This study aimed to investigate how lesson study perspective could help pre-service teachers (PSTs) to enhance their mathematical instruction. Four PSTs along with their 13 other peers who took a semester long secondary level mathematics teaching methods course in one of the large-midwestern universities in the US participated in this study. While four PSTs planned and taught a lesson in two different groups by two, other PSTs took the role of giving feedback to their classmates. PSTs enhanced their lesson plans based on the feedback from their peers and provided self-reflections on these changes. As a result of the investigation of the changes PSTs did on their lesson plans and the reflections they provided, it was revealed that they enhanced their instruction on some specific issues, such as getting students' attention, using time efficiently, maintaining student interaction, using technology. It is also suggested to future researchers that it would be beneficial to study on PSTs' assumptions on the difference between the real students and the PSTs who pretended as students during the peer-taught lesson study activity.

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Introduction: Textbook tasks are considered as tools for implementing, endorsing mathematical thinking and thereby creating chances for mathematics learning. Therefore, textbook tasks can potentially influence and structure the way students think and can serve to limit or to broaden their views of the subject matter with which they are engaged. Among the essential sources of textbook tasks include worked examples and exercises. Because these worked examples and exercises in the textbooks are mostly used by students either in the classroom or at home, they definitely affect students’ conceptual understanding of mathematics and may inspire students to work individually or collaboratively with their peers. Thus, given the importance of mathematical literacy for learning and understanding of math, one should investigate the chances students can have through it. This study aims to reveal the inclusion of the mathematical literacy demands in the fifth-grade mathematics textbooks from Turkey, Singapore, and Australia. Methods: Being qualitative in nature, the current study employed a document analysis method to examine the textbooks. The cycle of mathematical literacy processes, defined in PISA framework, was used as a framework during the analysis to investigate mathematical literacy demands. Results: Findings of the analysis of mathematical literacy demand in real life problems indicated that textbooks from all three countries had provided more opportunities for the competencies of two mathematical literacy processes, formulating and employing, while a small portion of these problems requires higher level cognitive skills to interpret/evaluate their mathematical solutions and make decisions for real life, which is the third process in the cycle; therefore, most of the real-life problems in the textbooks could not provide the chances for completing the whole mathematical literacy cycle. Moreover, textbooks from all three countries provided more chances for experiencing mathematical literacy processes in to-be-solved questions rather than worked examples. Discussion: In general, textbooks from all three countries have included a small portion of the problems relating real life. Related literature also proves evidence for lack of real-life opportunities in the mathematics textbook tasks. Moreover, textbooks from all countries had provided more opportunities for the competencies of formulating and employing while a small portion of these problems requires higher level cognitive skills to interpret/evaluate their mathematical solutions and make decisions for real life. These results are not in accordance with the mathematics education calls voiced in national and international standards of mathematics education: Raising individuals with both mathematical thinking and reasoning skills and a useful foundation of mathematical knowledge and skills needed in all areas of life. Most of the real-life questions in the textbooks could not provide the chances for completing the whole mathematical literacy cycle. Textbooks’ weaknesses in their inclusion of MLP may also cause impediments in the development of students’ skills of handling the problems that they confronted in daily life. Limitations: The present study only included one textbook from each country while these textbooks were representing the authenticity of the other textbooks in these countries. Moreover, this study examined the opportunities of mathematical literacy only provided in the textbooks while the actual implications of these opportunities may differ across classrooms in these countries. Conclusions: Students’ inappropriate practices with the real-life problems may cause them to not successfully solving these kinds of problems. Instead, employing more real-life problems in the classroom activities may result in higher student understanding. Moreover, examples and tasks from daily life are helpful to provide students with meaningful contexts and enable students to relate to their familiar experiences. The absence of providing necessary problem-solving opportunities in a range of different types in the textbooks may cause students to not solve specific types of problems. Moreover, textbooks should also include these problem-solving opportunities to construct students’ conceptual appreciations of problem structures. Thus, one implication this study can make is that Singaporean and Australian textbook creators should include more sufficient practices of the whole MLP cycle in their problems to make sure students acquire the principal latent components of the problems.

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