Mathematics Instructional Practices Research Articles

Professional Ability System and Effective Strategies in Enhancing Teaching Competence Among Mathematics Student Teachers

This study compares mathematics student-teachers' professional ability system and instructional practices. Content, pedagogical, technical, classroom management, and reflective practice were examined as part of their professional ability system. Modeling, guided practice, co-teaching, differentiation, technology integration, formative assessment, and collaborative learning were also assessed. The study also examined if student-teachers' professional ability system affects their math teaching practices. Content knowledge and effective teaching practices, especially modeling and guided practice, are strongly correlated. Teaching tactics and pedagogical knowledge are strongly correlated, underscoring their value in guided practice and collaborative learning. Although technological skill has a moderate association, it is essential for using digital tools in mathematics instruction. Collaboration in teaching is highly linked to classroom management skills. Modeling, guided practice, and formative assessment are strongly correlated with pedagogical content knowledge. Reflective practice is linked to all teaching styles, demonstrating its importance in improving mathematics education and permitting varied teaching methods. Modeling is linked to content, pedagogical, and reflective practice in teaching methodologies. Guided practice correlates well with content, pedagogical, and reflective practice. Classroom management and pedagogical content knowledge are closely related to co-teaching. Differentiation tactics strongly correlate with reflective practice and technical competency. Classroom management and reflective practice are strongly correlated with technology integration. The association between formative evaluation and reflective practice and differentiation is substantial. Reflective practice and differentiation are strongly linked in collaborative learning environments. For effective mathematics instruction, a full professional ability system must include topic knowledge, pedagogical understanding, technical competence, classroom management skills, and reflective practice. These components enable varied teaching methodologies, improving mathematical education. These components together shape effective mathematics instruction, as shown by the substantial correlations.

Teaching Mathematics in Kindergarten: How Does Instruction Differ by Classroom Ability?

Background/Context: Kindergarten mathematics instruction is critical for students’ future academic success. The nature and quality of this instruction may vary depending on classroom characteristics. However, little empirical work has examined how mathematics instruction in kindergarten might differ based on classroom performance levels. Purpose, Objective, Research Question, or Focus of Study: This study focuses on whether kindergarten teachers’ mathematics instructional practices differ based on reported performance levels of students in the classroom. In particular, we focused on whether mathematics instructional time, as well as the extent to which teachers use traditional versus ambitious mathematics practices, differed based on teaching a higher proportion of children performing below grade level. Research Design: This study used a nationally representative dataset of approximately 2,900 kindergarten teachers from the Early Childhood Longitudinal Study, Kindergarten Class of 2010–11. With these data, the study utilized a model that compared teachers to each other within the same school (i.e., school fixed effects). Conclusions or Recommendations: This study found that mathematics instructional time did not differ based on the proportion of children reported to be below grade level in the classroom. However, how teachers taught mathematics differed: teachers who reported having a greater percentage of students performing below grade level used ambitious practices less frequently. These findings were not moderated by measures of teacher background or teachers’ reported expectations of their students.

Mapping research trends in mathematical creativity in mathematical instructional practices: A bibliometric analysis

Mapping research trends in mathematical creativity in mathematical instructional practices: A bibliometric analysis

Pre-service teachers’ preparations for designing and implementing creativity-directed mathematical tasks and instructional practices

Pre-service teachers’ preparations for designing and implementing creativity-directed mathematical tasks and instructional practices

Using a Superfactorial Problem to Provide Extended Problem-Solving Experiences

ABSTRACT The purpose of this paper is to describe the use of a problem involving superfactorials (a specific product of factorials) that provides an in-depth and comprehensive mathematical experience, encompassing skills that mathematicians view as tantamount to exploration. The problem is easily accessible and fosters creativity and perseverance, thereby allowing participants to practice standard steps in developing a mathematical argument: from the problem, to simplifications, then conjecture, and finally proof. We present a brief solution to this problem and then discuss how the experience in trying to solve this problem may evolve during a professional development session for teachers. By providing teachers with extended time to investigate a single problem, we aim to provide professional development opportunities beyond the standard mathematical content or instructional practices. This problem also makes a welcome addition to any undergraduate mathematics curriculum and could be used in a mathematics for liberal arts course, capstone course, or any course with a focus on developing problem-solving skills and the process of doing mathematics.

