Engagement In Mathematics Research Articles

Providing Student Opportunities to Respond in Reading and Mathematics: A Look Across Grade Levels

The evidence for providing sufficient opportunities for students to respond has been established in terms of student engagement and achievement in reading and mathematics. Although supported by research, the question remains whether teachers are incorporating this effective practice in their classroom instruction. This study examines the analysis of data from direct teacher observations during reading and mathematics instruction. Results from the analysis indicate that there is a statistically significant difference between teachers' rate of opportunities for students to respond across grade levels during mathematics and reading instruction. Although opportunities for students to respond rates across grade levels may vary, the rates at all grade levels are lower than recommended. Implications and areas of future research will be discussed.

Identifying Systems of Interaction in Mathematical Engagement

Mathematical engagement is a complex process of interaction between the person and the world. This interaction is strongly influenced by the concepts and structure of the mathematical field, by the practical and symbolic tools of mathematics and by the focus of investigation in the world. This paper reports on research that involves a detailed analysis of the process of mathematical engagement by two postgraduate education students working together to solve a number of mathematical puzzles. A process model of mathematical engagement was developed, identifying coherent systems of ‘thinking in action’. Both mathematical and everyday systems were identified, as well as systems that mediated the interaction between the two. Four fundamental subsystems relate to the mathematical system: subsystems oriented to mathematical objects; mathematical actions; mathematical representations; and mathematical patterns and relationships. A further four functional subsystems relate to the interaction between the mathematical and everyday: subsystems relating to linking; orientation; evaluation; and strategic control. These subsystems are detailed through the analysis of a particular episode in the engagement data.

Supporting young ESL students from disadvantaged contexts in their engagement with mathematics: Teachers’ pedagogical challenges

Australian students from disadvantaged contexts who speak English as a second language (ESL) are at risk of being developmentally vulnerable when compared to their peers (Gonski et al., 2011). This article presents selected findings from a large-scale longitudinal study designed specifically for young students in disadvantaged contexts. It reports the positive students' gains, and the challenges teachers faced while engaging and supporting students in developing their understanding of mathematics. Data were collected from Early Years students (Foundation to Year 2) across three schools with large identified ESL cohorts (N = 379). Additionally, data were also collected from the participating students' teachers (N = 35). The students were tested twice yearly, while the teachers were interviewed three times during the year(s) they participated in the project. The improvements in the students' pre- and post-test scores were statistically and educationally significant. The teachers identified two main challenges as they implemented a program called Representations, Oral Language and Engagement in Mathematics (RoleM). First, relates to language and communication difficulties when teaching students whose first language was not Standard Australian English, and second, the teachers had to rethink their pedagogical practices after participating in RoleM professional learning. The results of this study add to the literature with regard to the pedagogical approaches used to teach mathematics to ESL students. In particular by providing evidence that the concepts of representing and communicating mathematics are intertwined, and thus teaching mathematics as a linguistic experience should be avoided.

Engagement in Mathematical Thinking and the Proficiency Level of Secondary Students

Engagement in Mathematics refers to the strategies to learn mathematics and confidence in the ability to succeed and emotional feelings about mathematics. It plays a vital role in the acquisition of mathematical skills and knowledge by being attracted to their work, persistent despite challenges and obstacles, and they take visible delight in work accomplishments.The purpose of the study was to determine the level of mathematical thinking and proficiency of secondary students of Davao del Norte, Philippines. The other intent of this undertaking was to find out the engagement of the students in mathematical thinking and the achievement of the fourth-year high school students. This study used the descriptive-correlation design. Pertinent data were gathered through the use of questionnaires in assessing the level of achievements of the 163 fourth-year students in Kapalong public secondary schools specifically Capungagan High School, Mabantao National High School and Sua-on National High School. This research employed statistical tools like Analysis of Variance (ANOVA), correlation, t-test and mean. The result revealed that the level of engagement of students in mathematical thinking was high that means that all the strategies are applied by the teachers in the class.

