# Constantinos ChristouUniversity of Cyprus · Department of Education

Constantinos Christou

## About

166

Publications

55,018

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2,684

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Citations since 2016

Introduction

Constantinos Christou currently works at the Department of Education, University of Cyprus. Constantinos does research in Mathematics Education. Their current project is 'Cognition', algebra thinking and technology impact on earning mathematics

Additional affiliations

June 1993 - present

## Publications

Publications (166)

In this article, existing research investigating how school performance relates to cognitive, self-awareness, language, and personality processes is reviewed. We outline the architecture of the mind, involving a general factor, g, that underlies distinct mental processes (i.e., executive, reasoning, language, cognizance, and personality processes)....

This study investigated the role of online applets in early algebra lessons. The effect of two different types of intervention modules on developing students’ early algebraic thinking abilities was compared. The first intervention module involved the use of open applets and real-life contexts (open-real). The second intervention module involved the...

Recognizing patterns is an important skill in early mathematics learning. Yet only few studies have investigated how first-grade students recognize patterns. These studies mainly analyzed students’ expressions and drawings in individual interviews. The study presented in this paper used eye tracking in order to explore the processes of 22 first-gra...

For researchers and practitioners, it is important to identify students at risk of developing mathematical difficulties. The aim of this pilot study was to investigate whether it is possible to identify first-grade students who are at risk of developing mathematical difficulties (RMD) through online measures in arithmetic and pattern tasks. In our...

Classroom assessment could contribute substantially to improving students’ mathematics learning. The process of classroom assessment involves decisions about how to elicit evidence, how to interpret it, and how to use it for teaching and learning. However, the field still needs to further explore how assessment tasks could guide forthcoming instruc...

Mathematical creativity is considered beneficial for learning mathematics. However, research studies that provide empirical evidence of students’ mathematical creativity in regular mathematics classrooms are relatively scarce. This study explores the idea of mini-creativity (mini-c), which is defined as the creative processes involved in the constr...

The present study had the purpose of investigating empirically the structure and relationships among mathematical imagination, mathematical knowledge and mathematical mindset. The three factors are constituent parts of the Innovation Engine model by Seelig (inGenius: A Crash course on creativity, HarperOne-2012) and can influence creative thinking....

A theoretical model describing young students’ (Grades 1–3) functional-thinking modes was formulated and validated empirically ( n = 345), hypothesizing that young students’ functional-thinking modes consist of recursive patterning, covariational thinking, correspondence-particular, and correspondence-general factors. Data analysis suggested that f...

In this paper, we discuss the theoretical foundation and implementation of two alternative instructional courses that aimed to support the development of elementary school students’ early algebraic thinking. Both courses approached three basic algebra content strands: generalized arithmetic, functional thinking and modelling languages. The courses...

Central in the frameworks that describe algebra from K-12 is the idea that algebraic thinking is not a single construct, but consists of several algebraic thinking strands. Validation studies exploring this idea are relatively scarce. This study used structural equation modeling techniques to analyze data of middle school students’ performance on t...

The purpose of the present study was to examine the structure and development of algebraic thinking across multiple dimensions. An algebraic thinking test was administered to 803 students aged 10–13 years old. One hundred and one students of different performance outcomes in the algebraic thinking test participated in semi-structured clinical inter...

The aim of this study was to propose a new conceptualization of early number sense. Six-year-old students’ (n = 204) number sense was tracked from the beginning of Grade 1 through the beginning of Grade 2. Data analysis suggested that elementary arithmetic, conventional arithmetic, and algebraic arithmetic contributed to the latent construct early...

The aim of this study is to better understand the notion of early algebraic thinking by describing differences in grade 4–7 students’ thinking about basic algebraic concepts. To achieve this goal, one test that involved generalized arithmetic, functional thinking, and modeling tasks, was administered to 684 students from these grades. Quantitative...

In this chapter we provide an overview of the state-of-the-art in mathematical creativity. To do so, we will use as a road map the 4Ps theory proposed by Rhodes in which four strands are used to capture the definition of creativity. In particular, (1) product: the communication of a unique, novel and useful idea or concept; (2) person: cognitive ab...

Based on a synthesis of the literature, a model for young children’s (Grades 1-3) functional thinking was formulated. The major constructs incorporated in this model were recursive patterning,correspondence relationships and covariational thinking. The study involved three hundred and forty five students. Data analysis validated the hypothesized mo...

