Human cognition is embodied, grounded in the human body, and in its location in space and time (Andrà et al., 2009). In the same way that motions with graphical calculators with sensors (Borba & Scheffer, 2004) and other sensory-motor coordination (Anna Shvarts, Alberto, Bakker, Doorman, & Drijvers, 2021), 3D virtual representation (Zhou et al., 2020) and augmented reality (Paulo, Pereira, & Pavanelo, 2020; (Zhou et al., 2020)), and touchscreen devices ((Assis & Bairral, 2022); Sinclair & de Freitas, 2014), eye-tracking movement integrate our sensory-motor (Nemirovsky, Kelton, & Rhodehamel, 2013) and our gaze behavior in its situational nature (Haataja et al., 2019). Eye tracking technology is used to understand individuals’ non-conscious, moment-to-moment processes during video-based learning. It’s a kind of non-verbal way to gather data and a specialized data analysis program to examine the positions and movements of an individual’s eyes as it happens(Deng & Gao, 2022).

Eyes are part of the body, and we have known for a long time that human cognition is embodied ((Glenberg, 2008); (Radford, 2014); (Wilson & Golonka, 2013)). Understanding what a person pays attention to in a cognitive task such as a recognition, identification, or classification, allows the researcher to better understand the task solving process (Garcia Moreno-Esteva et al., 2020). So it is not surprising to find in the literature that the relationship between eye-tracking and cognitive performance recognition seems to be a shared hypothesis (Andrá et al., 2015); (Andrzejewska & Stolińska, 2016);(Haataja et al., 2018); (Şimşek et al., 2020)); observing the parameters of eye movements, the fixation time, the dwelling time, the glance duration or the gaze and even the pupil dilation and blinks (Andrzejewska & Stolińska, 2016) all witness the way learners are reading and interpreting texts, graphic, drawings or screens and, in turn, how they learn or reflect on a given task.

Longer fixations are associated with more effortful cognitive engagement with a task: a higher mean fixation duration on a given location indicates a higher level of cognitive engagement with the information at that location (Hodds et al., 2014). In the case of task integrating the use of GeoGebra suggested that the long fixations are related both to instrument manipulation and cognitive processes (Hannula et al., 2019). According to the authors, these results suggest that using a digital tool increases the amount of both automatic scanning fixations and long fixations related to more elaborated processing. However, the qualitative examination of the long gazes in context suggests that a significant amount of these long fixations are related to interacting with GeoGebra, for example when selecting an option from a drop down menu or using mouse to place an object in the coordinate system.

For instance, concerning ET focusing on reading when the input is text, dwell time and number of fixations have values that make text close to formulas (namely, quite low), but fixation duration is similar to graph (low). The authors infer that text in the input is attended for a shorter time, both in terms of duration and in terms of the number of times the students come to see it (Andrá et al., 2015). Another example regarding fixations showed that tables concentrated students’ attention on the dependent variable data, whereas diagrams distributed students’ attention evenly across the numeric and visual elements of the task (Xolocotzin et al., 2020). The authors claim that an interpretation of results from a cognitive load framework would have been problematic and that diagrams should have produced less functional answers because they have more information and require more cognitive resources than tables. Research by (Soares et al., 2021) presented studies showing differences between people with high- or low-performance strategies during a reasoning task. Although they observed low performance students had difficulties in both reading and specific mathematics contents, they claim that the grade does not necessarily represent performance. According to them ET can facilitate interpreting the most prominent explanation for students’ difficulties and, without this equipment, some teachers would not have identified such problems.

From a socio-constructivist perspective, interactions in the classrooms, both among students and students with teacher, participate in learning and teaching. Group work plays an important role in engaging students in reflection by allowing them to help each other ((Dillenbourg, 1999); (Kanev et al., 2009); (Johnson et al., 2014)). In this context, the use of ET could be helpful to better understand the interactions in the classroom as well as the effect of the teacher's gaze on the students’ learning process. (Haataja et al., 2018) study through ET the amount of eye contacts which carries with it high dwell times of face-targeted gazes. Teachers can talk about different ways of interacting with students facing the same mathematical problem (Soares et al., 2021). But they can also analyze their students’ visual attention in problem-solving processes to make a prediction about their difficulties and help their students increase their problem-solving performance and academic achievement (Şimşek et al., 2020).

