How different perspectives on giftedness determine research and practice in the education of the mathematically gifted. We expand on the views of the group in this regard at the end of this report.

## July 11th Wednesday, 10:30 – 12:00

The session concluded with a round table discussion in which Nitsa Movshovitz-Hadar (Israel), the speakers and the audience discussed the scope and scope of the concept of mathematical literacy. In the study, 24 pairs of mathematically equivalent math problems were constructed so that each pair contained a language-rich version and a picture-rich version of "the same" problem.

## Friday 13th July, 15:00 – 16:30

In the first of three 15-minute presentations, Jeff Evans (UK) presented a comparative analysis of the definition of numeracy in PIAAC (Project for International Assessment of Adult Abilities) and the definition of mathematical literacy in PISA, 2006. next presentation, Jenna Tague (USA, with co-authors not present), dealt with two connected topics: the so-called STEM (Science, Technology, Engineering and Mathematics education) reform in the USA and a related development project at Ohio State University, reconceptualization of engineering courses by focusing on mathematical literacy.

## Saturday 14th July, 10:30 – 12:00

Mathematical literacy and numeracy are of the same nature, but mathematical literacy is (mainly) in the context of students and schools and numeracy in the context of the adult world. This conclusion served as a convenient prelude to the final part of the session, a combined round table conference and discussion among the participants.

## Students ’ Dif ﬁ culties and Teaching Methods

After further discussing the initially accepted proposals among the TSG-8 team members, four papers were accepted for long oral presentation (30 min presentation and 10 min discussion) and eight papers for short presentation (15 min presentation and 5 min discussion). Third, Wayne Hawkins from Australia presented four primary teachers' pedagogical content knowledge in teaching measurement for Year 3 and 4 students.

## Curricular Materials and Teaching Methods

By examining teachers' knowledge of mathematics alongside knowledge of students and teaching, Wayne helped the audience understand the complex nature of pedagogical content knowledge and provoked a discussion about the dynamic nature of such knowledge.

## Delving into Students ’ Understanding

This presentation helped participants understand the close relationship between curriculum documents, teaching methods and student learning outcomes. Third, Andrea McDonough from Australia reported on a design experiment to teach lower primary school students about measuring mass.

## Measurement Instrument and Its Use

16 of the oral presentations were short presentations (10 min for presentation and 5 min for discussion) and 9 were long presentations (20 min for presentation and 10 min for discussion). Xhevdet Thaqi compared the curricula of Spain and Kosovo and investigated "how potential teachers understand, learn and present each component of geometric transformations if there are differences between two different countries." The study concluded that the conceptual image of transformation as displacement and change of place is of importance among student teachers.

## Curriculum Development and Policies

There is a growing global interest in learning what kinds of knowledge teachers need to effectively teach probability concepts and how to facilitate the development of such teacher knowledge. To promote more discussion and research in this area, the plenary panel discussion was narrowed down to teacher knowledge for probability teaching.

## Research on Students ’ Thinking and Reasoning

He called for the need to address risk education and suggested that we can benefit from research relevant to other TSGs, such as mathematical applications and modeling in mathematics teaching and learning. The session challenged research to develop hands-on approaches to teaching probability through mathematical models.

## Probability Literacy and Instructional Challenges

Summarizing the session, Nilsson emphasized the need to develop research methodologies to investigate the semiotic nature of teaching and learning probability.

## Teacher Knowledge in Probability Teaching

Twelve longer presentations and discussions (10 + 5 min of discussion) to improve the overall themes of short presentations and posters; The structure for each of the four 90-minute sessions included some brief opening remarks by the committee co-chairs, followed by long presentations (20 minutes) and 3 short paper presentations (10 minutes each). Another large-scale survey – in this case conducted in China – was the starting point for the next talk given by Xuefen Gao.

Various issues related to teaching and learning of Calculus frequently appeared in the general discussions at the end of the oral sessions. Most of the papers (long and short presentations and posters) showed an interest in innovative approaches to different topics, in order to help students improve their knowledge and understanding of Calculus. Curriculum and textbook aspect; Cognitive aspect; Teaching and teacher training aspect, so that any paper of relevance to the overall focus of the Study Group.

Conception of Proof from Different Theoretical Perspective (10th July 2013)

## Proof in the Classroom: the Role of the Teacher (11th July 2013)

The discussion during the session, along with the content of the presentation, highlighted the difficulties for teachers in engaging students in mathematical activities involving proofs and proofs; an important issue concerns the possibility of making students aware of the need for proofs and proofs. Taking into account that geometry was the most represented mathematical domain in the articles and posters presented in the group, the following question was raised during the discussion: is this issue factually unavoidable, or is it possible to prove it in class? work in other mathematical domains. In the end, the participants agreed that while geometry is a relevant traditional domain in many countries for teaching reasoning, proofs and proofs in high school, there are also other relevant domains such as arithmetic, linear algebra, analysis etc., depending on the level.