In the present study, we are interested in the impact of an intervention course on the development of low-achieving sixth grade students’ abilities that are related to fraction understanding. An intervention course comprising of lessons for developing these abilities was implemented in a sample of low-achieving sixth grade students, while a control...

We investigated if learning relational reasoning in mathematics generalizes to other domains and general intelligence, including speed, attention control, and working memory. A total of 118 10-year olds were involved, allocated to an experimental and a control group. The experimental group was involved in 12 learning sessions addressed to various a...

This study sets out to develop and verify a theoretical model with regard to the construct of mathematical creativity. Moreover, it aims to investigate the effect of cognitive, developmental and personality characteristics in the emergence of mathematical creative behavior. Four hundred and seventy-six students, aged 9–12, participated in the study...

The purpose of this study was twofold. Firstly, to extend Technology Acceptance Model to assess secondary school teachers’ intention to use Dynamic Geometry Software (DGS) in geometry teaching and, second, to examine the relations among the parameters of TAM and the role of external factors. We enriched TAM by integrating in the model the notion of...

The aim of this study was to investigate the process followed by individuals during solving a mathematical creativity tasks. Therefore, 182 students of age 10-12 years old participated in individual interviews while solving a multiple solution mathematical task. Through the interviews we aimed to reveal the cognitive sub-processes that students fol...

The aim of this article was twofold. First, to propose a model for assessing mathematical challenging problems and second, to investigate the abilities of a group of in-service teachers to propose mathematically challenging problems based on the model suggested. The results indicated that mathematical challenging tasks may be characterised as those...

The present study aims to investigate whether creativity is domain general or domain specific, by relating students’ performance on two tests: the Creative Thinking Test and the Mathematical Creativity Test. Four hundred and seventy six students (Grades 4–6) participated in the study. Through confirmatory factor analysis we purported to compare the...

Σε αυτή την ερευνητική εργασίαεξετάσαμε τον ρυθμόανάπτυξης των παραμέτρων της «αίσθησης του αριθμού» μαθητών Α ́ τάξης δημοτικού σχολείου και διερευνήσαμε τη σχέση μεταξύ του ρυθμού ανάπτυξης των παραμέτρων αυτών με την επίδοσή των μαθητών στα μαθηματικά στη Β ́ δημοτικού. Οι τρεις συνιστώσεςτης αίσθησηςτου αριθμούπου χρησιμοποιήθηκαν είναι: (α) οι...

The present study adopted a theoretical model, suggesting that number sense consists of elementary number sense, conventional arithmetic and algebraic arithmetic, to trace the development of students’ early number sense. Two hundred and four 1st grade students were individually tested on five time-points. Data analysis suggested that number sense f...

Σε αυτή την ερευνητική εργασία, διαμορφώσαμε και εγκυροποιήσαμε ένα μοντέλο για την «αίσθηση του αριθμού» μαθητών Α΄ τάξης δημοτικού σχολείου. Οι τρεις βασικές συνιστώσες που περιλαμβάνονται σε αυτό το μοντέλο είναι: (α) οι βασικές αριθμητικές δεξιότητες, (β) ο τυπικός αριθμητικός συλλογισμός και (γ) ο αλγεβρικός αριθμητικός συλλογισμός. Τα αποτελέ...

The current study focuses in the description and presentation of challenging mathematical tasks as a means to identify mathematical giftedness.More specific, we will present the theoretical background which led to the development and use of certain types of tasks for the purpose of capturing giftedness in mathematics. We focus on identification pri...

The present study examines the effect of a number of cognitive factors onmathematical creativity,such as mathematical abilities, intelligence, working memory, speed and control of processing. Specifically,the aim of the study wasthreefold. Firstly, to assess whether a theoretically driven model fits the dataof the study. Secondly, to investigate wh...

This article reports the outcomes of an empirical study undertaken to investigate the effect of students' visual cognitive styles (spatial and object imagery preferences and experiences) on their three-dimensional (3D) geometrical abilities. A group of sixth grade students (N=121) completed a Greek modified version of the Object-Spatial Imagery Que...

The present study revalidated a measurement model describing the nature of early number sense. Number sense was shown to be composed of elementary number sense, conventional arithmetic and algebraic arithmetic. Algebraic arithmetic was conceptualized as synthesis of number patterns, restrictions and functions. Two hundred and four 1stgrade students...

