Mathematics Instruction Research Articles

Math-LIGHT problem posing by three experts with different fields of expertise: Why? What? and How?

The Math-LIGHT program is directed at promoting literacy-rich mathematical instruction in middle school. A team of designers with different types of expertise pose Math-Light problems. We perform comparative analysis of problem-posing activities by experts with different types of expertise. We demonstrate that Activity Theory (Leontiev, 1978) is a powerful theoretical framework for the analysis of the structure of problem posing activity. Framed by activity theory we ask “Why?” questions to understand the main goals of posing problems; “What?” questions are directed at the characteristics of the PP process and PP products; and “How?” questions are aimed at identifying the tools used by the designers to fit the conditions in which the problems are implemented. We find that the three designers’ problem-posing activities are complimentary and suggest that the cooperative problem posing process is essential for posing problems that integrate different perspectives and thus allow more goals to be attained.

Examining the elements of culturally relevant pedagogy captured and missed in a measure of high-quality mathematics instruction

Mathematics instruction is not race or culture neutral. For students who have been historically marginalized in mathematics classrooms, high-quality mathematics instruction, instruction that helps students build conceptual understanding, on its own might not be enough to disrupt inequities. These students might also need instruction that is culturally relevant, with teachers who demonstrate cultural competence, build critical consciousness, and support student learning. Our goal in this study was to understand which components of culturally relevant pedagogy (CRP) are captured and which are missed in a typical U.S. framework of high-quality mathematics instruction. To find the overlaps and gaps, we analyzed the mathematics lessons of three elementary teachers through both the lens of CRP and the Mathematics-Scan, a mathematics observation tool. We found the strongest overlap between the two frameworks in the patterns of strengths and weaknesses in the teachers’ lessons. When the teachers were delivering high-quality instruction, they were also often supporting students’ learning or showing cultural competence. When the teachers were delivering lower quality instruction, they were also often missing opportunities to enact CRP. At the same time, key elements of CRP including linguistic support for students, high expectations, critical consciousness, and nuances within cultural competence, were missed by the high-quality instruction framework. High-quality instruction was the foundation for CRP in the teachers’ classrooms, but CRP was more than just high-quality instruction. We conclude with recommendations for increasing the alignment between the frameworks and implications for international educators also grappling with equity in their own frameworks of mathematics instruction.

Indonesian Realistic Mathematics Education: Alternative Mathematics Learning Approach to Improve Fifth Grade Numeracy Literacy Skills

According to the findings of observations, students’ literacy numeracy skills are still considered to be weak. The findings of the computer-based national assessment show that fewer than 50% of pupils have attained the required level of ability. This study aims to analyze the impact of Indonesian realistic mathematics education on numeracy literacy skills of fifth grade students. The type of research used in this study is a quasi-experimental design with a non-equivalent control group design. The population of this study were all fifth-grade elementary school students as many as 123 people consisting of 8 classes contained in 8 public elementary schools. The entire population is equalized with a one-way ANOVA test after giving a pretest. If the entire population is declared equal, the sampling technique used is cluster random sampling. The data collection method was collected using a 3 questions description test, then the data was analyzed using descriptive statistical analysis techniques and inverential statistical analysis techniques with the Polled Variance T-Test. The result found that the Indonesian realistic mathematics education learning approach affects the Numeracy Literacy Skills of Fifth Grade Students by 52.9%. The findings of this study provide a theoretical foundation for applying the PMRI approach to mathematics instruction in elementary schools, with a focus on students’ numeracy literacy skills.