Exploring the Ups and Downs of Mathematics Engagement in the Middle Years of School

This study of 1,601 students in the middle years of schooling (Grades 5-8, each student measured twice, 1 year apart) from 200 classrooms in 44 schools sought to identify factors explaining gains and declines in mathematics engagement at key transition points. In multilevel regression modeling, findings showed that compared with Grade 6 students (upper elementary; the reference category), students in Grades 7 (typically the first secondary school year) and 8 have significantly declined in mathematics engagement from their previous year. Notably, in further analyses, these declines were found to be related to student (particularly mathematics self-efficacy and valuing), home (parent valuing of mathematics and availability of a computer for mathematics), classroom (class-average achievement and perceived climate), and school (socio-economic status and ethnic composition) factors. Implications for research and practice are discussed.

Exploring ESL students’ understanding of mathematics in the early years: factors that make a difference

Students living in disadvantaged contexts and whose second language is English (ESL) are at risk of not succeeding in school mathematics. It has been internationally recognised that students’ socioeconomic background and their achievements in mathematics is more pronounced for Australian students (Thomson et al. 2011). This gap is even more prominent for students who also have English as their second language (ESL). This paper explores the impact of the representations, oral language and engagement in mathematics (RoleM) learning experiences on ESL students’ performance in mathematics in the early years (foundation–year 2). All students participating in the study are from disadvantaged contexts (n = 461). The sample comprised 328 students who identified themselves as having English as a second language (ESL) and 133 mainstream students. Pre- and post-tests were conducted at the commencement and completion of each school year. All students demonstrated a significant improvement on their post-test scores, with ESL students displaying greater gains than the mainstream students. Additionally, students’ results were meeting norm-referenced expectations for students of the same age. A hypothesised taxonomy was developed to further investigate which types of test items foundation ESL students displayed greatest gains. ESL students again outperformed the mainstream cohort on all levels of test categorisation, including questions that were linguistically and conceptually challenging for foundation students.

Locally logical mathematics: An emerging teacher honoring both students and mathematics

This case study explores the mathematics engagement and teaching practice of a beginning secondary school teacher. The focus is on the mathematical opportunities available to her students (the classroom mathematics) and how they relate to the teacher's personal capacity and tendencies for mathematical engagement (her personal mathematics). We use a mathematical process-and-action approach to analyze mathematical engagement and then employ the teaching triad—mathematical challenge, sensitivity to students, and management of learning—to situate mathematical engagement within the larger context of teaching practice. The article develops the construct of locally logical mathematics to underscore the cogency of mathematical engagement in the classroom as part of a coherent mathematical system that is embedded within a teaching practice. Contributions of the study include the process-and-action approach, especially in tandem with the teaching triad, as a tool to understand nuances of mathematical engagement and differences in demand between written and implemented tasks.

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.

Engineering Technology Students’ Attitudes towards Engagement in Mathematics

The objective of this study is to understand and examine the attitudes of Engineering Technology (ET) students towards engagement in mathematics during their studies at the Faculty of Engineering Technology (FTK), Universiti Teknikal Malaysia Melaka (UTeM). In the study, a set of questionnaire that covers the questions on the students' attitudes towards engagement in mathematics was utilized. A total of 332 second year ET students at FTK, UTeM were requested to complete this set of questionnaire during the final week of semester two for 2013/2014 session. From the findings, a conclusion has been drawn regarding the attitudes of the ET students towards engagement in mathematics. The result showed that most of the ET students were very engaged in mathematics, and their engagement was more on behavioral types during the learning process of mathematics in class at FTK, UTeM.

Explanation of Academic Achievement Based on Personality Characteristics Psycho-Social Climate of the Classroom and Students’ Academic Engagement in Mathematics

This research explains academic achievement based on the personality characteristics, the psycho-social climate of the classroom in terms of academic engagement in mathematics. The population was high schoolboys and girls in Damghan city in Iran. Participants were randomly selected using a multi-stage cluster method (513 boys and girls) and they simultaneously completed three questionnaires: academic engagement, the psycho-social climate of the classroom and personality characteristics. Path analysis was used to analyze data. The results showed that the direct effects of personality characteristics and psycho-social climate of the classroom on academic achievement were not significant. The direct effects of openness, conscientiousness and psycho-social climate of classroom on academic engagement were significant. The indirect effects (with mediation of academic engagement) and overall effects of openness, conscientiousness and psycho-social climate of classroom on academic achievement were significant, also the effect of academic engagement on academic achievement was significant.

