Productive Struggle Research Articles

An Online Professional Development Model to Support Teachers' Abilities to Examine Student Work and Thinking

At the heart of the National Council of Teachers of Mathematics' (NCTM) Principles to Actions: Ensuring Mathematical Success for All (2014) is the development of professional practices such as eliciting and using evidence of student thinking, supporting productive struggle in learning mathematics, and posing purposeful questions. In this article, we share our emerging work in online professional development for teachers, which provides potentially cost-effective ways of scaling high-quality, effective professional development for mathematics teachers by employing the collaborative features of the Internet to mediate professional conversations and interactions. Specifically, we detail the characteristics of our model for online professional development and present cases to illustrate its potential impact on teachers' ability to analyze student work and provide productive feedback.

Not yet queer, here and now for sexualities and schooling

This paper represents our collective engagements and productive struggles with queer pedagogical-methodological (im)possibilities across a constellation of educational contexts. Following in the footsteps of queer theorists-pedagogues before us, we approach queerness as a horizon, a unique opportunity to experiment, take risks, explore new forms of undoing and to move-be-think-do otherwise. We begin by attending to the ways in which researchers-educators in the field of sexualities and schooling are pushing these conversations forward, followed by two vignettes from our own work. Our intention in sharing these vignettes is to slow down and expose some of the methodological-pedagogical processes that guide our work, our attempts to stay in the moment that trouble creates, and the challenge of staying in that moment to learn from it. This paper suggests that embracing new forms of enquiry, which account for queer methodological-pedagogical sensibilities, requires researchers-educators to actively embrace the failures of their own practice and engage with the contestations of theories that matter/materialise.

Supporting All Learners in Productive Struggle

To support a growth mindset in students, consider components involving cognitive, social, and emotional aspects so that students can work within their zone of productive stuggle.

Productive Struggle

From a teaching perspective, witnessing students struggle mathematically can be distressing because all teachers want their students to be successful. However, this struggle can ultimately lead to success when the teacher facilitates learning in the classroom in a manner that allows for think-time, teacher and student questioning, and collaboration. The act of struggling productively, as outlined in the following four articles, shows examples of how students are able to take ownership of mathematical understanding through this struggling process and ultimately have a lasting understanding because of the adversity. The articles also highlight steps that teachers need to take to ensure that this struggle is in fact productive and not arduous. Productive struggle in the classroom is equal parts teacher and student; when each role is clearly defined and enacted, students have a deeper understanding of mathematics and feel a sense of accomplishment that the understanding is in fact their own.

Productive Struggle for All: Differentiated Instruction

Consider strategies that create access while maintaining the cognitive demand of a mathematics task.

Scaffolding for Access to Productive Struggle

Examining two lessons using the same problem illuminates a way that scaffolding can support access to productive struggle.

Supporting Productive Struggle with Communication Moves

Read about ways to determine how your students are thinking, and then implement NCTM's mathematical teaching practices as students work on a task.

Patients and professionals learning together: an evaluation of an integrated change management fellowship programme for healthcare improvement

Improving the quality of healthcare involves collaboration between many different stakeholders to lead change. However, individuals are rarely taught to develop the skills to lead change effectively across professional boundaries. Collaborative learning theory suggests that teaching professionals alongside each other may enable them develop those skills, but there is little literature on how this works in practice. Additionally, though it is recognised that patients play a crucial role in improving healthcare, there are few examples of where they learn together alongside professionals. This study contributes to addressing this gap. Using the lens of collaborative learning, we report on a qualitative evaluation of an educational programme (the Collaboration for Leadership in Applied Health Research and Care (CLAHRC) Northwest London (NWL) Improvement Leader Fellowship) which is designed to build capacity to lead change through quality improvement methods in healthcare. This year long programme is a local case study as it enables patients/service users and healthcare professionals to learn together, as equals. Qualitative data were collected across six cohorts of the programme, through online evaluation forms and 34 semi-structured interviews with participants, data were analysed using a grounded theory approach. The overall finding was that the skills and capacity to lead change was valued and was enabled by the processes of learning together, discussing real world problems. The potential struggle Fellows faced to make sense of new concepts and work with new, unexpected methods and people within the Fellowship became a productive struggle, encouraging them to try new things, take a new perspective and step beyond their comfort zone. The integration of patients into the Fellowship appeared to enrich the experience for all fellows, with a clear exchange of learning with professionals and patients benefitting from the new perspectives brought into the group. The flattened hierarchy enabled a range of professions and patients to join as equal voices. This was achieved by faculty facilitation ensuring clear set ground rules and management to prevent one voice (patient or professional) from dominating the group. Fellows project's demonstrated a number of change outputs, from the implementation of patient booklet in mental health wards, to the increased use of co-production in a GP surgery.