The aim of this study is to examine students’ ability in interpreting and constructing plane representations of 3D shapes, and to trace categories of students that reflect different types of behaviour in representing 3D shapes. To achieve this goal, one test was administered to 279 students in grades 5–9, and forty of them were interviewed. The res...

This study aims to examine the structure of the relationship between intelligence and mathematical giftedness and build a comprehensive model to describe this relationship and the nature of mathe-matical giftedness. This study also purports to clarify the structure of components of mathematical ability. The third objective is to examine whether stu...

The study examines students’ ability to operate on unknowns through students’ levels of justification in generalized arithmetic tasks in which algebraic expressions are present. Two tasks about generalization of properties of numbers were administered to 73 fifth-grade elementary school students and then 10 semi-structured interviews were carried o...

Recently, a new cognitive style approach was introduced, which refers to two types of visualizers. This approach is based on neuropsychological evidence and neuroimaging results, which suggest the existence of two distinct imagery subsystems, the object and the spatial imagery subsystems. The goal of the study was twofold: first to examine a possib...

This study aims to investigate whether there is a relationship between mathematical ability and mathematical creativity, and to examine the structure of this relationship. Furthermore, in order to validate the relationship between the two constructs, we will trace groups of students that differ across mathematical ability and investigate the relati...

This paper investigates the relationship between the creative process in mathematical tasks and spatial, object and verbal cognitive styles. A group of ninety-six prospective primary school teachers completed the Object-Spatial Imagery and Verbal Questionnaire (OSIVQ) and took a mathematical creativity test. The results of a multiple regression ana...

A fundamental question regarding the use of technology in mathematics education is the way in which technology supports and promotes higher order thinking in mathematics. In this chapter, we try to describe and analyze the way in which SimCalc might develop and enhance elementary school students’ higher order mathematical thinking. To this end, we...

The aim of this paper is to propose a theoretical model to analyze prospective teachers’ reasoning and knowledge of real numbers, and to provide an empirical verification of it. The model is based on Sierpinska’s theory of theoretical thinking. Data were collected from 59 prospective teachers through a written test and interviews. The data indicate...

The purpose of this study is to describe and analyse a model for students’ transition
from comparing exponents to the monotonicity of exponential functions within the
context of operational and structural processes. The study was conducted with 193
11th grade students with the use of a test. The findings suggest that in this transition
there are th...

Based on a synthesis of the literature, a model for number sense was formulated, and validated. The major constructs incorporated in this framework were elementary number sense, conventional arithmetic and algebraic arithmetic. To trace the development of number sense components a longitudinal study was conducted. One hundred and forty 1st grade st...

Στόχοςτηςπαρούσαςεργασίαςήτανναπροτείνειέναμοντέλο,τοοποίοναεπεξηγείτηνεπίδρασημεταβλητώνπου σχετίζονται με το μαθητή, την τάξηκαιτη σχολικήμονάδαστηνεπίδοσητωνμαθητώνΔ’ δημοτικού σταμαθηματικά, αξιοποιώντας τα δεδομένα της έρευνας TIMSS2003. Για το σκοπό αυτό, έγινε χρήση τεχνικών πολυεπίπεδης ανάλυσης. Τα αποτελέσματα έδειξαν ότι οι μεταβλητές πο...

The aim of the present study was to investigate the effects of several structural and functional characteristics of the family
on the child’s actual school achievement. A structural equation model was constructed and its ability to fit the data was
tested. It was found that the child’s achievement is directly influenced by the socio-economic status...

This study purported to investigate whether the integration of technology improves prospective teachers’ creativity, in the field of mathematics. Furthermore, prospective teachers’ perceptions about the relationship of technology and creativity were examined. Forty two prospective elementary school teachers participated in the study. Participants w...

The purpose of this study was to examine how the involvement of prospective teachers in authentic exploration activities that integrate contemporary technological tools can enhance their Technological Pedagogical Content Knowledge (TPACK) in 3D shapes’ nets. The theoretical framework of TPACK was adopted because it provides a strong foundation abou...

Lamon (Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teachers,
2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005) claimed that the development of proportional reasoning relies on various kinds of understanding and thinking processes. The
critical components suggested were individuals’...

The present study aims to examine the structure and relationships among the components of mathematical giftedness and to identify groups of students that differ across these components. The proposed model is innovative in terms of integrating natural/cognitive, creative, and mathematical abilities leading to a new conceptualization of mathematical...