Teaching Quantitative Reasoning: A Better Context for Algebra

This editorial questions the preeminence of algebra in our mathematics curriculum. The GATC (Geometry, Algebra, Trigonometry, Calculus) sequence abandons the fundamental middle school math topics necessary for quantitative literacy, while the standard super-abundance of algebra taught in the abstract fosters math phobia and supports a culturally acceptable stance that math is not relevant to everyday life. Although GATC is seen as a pipeline to STEM (Science, Technology, Engineering, Mathematics), it is a mistake to think that the objective of producing quantitatively literate citizens is at odds with creating more scientists and engineers. The goal must be to create a curriculum that addresses the quantitative reasoning needs of all students, providing meaningful engagement in mathematics that will simultaneously develop quantitative literacy and spark an interest in STEM fields. In my view, such a curriculum could be based on a foundation of proportional reasoning leading to higher-order quantitative reasoning via modeling (including algebraic reasoning and problem solving) and statistical literacy (through the exploration and study of data).

Relational engagement: Proportional reasoning with bilingual Latino/a students

In this paper, we explored how engagement developed over time during a proportional reasoning unit for a group of US bilingual Latino/a students, with particular attention to aspects of social and cultural activity that supported students’ engagement. Our findings suggest that student mathematical engagement developed primarily as a relational process characterized by students’ social relations across time, their understandings about their relationships with mathematics, and the important relations emerging across proportional reasoning ideas.

Facilitating parental engagement in school mathematics and science through inquiry-based learning: an examination of teachers’ and parents’ beliefs

This study examined teachers’ and parents’ beliefs on the implementation of inquiry-based modeling activities as a means to facilitate parental engagement in school mathematics and science. The study had three objectives: (a) to describe teachers’ beliefs about inquiry-based mathematics and science and parental engagement; (b) to describe parents’ beliefs about inquiry-based mathematics and science and their engagement in inquiry-based problem solving; and (c) to explore the impact of an inquiry-based learning environment comprising a model-eliciting activity and Twitter. The research involved three sixth-grade teachers and 32 parents from one elementary school. Teachers and parents participated in workshops, followed by the implementation of a model-eliciting activity in two classrooms. Three teachers and six parents participated in semi-structured interviews. Teachers reported positive beliefs on parental engagement in the mathematics and science classrooms and the potential positive role of parents in implementing innovative problem-solving activities. Parents expressed strong beliefs on their engagement and welcomed the inquiry-based modeling approach. Based on the results of this aspect of a four-year longitudinal design, implications for parental engagement in inquiry-based mathematics and science teaching and learning and further research are discussed.

The Voces Project: Investigating How Latino/a Immigrant Children Make Sense of Engaging in School and School Mathematics

This study investigates how a group of Mexican immigrant children in the United States made sense of engaging in school and school mathematics. The research focused on a population of Latino/a middle school students who were a distinct minority, building a model that shows how a complex set of cognitive, sociocultural, and institutional factors mediated these students’ engagement and success in school. The results of this research will help educators understand the complex social environment that faces immigrant children and impacts their performance and engagement in school and school mathematics.

Young Australian Indigenous students’ effective engagement in mathematics: the role of language, patterns, and structure

This paper explores the outcomes of the first year of the implementation of a mathematics program (Representations, oral language and engagement in Mathematics: RoleM) which is framed upon research relating to effectively supporting young Indigenous students’ learning. The sample comprised 230 Indigenous students (average age 5.76 years) from 15 schools located across Queensland. The pre-test and post-test results from purposely developed language and mathematics tests indicate that young Indigenous Australian students are very capable learners of mathematics. The results of a multiple regression analysis denoted that their ability to ascertain the structure of patterns and to understand mathematical language were both strong predictors of their success in mathematics, with the latter making the larger contribution.

