Elementary Mathematics Classrooms Research Articles

Using Mixed Methods to Evaluate Modified Schema-Based Instruction in General Education Classrooms

In this convergent mixed methods design study, single-subject and qualitative data were collected concurrently to provide an in-depth picture of the impact of a modified schema-based instructional intervention. The intervention was delivered using instructional trials embedded across general education math lessons and a modified concrete-semi-concrete-abstract instructional sequence. This study investigated the impact of the intervention on the word-problem-solving, strategy use, and concept acquisition of three students with extensive support needs. The paraprofessional-delivered intervention was implemented in elementary general education mathematics classrooms using embedded instruction and focused on teaching students to solve addition and subtraction word-problems. Single-subject data indicated that all three students learned to solve word-problems given concrete materials but needed more time to master the use of semi concrete supports. Qualitative data indicated that students used taught and untaught strategies to solve word-problems, and mastered addition word-problems before subtraction when they were taught simultaneously. Data were integrated in narrative format to explore how strategy use and concept acquisition related to student word-problem-solving performance. Limitations and implications for research are discussed.

Relationships between elementary mathematics specialist certification, knowledge, beliefs, and classroom learning environments

AbstractWe report on the differences in mathematics learning environments in classes taught by certified Elementary Math Specialists (EMSs) (n = 28) and their peers (n = 33) as determined by observations of instruction. We used path analysis to examine how variables such as mathematical knowledge for teaching, beliefs, and background characteristics were related to the learning environment. We used the Classroom Learning Environment Measure (CLEM) observation protocol, which attends to aspects of mathematics lessons such as opportunities for students to justify their reasoning and attend to mathematical concepts. Our analysis revealed that learning environments incorporating such elements were significantly more prevalent in classes taught by EMSs, and that there were two paths indicating mediation effects on the relationship between EMS status and learning environment. One path was related to teachers’ beliefs about the primacy of computation in learning mathematics; the other path was related to teachers’ mathematical knowledge for teaching and their beliefs about the extent to which mathematical knowledge is constructed by the learner. We share implications for EMS programs and recommendations for future research on the impact of EMSs in elementary schools.

Exploring affordances and limitations of between-group movement in elementary mathematics classrooms

In this exploratory study, we examine how between-group movement, as an autonomy-promoting practice, might incentivize or disincentivize sixth-grade students’ engagement in two mathematical practices: (1) making sense of problems and persevering in solving them; and (2) constructing viable arguments and critiquing the reasoning of others. Between-group movement refers to a pedagogical strategy wherein teachers allow groups to physically move within the classroom while problem-solving to discuss strategies, ask for help, or check their work with other groups. Exploring both the affordances and limitations of between-group movement, we found that between-group movement supported groups to construct viable justifications, among other sense-making mathematical practices. However, we also found that some groups over-scaffolded during between-group conversations which disincentivized meaningful engagement in mathematical practices. Furthermore, between-group movement revealed some equity concerns in relation to status-based privileges. The findings imply that between-group movement can be a constructive pedagogical practice under specific conditions.

Spatial configuration of hundreds charts influences children's knowledge of base‐ten concepts

AbstractThe hundreds chart is a valuable tool for teachers in elementary mathematics classrooms. The present study investigated the effects of spatial configurations of virtual hundreds charts on children's knowledge of base‐ten concepts. Kindergarten and first‐grade students were assigned to three instructional conditions in which they worked with a researcher to solve arithmetic word problems. The charts used in the conditions differed by the spatial configuration of the numbers: (a) top down, with numbers increasing from top to bottom; (b) bottom up, with increases from bottom to top; and (c) explicit bottom‐up, with a bottom‐up chart and an explicit visual cue that prompted a comparison between the “up‐is‐more” structure to a cylinder filling with water. Participants were more likely to count by tens than by ones to solve problems when the numbers in the chart increased from top to bottom than when they increased from bottom to top. No effects of spatial configuration on place‐value knowledge was observed. One account of the findings is that participants were more accustomed to the movements in the top‐down chart because they matched the direction in which children learn to read. The role of spatial affordances of instructional materials in children's mathematics learning is discussed.