The quality of prospective mathematics teachers' dynamic geometry tasks in terms of the coordination between mathematical depth levels and technological actions

AbstractBackgroundTeachers must have the skills to find, select, design and use technology‐based mathematical activities that focus on high‐level cognitive demands—supporting student reasoning. However, they experience various difficulties in creating, planning and making decisions about how and when to utilize technological affordances.ObjectivesThis study aims to examine the quality of prospective school mathematics teachers' (PMTs) tasks containing the use of dynamic geometry software through the analysis of the coordination between mathematical depth levels (MDLs) and technological actions (TAs), according to Trocki and Hollebrands', Digital Experiences in Mathematics Education, 2018, 4, 110–138, Dynamic Geometry Task Analysis Framework.MethodsWithin groups, PMTs designed lesson plans that included dynamic geometry tasks (DGTs) based on the learning outcomes of the middle school mathematics curriculum. They then created micro‐teachings of these tasks. The participants' DGTs and transcripts of their microteaching videos were the main data sources.ResultsWe found that many prompts included no TA or a single TA, regardless of the prompts' MDLs. Moreover, the results showed that the high‐depth prompts aimed to contribute to students' reasoning processes on geometric concepts through the TAs, which required specific tools such as dragging and sliding to get generalizations. Although the groups differed in the quality and number of DGTs, the groups' lesson plans mostly contained low‐ or medium‐quality DGTs regarding the coordination between MDLs and TAs.ConclusionsInforming PMTs about high‐quality technology tasks and increasing their awareness on this matter is a priority to encourage them to incorporate innovative technological activities in their mathematics instruction.

The Worked-Example Effect and a Mastery Approach Goal Orientation

This study aimed to explore the impact of a mastery approach goal orientation (MAGO) on learning from worked examples. In this experiment (N = 98, mean age = 13.9 years), learners had their MAGO measured, and received instruction in mathematics, either through a worked-example or a problem-solving strategy. The study demonstrated that the worked-examples approach resulted in enhanced retention (but not transfer) and decreased cognitive load when compared to the problem-solving approach. However, there was a significant interaction between instructional strategy and the MAGO, indicating that only learners with a high MAGO benefited from worked examples. Learners with higher MAGO levels also experienced less cognitive load than learners with a lower MAGO. These results indicate a moderating role of MGO in enhancing the effectiveness of worked examples. This study also found that prior knowledge was the only factor influencing transfer performance, highlighting the importance of studying its impact.

Elementary Teachers Designing Culturally Grounded Cases for Preservice Teachers: A Process for Reciprocal Learning

Connecting university methods courses and teacher daily practice is a persistent challenge in teacher education. Another challenge is preparing teachers to enact equitable instruction that meets the needs of an increasingly diverse student population. We take on these challenges by supporting practicing elementary teachers to design case-based teaching scenarios for preservice teachers that engage them with enacting culturally grounded mathematics and science instruction. We draw on data from workshops with teachers to illustrate how the design process elevates teachers’ voices while also supporting their own learning. Workshop features that proved powerful for teachers included collaborating with colleagues, offering and receiving peer feedback, and working with a table describing key features of culturally grounded pedagogy in mathematics and science.

Centering First-Year Teachers’ Instructional Visions and Professional Voices in a Community of Practice

First-year teachers often experience tensions between their visions of high-quality and equitable mathematics instruction and the realities of school culture and politics. Subsequently, first-year teachers need a professional learning space where they can be supported in enacting their instructional visions while developing their professional voices. In this paper, we share the voices of four first-year teachers and how a community of practice supported them to navigate the individual challenges of their classroom practices. Findings from this study yielded two major themes: 1) the community of practice supported them to reflect, envision, and articulate alternative realities; and 2) instructional visions were filters that empowered them to strengthen their professional voices while developing as equitable mathematics teachers.

Experiences of Learners with Mathematics Learning Difficulties in Regular Classrooms in Malawian Secondary Schools

The purpose of this study was to establish the experiences of learners with mathematics learning difficulties in regular classrooms in Malawian secondary schools. The study embraced the qualitative approach and it was conducted in the Central West Educational Division in Lilongwe, at one secondary school with the learners’ population of 1,100. Forty learners were sampled at the school to be involved in the study. Data was analyzed using the thematic method. Out of the results of the study, it was concluded that students experienced lack of support from their teachers as most teachers had negative attitude towards them. Teachers’ use of poor Mathematics Instruction techniques caused the learners to have difficulties in the subject. Furthermore, lack of teaching and learning materials made the teaching and learning of Mathematics more theoretical than practical, which made the subject even more difficult for learners with Mathematics Learning Difficulties. The study recommends that the Ministry of Education needs to orient the general education teachers in mainstream schools on the effective teaching of learners with learning challenges such as those with Mathematics Learning Difficulties. Furthermore, there should be school based Continuous Professional Development programs for teachers of Mathematics to improve their classroom delivery of Mathematics lessons. The Ministry of Education should provide required teaching and learning materials in order to facilitate the teaching and learning of Mathematics.

