Andreas J. Stylianides

• PhD
• Professor (Full) at University of Cambridge

Mathematical problem posing, a form of authentic mathematical inquiry and creation, has been acknowledged as important by educators and curriculum frameworks internationally and has been the focus of several intervention studies with students and teachers. However, the intervention components and measured outcomes of these prior studies varied, hig...

Mathematical problem posing, generally defined as the process of interpreting given situations and formulating meaningful mathematical problems, is academically important, and thus several interventions have been used to enhance this competence among students and teachers. Yet little is known about the interventions’ various components and their re...

Situated in the education reform launched by the Egyptian Ministry of Education (MOE), which called for a socially-foreign shift away from memorization-based mathematics instruction, this paper explores the role of school-based teacher professional networks in implementing reform. Adopting the Goodson Change Model as a theoretical framework, we map...

Assumptions play a fundamental role in disciplinary mathematical practice, especially concerning the relativity of truth. However, much is still unclear about ways to help students recognize key aspects of this role. In this paper, we propose a set of principles for task design to introduce students to the role of assumptions in mathematical activi...

Although mathematics pedagogy in Chinese classrooms is presumed to be mostly teacher-centered, the Dulangkou secondary school has a strong national reputation of having reformed its pedagogy to be student-centered. In this comparative case study, we used the Reformed Teaching Observation Protocol (RTOP) to investigate whether the pedagogy used at D...

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This systematic review aims to provide a complementary to existing synopses of the state-of-the-art of mathematics education research on proof and proving in both school and university mathematics. As an organizing framework, we used Cohen et al.’s triadic conceptualization of instruction, which draws attention not only to the main actors of the di...

Although the notion of assumptions is important in mathematical activity as early as the elementary school, there is limited research on how to help elementary teachers develop mathematical knowledge for teaching related to assumptions. In this paper, we discuss the theoretical foundation and implementation of an intervention that aimed to promote...

As the goals of mathematics instruction have broadened over the past few decades, there has been a growing appreciation of the idea that there is value in students’ classroom mathematical activity, even in the elementary school, being a representation of some core aspects that are characteristic of mathematicians’ activity in the discipline of math...

Although the notion of proof is important for all learners’ mathematical experiences, there has been limited attention to what it might involve and look like to introduce students and prospective teachers to proof. In this paper we argue for the importance of having a coherent approach to introducing students and prospective teachers to proof, and...

The terms (mathematical) argumentation, justification, and proof are or can be related, and they have been used in various ways in the mathematics education literature, often without an explicit definition. In this chapter we reflect on issues of terminology with regard to these terms, and we explore implications of using alternative definitions th...

Talk for the Collaborative Innovation Centre of Assessment toward Basic Education Quality Beijing Normal University, China, 25 Feb 2022

The field of knowledge brokering in education—aiming to better connect research to practice—is currently emerging. Evidence of a community dissonance between researchers and practitioners in education suggests that models of knowledge brokering that consider the perspectives and priorities of both groups are required. It is also a priority to ident...

Underpinned by the Human Condition Theory, this case study casts light on how an Egyptian mathematics teacher navigates his instructional approach with regards to problem solving while operating within a centralised governance model of national schooling. The study investigates multiple layers of contextual power dynamics affecting the teacher’s pe...

https://pdf.medrang.co.kr/JERM/2020/030/jerm-30-sp-69.pdf The concept of proof is central to every undergraduate mathematics curriculum, but it is also a difficult concept for university students to understand and for university instructors to teach. Prior studies have contributed useful research knowledge about the nature and sources of undergrad...

This paper presents a contextual investigation of social, cultural and political factors hindering the integration of mathematical problem solving in Egyptian classrooms. Centered around a one-size-fits-all mathematics curriculum and examination scheme, the current national agenda for schooling seeks to govern all schools in Egypt. Using the Goodso...

In this paper, we argue that posing new researchable questions in educational research is a dynamic process that reflects the field’s growing understanding of the web of potentially influential factors surrounding the examination of a particular phenomenon of interest. We illustrate this thesis by drawing on a strand of mathematics education resear...

Mathematics education researchers have highlighted the importance of assumptions in school mathematics given their vital roles in mathematical practice. However, there is scarcity of research aiming at enhancing students' recognition of different roles that assumptions play in mathematical activity. In this paper, we begin to address this issue by...

Prior research showed that many secondary students fail to construct arguments that meet the standard of proof in mathematics. However, this research tended to use survey methods and only consider students presenting their perceived proofs in written form. The limited use of observation methods and the lack of consideration of students presenting t...

The notions of mathematics teachers’ knowledge and beliefs have been conceptualized in manifold ways in the literature. Notwithstanding these different conceptualizations, however, the point stands that mathematics teachers’ knowledge and beliefs are important factors to consider both in the study of classroom instruction in mathematics and in thin...

