Productive Struggle Research Articles

Number Talks as Access to Teaching Practices: Pre-Service teachers’ Attention to Mathematical Teaching Practices While Reflecting on Number Talks Enacted in a Field Placement

ABSTRACT Number Talks are increasingly used in classrooms to support student’s number sense. While Matney et al. (2020) documented little empirical evidence about the effectiveness of Number Talks in improving student outcomes, we considered the potential benefits of Number Talks for teachers and their practices. We ask to which of NCTM’s Mathematical Teaching Practices do pre-service teachers attend while reflecting on Number Talks implemented in a field placement and what was the nature of their attention? Using a constructivist lens, we analyzed the reflections of ten pre-service elementary teachers on three Number Talks in a field placement. As they implemented Number Talks, the participants in this study constructed their own understanding of both the process and purpose of a Number Talk. By doing so, we found that not only was it possible for pre-service teachers to attend to each of the Mathematical Teaching Practices, but three practices were regularly attended to by participants: posing purposeful questions, facilitating mathematical discourse, and supporting productive struggle. Thus, Number Talks may serve pre-service teachers as important vehicles for developing these practices.

Building mathematical micro-identities through supporting productive struggle

ABSTRACT We designed a series of lessons that adopted supporting productive struggle practices, and explored how mathematical micro-identities emerged in the moments of productive struggle and what connections exist across micro-identities and productive struggle. We found that the low-achieving students had moments of both mathematically capable and incapable micro-identities, when offered, which reciprocally created moments of productive struggle and no struggle; and that the positions a teacher takes, between supporting productive struggle or not, directly impact the formation of micro-identities. The results suggest that supporting productive struggle strategies could be an avenue to develop mathematically capable micro-identities.

Productive Struggle as a Boundary Object between Co-Teachers in Grade 6 Mathematics Classrooms in the United States

Teachers’ attitudes are prerequisite to the implementation of inclusive practices, and teachers’ professional development through their teacher preparation programmes is important for inclusive classroom practice in schools. This study investigated pre-service teachers’ understandings of inclusive practice in Scotland and Finland. The aim was to have an in-depth understanding of some pre-service teachers’ views with examples and gain ideas that could count as evidence of inclusive practice, contributing to the dialogue about good inclusive practice. Data were drawn from focus group interviews with second- and fourth-year pre-service teachers from both countries. The findings indicate that a focus on values and pedagogy in both teacher preparation programs is needed with more explicit links between key ideas and practice. It is suggested that the idea of inclusion is embedded in the programs rather than focusing solely on special education modules. This study offers empirical evidence and contributes to inclusive education research, teachers’ professional preparation, policy goals and practice.

How Students Make Model and Promote Productive Struggle in Solving Mathematical Problems

How Students Make Model and Promote Productive Struggle in Solving Mathematical Problems

Facilitating Productive Struggle in an Online Secondary Education Mathematics Methods Course: Experiences of Pre-Service Teachers

This research investigated preservice teachers’ (PSTs) experiences with productive struggle in an online environment, and how it influenced their pedagogical knowledge. This action research study reports on secondary mathematics pre-service teachers (PSTs) who completed mathematical tasks in weekly synchronous Zoom sessions to develop their understanding of productive struggle. Vygotsky’s (1978) Social Constructivist Theory and the growth mindset framework (Boaler, 2016; Dweck 2006; 2008) provided the lenses through which the research was designed and analyzed. Findings show that presenting opportunities for PSTs to experience productive struggle informs their pedagogical practice, and that providing this experience in an online environment is possible. PSTs gained an increased understanding of the importance of collaborative work, asking purposeful questions, and the alignment between productive struggle and improved mathematical understanding.

Using Simulations or Rehearsals in Teacher Preparation Coursework: Learning from Preservice Social Studies Teacher Experiences to Inform Future Practice

Research on practice-based teacher education [PBTE], such as rehearsals or teaching simulations, assumes that preservice teachers [PSTs] prefer such practical approaches in comparison to more theoretical work. Few studies test this assumption or incorporate PSTs voices and perspectives on PBTE approaches. This study draws on survey data and interviews from secondary history/social studies PSTs to investigate the benefits and challenges they experienced with practice-based coursework. PSTs found more authentic and active aspects of preparation (e.g., clinical work, teaching simulations, and instructional feedback) as more important for developing their practice than passive and theoretical activities (e.g., readings, discussion, and essays). Teaching simulations also cultivated communities of practice where PSTs engaged in productive struggle and surfaced equity considerations. Participants reported that rehearsals can serve as representations of practice that supplement, and in some cases supplant, experiences in clinical placements. Considerations for effectively enacting rehearsals or simulations within preparation coursework are also discussed.