Perceptions of Malaysian University Mathematics Instructors of the Challenges they Face in Implementing Effective Distance Learning

Perceptions of Malaysian University Mathematics Instructors of the Challenges they Face in Implementing Effective Distance Learning

Understanding the onto-semiotic approach in mathematics education through the lens of the cultural historical activity theory

Research in mathematics education can be understood as a system of activities addressing the basic and applied problems related to teaching and learning of mathematics. Such a system includes the activities of foundation, planning, implementation, evaluation of mathematics instruction, and teacher professional development, which are supported by different theories. This diversity of theories raises interest in their comparison, coordination, and possible integration. The paper aims to present a case of application of the Cultural Historical Activity Theory (CHAT), in its 3rd and 4th generation versions, to analyze the emergence of the Onto-semiotic Approach to mathematical knowledge and instruction as a theoretical framework that addresses the study of the five partial activities mentioned above. This use of the CHAT can be useful in studies on theory articulation by focusing not only on the subjects, the object, and the instruments but also on the community context, the ecological-normative environment in which these activities take place, and the dilemmas or contradictions between theories.

Learning and constructions of us and them in teachers’ collaborative groups

ABSTRACT Background Many studies have pointed to the importance of trust and inclusiveness in teachers’ collaborative groups. Here, we investigate how teachers negotiate dividing lines between “us” and “them” in moment-to-moment interaction. We also examine relationships between these negotiations, local arrangements, and teachers’ opportunities to learn. Methods We analyzed video recordings of two teacher groups, both oriented toward equitable mathematics instruction. We coordinated microinteractional analyses of four episodes with analyses of local arrangements that shaped interaction. Findings In both groups, participants worked to construct a sense of solidarity as “us.” Yet the threat of being positioned outside this “us”—as one of “them”—narrowed opportunities for teachers in both groups to engage in the vulnerable work of grappling with tensions and contradictions together. The salience of this threat was greater in one group than the other, however. We trace this to local arrangements that were differently designed, with different affordances for constructing “us” and “them.” Contribution The social negotiation of exclusion and belonging in teacher groups is highly consequential for teacher learning. Better supporting teacher learning is not just a matter of remediating individuals’ skills or dispositions; it requires learning environments designed to support engagement with the tensions inherent in teaching..

Exploring the enactment of a coaching stance: Findings from one coach–teacher dyad

AbstractCoaching teachers is complex work as coaches must navigate multiple and competing roles of expert and colleague. Within mathematics education, there is a lack of research exploring how coaches enact their stance for coaching, balancing the roles of expert and colleague, in ways that best support teacher learning. Furthermore, little is known about the specific discursive practices coaches use when enacting different stances during mathematics interactions with teachers. Drawing on data collected from one coaching cycle for one coach–teacher dyad during mathematics instruction, including transcripts of two planning meetings, one modeled lesson, one reflection meeting, and five semi‐structured interviews, this study explores one instructional coach's discursive enactment of their coaching stance. Qualitative analyses indicate that the coach had the goal of enacting a responsive coaching stance, and in her practice the coach discursively enacted multiple coaching stances. Furthermore, findings indicate that the coach's disciplinary expertise seemed to influence the discursive enactment of her coaching stance. Implications for research and practice are discussed.

