This study employed a qualitative case study design to explore pre-service mathematics teachers’ engagement in lesson design and enactment within an integrated PjBL and Lesson study structure. A case study was appropriate because the study investigated a contemporary teacher-learning process within its specific course context and drew on multiple forms of qualitative evidence (Yin, 2003). The bounded case was the PjBL-organized lesson-design project implemented within one 15-meeting Elementary Mathematics Instruction course at a private Indonesian university. The course began with five theoretical meetings, followed by a project phase in Meetings 6–15. Within this project, the seven-meeting Lesson study component occurred during Meetings 9–15.

The case was bounded by one course, one semester, 13 participating PSTs, and the collaborative production and peer-teaching enactment of elementary mathematics lessons. The three lesson-design groups constituted the embedded units of analysis. Each group selected a different mathematical topic and collectively undertook two Plan–Do–See–Redesign cycles. The case was selected because it provided an information-rich setting in which PSTs moved from studying elementary mathematics pedagogy to designing, enacting, reflecting on, and redesigning instruction within a sustained course project. The analysis examined patterns across the three groups while retaining topic-specific and group-level variations.

The participants were 13 third-year pre-service mathematics teachers enrolled in a four-year undergraduate Mathematics Education program at a private university in Indonesia. Although they were preparing for professional roles as mathematics teachers, the study was conducted within an Elementary Mathematics Instruction course focusing specifically on the design and enactment of mathematics lessons for elementary-school learners. Before taking this course, the participants had completed foundational coursework in mathematics, mathematics pedagogy, and general educational studies.

The PSTs were organized into three groups of four to five members. Each group selected one topic from the primary mathematics curriculum: fractions, three-dimensional shapes, and measuring angles. During the lesson study cycles, the PSTs assumed complementary roles as lesson designers, model teachers, observers, and peers simulating primary learners. All lesson enactments were conducted through peer teaching at the university.

PjBL functioned as the macro-pedagogical architecture of the course project. It organized PSTs’ work around the authentic professional problem of designing mathematics instruction responsive to difficulties commonly experienced by primary learners. The project involved sustained inquiry, collaborative decision making, selection of mathematical topics and pedagogical approaches, development of instructional media and worksheets, peer feedback, lesson enactment, and production of a finalized lesson design. The groups exercised agency in selecting their topic, distributing responsibilities, designing tasks, choosing representations, and determining the pedagogical support incorporated into their lessons.

Lesson study operated within this broader project as the micro-cycle of professional inquiry. Each group completed two cycles. During Plan, group members collaboratively developed a lesson design containing learning objectives, anticipated difficulties, task sequences, predicted learner responses, and proposed teacher support. During Do, the design was enacted through peer teaching while other PSTs assumed observer or simulated-learner roles. During See, participants and the course instructor discussed the enactment, with attention to learner responses, task accessibility, teacher questioning, and departures from the plan. During Redesign, each group reconsidered its tasks, prompts, scaffolding, and lesson sequence before the subsequent cycle or final submission. Thus, PjBL organized the overall course project, whereas lesson study provided the recurring process connecting planning, enactment, reflection, and redesign. Table 1 presents an overview of how PjBL and Lesson Study integrate.

The analyzed data comprised two complementary sources including final lesson designs and semi-structured group interviews. The three final lesson designs, one from each group, were submitted after completion of the lesson study cycles. Each document included learning objectives, anticipated content-specific difficulties, task sequences, predicted learner responses, proposed teacher support, group activities, and assessment or reflection components. The documents provided evidence of the pedagogical decisions represented in the groups’ final plans; because earlier versions were not included in the analyzed corpus, they were not used to establish developmental change across cycles.

Three semi-structured group interviews were conducted after completion of the lesson study, with one interview for each group. Each interview lasted approximately 20–30 minutes and addressed collaborative planning, peer-teaching enactment, reflection, redesign, pedagogical insights, and difficulties in translating inquiry-oriented plans into practice. All 13 PSTs participated in their respective interviews. The interviews were conducted by the research team in Indonesian, audio-recorded with permission, and transcribed verbatim. Quotations selected for reporting were translated into English while preserving their intended meaning and checked against the Indonesian transcripts.

Data were analyzed using a thematic analysis approach within the case study framework. The analysis began with open coding of interview transcripts and lesson plans, followed by axial coding to identify themes related to pedagogical reasoning, collaborative practices, and professional insights. Analysis began with repeated reading of the three lesson designs and interview transcripts to establish familiarity with each group’s account. The primary researcher then conducted open coding across both data sources. Initial codes captured content-specific anticipation, task selection and sequencing, predicted learner responses, instructional scaffolding, collaborative decision making, reflective reconsideration, reported redesign, and departures from the lesson design.

