Education Research International

Volume 2019, Article ID 3402035, 19 pages

https://doi.org/10.1155/2019/3402035

## Learning Mathematics in Metacognitively Oriented ICT-Based Learning Environments: A Systematic Review of the Literature

^{1}Center for Instructional Psychology and Technology, KU Leuven, Leuven, Belgium^{2}David Yellin Academic College of Education, Jerusalem, Israel

Correspondence should be addressed to Lieven Verschaffel; eb.nevueluk@leffahcsrev.neveil

Received 4 March 2019; Revised 30 June 2019; Accepted 21 July 2019; Published 16 September 2019

Academic Editor: Christos Troussas

Copyright © 2019 Lieven Verschaffel et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This article encompasses a systematic review of the research on ICT-based learning environments for metacognitively oriented K-12 mathematics education. This review begins with a brief overview of the research on metacognition and mathematics education and on ICT and mathematics education. Based on a systematic screening of the databases Web of Science and ERIC wherein three elements—ICT-based learning environments, metacognitive pedagogies, and mathematics—are combined, 22 articles/studies were retrieved, situated at various educational levels (kindergarten, elementary school, and secondary school). This review revealed a variety of studies, particularly intervention studies, situated in elementary and secondary schools. Most studies involved drill-and-practice software, intelligent tutoring systems, serious games, multimedia environments, and computer-supported collaborative learning environments, with metacognitive pedagogies either integrated into the ICT software itself or provided externally by the teacher, mainly for arithmetic or algebraic word problem-solving but also related to other mathematical topics. All studies reported positive effects on mathematical and/or metacognitive learning outcomes. This review ends with a discussion of issues for further theoretical reflection and empirical research.

#### 1. Introduction

In *How People Learn*, Bransford et al. [1] propose the support and exploitation of metacognition as one of the three core instructional design principles. This proposal is based on the vast amount of research showing that (a) learners with better metacognitive knowledge and skills will acquire domain-specific knowledge and skills more effectively and efficiently and will transfer their knowledge and skills more easily to other domains and contexts and (b) well-designed metacognitively oriented instruction embedded in a specific content domain has a positive impact on learners’ metacognitive behavior as well as their learning within that domain [2–7].

This article encompasses a systematic review of the research on learning mathematics in metacognitively oriented ICT-based learning environments: research describing and evaluating attempts to increase the power of ICT-based learning environments for K-12 mathematics education by enriching them with a metacognitive pedagogy, or the reverse, that is, attempts to increase the power of metacognitive pedagogies for K-12 mathematics education by embedding them in ICT-based learning environments. We begin with a brief overview, first, of the research on metacognition and mathematics education. Afterwards, we briefly review the research on ICT and mathematics education. Finally, we explicate the aims and scope of our literature review wherein these three elements—metacognition, ICT, and mathematics education—are combined.

##### 1.1. Metacognition and Mathematics Education

Since the 1980s, it is commonly accepted that the cognitive system depends on higher-order processes that enable it to work efficiently. Examples of metacognitive components are planning, monitoring, control, and reflection (e.g., [8]). From the very beginning, researchers ([8]; see also [9, 10]) distinguished between two closely interrelated components of metacognition: (1) knowledge of cognition (e.g., knowledge about the task, strategies appropriate for solving the task, and personal characteristics relevant to the task) and (2) regulation of cognition (e.g., monitoring, control, and reflection). (The term “metacognition” is closely related to the term “self-regulation.” According to some researchers, self-regulation refers to the second component of the metacognitive system, namely, one’s ability to control, evaluate, and modify his or her cognitive processes in the pursuit of a particular goal [11]. Others conceive self-regulation more broadly, referring not only to the ways that learners systematically activate and sustain their cognitions towards the attainment of their goals but also to their behaviors, motivations, and affects [6]. In this article, we take the former perspective, implying that we conceive metacognition as the most general concept and self-regulation as the second, regulatory component of metacognition.)

While the early research on metacognition assumed that children younger than 10 years have little or no metacognition, from the late nineties on, researchers started to report evidence demonstrating that kindergarten children can already spontaneously plan, monitor, control, and reflect on their mathematics activities [12–15].