The Effect of Training Program Based on Instructional Practices According to the (NCTM) Standards on Improving the Pedagogical Knowledge among Mathematics Teachers in Jordan

The current study aims at revealing the effect of a training program based on teaching practices according to NCTM standards in improving the pedagogical knowledge of mathematics teachers. The study followed the semi- experimental method. To achieve the aims of the research, a training program that is based on the standards of NCTM was designed. The program consists of eight packages which are (Establish mathematics goals to focus learning, implement tasks that promote reasoning and problem solving, Use and connect mathematical representations, facilitate meaningful mathematical discourse, pose purposeful questions, build procedural FLuency from conceptual understanding, support productive struggle in learning mathematics, Elicit and use evidence of student thinking). After confirming the validity of the tool, a sample of (20) male and female teachers from Deir Ala Directorate of Education in the academic year 2020-2021.To reveal the effectiveness of the program, a test in pedagogical knowledge was prepared. The test consists of six respects which are identification of mathematics content, the pedagogical knowledge of the mathematical content and knowing students' thinking. The test validity and reliability were checked. The results of the study showed that there were statistically significant differences between measuring averages in the post application of the test. These results were pro- sample in all dimensions and in the total degree. Depending on these results, the study asserted the necessity for the training department in the Jordanian Ministry of Education to benefit from the suggested and used program in the study to focus more on the teaching practices.

أثر استخدام إستراتيجية "Productive Struggle" في تحسين الفهم المفاهيمي في الرياضيات لدى طلبة الصف الخامس الأساسي

Objectives: The study aimed to identify the effect of using the “Productive Struggle” strategy in improving conceptual understanding of mathematics among fifth-grade students. Methodology: The study used the quasi-experimental method with a pre-post measurement. The study sample consisted of (30) students who were distributed equally into the two groups of the control and experimental study. And to achieve the objectives of the study, a conceptual understanding test was constructed with the three demonstrations (Explanation, Interpretation, Application), and its validity and reliability were verified in addition. To the observation card to determine the level of employment of “Productive Struggle” types among fifth grade students. Results: The results of the study showed that there were statistically significant differences between the arithmetic averages of the performance of students in the experimental and control groups in the conceptual understanding test and each of its manifestations and in employing the “Productive Struggle” types due to the teaching method and in favor of the experimental group. Conclusion: In light of the results of the study, the researchers recommend the necessity of employing the “Productive Struggle” strategy in teaching mathematics to fifth-grade students.

Learning to Struggle: Supporting Middle-grade Teachers' Understanding of Productive Struggle in STEM Teaching and Learning.

This qualitative study examines the influence of a 3-year professional development project for middle school mathematics, science, and special education teachers focused on integrating science, mathematics, and engineering in classroom instruction on participants' understandings of productive struggle in learning. Multi-disciplinary teams of teachers engaged as learners to use engineering design as a framework for integrating significant mathematics and science content supported by effective teaching practices. In this paper, we describe how the components of our professional development design supported teacher-participants to make sense of productive struggle in learning. In particular, participants noted that being able to experience design-based activities as learners and working through solutions with their colleagues supported their understanding of what it means to productively struggle, resulting in their growth as individuals and as teachers. The significance in this work lies in understanding how to effectively support teachers to buy-in to the meaning and value of productive struggle and how engaging in integrated science, technology, engineering, and mathematics (STEM), design-based professional learning experiences facilitated that effort.

The Effectiveness of an Educational Program in Developing Mathematical Achievement as well as Developing Productive Struggle among Students of Intermediate Stage

The Effectiveness of an Educational Program in Developing Mathematical Achievement as well as Developing Productive Struggle among Students of Intermediate Stage

Struggling as part of success: International Baccalaureate students’ productive struggle is strongly correlated to mathematical achievement

Productive struggle is an effective mathematics teaching practice that provides students opportunities to grapple with challenging mathematical concepts, connect prior knowledge, discover new ideas, and develop their critical thinking skills. Research has documented the benefits of secondary mathematics students engaging in productive struggle. Additional work is needed to detail how productive struggle relates to students’ mathematical achievement, specifically in the International Baccalaureate (IB) classroom. This study examined what correlation existed between 68 U.S. grade 11 and 12 IB mathematics students’ level of productive struggle exhibited during tasks of varying levels of cognitive demand and their mathematical achievement based on 10 IB established markschemes and a summative assessment. A strong, positive correlation was found between the level of productive struggle and mathematical achievement across all cognitive demand levels. These results support prior work emphasizing the importance of teachers making productive struggle a consistent, pervasive practice in their classrooms to foster student mathematical achievement and understanding.