Lamon (Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teachers, 2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005) claimed that the development of proportional reasoning relies on various kinds of understanding and thinking processes. The critical components suggested were individuals’...

This paper focuses on the comparison between gifted and non - gifted elementary school students’ answers on multiple solution tasks. More specific, the number of correct responses provided, the different mathematical ideas employed, as well as the originality of the solutions of these two groups are compared. The study was conducted among 9 mathema...

Σκοπό της εργασίας αποτέλεσε: (α) η εξέταση της τεχνολογικής παιδαγωγικής γνώσης
περιεχομένου (ΤΠΓΠ) φοιτητών για τα λογισμικά δυναμικής γεωμετρίας (ΛΔΓ) και (β) η πρόταση ενός μοντέλου επιπέδων ανάπτυξης της ΤΠΓΠ για τα ΛΔΓ, βασισμένο στα
επίπεδα της Niess (2007). Συμμετείχαν 58 φοιτητές οι οποίοι παρακολούθησαν μαθήματα ενσωμάτωσης της τεχνολογία...

This paper focuses on the development of a theoretical model in which mathematical
creativity constitutes a predictor of mathematical ability. Furthermore, we examine
the existence of groups of students that differ across mathematical ability and investigate whether these groups present differences in their mathematical creativity. The study was co...

Η παρούσα εργασία επικεντρώνεται στην περιγραφή και παρουσίαση κατάλληλων δραστηριοτήτων για ενίσχυση της δημιουργικότητας στην τάξη των μαθηματικών. Πιο συγκεκριμένα, γίνεται αναφορά στην έννοια της μαθηματικής δημιουργικότητας, στα
στοιχεία που χαρακτηρίζουν τις δημιουργικές δραστηριότητες και στις κατηγορίες δραστηριοτήτων που ενισχύουν τη δημιο...

This study purports to develop a multiple criteria identification process for mathematically gifted students, in an effort to clarify the construct of mathematical giftedness. The study was conducted among 359 4th, 5th and 6th grade elementary school students in Cyprus, using four instruments measuring mathematical ability, mathematical creativity,...

Είναι ευρέως αποδεκτό ότι ένας σημαντικός στόχος της εκπαίδευσης είναι η ενίσχυση και η ανάπτυξη της δημιουργικότητας των εκπαιδευτικών και των μαθητών τους. Η εκπλήρωση του στόχου αυτού συνδέεται άμεσα με την κατανόηση των παραγόντων που σχετίζονται με τηδημιουργικότητα και τη διασαφήνιση του ρόλου τους. Ένας τέτοιος παράγοντας μπορεί να είναι τα...

This paper investigates the relations of students’ spatial and object visualisation with their analytic, creative and practical abilities in three-dimensional geometry. Fifty-three 11-year-olds were tested using a Greek modified version of the Object–Spatial Imagery Questionnaire (OSIQ) (Blajenkova, Kozhevnikov, & Motes, 2006) and two mathematics t...

The aim of this study is to describe and analyse the structure of 3D geometry thinking by identifying different types of reasoning
and to examine their relation with spatial ability. To achieve this goal, two tests were administered to students in grades
5 to 9. The results of the study showed that 3D geometry thinking could be described by four di...

This study focuses on the structures and relationships involved in one-step additive and multiplicative problems. Thirty-three problems were given to 450 students in grades 2, 3 and 4. The analysis of results showed that the facility ratio of the problems differs by structure, by situation and by the sequence of the data within the same situation....

In this study, we report on an analysis of the mathematization processes of one 6th and one 8th grade group, with emphasis
on the similarities and differences between the two groups in solving a modeling problem. Results provide evidence that all
students developed the necessary mathematical constructs and processes to actively solve the problem th...

The aim of this study was to investigate sixth grade students’ analytical, practical and creative abilities (e.g., Sternberg, 1997, 1999) in nets and three-dimensional rectangular arrays of cubes. A group of fifty three sixth grade students completed two mathematical tests: one on nets of cubes and cuboids and one on rectangular arrays of cubes. Th...

The present study examines a number of cognitive factors that may predict creative ability in mathematics. The study was conducted among 359 elementary school students in Cyprus, using four different instruments. The results revealed that students’ mathematical creativity may be predicted only by students’ mathematical abilities. In particular, the...

This study explores the differences mathematical abilities of high IQ and low creativity
students (H IQ L C) and with low IQ and high creativity (L IQ H C ) students. The two groups were also compared to the abilities of students with high IQ and high creativity
(H IQ H C ). A mathematics test , a mathematical creativity test and an IQ test (WASI)...