The proliferation of instructional resources and the potential impact of teachers’ resource selection on students’ learning opportunities create a need for research on teachers’ selection of resources. We report results from an interview study with 36 secondary mathematics teachers in England, designed to find out (1) what instructional resources t...

Research has provided a strong empirical and theoretical basis about major difficulties students face with proof, but it has paid less attention to the design of interventions to address these difficulties. In this chapter we highlight the need for more research on classroom-based interventions in the area of proof, and we discuss what might be imp...

This Working Group aims to engage PME participants in discussion and debate about principles for the design of i.e. documents such as the Common Core State Standards in the USA and the National Mathematics Curriculum in Eng-land. Such documents set out expectations about what mathematical ideas should be taught and when and include learning goals t...

In this exploratory study, we investigated the personal epistemologies of statisticians in academia with the aim of offering some insight into what might be an availing epistemology for learning statistics. Findings from in-depth , semi-structured interviews with six academics currently researching within the field of statistics showed that their s...

In this exploratory study, we investigated the personal epistemologies of statisticians in academia with the aim of offering some insight into what might be an availing epistemology for learning statistics. Findings from in-depth, semi-structured interviews with six academics in the UK currently researching within the field of statistics showed tha...

The concept of proof has attracted considerable research attention over the pastdecades in part due to its indisputable importance to the discipline of mathematics and tostudents’ learning of mathematics. Yet, the teaching and learning of proof is an instructionallyarduous territory, with proof being recognized as a hard-to-teach and hard-to-learn...

The benefits of problem-based learning (PBL) to student learning have prompted researchers to investigate this pedagogical approach over the past few decades. However, little research has examined how PBL can be applied to mathematics learning and teaching, especially in countries like Taiwan, where the majority of teachers are accustomed to lectur...

The benefits of problem-based learning (PBL) to student learning have prompted researchers to investigate this pedagogical approach over the past few decades. However, little research has examined how PBL can be applied to mathematics learning and teaching, especially in countries like Taiwan, where the majority of teachers are accustomed to lectur...

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Ambitious teaching is a form of teaching that requires a high level of teacher responsiveness to what students do as they actively engage with the subject matter. Thus, a teacher enacting ambitious teaching is often confronted with uncertainties about how to advance students’ learning while also building on students’ contributions. In this article...

Many students of all levels of education have certain beliefs about mathematical problem solving that tend to influence negatively these students’ ability or willingness to engage productively with problem solving. Previous interventions that achieved a positive impact on such student beliefs tended to last over extended periods of time, thereby pr...

The activity of reasoning-and-proving is at the heart of mathematical sense making and is important for all students’ learning as early as the elementary grades. Yet, reasoning-and-proving tends to have a marginal place in elementary school classrooms. This situation can be partly attributed to the fact that many (prospective) elementary teachers h...

This paper examines ways to engage young children in constructing and interpreting narratives to develop their understanding of parity. It reports on a teaching intervention that was developed over three research cycles of a classroom-based design experiment, and focuses on the last of these cycles. The teaching intervention set out to investigate...

Research on classroom-based interventions in mathematics education has two core aims: (a) to improve classroom practice by engineering ways to act upon problems of practice; and (b) to deepen theoretical understanding of classroom phenomena that relate to these problems. Although there are notable examples of classroom-based intervention studies in...

In the United States, elementary teachers (grades 1–5 or 6, ages 6–11 years) typically have weak knowledge of reasoning-and-proving, and may have few opportunities to learn about this important activity after they complete their teacher education program. In this study we explored how reasoning-and-proving is treated in the 16 extant textbooks writ...

In this chapter, we make a case for considering culture in research on teachers’ mathematical knowledge, and we review Chapters 7-10 with a focus on the interplay between the cultural context and mathematical knowledge for/in teaching. Our review illuminates three different, but complementary, aspects of the cultural embedding of mathematical knowl...

The concept of proof is central to meaningful learning of mathematics, but is hard for students to learn. A serious misconception dominant amongst students at all levels of schooling is that empirical arguments are proofs. An important question, then, is the following: What knowledge might enable teachers to help students overcome this misconceptio...

Research showed that children’s school-entry academic skills are strong predictors of their later achievement, thereby highlighting the importance of children’s achievement at kindergarten entry. This article defines a particular type of parental involvement in children’s education and uses a representative sample of American urban kindergarteners...

This article first examines why mathematics educators need to teach proof, as reflected in the needs that propelled proof to develop historically. We analyse the interconnections between the functions of proof within the discipline of mathematics and the needs for proof. We then take a learner’s perspective and discuss learners’ difficulties in und...