Shona Mathematical Instructional Practices in Bilingual Primary Schools in Zimbabwe

Many Zimbabwean mathematics classrooms have student populations from diverse cultural backgrounds who speak diverse Shona dialects. Most of the mathematics teaching is not related to the learners’ world or everyday experiences because it is taught in English, a second language for most of these learners. Teachers therefore play a fundamental role in making sure that learners in this bilingual setup understand the mathematical concepts being taught. The debate on whether English or indigenous languages are suitable for use in education is increasing. This paper explores possible instructional practices to assist bilingual learners. A qualitative approach was used to explore the instructional practices used by primary school teachers during the teaching and learning of mathematics in Zimbabwe. The findings indicated that teachers code-switched between English and Shona and also used examples from the learners’ environment. It was concluded that there was a possibility of using a bilingual model including Shona and English when teaching mathematics to bilingual learners. The idea is to create a caring, colourful, exciting, stimulating, and reflective environment as a way of engaging learners even if they are from diverse cultural and social backgrounds. The latter would also reduce marginalisation of bilingual learners.

Learning about Active Learning While Actively Learning: Insights from Faculty Professional Development

ABSTRACT With knowledge in hand that teaching mathematics through active engagement leads to better learning outcomes for students, the field of mathematics is now tasked with researching effective facilitation of professional development for faculty. Our university embarked on an initial year of active learning professional development for mathematics faculty, implementing and researching a variety of professional development formats. We conjectured that effective faculty professional development, like effective mathematics instruction of students, would engage faculty in active learning experiences. Initial results indicate that effective professional development for faculty is tightly aligned with effective classroom instruction of students. This paper provides a framework of professional development practices for faculty, informed by a subset of mathematics instructional practices.

Using Direct Observation to Document “Practice-Based Evidence” of Evidence-Based Mathematics Instruction

Implementation of evidence-based practices (EBPs) is paramount to students’ development of mathematics proficiency. This study investigated “practice-based evidence” of interventionists’ actual use of explicit mathematics instruction, a well-established EBP. Specifically, this study analyzed direct observation data collected in a federally funded efficacy trial involving a Tier 2 first-grade mathematics intervention to examine whether the quantity and quality of explicit mathematics instruction was associated with the mathematics outcomes of 470 first-grade students with or at risk for mathematics learning disabilities. Associations between group-level pretreatment skill levels and the quality and quantity of explicit mathematics instructional practices used in the intervention were also explored. Findings suggested significant associations between positive gains in student mathematics outcomes and (a) lower rates of incorrectly answered mathematics-focused questions, and (b) the rate in which interventionists delivered group-level practice opportunities and offered academic feedback. Significant associations were also found between initial student mathematics performance and rates of student errors and the quality of explicit instruction. Implications for using direct observation to document enacted EBPs are discussed.

Examining the Alignment of Mathematics Instructional Practices and Mathematics Vocabulary between Core and Intervention Materials

AbstractWithin a multitiered system of support (MTSS), students who struggle to learn mathematics often receive core instruction and supplemental intervention in different settings, with different teachers and different sets of curriculum materials, all of which can result in poor alignment. This curriculum crosswalk describes how three sets of materials commonly used to provide core instruction and intervention differ with regard to mathematics practices and vocabulary. The results indicate that there is little overlap among all three programs for the majority (n = 6) of the mathematics practices, and very little overlap in mathematics vocabulary (ranging from 6.3 to 24 percent). We also provide a set of research‐based instructional recommendations intended to help teachers address gaps and improve alignment of core instruction and intervention.

Math Instructional Practices in General Education Classrooms With and Without Students With High-Incidence Disabilities

This study compares mathematics instructional practices in classrooms that do and do not contain students with high-incidence disabilities (HIDs). To do so, we examined a national data set of responses from kindergarten teachers about instructional practices. We do find that in classrooms with students with HIDs, teachers reported different frequencies of math activities as well as skills instruction. These differences depended on type of HID. There were no differences in the frequency of time spent on math, meaning that classrooms with and without students with HIDs reported the same amount of math instruction per week. Differences in these findings arose based on teacher qualifications. Implications for policy are discussed.

Elementary teachers’ mathematical beliefs and mathematics anxiety: How do they shape instructional practices?

AbstractThis quantitative study investigated the relationships among practicing elementary teachers’ (N = 153) beliefs about mathematics and its teaching and learning, mathematics anxiety, and instructional practices in mathematics. When viewed singly, the findings reveal the teachers with higher levels of mathematics anxiety tend to use less standards‐based instruction and those with beliefs oriented toward a problem‐solving view of mathematics reported more standards‐based teaching. A combined analysis shows that after controlling for mathematical beliefs, teaching longevity, and educational degree attainment, there is no relationship between teachers’ mathematics anxiety and instructional practices. These findings suggest a spurious relationship between anxiety and practices, with beliefs having the strongest relationship with practices. Several suggestions for positively influencing the mathematical beliefs and affect in general of elementary teachers while learning mathematics are offered.

