Designing and enacting mathematics lessons: Insights from pre-service teachers’ learning through project-based learning and lesson study
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Abstract
Bridging lesson design and instructional enactment remains a challenge in mathematics teacher education. This qualitative case study explored how Project-Based Learning (PjBL) and lesson study supported pre-service mathematics teachers (PSTs) in addressing this challenge. PjBL provided the macro-pedagogical architecture for a seven-week collaborative project, while LS structured the micro-cycles of Plan, Do, See, and Redesign. Participants were 13 third-year PSTs enrolled in an undergraduate Mathematics Education program and taking an Elementary Mathematics Instruction course at an Indonesian university. Organized into three groups, they selected an elementary mathematics topic, designed a two-meeting lesson sequence, and completed two lesson study cycles through peer teaching. Data consisted of lesson designs and semi-structured group interviews and were analyzed thematically. The findings revealed that participants engaged in pedagogical reasoning, designed tasks intended to promote mathematical reasoning and communication, considered simulated learner responses, and used reflection to redesign their lessons. However, interview data revealed instances of reverting to direct explanation when simulated learners hesitated or required additional time. These findings identify a design–enactment discontinuity in which the capacity to construct student-centered lessons did not automatically translate into responsive enactment. The study suggests that combining sustained project work with iterative professional inquiry can provide a useful structure for lesson design, but PSTs also require repeated and scaffolded opportunities to rehearse responding to learner thinking.
INTRODUCTION
Preparing pre-service teachers (PSTs) to design and deliver effective instruction in elementary classrooms has become a central concern in teacher education. Beyond content knowledge, novice teachers must develop the capacity to plan instruction that promotes conceptual understanding, addresses student misconceptions, and engages diverse learners(Allmendinger et al., 2023). This includes selecting and sequencing meaningful tasks, anticipating learners’ possible responses, and determining appropriate pedagogical support(Sujadi et al., 2025). However, this instructional design competence cannot be developed in isolation from practice. Research has consistently shown that traditional university-based coursework tends to separate theoretical knowledge from the practical demands of real teaching, leaving teacher candidates underprepared for the complexity of the classroom(Christiansen & Erixon, 2024; Hoover & Ball, 2021). A particularly persistent challenge is the design–enactment gap: the presence of student-centered elements in a lesson design does not necessarily ensure that novice teachers can enact those elements responsively in practice.(Farrow et al., 2024; Fitriati & Novita, 2018). In response, there is growing interest in embedding practice-based approaches into teacher education programs, emphasizing teaching as a form of disciplined inquiry and design(Mancenido et al., 2026).
Project-Based Learning (PjBL) has emerged as a promising approach in teacher preparation because it positions pre-service teachers (PSTs) as active designers and decision makers. Through authentic, extended projects, PSTs learn to connect theory with practice, collaborate to solve instructional problems, and create meaningful products such as lesson designs(Farrow et al., 2022; Pratiwi et al., 2025; Qi et al., 2025). In Indonesia, the use of project-oriented learning in higher education has been reinforced through the national Key Performance Indicators for higher education. Under KPI 7, collaborative and participatory learning is recognized through the use of case methods or team-based projects, in which students work collaboratively on authentic problems or complex questions and present a final product for feedback (Directorate General of Higher Education, 2021;Ministry of Education Culture Research and Technology, 2023). Through PjBL, PSTs are encouraged to structure lessons around rich problems, anticipate student strategies, and design learning trajectories that promote inquiry of learning in the 21st century. However, while PjBL strengthens PSTs’ conceptual understanding of instructional models, research indicates that novice teachers often struggle to enact these designs in real classrooms without additional guided practice(Liang et al., 2025; Magaji et al., 2024).
Lesson study offers a complementary structure by situating PSTs’ learning within cycles of collaborative planning, observation, reflection, and revision(Fitriati et al., 2023; Tan et al., 2024). In lesson study, teachers jointly plan a lesson, often called a research lesson, observe its implementation in a real classroom, and engage in structured reflection based on student learning evidence(Lewis, 2016; Lewis & Hurd, 2011; Murata, 2011). The process enables PSTs to focus deeply on teaching and learning, to test and refine ideas, and to grow professionally through collective inquiry(Dudley, 2014; Lewis, 2016). While lesson study has traditionally been used for in-service teacher development, recent studies have highlighted its potential in teacher education, especially for enhancing PSTs’ skills in lesson planning, pedagogical reasoning, and classroom observation(Fitriati et al., 2025; Tan et al., 2024; Wood et al., 2019).
The inclusion of lesson study in initial teacher education aligns with a broader shift toward pedagogies of enactment, which situate professional learning within approximations of teaching practice. AsLewanowski-Breen et al. (2021)argue, such pedagogies provide opportunities that allow PSTs not only to apply knowledge for teaching mathematics but also to develop pedagogical reasoning by connecting instructional purposes, anticipated learner responses, teaching decisions, and reflection on enactment. In mathematics education, pedagogical reasoning is closely related to professional noticing, commonly understood as teachers’ capacity to attend to, interpret, and respond to learners’ mathematical thinking(Bakker et al., 2022). Research indicates that noticing does not develop automatically; PSTs require structured opportunities to anticipate responses, examine evidence from enactment, and reconsider instructional decisions (Ekawati et al., 2023;Yilmaz & Yetkin Ozdemir, 2023). In this study, pedagogical reasoning and professional noticing therefore provide complementary lenses for examining how PSTs justify lesson-design decisions and interpret simulated learner responses during peer teaching.
Recent research indicates that PSTs benefit from opportunities to design contextually meaningful mathematical tasks, anticipate possible responses, and revise instruction through collaborative inquiry (Sujadi et al., 2025;Yilmaz & Yetkin Ozdemir, 2023). Lesson study supports these processes by connecting planning, enactment, reflection, and redesign(Fitriati et al., 2025; Fitriati et al., 2023; García et al., 2024), while PjBL provides sustained engagement with an authentic professional project. The two approaches therefore contribute at different but complementary levels. PjBL provides the macro-pedagogical architecture that organizes the extended lesson-design project, participant collaboration, project milestones, feedback, and final products. Lesson study operates within that architecture as a micro-cycle of professional inquiry through Plan, Do, See, and Redesign. This nested relationship is consistent with recent mathematics education research showing that PjBL and Lesson study can be combined to support teachers’ interpretation and adaptation of instructional resources(Qi et al., 2025). However, evidence of successful lesson design should not be equated with successful enactment, as student-centered features in planned lessons may not transfer directly into instructional practice(Farrow et al., 2024).
Despite growing research on lesson study in teacher education(Baumfield et al., 2022; Larssen et al., 2018; Tan et al., 2024), two issues remain insufficiently examined.
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