Creating a context for graduate student learning through constructivist inquiry: Introduction to academia as learning through play

ABSTRACT In this article, I explore the impact of receiving mentorship into research and theory of the field that was guided by a social constructivist learning lens. I reflect on the ways that my conception of research and research agenda were framed subconsciously by early experiences investigating my secondary mathematics teaching practice under the mentorship of Dr. Terry Wood. Terry mentored through listening, posing questions, creating cognitive conflict, and encouraging my autonomous exploration. What stood out from this process are the parallels between her words about constructivism, applied to the elementary mathematics classroom, and her ways of mentoring me into the space of mathematics education research, theory, and practice. Her patient and student-centered mentorship had a profound impact on my ways of framing and studying teacher learning.

Impacting teachers’ reflection on elementary mathematics classroom videos in online asynchronous professional learning contexts

Video-based learning (VBL) aids STEM teacher professional development. In synchronous, in-person settings, researchers have linked changes in teachers’ reflective comments about videos to changes in their beliefs and classroom practices, which are associated with improved student outcomes. However, questions remain about VBL on asynchronous professional development websites, without facilitator support. This study experimentally examined how prompts, mathematical content, camera focus, and motivation for commenting impacted 300 educators’ reflective comments on videos in an online learning community. Results indicated that prompts targeted at specific focal areas (teachers, students, mathematics) produced more reflection on those focal areas, but less reflection in non-focal areas.

Building Teacher Capacity and Leadership in Elementary Mathematics Classrooms in Nova Scotia: Review of the Certificate in Elementary Mathematics Pedagogy

Building Teacher Capacity and Leadership in Elementary Mathematics Classrooms in Nova Scotia: Review of the Certificate in Elementary Mathematics Pedagogy

Multiple Scaffolds Used to Support Self-Regulated Learning in Elementary Mathematics Classrooms

This study uses the knowledge structure of the adaptive learning platform to explore the model of elementary school students' self-regulated learning of mathematics. The research objects are 85 students who are in grade five. In the two experimental groups, students are divided into groups to carry out scaffold-support self-regulated learning and experimental teaching. The control group conducts traditional teaching. The results of the study show that: 1) The self-regulated learning model supported by multiple scaffolding performs better than the traditional teaching models in learning mathematics. And it is also superior to the traditional narrative of only teaching materials provided by the digital learning platform. 2) The learning performance of high achievement students is higher in Experimental Group 1 compared to all the other groups. 3) Students in Experimental Group 1 have more confidence in themselves as compared to those of Experimental Group 2 with regards to these five aspects including self-regulated learning/planning, self-monitoring, evaluation, reflection, and effort.

Creating Complexity in the Elementary Mathematics Classroom

Complexity thinking provides a unique perspective on classroom interactions, student engagement and classroom management as well as insight into innovative pedagogies for teachers in the elementary mathematics classroom. A novel meeting strategy for classroom organization offers teachers the opportunity to observe complexity in action and to promote student participation through mathematical conversations thereby building the learning community and fostering the discourse of mathematics. The intervention of mathematical conversations created conditions for complexity in an elementary classroom and provided qualitative data for analysis. Transcripts and classroom mapping showed increased student engagement with students afforded more freedom, mobility and choice to host or participate in small-group conversations. An analytic framework indicated three types of conversations emerging: sharing information, building knowledge and exploring possibilities as well as instances of blocking behavior. Findings suggest possibilities for building student capacity for conversation skills, disciplinary integration and differentiating learning significantly for students.

Impact of Interactive Pedagogies on Students’ Academic Achievement in Mathematics at Elementary School Level in Quetta City, Balochistan.