The Critical Roles of a Mathematics Specialist in Establishing Effective, Coordinated Professional Development Systems

ABSTRACT For nearly three decades, mathematics research has indicated the need for high-quality mathematics instruction including both ambitious and equitable practices, as well as continuous, innovative learning opportunities for educators. Teaching practices and standards for mathematical practice have been identified to provide guidance. While research connects effective professional development (PD) to improved instructional practices, there is a need for additional research on the role mathematics specialists play in developing and sustaining PDs. This qualitative case study examined the multiple roles of a specialist while laying the foundational components for a coordinated PD system to improve and strengthen mathematics teaching and learning in elementary classrooms. The PD efforts included the implementation of a teacher subsystem where a specialist led all components consisting of pull-out PD, mathematics coaching, collaborative time, and teacher networks. This study took place at a rural, pre-K through fourth-grade school in a southeastern state. Analysis of the data identified the specialist’s key roles in each component of the teacher subsystem. The results indicated that the development and implementation of a teacher subsystem impacts the overall effectiveness of PD. Findings serve as a foundation for specialists to design and implement coordinated efforts that can have positive impacts on the teaching and learning of mathematics.

Factors Influencing E-learning Adoption when Teaching Science, Technology, Engineering, and Mathematics (STEM) Disciplines at a Science and Technology University in Ethiopia

eLearning technology in Science, Technology, Engineering, and Mathematics (STEM) instruction may positively impact the quality of education in preparing a competent 21st-century workforce in developing countries. Adopting eLearning technology in higher education institutions' STEM departments in developing countries is critical in allowing its graduates to compete in the global workforce. Information technology integration into STEM disciplines in higher education in developing countries may have two purposes: course access and technology skill development. Training this labor force with skills to use eLearning integrated into STEM disciplines increases their technical competencies. However, using eLearning to teach STEM disciplines in higher education institutes in developing countries still needs improvement. Understanding the factors influencing eLearning adoption and use is critical to understanding this phenomenon. This case study explored factors influencing eLearning adoption when teaching STEM disciplines. The study occurred at a mid-sized science and technology university in Ethiopia. A qualitative research approach examined how faculty members describe factors influencing eLearning technology adoption and use in the STEM departments on campus: the data collection method combined semi-structured individual interviews, focused group interviews, and document reviews. Seven faculty members and department heads participated in the personal interviews, and three participated in focus group interviews. An inductive method was used to analyze data collected from participants. Five themes emerged from qualitative data analysis: nature of the course, technology, institution, user's attitude, and environment. Challenges related to technology infrastructure, lack of training and technical support, the course nature, and lack of eCurriculum design were significant factors in adopting and using eLearning. The concerted effort of stakeholders, specifically faculty members, institutional leaders, and technical support teams, to adopt and use eLearning in STEM instruction positively impacts the quality of education in preparing a competent 21st-century workforce in developing countries.

A Study of Problems Faced by Engineering Students in Mathematical Subjects using Fuzzy Cognitive Mappings

Introduction: One of the main concerns and issues for educators, particularly for engineering students, has been the caliber of mathematics instruction and learning. There are many different concepts and skills that make up mathematics. The improvement of problem-solving skills is one of mathematics' key functions. Numerous colleges struggle with the issue of students quitting because of mathematics because it is frequently thought of as a topic that students find difficult to master. Objectives: The study's goal is to examine the reasons why engineering students struggle with math. In this research, using fuzzy cognitive map techniques (FCM), we analyze the challenges engineering students encounter when trying to earn grades in math-related courses. FCM is a blend of some fuzzy logic and neural network ideas. FCM is made up of collections of concepts and all the different causal relationships that connect them. Methods: We created a model of the issues and causal relationships that engineering students faced when trying to succeed in mathematics classes. Both statically and dynamically, utilizing concepts from graph theory and simulations, the model is examined. Also we applied DEMATEL one of the Multi Criteria Decision Making method. Results: The analysis reveals that the main issue is not just the students' lack of mathematical background knowledge, but also their attitude toward learning, psychological response to the first failure, and lack of effort to complete additional tasks or attend tutorials. Conclusions: Using the FCM method, a model was created for the case of problems faced by engineering college students in scoring marks in mathematical related subjects based on the opinion of a domain expert. The model was first examined statically. The model was then simulated in a dynamic and it was predicted that there should be an attitude change in teachers and as well as students. Through the above static and dynamic studies of the FCM model was identified as important and useful decision support system, since it capable to provide support to decision makers, by making predictions on various scenarios that are imposed on the FCM model.