Eye-tracking method provides a promising channel for educational researchers to connect learning outcomes to cognitive processes (Lai et al., 2013) and in agreement with (Wilson & Golonka, 2013) research programs based on embodiment cognition should follow - as a first step - a task design analysis. Since most results on the paper in our review are mainly focused on the eye-movements, we could add reflections concerning the demand of the task to enrich the studies on eye tracking. Considering the advance of digital technology and the devices to gather a great amount and detailed data from gaze we think it could be important to reflect about the kind of proposed task.

Tasks are mediating strategies for teaching and learning mathematics, and the way in which they are designed and used for learning and knowledge production is considered by researchers (Source Title, 2021). In mathematics education, the concept of task is broad and covers a wide variety of activities: lists of exercises, construction of geometric objects using dynamic geometric environment, construction of handling models of geometric solids, providing examples of definitions or statements, problem-solving, carrying out an experiment or investigation, games, etc. (Bairral, 2021).

The relationship between teaching and learning that links dimensions of instructional tasks with gains in student learning outcomes was examined using a conceptual framework based on cognitive task demand(Stein & Lane, 1996). According to the researchers, the greatest student gains on a performance assessment consisting of tasks that require high levels of mathematical thinking and reasoning were related to the use of instructional tasks that engaged students in the “doing of mathematics” or the use of procedures with connections to meaning. In addition, student performance gains were greater for those sites whose tasks were both set up and implemented to encourage the use of multiple solution strategies, multiple representations, and explanations. Whereas student performance gains were relatively small for those sites whose tasks tended to be both set up and implemented in a procedural manner and that required a single solution strategy, single representations, and little or no mathematical communication (Mary Kay Stein, Engle, Smith, & Hughes, 2008, (Stein et al., 2000)).

Based on the framework of(Stein & Smith, 1998) and of (Stein et al., 2000), In this document, we have associated the two levels of cognitive demand for the proposed tasks. Speaking of “level” does not imply comparing the tasks in terms of better or worse, easy or difficult but rather to point out the mathematical concepts and procedures involved in the tasks. The levels serve only to distinguish the cognitive load of the tasks, and not to personify abilities and understandings (Stein & Smith, 1998). In other words, levels don’t refer to classifying better or worse learning, but the possibility of mathematical thinking processes which could be achieved when solving a task. It's not a question of thinking in terms of levels of learning, but of the cognitive load that involves time consumption and complex thinking. (Moutsios-Rentzos & Stamatis, 2015). Demand implies reasoning, emerging strategies, and different kinds of representations (graphical, pictorial, table, algebraic, geometrical etc.)

In all five steps, we didn’t consider or classify the studies according to the eye-tracking device used and/or regarding the theoretical framework adopted. The main exclusion criterion was when the article didn’t present a provided mathematics task. Articles in our review are based on eye-tracking studies using explicitly the whole mathematics tasks or part of them. In that case, part of the task presented allows us to infer about the task demand, for example, in(Campbell et al., 2009) and (Espino et al., 2005) studies, or in a paper we saw the provided tasks in the analysis section (Şimşek et al., 2020). If the paper comes from the same research project or team – using the same task – we have considered the article which contains the proposed task (Salminen-Saari et al., 2021). When the paper presents mathematics and non-mathematics tasks, we consider only the mathematical one (Werner & Raab, 2014).

According to (Strohmaier et al., 2020) reviewing problem solving was examined in four studies (2%), investigating relations between eye movements and objective/subjective task difficulty (Andrzejewska & Stolińska, 2016), insight problem solving (Knoblich et al., 2001), and the association of body movements and problem solving processes, assuming effects of embodied cognition (Werner & Raab, 2014), and the use a collaborative problem-solving task to investigate a teacher’s attention during scaffolding (Haataja et al., 2018).