This proposed research tested the impact of interactive pedagogies (demonstration and discussion pedagogies) on students’ academic achievement in Mathematics at elementary school level. This study was limited to Quetta city of Baluchistan, Pakistan. This study was emphasized, to analyse the current pedagogies in use at elementary Mathematics’ classrooms, to highlight the difficulties which students are facing in understanding the Mathematics, to explore the impact of interactive pedagogies on students’ academic achievement in Mathematics and to find out the strategies for implementing the interactive pedagogies in an effective way. The sample size was the 235. (N#235). 200 students (grade 11 & 12), 30 teachers (mathematics teachers) and 5 experts were the sample of this research study. This study used mixed method in design. Both quantitative and qualitative data was collected. The quantitative data was collected through observation checklist, pre-test, and post-test while qualitative data was collected through interview. The quantitative data collected through observation was analysed through frequency and %ages while pre-test, post-test was analysed through paired sample t-test by entering the data into SPSS 20 version. Qualitative data collected was analysed through thematic analysis.

An Analysis of Elementary Mathematics Teachers' Feedback Use and Mathematics Classroom Culture

An Analysis of Elementary Mathematics Teachers' Feedback Use and Mathematics Classroom Culture

Understanding Meaningful Exchanges: Mathematics Discourse Analysis and Complexity Thinking

The focus in this paper is on the analysis of student-centered discourse through applying a discourse analysis tool that I developed to analyze data from an elementary mathematics classroom. The purpose of the analysis tool is to understand the impact of the complex learning system on the emerging classroom discourse. The minimum conditions for complexity created an invitational space for students that allowed interactions and meaningful exchanges to flourish through exploration of mathematical concepts and collective participation in classroom discourse. The analytic lens provides the teacher with a tool to understand more clearly the dynamics of meaningful exchanges identified as sharing, building, exploring and blocking.
 Keywords: Classroom discourse; mathematics education; complexity

Investigating Elementary Students’ Problem Solving and Teacher Scaffolding in Solving an Ill-Structured Problem

This study investigated the features of elementary students’ problem solving skills, when teachers provide scaffolding in the process of solving an ill-structured problem in an elementary school mathematics classroom in Seoul, South Korea. In this study, participants solved the ill-structured problem following the phases of Analyze, Browse, Create, Decision-making, and Evaluate. When problem solving was completed without the phase of the Evaluate, to provide metacognitive scaffolding helped to analyze the information of the problem in more depth by returning to identifying related information, which was the sub-phase of Analyze and Browse. When there were difficulties in deepening their understanding of the information from the problem situation, to provide strategic scaffolding helped to access information in an organized way and facilitated solving an ill-structured problem. Based on these results, this study draws implications about scaffolding that can help in the process of solving ill-structured problems, and ultimately suggests the direction to advance to improve problem solving ability in mathematics education.

Baseline Assessment in the Elementary Mathematics Classroom: Should it be Optional or Mandatory for Teaching and Learning?

Too few mathematics teachers have the expertise to apply baseline assessment for differentiated learning in mathematics classes. This empirical study was conducted in a focus group of sixty learners and three teachers in a grade four mathematics class. It proved that teachers of mathematics in elementary grades could profitably learn to conduct baseline assessments; developing activities to benchmark learners’ abilities and learning needs. The exploratory research design was utilized to set up the general sample and the focus group, and mixed research methods; qualitative and quantitative instruments to collect data and analyzing data. The records of scores obtained by learners from the assessment activities and the interviews with teachers were the main sources of data. Data analysis followed quantitative procedures and presented in figures and categorized them in frequency distribution tables. Findings highlighted that learners can reach their optimal levels in learning mathematics in a free and flexible environment. This paper concludes that the lack of knowledge about how to conduct baseline and its value is one of the attributes of the high failure rate of children in the middle class. This article recommends the consideration of baseline assessment to be an essential aspect of a continuous professional development program for mathematics teachers. https://doi.org/10.26803/ijlter.19.8.18

“So what are we working on?”: how student authority relations shift during collaborative mathematics activity

This paper explores peer interactions in an elementary mathematics classroom (ages 9–10) where the teacher intentionally shared authority with her students and supported them in learning to share authority with one another. Authors examine how students shifted between shared, concentrated, and contested social and intellectual authority relations in partner and small group work during a three-week unit on place value. Findings show that (a) students were able to share both social and intellectual authority, and did so often; (b) the distribution of social authority was more dynamic than that of intellectual authority; and (c) when groups shifted into shared intellectual authority, shifts were usually preceded by a student making some aspect of the collaborative task public. We connect these findings to research on authority in mathematics classrooms that serve racially and linguistically minoritized students and offer directions for future work.