Despite the importance of proof and refutation in students' mathematical education, students' conceptions about the relationship between proof and refutation have not been the explicit focus of research thus far. Nevertheless, the combined consideration of findings from different studies suggests that some students believe it is possible to have a...

In this article we elaborate a conceptualisation of mathematics for teaching as a form of applied mathematics (using Bass's idea of characterising mathematics education as a form of applied mathematics) and we examine implications of this conceptualisation for the mathematical preparation of teachers. Specifically, we focus on issues of design and...

In this article, we focus on a group of 39 prospective elementary (grades K-6) teachers who had rich experiences with proof, and we examine their ability to construct proofs and evaluate their own constructions. We claim that the combined “construction–evaluation” activity helps illuminate certain aspects of prospective teachers’ and presumably oth...

Although students of all levels of education face serious difficulties with proof, there is limited research knowledge about how instruction can help students overcome these difficulties. In this article, we discuss the theoretical foundation and implementation of an instructional sequence that aimed to help students begin to realize the limitation...

This article is situated in the research domain that investigates what mathematical knowledge is useful for, and usable in, mathematics teaching. Specifically, the article contributes to the issue of understanding and describing what knowledge about proof is likely to be important for teachers to have as they engage students in the activity of prov...

Mathematical tasks embedded in real-life contexts have received increased attention by educators, in part due to the considerable levels of student engagement often triggered by their motivational features. Nevertheless, it is often challenging for teachers to implement high-level (i.e., cognitively demanding), real-life tasks in ways that exploit...

There are currently increased efforts to make proof central to school mathematics throughout the grades. Yet, realizing this goal is challenging because it requires that students master several abilities. In this article we focus on one such ability, namely, the ability for deductive reasoning, and we review psychological research to enhance what i...

The notion of assumptions permeates school mathematics, but instruction tends to highlight this notion only in the advanced grades. In this article, I argue that it is important for even young children to develop a sense of the role of assumptions in proving, and I investigate what it might mean and look like for instruction to promote this goal. T...

There is a growing effort to make proof central to all students’ mathematical experiences across all grades. Success in this goal depends highly on teachers’ knowledge of proof, but limited research has examined this knowledge. This paper contributes to this domain of research by investigating preservice elementary and secondary school mathematics...

Despite increased appreciation of the role of proof in students’ mathematical experiences across all grades, little research has focused on the issue of understanding and characterizing the notion of proof at the elementary school level. This paper takes a step toward addressing this limitation, by examining the characteristics of four major featur...

Learning with understanding has increasingly received attention from educators and psychologists, and has progressively been elevated to one of the most important goals for all students in all subjects. However, the realization of this goal has been problematic, especially in the domain of mathematics. To this might have contributed the fact that,...

Many researchers and curriculum frameworks recommend that the concept of "proof" and the corresponding activity of "proving" become part of students' mathematical experiences throughout the grades. Yet it is still unclear what "proof" means in school mathematics, especially in the elementary grades, and what role the teacher has in cultivating proo...

This paper discusses issues concerning the validation of solutions of construction problems in Dynamic Geometry Environments (DGEs) as compared to classic paper-and-pencil Euclidean geometry settings. We begin by comparing the validation criteria usually associated with solutions of construction problems in the two geometry worlds – the ‘drag test’...

Literature suggests that the type of context wherein a task is placed relates to students' performance and solution strategies. In the particular domain of logical thinking, there is the belief that students have less difficulty reasoning in verbal than in logically equivalent symbolic tasks. Thus far, this belief has remained relatively unexplored...

Many researchers and curriculum frameworks, especially in the United States, recommend that proof by made central to all students' mathematical experiences as early as the elementary grades. However, the development of proof in school mathematics has been uneven. Proof has historically been associated only with tenth- grade courses on Euclidean geo...

In this paper, we discuss issues of content knowledge that is important for mathematics teaching. Specifically, we present a framework for the content knowledge of "reasoning and proving" that is important for teaching elementary school mathematics, and we consider how this knowledge can be effectively promoted in mathematics courses for preservice...

This paper investigates prospective elementary and secondary school teachers' understanding of proof in a case where the truth set of an open sentence is broader than the set covered by a valid proof by mathematical induction. This case breaks the boundaries of students' usual experience with proving tasks. The most important finding is that a sign...

Research suggests that teachers need to have mathematics content knowledge that allows them to effectively deal with the particular mathematical issues that arise in their everyday practice. This implies the importance of providing teachers with learning opportunities that prepare them to both recognize situations in their practice where these math...

In this article we elaborate a conceptualization of mathematics for teaching as a form of applied mathematics (building on Bass's idea of characterizing mathematics education as a form of applied mathematics) and we examine implications of this conceptualization for the mathematical preparation of teachers. Specifically, we discuss issues of design...