Examining teachers' relational noticing: promoting equity through positive interactions in mathematics education

AbstractHow teachers attend to and interpret positive relational interactions shapes how they enact instructional practices for equity. We draw on frameworks from equitable mathematics instruction, relational interactions, and teacher noticing to conceptualize mathematics teachers’ relational noticing. Using noticing interview and classroom observation data from a research collaborative between secondary mathematics teachers and university-based teacher educators, we document the range and diversity of ten teachers’ relational noticing. We use this analysis to examine how teachers’ relational noticing supports enacting equitable instructional practices. Our findings indicate five themes of teachers’ relational noticing that are informed by their personal histories, understanding of dominant narratives of mathematics education, and their local sociopolitical school context. Additionally, teachers enacted a range of practices for creating positive relational interactions, with attending to student thinking being the most enacted practice. Our findings suggest that mathematics teachers’ relational noticing can support the three axes of equitable instruction.

Toward a Better Understanding of the Nature of Pedagogical Content Knowledge for Fractions: The Role of Experience

ABSTRACT Mathematical knowledge for teaching (MKT) is a professional knowledge crucial for effective mathematics instruction, encompassing both content knowledge (CK) and pedagogical content knowledge (PCK). The purpose of this study is to investigate the hierarchical structure of PCK for fractions by seeking further evidence for the PCK-Fractions assessment. The PCK-Fractions measure is designed to examine the effectiveness of teacher education program and field experiences in facilitating preservice teachers’ (PSTs) PCK for children’s fraction reasoning in grades 4–6. Emplying165 undergraduate students, the research investigates how different levels of coursework and field experience influence PCK-Fractions scores. Results suggest that both completing coursework in a teacher education program and having grades 4–6 field experience each led to higher PCK-Fractions scores. Additionally, this study provides further evidence supporting the validity of the PCK-Fractions measure as a reliable indicator of PSTs’ proficiency in teaching fractions. Implications for mathematics teacher education and educational research are discussed.

Seeing Through the Eyes of Classroom Observers: The Case of Rating Contrasted Groups of Lessons With Classroom Observation Measures

Classroom observations are commonly employed to assess quality of instruction in research and practice in mathematics education. However, there is more to be learned about how sensitive classroom observation protocols are to exemplars of strong mathematics instruction, and continuous refinements to observation protocols or rating processes that may be warranted. In this study, we use the public-released mathematics videos from the Third International Mathematics and Science Study (TIMSS) to examine how classroom observers, using two contemporary classroom observation instruments, rate a set of lessons whose instructional quality is in theory expected to differ, also referred to as contrasted groups. We find that descriptively, the pattern of findings is distinct from prior studies’ conclusions about the relative instructional quality reflected in the TIMSS video pool. We provide qualitative examples to illustrate the findings, and discuss implications for future research. We point to the potential value of exploring classroom observation rubrics’ performance using ‘contrasted groups’ of lesson videos, as a tool to broaden our understanding of how observation instruments are functioning.

On Some Guiding Principles of Enacting Mathematical Problem Solving for Classroom Instruction

In addressing the key role that problem solving has been playing in mathematics instruction for K-12, this paper aims to assist mathematics teachers and educators to consider a set of guiding principles for designing problem solving tasks for classroom instructions. The set of guiding principles was synthesized and proposed through the researchers’ systematic review of existing education literature on problem solving.

You can count on your fingers: Finger-based intervention improves first-graders’ arithmetic learning

The question of whether finger use should be encouraged or discouraged in early mathematics instruction remains a topic of debate. Scientific evidence on this matter is scarce due to the limited number of systematic intervention studies. Accordingly, we conducted an intervention study in which first-graders (Mage = 6.48 years, SD = 0.35) completed a finger-based training (18 sessions of ∼ 30 min each) over the course of the first school year. The training was integrated into standard mathematics instruction in schools and compared with business-as-usual curriculum teaching. At the end of first grade and in a follow-up test 9 months later in second grade, children who received the finger training (n = 119) outperformed the control group (n = 123) in written addition and subtraction. No group differences were observed for number line estimation tasks. These results suggest that finger-based numerical strategies can enhance arithmetic learning, supporting the idea of an embodied representation of numbers, and challenge the prevailing skepticism about finger use in primary mathematics education.