FACE-TO-FACE AND ONLINE PROFESSIONAL DEVELOPMENT FOR MATHEMATICS TEACHERS: A COMPARATIVE STUDY

The study compared the effects of a professional development course delivered in an online and a face-to-face format. The effects examined included changes in teachers’ pedagogical beliefs, instructional practices, and understanding of teaching number-sense and related mathematical concepts. The study randomly assigned participants to either the online or the face-to-face format and employed the same instructors, reading materials, and instructional activities for both formats of the course. Both formats of the course were also delivered over the same eight-week period and required participants to invest approximately the same amount of time each week engaging in learning activities. Both formats of the course showed significant impacts on teachers’ mathematical understanding, pedagogical beliefs, and instructional practices. Consistent with prior research on online versus face-to-face instruction, the positive outcomes were comparable across both formats. Interestingly, teachers who participated in the online course reported that they were more willing to take courses in the future online than did teachers in the face-to-face condition. Further research is needed to determine whether this finding is limited to self-selectedteachers, the specifics of this course, or other factors that limit generalizability.

Affective Factors and Instructional Practices in Mathematics Among Elementary School Teachers

The purpose of this quantitative, correlational study was to explore the relationships between mathematical beliefs, mathematical attitudes, mathematics anxiety and instructional practices in mathematics of the elementary school teachers in Guiuan districts. This study included 143 elementary school teachers handling mathematics classes. The Pearson-Product Moment Coefficient was the statistical tool used to examine the relationships between variables. Results indicated a statistically significant positive relationship between mathematical beliefs and instructional practices in mathematics, significant positive relationship between mathematical attitudes and instructional practices in mathematics, and significant negative relationship between mathematics anxiety and instructional practices in mathematics. The teachers-respondents hold a constructivist belief about mathematics, have a positive attitude towards mathematics, experience neutral level of mathematics anxiety, and utilizes student-centered instructional practices in mathematics. Their instructional practices in mathematics is significantly affected by their mathematical beliefs, mathematical attitudes and mathematics anxiety. This study suggests that in curriculum implementation, affective factors like beliefs, attitudes, and anxiety must be given importance just like content knowledge. This study further suggests that teacher educators should strive to minimize mathematics anxiety among prospective teachers more than just teaching mathematical pedagogies and content knowledge as this will eventually lead to the development of effective student-centered instructional practices in mathematics.

Learning Lessons from Instruction: Descriptive Results from an Observational Study of Urban Elementary Classrooms

Background For nearly three decades, policy makers and researchers in the United States have promoted more intellectually rigorous standards for mathematics teaching and learning. Yet, to date, we have limited descriptive evidence on the extent to which reform-oriented instruction has been enacted at scale. Purpose The purpose of the study is to examine the prevalence of reform-aligned mathematics instructional practices in five U.S. school districts. We also seek to describe the range of instruction students experience by presenting case studies of teachers at high, medium, and low levels of reform alignment. Participants We draw on 1,735 video-recorded lessons from 329 elementary teachers in these five U.S. urban districts. Research Design We present descriptive analyses of lesson scores on a mathematics-focused classroom observation instrument. We also draw on interviews with district personnel, rater-written lesson summaries, and lesson video to develop case studies of instructional practice. Findings We find that teachers in our sample do use reform-aligned instructional practices, but they do so within the confines of traditional lesson formats. We also find that the implementation of these instructional practices varies in quality. Furthermore, the prevalence and strength of these practices corresponds to the coherence of district efforts at instructional reform. Conclusions Our findings suggest that, unlike other studies in which reform-oriented instruction rarely occurred, reform practices do appear to some degree in study classrooms. In addition, our analyses suggest that implementation of these reform practices corresponds to the strength and coherence of district efforts to change instruction.

Creating a Virtual World for Mathematics

A virtual world was created using the popular sandbox game Minecraft to support the development of preservice teachers’ knowledge for teaching mathematics. Preservice teachers explored the virtual world for a geometry activity involving area and volume problems. They then discussed how this integration of technology could support students’ effective learning of mathematics in a meaningful way. The findings of the study demonstrated that to a certain extent the Minecraft activity supported the transfer of knowledge from preservice teachers’ mathematics content knowledge to their mathematics pedagogical and instructional practice knowledge. Preservice teachers appreciated the usefulness and effectiveness of the Minecraft activity in enhancing the teaching and learning of mathematics by visualizing mathematical concepts in the virtual world. This integration of technology also gave them an opportunity for professional growth. Although this study focuses on preservice teachers’ perspectives on the Minecraft activity, the technology integration using Minecraft will also be beneficial for students because it engages them in active and discovery learning.