Why do teachers vary in their instructional change during science PD? The role of noticing students in an iterative change process

AbstractInstructional shifts required by equitable, reform‐based science instruction are challenging, especially in the elementary context. Such shifts require professional development (PD) that supports teacher internalization of new pedagogical strategies as well as changes in beliefs about how students learn. Because of this complexity, many PD programs struggle to foster lasting pedagogical shifts, necessitating further investigation into why some teachers successfully embrace reform practices while others do not. This qualitative study uses a nonlinear, iterative model of teacher learning (Interconnected Model of Professional Growth; Clarke & Hollingsworth, 2002) alongside professional noticing to help understand why elementary teachers in science PD differentially make sense of and internalize new pedagogies. Findings indicate that teachers most likely to adopt reform‐based instructional practices from the PD were those who clearly connected student learning to their instructional moves. In addition, teachers who more actively attended to student sensemaking and productive struggle took up pedagogies from the PD more substantively than did colleagues who attended solely to student engagement and affect. Finally, teachers who attended to and valued novel ideas from students’ lived experiences were more likely to change their beliefs about students’ capacity to learn science, and thus more likely to see the value of instructional practices from the PD. In sum, structuring PD to build on these specific teacher noticing skills can encourage more teachers to move away from traditional, teacher‐directed instructional practice, and more fully support reform‐based instructional practices.

There’s ‘learning in that struggle’: journey mindsets and agency in action research and culturally responsive education

ABSTRACT Working with ethnoracially diverse student groups is a reality in most K-12 classrooms. However, studies of the impacts of professional development for cultural responsiveness have tended to use a range of approaches such as action research, video reflections, and coaching, making it difficult to tease apart the effects of each one. The purpose of this study was to focus on how action research, specifically, influences educators’ culturally responsive practices. Participants found that the action research process promoted their agency to effect positive change in their schools, a key component of culturally responsive education. Although participants found it challenging to balance learning the nuances of action research and culturally responsive education simultaneously, they appreciated this as a productive struggle and adopted the same growth mindset for themselves that they encouraged in their students. Based on our results, action research appears to be a promising form of professional development for enhancing culturally responsive practices.

An exploratory mixed methods study about teacher candidates’ descriptions of children’s confusion, productive struggle, and mistakes in an elementary mathematics methods course

Recognizing and describing children's mathematical thinking in humanizing ways, especially when students engage in confusion, productive struggle, and mistakes, is a complex and challenging process. This paper describes an exploratory, mixed-methods study about how elementary teacher candidates (TCs) describe children's thinking as a right to exercise and to value their humanity when learning mathematics. The study analyzed transcripts from 64 TCs' summative assessments, which consisted of mock parent-teacher conferences (MPTC). Findings suggest that TCs described children's confusion, productive struggle, and mistakes (RotL 1 and 2) as: a teacher's observation, an opportunity for students to correct or clarify their thinking, an opportunity for teachers to adjust instruction or provide support, and as a normal part of the learning process. More importantly, some TCs reassured children that learners have fundamental rights when learning mathematics, especially when feeling confused and claiming a mistake. Implications for research and teacher education are discussed. Keywords: Elementary, teacher education, mathematics, mixed methods, rehumanizing, Torres’ rights of the learner

Ways of Developing Creative Thinking and Reasoning of Students in Mathematics Learning

Reasoning skill is one of the main components of mathematical competency (NCTM, 2014). Mathematics students use mainly two types of reasoning skills namely imitative reasoning and creative reasoning in solving mathematical tasks. The textbook tasks in our context are of routine types which are solvable using imitative reasoning. Most mathematics teachers use prescribed textbooks in lesson planning and teaching (Thomson & Fleming, 2004) which ultimately promotes imitative reasoning among the students as compared to creative reasoning. Moreover, many mathematics teachers still follow the traditional chalk-and-talk banking pedagogy which does not support the enhancement of creative thinking and reasoning skills. This literature-based research study has identified some of the ways to develop the creative thinking and reasoning skills of mathematics students through the intense study of the available research articles, thesis, and books in the field of mathematical thinking and creativity. This study has found the positive impact of productive struggle and adversity quotient on students’ creative thinking and reasoning skills. Likewise, problem-posing and problem-solving skills have been found to be essential skills for enhancing creativity. This study has also found modern student-centric teaching approaches like the ADI (Argument-Driven Inquiry) approach and the RME (Realistic Mathematics Education) approach beneficial in improving reasoning skills. This study also found CMR (Creative Mathematically Founded Reasoning) tasks to be helpful in increasing the creative reasoning skills of mathematics students.

