of a preand post-survey, a teacher-created unit test, random interviews, and a focus group session. In addition, the researcher documented observations, experiences, thoughts, and insights regarding the intervention in a journal on a daily basis. Quantitative results and qualitative findings revealed the student participants responded favorably to the flipped model of instruction and experienced an increase in their engagement and communication when compared to the traditional classroom experience. The student participants also recognized improvements in the quality of instruction and use of class of time with the flipped model of instruction. In terms of academic performance, no significant changes

I know how to add them, I didn't know I had to add them

: Ten non-English speaking immigrant students shared their lived experiences in their secondary school mathematics classrooms in New Zealand. Through the voices of these students some understandings of the challenges they experienced as second language learners are brought to the fore. The students’ perspectives of the language-related challenges that they faced, how they made sense of learning in an environment where the medium of instruction was dissimilar to their first language, and the impact that language-related challenges may have had on their perceptions of their ability in their new environment compared to their home country, form the basis of this paper.

Examining Classroom Interactions in Secondary Mathematics Classrooms in Brunei Darussalam

This study examined the classroom interactions in three secondary mathematics classrooms in Brunei Darussalam. Investigations were conducted on whether the types of classroom interactions (be it public or private) may have any direct effects on Year 10 students’ learning of mathematics. The participants involved in this study were three mathematics teachers and 78 Year 10 students. Data were collected by video-recording a sequence of three lessons for each of the three classes, the use of lesson feedback forms (which included a questionnaire on code-switching) distributed to the students and student interviews. The results of the study revealed that majority of the lesson time for all three classes were spent on public interaction (78.9%) rather than private interaction (10.4%). Moreover, it was found that the types of interaction have no direct effect on the students’ learning; rather it is how the teacher carried out these interaction types that can affect the students’ learning. From the results of the questionnaires on code-switching, there was an almost evenly divided preference for code-switching (Malay and English) and using ‘English only’ as the medium of instruction among the student participants. It seems that code-switching is only useful in helping the students to understand the lesson better; however it does not necessarily mean that the secondary students learned better when the teacher code-switched during the lesson.

EXPLOITING UNEXPECTED SITUATIONS IN THE MATHEMATICS CLASSROOM

The professional development of mathematics teachers needs to support teachers in orchestrating the mathematics classroom in ways that enable them to respond flexibly and productively to the unexpected. When a situation arises in the classroom which is not connected in an obvious way to the mathematical learning intentions of the lesson, it can be challenging for the teacher to improvise so as to craft this situation into an opportunity for doing and learning mathematics. In this study, as teacher-researcher I maintained a record of unexpected situations as they arose in my own secondary mathematics classroom. Details are given of four unexpected situations which I found ways to exploit mathematically, and these are analysed to highlight factors which may enhance a mathematics teacher’s preparedness for dealing with the unexpected. The results of this study indicate that deviating from the intended lesson to exploit an unexpected situation in which students have shown some interest can lead them into enjoyable and worthwhile mathematical engagement.

Teacher support for collective argumentation: A framework for examining how teachers support students’ engagement in mathematical activities

We propose a framework for examining how teachers may support collective argumentation in secondary mathematics classrooms, including teachers’ direct contributions to arguments, the kinds of questions teachers ask, and teachers’ other supportive actions. We illustrate our framework with examples from episodes of collective argumentation occurring across 2 days in a teacher’s classroom. Following from these examples, we discuss how the framework can be used to examine mathematical aspects of conversations in mathematics classrooms. We propose that the framework is useful for investigating and possibly enhancing how teachers support students’ reasoning and argumentation as fundamentally mathematical activities.

A Literature Review on Disciplinary Literacy

Current adolescent literacy rates cause concerns at the number of students who graduate high school with basic or below-basic reading skills. The Common Core State Standards promote disciplinary literacy, which presents advanced literacy skills embedded in content area instruction. Disciplinary literacy is argued as a way to raise adolescent literacy rates. This literature review examines how Discourse theory frames disciplinary literacy as an apprenticeship model, and how instruction in mathematical Discourses focuses on communication and reasoning at the secondary level. Mathematical standards are analyzed for literacy features, and then studies of secondary mathematics classrooms are reviewed in light of these features. The review is offered to help mathematics teachers and literacy specialists build a shared knowledge base of mathematical literacy in secondary classrooms.

A Glance into Interactions in Some South African Township Mathematics Classrooms

This paper examines the classroom interactions between teachers and students in some secondary mathematics classrooms in South Africa. Cases of twelve lessons of eight teachers were analyzed using the Secondary Teaching Analysis Matrix framework of Gallagher and Parker (1995) to classify teaching into didactic, transitional and conceptual teaching about classroom interactions. Classroom interactions were found to be predominantly didactic. This means among other things that there was little student interaction about the subject matter; short answers predominated; there were few student questions and student-student interaction was rare. The findings will be used for professional development intervention programs to guide teachers to improve dialogue during mathematics instruction. DOI: 10.5901/mjss.2013.v4n13p435