Korean elementary school teachers’ implementation of mathematics instruction for students struggling to learn mathematics in inclusive settings

In this study, the researchers used a researcher‐developed online survey to examine the beliefs of elementary school general and special education teachers regarding inclusion and their implementation of mathematics instructional practices. Participants were 55 general and 38 special education teachers. The data analysis was performed using frequency analyses, crosstabs statistics (Fisher's exact test) and independent t‐tests. Results indicated that both general and special education teachers recognised the importance of and need for inclusive education. Further, the most frequently used instructional groupings were a whole class and an individualised grouping for general and special education teachers respectively. The two groups’ responses about the use of instructional materials and practices varied considerably. Finally, both groups reported a relatively high level of confidence in mathematics topics in general. Limitations, recommendations for future research and instructional practices are discussed.

Educating the Whole Child: Kindergarten Mathematics Instructional Practices and Students’ Academic and Socioemotional Development

Background To date, school policies and practices have emphasized early-schooling mathematics instructional practices only as a way to boost academic achievement. However, because young children spend a large part of their formative years in classroom settings, it is important to understand not only the link between instruction and achievement but also the link between instruction and socioemotional development. Our study addressed this issue. Using a nationally representative dataset of kindergarten students, we inquired into which early mathematics instructional practices might be linked to a range of child outcomes, including both achievement and socioemotional development. We also investigated whether these associations varied across different subpopulations of students. Population The ECLS-K: 2011 dataset for a nationally representative sample of kindergartners in 2010–11 was used. Children were assessed in mathematics at kindergarten entry and at the end of the kindergarten year. Their socioemotional development was also rated by teachers and parents. Research Design We used student-level multiple regression analyses with school fixed effects, a rich set of individual, family, and classroom covariates, and school cluster-adjusted standard errors to estimate the associations between kindergarten mathematics instructional practices and achievement and multiple socioemotional outcomes. Conclusions We found that several instructional practices were associated with multiple types of outcomes, often with different results for different types of students. Thus, an exclusive focus on achievement likely obscures the full range of influence that teaching practices have on student success. As school systems increasingly seek to foster socioemotional learning, it is important to establish a research base that considers the links between pedagogy and all facets of childhood development.

A Survey of Elementary School General Education Teachers' Beliefs on Inclusive Education and Mathematics Instructional Practices for Students with Disabilities and Learning Difficulties

A Survey of Elementary School General Education Teachers' Beliefs on Inclusive Education and Mathematics Instructional Practices for Students with Disabilities and Learning Difficulties

Factors Associated with Alignment between Teacher Survey Reports and Classroom Observation Ratings of Mathematics Instruction

AbstractWe investigated the alignment between a teacher survey self-report measure and classroom observation measure of ambitious mathematics instructional practice among teachers in two urban school districts using two different standards-based mathematics curricula. Survey reports suggested mild differences in teachers’ instructional practices between the two districts, whereas observation ratings indicated starker differences. That said, teachers’ survey and observer ratings were significantly correlated in both districts. Factors significantly predicting the extent of survey-observation alignment included teachers’ grade level, Mathematical Knowledge for Teaching, cognitive demand, and—for one district—teachers’ adherence to the surface-level aspects of their curriculum. Qualitative analyses suggested that teachers’ survey-observation alignment could be a function of their interaction with colleagues who provided instructional models against which they could gauge the extent of their standards-based i...

Developing a Mathematics Instructional Practice Survey: Considerations and Evidence

As mathematics teacher educators, it is imperative that we have high-quality tools that conceptualize and operationalize mathematics instruction for large-scale examination. We first describe existing instructional practice survey scales, including their conceptualization of practice and related validity evidence. We then present the framework and initial validity evidence for our mathematics instructional practice survey. Survey participants were inservice teachers in a statewide mandated mathematics professional development course. Statistical analyses indicate the items measure two constructs: social-constructivist and transmission-based instructional practice. Of particular interest is the result that these two constructs were negligibly correlated. This is in contrast to the generally accepted notion that social-constructivist and transmission-based instructional practices are the two polar ends of a single construct for describing instructional practice.