The relationship between metacognition and mathematical reasoning and problem-solving is well documented in the research literature (e.g., [16, 17]). Research has indicated that learners at all ages, from kindergartners to adult learners, who plan, monitor, evaluate, and reflect on their problem-solving processes, perform better on mathematics reasoning tasks and solve mathematical problems better than those who do not use these activities, or use them less frequently (e.g., [18]). This phenomenon has been documented by applying a large variety of off- and online measurements, including questionnaires, observations, think-aloud and retrospective techniques, (semi)structured interviews, various types of brain coding techniques, and analysis of peers explaining the solutions to one another or working in small groups. In general, these studies reported high positive correlations between metacognition and mathematical reasoning or problem-solving, even after controlling for IQ [13, 19].

Given the well-documented positive association between metacognition and mathematical reasoning or problem-solving [1], researchers started to look for ways of improving learners’ mathematical reasoning and problem-solving, based on the teaching of metacognitive knowledge and/or skills [6, 16]. Over the years, several such “metacognitive pedagogies” have been designed for the area of mathematics learning, for various age levels and embedded in different parts of the mathematics curriculum.

Most of these methods were routed in the seminal work of Schoenfeld [5, 20]. In his classic studies from the 1980s, Schoenfeld [20] worked with undergraduates on improving their problem-solving by regularly prompting them to consider metacognitive questions such as “What are you doing?” “How are you doing it?” and “How does it help you?” He found that, by asking students these questions throughout a one-semester course, the students themselves began asking and answering these questions, which in turn yielded greater metacognitive awareness of their problem-solving as well as more efficient problem-solving.

These results about the possibility of improving mathematical competence through metacognitively oriented instruction were confirmed in a number of subsequent studies throughout the nineties and into the 2000s not only with university students but also with learners as young as kindergartners (e.g., [16, 21–28]).

In particular, Kramarski, Mevarech, and colleagues engaged in a robust program of research related to metacognition instruction in mathematics for more than 20 years (e.g., [16, 25, 26]). They designed and investigated an instructional method that they refer to as IMPROVE, an acronym representing the series of following teaching steps:(i)Introducing the new materials, concepts, problems, or procedures using metacognitive scaffolding(ii)Metacognitive self-directed questioning in small groups or individually(iii)Practicing by employing the metacognitive questioning(iv)Reviewing the new materials by teacher and learners, using the metacognitive questioning(v)Obtaining mastery on higher-order and lower-order cognitive processes(vi)Verifying the acquisition of cognitive and metacognitive skills based on feedback-corrective processes(vii)Enrichment and remedial activities

The core component of the IMPROVE program consists of training the learners to use four kinds of metacognitive self-directed questions:(i)Comprehension: What is the problem all about?(ii)Connection: How is the problem at hand similar to or different from problems you have solved in the past?(iii)Strategies: What strategies are appropriate for solving the problem and why?(iv)Review: Does the solution make sense? Can you solve the problem differently, how? Are you stuck, why?

However, in many cases, the positive effects of all these interventions were moderate rather than strong, implying that improving learners’ competence in mathematical reasoning and problem-solving by means of metacognitively oriented interventions is a complex and demanding matter, which comes with a cost, in terms of effort, time consumption, and reduction of the curriculum in the traditional sense [13].

##### 1.2. Metacognition and ICT

Similar to the research literature on metacognition and mathematics education, the literature on metacognition and ICT is immense. In the early days of ICT, a computer’s potential was mainly seen as a machine for drill-and-practice in basic arithmetic and algebraic skills [11]. But as a result of emergence of new theoretical approaches to learning and instruction (e.g., constructivism), on the one hand, and new technological advancements, on the other hand, researchers started to explore its potential for developing learners’ higher-order cognitive and metacognitive competencies by means of more advanced learning technologies such as intelligent tutoring systems, simulations, programming, serious games, hypermedia, computer-supported collaborative learning environments, and virtual reality [11, 29–31].

So, already for several decades, ICT is being considered a powerful tool for teaching higher-order processes such as metacognition and self-regulation, in various domains including mathematics. As argued by Mayer (2010, in [16]; p. 148), “ICT is particularly useful for approaching such complex and unfamiliar problem-solving tasks because it enables the learner to search for information on the web, look for similar problems and sub-problems on-line, and use various computerized tools that can carry out the tedious work that is sometimes associated with solving mathematics problems (such as plotting graphs or doing computations) and hence release cognitive energy for higher-order cognitive processes [32]. Furthermore, search tools and online information sources (…) may lead users to reflect on the given information, decide which piece of information is most applicable to the given problem (…). Computer supported collaborative learning (e.g., asynchronous learning networks, forums, even emails) can become a powerful reflection tool, enabling students to be aware of how and why a solution path was chosen (…).”