How Productive is the Productive Struggle? Lessons Learned from a Scoping Review

Since its first notable appearance in the Second Handbook of Research on Mathematics Teaching and Learning, the phrase productive struggle has garnered support from a few, yet very influential, educational researchers. However, since the phrase was popularized by Hiroko Warshauer in 2011, examinations of the productive struggle have grown substantially within mathematics education. In this article, we present a systematic review of the literature on the productive struggle to quantify the breadth and depth of existing work in the area. Our analysis indicates that many studies: (1) provide a direct implementation of the productive struggle; (2) primarily involve teachers and not students; (3) present primarily qualitative or non-empirical research approaches; and (4) specify the NCTM content area focus less often across studies. Thus, we conclude that there are opportunities for rigorous research designs reporting on observable trends in the implementation of the productive struggle, explicitly targeting underexamined NCTM content and process standards, and focusing on how the productive struggle can support equity in mathematics. We believe that these opportunities should be investigated to provide a broader evidence base for developing meaningful experiences in mathematics for school-aged children that capitalize on the interconnectedness of attribution, meta-cognition, and controlled frustration in mathematics learning.

Following the Mentorship Model of Jesus: The Role of Storytelling

Drawing from research in the learning sciences, this article argues that educators, like Jesus, should use stories as we mentor students to move beyond passive reception of information and truly apply their learning to novel situations. Thus, students can go beyond “hearing” to “bearing fruit.” This storytelling approach to mentorship strikes at the common query of students, “When will we ever need to know this?” Part of the disconnect sometimes experienced by students is that the moment of learning often looks very different than the moment when their learning needs to be deployed. In the Gospel of Luke, Jesus acknowledges this disconnect by making the distinction between “hearing the word” and the later “bearing of fruit with patience” and does so by employing a parable, a concrete story of a sower, seeds, and soils. Although stories may appear to conceal truths when compared to straightforward statements, research in the learning sciences suggests that learning from stories is better for producing understanding that could be applied to future situations. Why are stories so effective? To achieve transferable learning, students need to engage in productive struggle to make connections. Stories engaged Jesus’s disciples in struggling with what parables meant because the truths did not lie at the surface. Instead, parables required disciples to actively make connections. Jesus, instead of removing their struggles, supported their struggle to make it more productive. Research has shown that the understanding that results from productive struggle is profound, useful, and transferable. As academic mentors, we should emulate Jesus to engage our students in making productive connections by integrating storytelling into our pedagogical practice.

Exploring non-dominant youths’ engineering identity through productive struggle in a making summer program

Exploring non-dominant youths’ engineering identity through productive struggle in a making summer program

Equitable STEM+CS learning experiences for girls of color: nurturing an independent learning approach via a learning ecosystem

PurposeThere is a critical need to understand how to attract Black girls and other girls of color to the science, technology, engineering, math, and computer science (STEM+CS) field. This study aims to look at the design and implementation of a CS learning ecosystem that supports girls of color in acquiring critical CS skills starting in middle school.Design/methodology/approachThis mixed-method case study included 53 girls, between the ages of 11 and 13, in four US middle schools. Study methods included the analysis of a pre-program student survey, longitudinal interviews and focus groups, weekly observations and computing artifacts.FindingsProgram participants were interested in CS, were confident in their ability to learn CS, had prior coding and CS experience and had parents and teachers who encouraged them to learn CS. But some students showed dependent learning behaviors while engaging in CS activities. These included relying on instructors and being reticent to make mistakes–behaviors that limit learning. The CS learning ecosystem supported students as they shifted from applying dependent learning approaches to applying independent learning approaches. Instructors sustained a growth mindset and supported productive struggle as students learned CS skills.Originality/valueA CS learning system supported equitable learning experiences and helped students develop independent learning behaviors that led to deeper engagement in CS.

Distinguishing between Grit, Persistence, and Perseverance for Learning Mathematics with Understanding

Learning mathematics with understanding involves productively struggling to make connections between different mathematical ideas. Such productive struggle is associated with three primary constructs: grit, persistence, and perseverance. Each of these constructs has a distinct definition, background, and implied utility in mathematics education research. However, these constructs are often colloquially conceptualized as synonyms, leading to a misconception of what can be learned through the lens of each construct. The purpose of this paper is to carefully examine the literature on grit, persistence, and perseverance and to review and distinguish the ways in which these constructs offer insights into learning mathematics with understanding.