This study purports to develop a self - report instrument for identifying mathematically gifted students and to investigate the relationship between students’ self - perceptions
and mathematical giftedness. The study was conducted among 359 4th, 5th and 6th
grade elementary school students in Cyprus, using a self - report questionnaire of 20 statem...

This paper reports the outcomes of two empirical studies undertaken to investigate the relationship of sixth grade students’ spatial and object visualisation preferences and experiences and their abilities in nets and three-dimensional rectangular arrays of cubes. The results of both studies suggest that whereas the spatial cognitive style is a sta...

This paper reports the outcomes of an empirical study undertaken to investigate the relationship of prospective teachers’ cognitive styles and levels of performance in measurement and spatial tasks. A total of 116 prospective kindergarten school teachers were tested using the VICS and the extended CSA-WA tests (Peterson 2005) in order to place them...

This paper reports the outcomes of an empirical study undertaken to investigate the effect of students’ cognitive styles on
achievement in measurement tasks in a dynamic geometry learning environment, and to explore the ability of dynamic geometry
learning in accommodating different cognitive styles and enhancing students’ learning. A total of 49 6...

In this study we report on an analysis of the mathematical developments of twenty two 11 year old students as they worked on a complex environmental modeling problem. The activity required students to analyse a real-world situation based on the water shortage problem in Cyprus using Google Earth and spreadsheet software, to pose and test conjecture...

Η παρούσα εργασία έχει σκοπό να αναλύσει τον τρόπο σκέψης υποψηφίων εκπαιδευτικών όσον αφορά τη δομή και τις ιδιότητες των πραγματικών αριθμών, με βάση το μοντέλο θεω-ρητικής σκέψης της Sierpinska (Sierpinska, Nnadozie, & Okta, 2002). Τα δεδομένα συνελέ-γησαν από δοκίμια και συνεντεύξεις που έγιναν σε 59 φοιτητές. Από την ανάλυση των δεδο-μένων προ...

In our increasingly technological world, it is more and more important to encourage students to develop their abilities to reason and think creatively, especially in mathematics. The aim of this study is to investigate whether individuals’ cognitive styles are related to their mathematical creativity. Mathematical creativity is measured in terms of...

This study analyzed the processes used by students when engaged in modeling activities and examined how students' abilities to solve modeling problems changed over time. Two student populations, one experimental and one control group, participated in the study. To examine students' modeling processes, the experimental group participated in an inter...

The tangent line is a central concept in many mathematics and science courses. In this paper we describe a model of students’ thinking – concept images as well as ability in symbolic manipulation – about the tangent line of a curve as it has developed through students’ experiences in Euclidean Geometry and Analysis courses. Data was collected throu...

Mathematical modelling is a complex mathematical activity, and the teaching and learning of modelling and applications involves many aspects of mathematical thinking and learning (Burkhardt & Pollak, 2006; Niss, 1987; Kaiser, Blomhøj & Sriraman, 2006). An increasing number of mathematics education researchers have begun focusing their research effo...

This is a case study of an experienced teacher concerning her knowledge about calculus teaching. Specifically, we investigated aspects of this knowledge, and the way in which these affected this teacher’s practice and professional development. The data collected from a number of observations of this teacher’s calculus teaching, informal discussions...

In this paper we address some issues about the nature of secondary teacher mathematical knowledge in the area of Calculus. Our research data comes from observing classroom teaching of nine teachers and from interviews with them. In particular, we indicate some qualitative characteristics of the specialised mathematical knowledge for teaching that a...

The aim of this study is to describe and analyze students’ levels of understanding of exponents within the context of procedural and conceptual learning via the conceptual change and prototypes’ theory. The study was conducted with 202 secondary school students with the use of a questionnaire and semi-structured interviews. The results suggest that...

While, commonly across the world, selected key ideas of the Calculus are introduced to students in the final years of schooling, and are thence built upon as students take a full course in Analysis at University, there remains much to learn about how best to introduce such ideas and how to develop and expand the ideas at University level. This pape...

This paper reports on the design of a dynamic environment for the learning of stereometry (DALEST) and the teaching of spatial geometry and visual thinking. The development of the software was in the framework of DALEST project which aimed at developing a dynamic three-dimensional geometry microworld that enables students to construct, observe and...