Middle School Mathematics Teachers’ Perceptions of the Common Core State Standards for Mathematics and Its Impact on the Instructional Environment

This study examines Middle School Mathematics Teachers’ (MSMTs') (N = 1,241) perceptions of the Common Core State Standards for Mathematics (CCSSM) and its impact on the instructional environment. A total of eight factors appear in the data. These factors include professional support, teachers’ use of district‐adopted and non‐district‐adopted curricular resources, influence of CCSSM assessment and teacher evaluation on the instructional environment, influence of the CCSSM on classroom instruction, teachers’ planning practices, and perceived rigor of the CCSSM. The data suggest that teachers’ use of digital resources located online was disconnected from their district‐adopted resources suggesting a lack of curricular coherence. MSMTs note that the CCSSM had caused them to incorporate more reform‐oriented practices such as exploration and productive struggle into their daily instruction. MSMTs also perceive that the CCSSM includes new content that is more rigorous than previous state standards. Sampled MSMTs state that while state assessments will measure CCSSM content, they are less likely to include more complex problems or the standards for mathematical practice. Teachers are more likely to read teacher resources than student textbook activities online and to use digital resources for remediation instead of inquiry activities. Over one‐third of MSMTs wanted more CCSSM professional development.

Replacing textbook problems with lab experiences

End-of-the-chapter textbook problems are often the bread and butter of any traditional physics classroom. However, research strongly suggests that students be given the opportunity to apply their knowledge in multiple contexts as well as be provided with opportunities to do the process of science through laboratory experiences. Little correlation has been shown linking the number of textbook problems solved with conceptual understanding of topics in mechanics. Furthermore, textbook problems as the primary source of practice for students robs them of the joy and productive struggle of learning how to think like an experimental physicist. Methods such as Modeling Instruction tackle this problem head-on by starting each instructional unit with an inquiry-based lab aimed at establishing the important concepts and equations for the unit, and this article will discuss ideas and experiences for how to carry that philosophy throughout a unit.

A typological analysis: understanding pre-service teacher beliefs and how they are transformed

ABSTRACTThis article describes the beliefs and their transformations of members of a cohort of early-childhood, elementary and middle-level pre-service teachers (PSTs) as they professionally develop. A typological analysis of both quantitative and qualitative data collected between August 2011 and May 2013 was utilized to categorize how 40 PSTs’ beliefs transformed throughout their formal teacher preparation. Five typologies were identified, showing variation in how PST beliefs transform or remain static.Among the findings, strong support related to the development of innovative beliefs during coursework coupled with at least one transformative experience where innovation was observed ‘working’ in the field were sufficient for the transformation to innovative beliefs, despite potential constraints by supervisors, cooperating teachers and/or mandated curricula (Typology 3). Another finding revealed disguised growth toward innovation among those in Typology 5, who reported being innovative and having productive beliefs but described extremely traditional practices. Implications call for improved connections between mathematics methods professors and field supervisors, particularly during clinical internships when PSTs are no longer enrolled in methods courses, to enhance PSTs’ productive struggle in their development of innovative beliefs (T3) and to increase opportunities for disconnects between innovative beliefs and traditional practices to be made explicit and negotiated (T5).

Developing an improvement leaders fellowship programme and the evaluation of the integration of patient fellows

1) The National Institute for Healthcare Research (NIHR) Collaboration for Leadership in Applied Health Research and Care (CLAHRC) Northwest London (NWL) has run an Improvement Leader Fellowship programme since 2010. A one year multi-disciplinary, improvement science capacity building programme built around a work based learning model and an improvement project delivering healthcare improvement on the ground. This innovative educational programme works to engage patients and mobilise knowledge across patient professional boundaries. 2) The multidisciplinary perspective of quality improvement and the pedagogical theory behind improvement science teaching and application are considered along with the challenges and practicalities of co-producing education with patients in this programme. Patients have been involved in the programme since 2012, the evaluation considers the impact of involving patients both for the patients themselves and the other Fellows in the multi-disciplinary group. 3) Eighty five Fellows have passed through the programme, fifteen of whom have been patients. The session will discuss the independent evaluation of four cohorts and considers the impact of the integration of patient fellows in the programme. Patient Fellows have delivered sessions within the programme, these co-produced sessions highlight the expertise that patient leaders can bring to the table. 4) Semi-structured interviews were conducted with 34 fellows, and analysed using grounded theory. Thematic analysis shows the Fellows responded positively to the multi-disciplinary approach. The inclusion of patient Fellows in the cohort resulted in a period of adjustment for both professionals and patients, independently reported by either group. 5) Concepts such as the zone of proximal development, productive struggle and participatory knowledge spaces are highlighted as theoretical underpinnings to explore the observed phenomena in the Fellowship. 6) The lesson learned were multiple, the challenges arising from the integration of patients rose a number of levels including practical (financial) and human (conflict resolution, unfounded fears) 6) Limitations included the small cohort sizes, also the intangibility and difficulty in capturing methodologically the personal development of fellows. 7) Future research may wish to consider a social network analysis of alumni fellow groups to more fully capture the education and personal development of both clinician and patient fellows.