This claim has been reiterated by scholars working in research projects that are aimed at realizing learning outcomes in various curricular domains, including mathematics, through advanced learning technologies such as simulations, serious games, hypermedia, computer-supported collaborative learning environments, and virtual reality. According to these researchers, several design characteristics of these advanced learning technologies (such as learners’ access to nonlinear information, to multiple representations, or to input or ideas from other learners) may play a critical role in the development of their metacognitive or self-regulatory skills and, consequently, lead to improved learning outcomes in the curricular domain at stake [30, 33–35].

However, the above-mentioned design features of these advanced learning technologies also require learners to actively, deliberately, and critically consider and monitor the logical relations between various pieces of information, different kinds of representation, or the varied input from co-learners, in relation to the progression in their own learning process. Clearly, all these processes can be characterized as metacognitive or self-regulatory [6]. So, learners’ ability to monitor, control, and reflect on their learning in these advanced technological learning environments will also have a significant impact on their learning outcomes [16, 33]. Indeed, successfully navigating nonlinear information, integrating information from various representations of the same concept, or integrating input from a peer learner requires learners to actively regulate their own learning, and learners’ inability to do so will undermine their learning success with these technologies. In response to this challenge, researchers have developed various kinds of scaffolds or prompts designed to stimulate, guide, and support learners’ metacognition or self-regulation while working with these advanced learning technologies [30, 33]. While initially these metacognitive scaffolds or prompts embedded in available ICT environments were typically general and static in nature, researchers are increasingly striving for more individually tailored pathways involving adaptive scaffolding, prompts, assessments, and navigation, by making use of techniques of artificial intelligence, learning analytics, etc. [33, 36].

Learners’ inability to monitor, control, and reflect on their learning with advanced learning technologies is not the only reason why the potential of advanced technologies in (mathematics) teaching and learning may not be fulfilled. Other reasons for that failure given in the literature are (1) the very nature of ICT, which calls for “trial-and-error” and does not encourage learners to reflect on their problem-solving processes, and (2) the cognitive overload in learners that these ICT-enhanced learning environments might be induced by the multitude of information and extra tools they offer [16].

##### 1.3. Aims and Scope of This Review

This article reviews research on enriching ICT-enhanced environments by metacognitive scaffolds or prompts, or the reverse, that is, attempts to increase the power of metacognitive pedagogies by embedding them in ICT-based learning environments in the domain of K-12 mathematics education. So, our review covers research on how to embed metacognitive pedagogies in available ICT environments to increase the quality and efficiency of mathematics learning, as well as research on how to apply ICT to increase the quality and efficiency of metacognitively oriented mathematics learning environments.

With this systematic review, we hope to answer the following questions concerning the available research on mathematics learning in metacognitively oriented ICT-based learning environments:(i)What is the educational level of the learners (ranging from kindergarten to secondary education)?(ii)What are the characteristics of the learners (e.g., regular learners, low- or high-achieving learners, or learners with special needs)?(iii)What kind of ICT environment is being used (e.g., computer-supported practice, educational e-books, intelligent tutoring systems, serious games, multimedia, simulations, hypermedia, computer-supported collaborative learning environments, and virtual environments)?(iv)What is the nature of the mathematical subdomain being addressed (e.g., early number sense, arithmetic, geometry, algebra, graphing, and word problem-solving)?(v)What research methodology is being used (e.g., observational study, case study, correlational study, (quasi-)experimental intervention study, and design research)? and in case of intervention studies, What is the nature of its conditions?(vi)What kind of metacognitive training, guidance, or support is provided (e.g., utilizing software features that help the learner to navigate within a math learning environment, providing assistance in solving problems or processing information by offering metacognitive scaffolds, and increasing the awareness of the problem-solving or learning process with mirroring tools [13])? And how is the metacognitive support delivered? Is it embedded in the ICT environment itself, provided outside by the teacher or other instructional means (e.g., cue cards), or both?(vii)What are the targeted learning outcomes of the learning environment (i.e., cognitive knowledge and skills in a given content domain, metacognitive knowledge and self-regulatory skills, improved performance in the specific mathematical subdomain being addressed, or affective or motivational learning outcomes)?(viii)What are the main findings?

#### 2. Method

We conducted a systematic review of the research literature regarding technology-mediated K-12 mathematical learning environments implementing a metacognitive pedagogy, making use of the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses [37]) guidelines. These guidelines consist of a checklist and a flow diagram and help improve the reporting of this review. A summary of the search and selection process, which consists of four consecutive phases, is presented in Figure 1 and is based on the PRISMA statement.