Evaluation of Proofs (13th July 2013)

## Curriculum and Materials (14th July 2013)

In this particular study, the author relies on the application of the anthropological theory of didactics, a framework commonly used in the French mathematics education tradition. Museum View was the guiding image in the design of VisualMath's interactive eBooks in Algebra, Functions, and Calculus. Peter Stender also focused on the role of the teacher on modeling in mathematics education, the development of forms of intervention and their placement in teacher education, and Dominik Leiss on flexible teacher interventions in mathematical modeling.

One way to get an overview of the picture of the field presented in the subject study group is to look at the different ones. Therefore, a wide range of the applicable educational technologies is present in the subject study group. In ICME12, the role of technology in mathematics education was divided into two separate study groups: Analysis of uses of technology in teaching (TSG 18) and learning (TSG 19) in mathematics.

Theme 1: Theoretical and Methodological Considerations)

## Theme 2: Instructional Context, Reflection, and Improvement)

In the following sections, we briefly summarize the paper presentations and discussions during these sessions. Giménez and Font i Moll illustrated the use of a two-dimensional grid to identify nine types of democratic mathematical practices in the classroom.

Theme 3: High-Quality Instructional Practices)

## Theme 4: Students ’ Perception, Class Work, and Learning)

The authors also investigated teacher change processes by supporting teachers' systematic reflection and iterative improvement of their lessons. The authors argued that the strong direct role of the teacher can help students master their mathematical content.

Theme 5: Teaching and Learning Elementary Mathematics)

## Theme 6: Teachers ’ Questioning and Response in Classroom Instruction)

The Chinese teacher's questions usually only required a short answer, in a short time and without the help of the teacher. On the contrary, the Czech teacher's questions were more cognitively demanding, but he offered no guidance. Taken together, these articles demonstrate the growing interest in teacher questioning practices as a result of the recognition of its pedagogical value for student learning.

Some professional cultures seem to value the power of questioning for a long time, but the nature and goals of the questions the teachers ask differ substantially from setting to setting.

Theme 7: Instructional Design and Practice)

## Theme 8: Curriculum/Task Implementation)

The second presentation “The Ladder of Knowledge: A Knowledge Model for Second Level Mathematics Teachers” was presented by Niamh O'Meara (Ireland). The fifth presentation “the structure of the knowledge of student teacher teaching on the topic of distance formulation” was presented by Lin Ding (China). The sixth presentation “The Project: Collaborating to Advance the Mathematics Proficiency of Secondary School Teachers” was presented by Pier Junior Clark (USA).

Empirical research to explore the relationship between teachers' teaching learning (both pre-service and in-service) and students' mathematics learning, eg, the effect of mathematics teaching knowledge on student achievement, innovative approaches and creative development of the effect of mathematical knowledge for teaching on student learning and achievement. While this is often portrayed as a 'problem', the papers presented at TSG show that mathematics educators are dealing in subtle and important ways with the complex issues involved. The third session highlighted how important the teaching method is to capture the students' interest – the girls of the study value being responsible and active.

It was also noted that although TSG 30's title and topics included "multilingualism" and "multiculturalism," the papers and discussions tended to focus on issues related to multilingualism. Issues and examples related to the implementation of classroom practices that reflect current thinking in mathematics assessment and education (eg, using assessment for learning, teaching and learning in mathematics classrooms).

## Large-Scale Assessment and the Implications for the Development of Teaching and Learning

Papers were then categorized according to these three threads, and after our first meeting to introduce the topics and structure of the group, each day consisted of the presentation of plenary papers or posters connected to these three threads, and then a division into three subgroups with a subgroup focused on each strand. The following presents a summary of the main themes presented and discussed in each of the strands. We have also included the ideas from the plenary papers, which typically spanned several threads.

Classroom Assessment and Developing Students ’ and Teachers ’ Knowledge

## Task and Test Design, Various Perspectives

In the words of the discussion document for ICMI Study 16, "Mathematics is engaging, useful, and creative. Does engaging students in challenging contexts affect their ability to learn mathematics? In keeping with the already established tradition of research in the history of mathematics education, the International Program Committee for ICME-12 included in the scientific program a TSG 35 with the title "The history of teaching and learning mathematics".

Despite the time constraints, the contributions to ICME-12 on the history of the teaching and learning of mathematics have enabled reflection on the dual aspect of this topic. Eds.) (2012). Proceedings of the Second International Conference on the History of Mathematics Education. Caparica, Portugal:. They tried to emphasize the role of cultural mathematics in the development of the ability to make mathematical connections.