Principles for designing mathematical tasks that enhance imitative and creative reasoning

The design research programme learning by imitative and creative reasoning (LICR) studies whether, how and why tasks and teaching that enhance creative reasoning lead to a more productive struggle and more efficient learning than the common but inefficient task designs based on imitating given solution procedures. The purpose of this paper is to synthesise the research outcomes determined to date by providing the following: a conceptual framework for key concepts and relationships among teaching, tasks, student activities and learning; a theoretical basis for analyses of causal effects between task/teaching design and learning outcomes; a design research methodology for transforming initial design ideas, through cycles of evaluation and revision, into firmer design principles; and an application of this theory and methodology to empirical studies carried out to date, in order to propose task-design principles related to imitative and creative reasoning.

Supporting Opportunities for Productive Struggle: Implications for Planning Mathematics Lessons

This department publishes brief news articles, announcements, and guest editorials on current mathematics education issues that stimulate the interest of TCM readers and cause them to think about an issue or consider a specific viewpoint about some aspect of mathematics education.

Call for Manuscripts for the 2018 Focus Issue: Productive Struggle

Call for Manuscripts for the 2018 Focus Issue: Productive Struggle

Parental Beliefs on the Efficacy of Productive Struggle and Their Relation to Homework-Helping Behavior

Productive struggle—expending effort to make sense of something beyond one’s current level of understanding—aids in learning mathematics concepts and procedures. In this study, we surveyed 197 parents with children in the 1st to the 5th grade on their beliefs about productive struggle. Beliefs were assessed via questionnaire and rating of a recorded lesson involving productive struggle. Parents also reported how often they helped with math homework and their child’s ability in math. The results show that parents had diverse beliefs about the efficacy of productive struggle, with fathers favoring it more than mothers. A significant relation was found between parents’ beliefs about productive struggle and reports of their child’s ability in math. The findings of this study suggest that for productive struggle to be effective, parents must intentionally facilitate experiences through student-centered approaches. Programs for parents should emphasize specific evidence-based behaviors rather than broad generalizations about increased involvement with homework. Schools and educators should also provide guidance for parents to explain the potential harmful effects of gender stereotypes and parents’ own math anxiety and to teach methods for limiting homework interaction while students grapple with difficult problems.

Productive Struggle in a Geometry Class

Struggle and its connection to learning are central to improve student learning and understanding of mathematics. A description of what a student’s productive struggle looks like in the setting of classrooms can provide insight into how teaching can support or hinder the student’s learning process. In order for any struggle to be productive, these struggles with mathematics must be documented. However, prior studies on student struggles are limited and have primarily focused on examining whether or not struggle occurred. Thus, the purpose of this study is to describe pre-service middle grade teachers’ (PSTs) struggle types in details as well as to investigate how enagaging in a non-routine high level task (doing mathematics) fosters (or inhibits) productive struggle during instruction.

Build me—if you can

In this month's problem scenario, students engage in productive struggle to explore the part-whole fraction relationship by building triangles represented with pattern blocks. Each month, elementary school teachers receive a problem along with suggested instructional notes. Teachers are asked to use the problem in their own classrooms and report solutions, strategies, reflections, and misconceptions to the journal audience.

Discovering and addressing errors during mathematics problem-solving—A productive struggle?

The present study investigates students’ struggles when encountering errors in problem-solving. The focus is students’ problem-solving activities that lead to productive struggle and what the students might gain therefrom. Twenty-four students between the ages of 16 and 17 worked in pairs to solve a linear function problem using GeoGebra, a dynamic software application. Data in the form of recorded conversations, computer activities and post-interviews were analyzed using Hiebert and Grouws’ (2007. Second handbook of research on mathematics teaching and learning (Vol. 1). 404) concept of productive struggles and Schoenfeld's (1985. Mathematical problem solving: ERIC) framework for problem-solving. The study showed that all students made errors concerning incorrect prior knowledge and erroneously constructed new knowledge. All participants engaged in superficial, unproductive struggles moving between a couple of Schoenfeld's episodes. However, a majority of the students managed to transform their efforts into productive struggle. They engaged in several of Schoenfeld's episodes and succeeded in reconstructing useful prior knowledge and constructing correct new knowledge—i.e., solving the problem.

Call for Manuscripts for the 2018 Focus Issue: Productive Struggle

Call for Manuscripts for the 2018 Focus Issue: Productive Struggle