Transition from Primary to Secondary School Mathematics: Students’ Perceptions

During a longitudinal case study on engagement in Australian middle school years mathematics, 20 students in their first year of secondary school in Western Sydney, New South Wales, were asked about their experiences of the transition to secondary school in relation to their experiences of mathematics teaching and learning. Changes and disruptions in teacher-student relationships were a major cause of concern. This was due to fewer opportunities for teacher-student interactions and a heavy usage of computer-based mathematics lessons during the first months of secondary school. Findings indicate that a strong pedagogical relationship is a critical foundation for sustained engagement in mathematics during the middle years.

Teacher Beliefs as Predictors of Adolescents’ Cognitive Engagement and Achievement in Mathematics

ABSTRACT The authors explored the moderating effect of teachers’ expectancies and general sense of efficacy on the relationship between students’ achievement and their cognitive engagement and achievement 1 year later. They used hierarchical linear modeling with a longitudinal sample of 79 mathematics teachers and their 1,364 secondary school students coming from 33 schools serving disadvantaged communities in Québec (Canada). Results indicate that teachers’ self-reported beliefs directly influenced student academic experience. However, they did not influence more importantly low-achieving than high-achieving students. Such findings suggest that in schools serving low socioeconomic status students, teachers should be made aware of the role their attitudes can play on students’ cognitive engagement and achievement. Special efforts should also be made to help them develop positive attitudes toward all students.

Cultivating Mathematics Identities In and Out of School and In Between

ERICA N. WALKER is an associate professor of matheamtics education at Teachers College, Columbia University, Box 210, 525 West 120th Street, New York, NY 10027; email: ewalker@tc.edu. Her research focuses on social and cultural factors as well as educational policies and practices that facilitate mathematics engagement, learning, and performance, especially for underserved students. Cultivating Mathematics Identities In and Out of School and In Between

Overly Scripted: Exploring the Impact of a Scripted Literacy Curriculum on a Preschool Teacher's Instructional Practices in Mathematics

As part of a renewed focus on early childhood mathematics education, researchers have recently called for increased attention to preschool mathematics curricula. This article, which is based on a multiyear ethnographic study in a rural preschool primarily serving African American children, contributes to this area of interest by documenting the instructional practices a teacher learned from her mandated literacy curriculum. This curriculum, which was highly scripted, shaped the teacher's instructional practices in mathematics as well as in literacy. The teacher's mathematical engagement with children, during formal lessons and informal play, reflected the instructional beliefs of the literacy curriculum, which was demonstrated by a focus on efficiently completing planned tasks, rather than pursuing children's thinking, and by narrowing mathematics to the use of proper grammar and posing simple questions. This study argues that the curriculum's highly structured scripts made it less likely that the teacher would engage in innovative practices in mathematics, which reduced opportunities for children in the classroom to reason and problem solve mathematically. In addition, because of the adoption patterns of scripted curricula, teachers of low-income, minority children are more likely to have their mathematics teaching shaped in this way.

Supporting Teachers’ Professional Learning at a Distance: A Model for Change in At-risk Contexts

This paper examines the effectiveness of a professional learning model developed to support early years teachers in rural and remote communities in Queensland as they began to implement the Australian Curriculum in Mathematics. The data are drawn from 35 teachers at the initial stage of a large, four year longitudinal study RoleM (Representations, oral language and engagement in Mathematics). The particular aims of the longitudinal study are to (a) identify effective pedagogical practices that may assist young Indigenous Australian students to negotiate Western mathematical understanding, and (b) investigate professional learning models that best support teachers within this context. The data was collected throughout the first year of the study. The findings indicate that as the year progressed participating teachers experienced significant and positive changes in: a) their attitudes, beliefs and pedagogical practices in relation to teaching mathematics; b)their expectations of student learning in mathematics; c) their confidence levels to be innovative, creative and experimental implementers of the new national mathematics curriculum; and d) their ongoing development from novice teacher to expert.