Book Review: Andreas J. Stylianides (2016) Proving in the elementary mathematics classroom

Book Review: Andreas J. Stylianides (2016) Proving in the elementary mathematics classroom

Learning and teaching with preservice teachers: An action research for modelling and building faculty-school collaboration

To make refinements in school curricula is not solely enough to improve the quality of education. We need to provide professional development for both in-service and preservice teachers to enable them implement those reforms in their classes. For preservice teachers, field experiences are the best opportunity to observe experienced teachers, make practice of reforms in a classroom setting and learn from their own teaching experiences. In this study, we aim i) to propose a model for faculty-school collaboration in which teacher educators and preservice teachers teach together in an elementary mathematics classroom and ii) to discuss the effects of this model on preservice teachers’, mathematics teachers’ and students’ views and practices. An action research was employed in a 7th grade mathematics classroom to investigate the impacts of the proposed model. The results revealed that our model made meaningful contributions to i) preservice teachers’ understanding and practice of teaching mathematics, ii) mentor teacher’s classroom practices and iii) elementary school students’ participations in mathematics lessons.

Learning and Teaching with Preservice Teachers: An Action Research for Modelling and Building Faculty-School Collaboration

To make refinements in school curricula is not solely enough to improve the quality of education. We need to provide professional development for both in-service and preservice teachers to enable them implement those reforms in their classes. For preservice teachers, field experiences are the best opportunity to observe experienced teachers, make practice of reforms in a classroom setting and learn from their own teaching experiences. In this study, we aim i) to propose a model for faculty-school collaboration in which teacher educators and preservice teachers teach together in an elementary mathematics classroom and ii) to discuss the effects of this model on preservice teachers’, mathematics teachers’ and students’ views and practices. An action research was employed in a 7th grade mathematics classroom to investigate the impacts of the proposed model. The results revealed that our model made meaningful contributions to i) preservice teachers’ understanding and practice of teaching mathematics, ii) mentor teacher’s classroom practices and iii) elementary school students’ participations in mathematics lessons.

Teachers’ responses to student mathematical thinking in Chinese elementary mathematics classrooms

AbstractRecent research on teachers’ use of student mathematical thinking (SMT) and recommendations for effective mathematics instruction claim that how teachers respond to SMT has great impact on student mathematical learning in the classroom. This study examined some Chinese mathematics teachers’ responses to student in‐the‐moment mathematical thinking that emerged during whole class discussion. The findings of this study revealed that the majority of Chinese elementary mathematics teachers in the data involved the whole group of students to make sense of in‐the‐moment SMT. They either invited students to digest SMT involved in the instance or provided an extension of the instance to further develop student mathematical understanding.

Enhancing achievement and interest in mathematics learning through Math-Island

Conventional teacher-led instruction remains dominant in most elementary mathematics classrooms in Taiwan. Under such instruction, the teacher can rarely take care of all students. Many students may then continue to fall behind the standard of mathematics achievement and lose their interest in mathematics; they eventually give up on learning mathematics. In fact, students in Taiwan generally have lower interest in learning mathematics compared to many other regions/countries. Thus, how to enhance students’ mathematics achievement and interest are two major problems, especially for those low-achieving students. This paper describes how we designed a game-based learning environment, called Math-Island, by incorporating the mechanisms of a construction management game into the knowledge map of the elementary mathematics curriculum. We also report an experiment conducted with 215 elementary students for 2 years, from grade 2 to grade 3. In this experiment, in addition to teacher-led instruction in the classroom, students were directed to learn with Math-Island by using their own tablets at school and at home. As a result of this experiment, we found that there is an increase in students’ mathematics achievement, especially in the calculation and word problems. Moreover, the achievements of low-achieving students in the experimental school outperformed the low-achieving students in the control school (a control group in another school) in word problems. Moreover, both the low-achieving students and the high-achieving students in the experimental school maintained a rather high level of interest in mathematics and in the system.