The analysis proceeded in two stages. First, the lesson design and interview for each group were examined as an embedded unit to identify alignments and tensions between planned instruction and participants’ retrospective accounts of enactment. Second, codes were compared across the three groups to identify recurring patterns, topic-specific variations, and discrepant evidence. Related codes were clustered into provisional categories and refined into four themes: developing pedagogical reasoning in planning, designing mathematical tasks for reasoning and communication, attending to simulated learner responses, and using reflection to inform lesson redesign. A design–enactment discontinuity was retained as a cross-cutting pattern because it appeared across all three group interviews and challenged a uniformly developmental interpretation of the project.

The primary researcher developed the initial coding and thematic organization. A second researcher familiar with Lesson study and mathematics teacher education reviewed the coded evidence, theme boundaries, and interpretations. Differences were discussed and resolved through re-examination of the original lesson designs and Indonesian interview transcripts.

Several strategies were used to strengthen the credibility of the findings. Comparison between the final lesson designs and group interviews enabled source triangulation between planned pedagogical representations and participants’ interpretations of their experiences. Member checking was conducted by inviting participants to review summaries of their interview responses for accuracy. Peer debriefing with a researcher familiar with Lesson study and mathematics education was used to examine the plausibility of the codes and themes. Disconfirming evidence was retained in the analysis, particularly participants’ reported reversion to direct instruction despite inquiry-oriented lesson designs.

The research team also recognized that the course-based setting and the instructor’s pedagogical role could influence participants’ responses. Participation in course activities was part of the course, but participation in the research was voluntary. Participants received information about the study and provided written consent before their data were used. They were assured that participation or withdrawal would not affect their academic evaluation. All data were anonymized during analysis, and quotations were reported using group and participant identifiers, such as G1-M1.

This section presents the findings in relation to the two research questions: (1) How do PSTs engage in lesson design and enactment within a PjBL-organized course structured through lesson study cycles? and (2) What pedagogical reasoning, professional insights, and design–enactment tensions emerged from their participation in these cycles? The discussion is organized around these questions and grounded in both participant data and relevant literature.

The data corpus comprised three final lesson designs addressing fractions, three-dimensional shapes, and angle measurement, together with three semi-structured group interviews. The lesson designs represented the participants’ planned pedagogical decisions, including anticipated learning difficulties, task sequences, predicted learner responses, and proposed teacher scaffolding. The interviews provided retrospective accounts of collaborative planning, peer-teaching enactment, reflection, and intended redesign. Across data sources, four themes consistently emerged: (1) developing pedagogical reasoning in planning, (2) designing mathematical tasks for reasoning and communication, (3) attending to simulated learner responses, and (4) using reflection to inform lesson redesign. A design–enactment discontinuity also emerged across all three groups as a cross-cutting pattern. Table 2 summarizes the four themes and highlights representative evidence from each data source.

The findings indicate that the PjBL and Lesson study arrangement created opportunities for PSTs to engage with lesson design as a reasoned and collaborative activity rather than merely as the completion of a planning template. The planning evidence reflects an emerging form of pedagogical reasoning in which mathematical content was transformed into instructional sequences responsive to anticipated learner difficulties. For example, the groups planned transitions from concrete or visual representations to more formal mathematical ideas and incorporated sharing and jumping tasks to extend reasoning. This finding is consistent with Shulman (1987) conception of pedagogical reasoning as the transformation of subject matter for teaching. It also complements recent research showing that lesson study can support PSTs in anticipating student strategies, selecting mathematically productive tasks, and preparing classroom discussions (Cardoso et al., 2025; Clivaz & Ni Shuilleabhain, 2019; Fitriati et al., 2025; Nguyen & Tran, 2023). The present study adds that these forms of reasoning were visible across three distinct elementary mathematics topics such as fractions, three-dimensional shapes, and angle measurement, although the available data do not establish a longitudinal increase in competence.

The PSTs’ attention to possible misconceptions and solution strategies can also be interpreted through professional noticing (Qi et al., 2025; Yilmaz & Yetkin Ozdemir, 2023). Their lesson designs showed evidence of preparing to attend to learner responses, while the interviews demonstrated retrospective efforts to interpret why particular tasks or representations did not function as expected. Lesson study has similarly been found to support PSTs’ attention to and interpretation of mathematical thinking through collaborative planning and reflection. However, the current findings also expose an important limitation. Because the enactments involved peers simulating primary students, the observed responses cannot be equated with authentic students’ mathematical thinking. Consequently, the evidence supports emerging attention to simulated learner responses, not fully developed professional noticing in actual primary classrooms. Moreover, noticing requires more than anticipating or recognizing a response, it also involves selecting an appropriate instructional response in the moment. The PSTs’ difficulty at this responding stage became particularly visible during enactment.

The cross-cutting design–enactment discontinuity provides the study’s central theoretical contribution. Although all three groups designed lessons intended to promote exploration, explanation, and comparison of strategies, their interview accounts indicated that they sometimes returned to direct explanation when peer learners hesitated, remained silent, or required more time. The groups associated this reversion with time pressure, limited confidence in probing learner thinking, short wait time, and familiarity with teacher-centered instruction. Thus, producing an inquiry-oriented design did not ensure responsive enactment. From the perspective of pedagogical reasoning and action, PSTs could formulate pedagogical intentions during planning but found it more difficult to adapt those intentions under the uncertainty of interaction. From the perspective of professional noticing, they could anticipate possible responses but did not consistently translate attending and interpreting into productive responding. This distinction is consistent with recent evidence that instructional intentions may exceed PSTs’ capacity to enact inquiry-oriented teaching when contextual uncertainty and limited opportunities for supported practice intervene (Tsakeni et al., 2026).

The collaborative and inquiry-oriented nature of PjBL and lesson study is consistent with a social constructivist perspective, in which professional knowledge is constructed through participation, dialogue, and shared examination of practice (Schunk, 2014). Through PjBL and lesson study activities, PSTs construct their knowledge by working collaboratively with peers and experts to plan the lesson, implement and observe the lesson and reflect on it. Interaction with peers and experts is seen as an effective way for teachers as learners to construct new knowledge and skills. Similar findings appear in contemporary lesson study research, where collaborative cycles have been shown to support shared professional judgment and the examination of mathematics teaching practices (Fitriati et al., 2026; Fitriati et al., 2023; Nguyen & Tran, 2023). In the present study, this collaborative process was particularly evident in participants’ discussions of task accessibility, learner participation, and the need to provide opportunities for mathematical explanation rather than merely correct answers.

The findings also clarify the distinct functions of PjBL and lesson study within the course. PjBL served as the macro-pedagogical architecture as it organized the extended project through which the PSTs identified a problem of practice, selected a mathematical topic, and produced a final lesson design. This function is consistent with research positioning projects as structures for sustained investigation and the production of meaningful instructional artifacts (Farrow et al., 2024). Lesson study operated within that architecture as the micro-cycle of professional inquiry through which each design was planned, enacted through peer teaching, examined, and redesigned. In this sense, PjBL provided continuity and a shared project outcome, whereas lesson study supplied the iterative mechanism for examining instructional decisions. Their interaction is reflected in the movement from problem identification to repeated lesson-design cycles. However, because the analyzed corpus comprised final lesson designs and retrospective group interviews, the study cannot isolate the causal effect of PjBL or determine whether the same outcomes would have occurred through lesson study alone. The contribution is therefore conceptual and interpretive: the case demonstrates a feasible division of pedagogical functions rather than comparative evidence of effectiveness. This interpretation is compatible with recent work showing that PjBL and Lesson study may be coordinated while retaining analytically distinct roles (Qi et al., 2025).

A key indicator of teacher learning is the ability to revise instruction based on evidence rather than habit. In this study, PSTs revised tasks, scaffolds, and representations based on mismatches between the lesson designs and peer-teaching enactments. This aligns with research indicating that lesson study supports adaptive instructional decision-making by making learner responses visible and providing structured opportunities for collaborative reflection and evidence-based refinement (García et al., 2024; Lewis, 2016; Nguyen & Tran, 2023). In this study, PSTs reconsidered representations used to introduce volume, clarified prompts related to fraction denominators, and adjusted task guidance and waiting time. These revisions reflected emerging attention to responsive teaching, although the available data did not establish developmental change across the two cycles.

The findings highlight several actionable implications for strengthening mathematics teacher preparation. First, integrating structured lesson design should become a core component of coursework and practicum. Explicit attention to constructing didactic situations, anticipating student responses, and planning teacher moves enables PSTs to engage in deeper pedagogical reasoning. Embedding these elements in methods courses can better prepare PSTs for the complexities of classroom instruction since designing effective mathematics instruction is not an easy task for them (Fitriati & Novita, 2018). Second, lesson study offers a productive practice-based framework for developing these competencies. Its iterative cycles create authentic opportunities for PSTs to plan tasks for reasoning and communication, test predictions about student thinking, and revise designs using evidence from peer-teaching enactments and collaborative reflection. Embedding Lesson study within school–university partnerships can enrich practicum experiences by connecting coursework with real student learning. Finally, teacher educators should foreground the practice of noticing and evidence-based revision as essential habits of mind. Structured observation tools, guided reflection, and collaborative debrief can help PSTs learn to interpret student thinking and make principled instructional decisions. By cultivating these practices, teacher education programs can better equip future teachers to design mathematically rich and responsive learning experiences.

Finally, this study is bounded by its small sample and single institutional context, which may limit transferability of the findings. Each group designed and enacted lessons for only one mathematical topic; therefore, the identified patterns may partly reflect topic-specific features and do not demonstrate whether the same PSTs would make similar planning and enactment decisions across different mathematical domains. Moreover, the lessons were enacted through peer teaching rather than with primary pupils, and the analyzed corpus was limited to final lesson designs and retrospective group interviews. Future research should examine repeated lesson study cycles across multiple topics and authentic classroom settings.