Since affective factors represent an important aspect of learning throughout mathematics problem solving, we decided to analyze the two studies linking eye movements to mathematics-specific affective variables, namely mathematical self-concept (Strohmaier et al., 2017) and mathematics anxiety (Hunt et al., 2015). The provided tasks are only indicated in the last study.

Since only one(Haataja et al., 2018) of the six papers found in steps 1 and 2 were from mathematics education, we thought that finding other related papers from their research team to know more about the problem provided by them could be helpful in our task analysis. On step 3 we found eight more papers from Hannula's research team focusing on joint attention. Six of them refer – explicitly on paper or in some reference – to a problem of four cities¹ and we supposed in M. S. (Hannula et al., 2019) that they also used the same problem. We use all the papers related to the cable cities problem and recurring on (Heyd-Metzuyanim et al., 2023) because it presents detailed students’ solutions during various stages of the lesson.

Inspired by papers from the third step based on the four cities, which provided us insight about the kind of task provided and considering such type of task is usually proposed on studies in proofing, we decided on step 4 to look back in Anselm(Strohmaier et al., 2020) now focusing on the twelve papers concerning reasoning and proof. In this strand we excluded the paper from (Panse et al., 2018) because it includes the same tasks as those in(Inglis & Alcock, 2012). Concerning the two-paper gathered on proportional reasoning, we consider (Abrahamson et al., 2015) because it presents detailed design of the task shortly commented on (Duijzer et al., 2017). Papers concerning reasoning and proof, in this strand we excluded the paper from Panse, Alcock, & Inglis (2018) because it includes the same tasks as those in (Inglis & Alcock, 2012). Concerning the two-paper gathered on proportional reasoning, we consider (Abrahamson et al., 2015) because it presents detailed design of the task shortly commented on (Duijzer et al., 2017).

Finally, on step 5, we selected randomly other papers that focused on eye-movements and still referring to mathematical problem solving which explicitly show the task or part of it, mainly a mathematical task, even if the focus was not strictly linked to learning or teaching mathematics such as (Andrzejewska & Stolińska, 2016). In(Kosko, 2022)) we encounter more details about the task shortly commented in (Kosko et al., 2023).

Based on such criteria of inclusion and exclusion, we generated Table 1 with the description of the number of papers included or not in our review concerning task demand analysis. All studies are important in the theoretical framework and for future analysis.

[1] The students were asked to find the shortest possible way to connect four cities located at the vertices of a square. This problem is the four-point version of the Steiner tree problem.

We are not presenting many details of data collecting settings, considering them to categorize the task. We are interested in focusing only on the type of the provided mathematical task. Some tasks could be of low demand but depending on the classroom dynamic, the semiotic mediation and interaction among teacher and students, they could make another version of the task arise (based on the first) which could be in a higher level of demand. To avoid comparing the studies we decided not to consider the dynamic for collecting data. In other words, we did not analyze the task demand related to the data collection setting.

In the amount of analyzed papers we found 4 high demand tasks level 2 and 3 level 1. In the low level we found 8 tasks in each level. It is a significant amount of low demanding tasks.

Tasks provided in HD1 and HD2 normally do not give the solutions or procedures explicitly. They also explore different representations and mathematical thinking processes, not only based on memorization or shape identification. The tasks captured in this level aim to observe regularities, reading statements with self-explanation, contrasting, and using different ways of interpreting mathematical concepts and some tasks are not usual in the classroom.

In the different studies, dwell and time duration were used with the hypothesis that dwelling indicates a particular attention significant to a cognitive effort on a particular point. In the case of reading proofs, dwell time is used to compare the way students read and understand what they read. It allows a better cognitive engagement of students trained to a specific behavior in one case (Hodds et al., 2014); and it allows one to better understand the difference of behavior when reading a mathematical proof on a screen or in a textbook (Roy et al., 2017). The possible students’ failures with proofs are due not to some inherent intellectual incapacity. Eye-tracking results indicated that undergraduate students do have at least some of the skills and understanding they need to read proofs effectively, and that a light-touch intervention can lead to better mobilization of these skills and thus to considerably better proof comprehension. They argue that ‘transition to proof’ courses should incorporate self-explanation training. On the other hand, eye-tracking allows us to compare the students' engagement regarding the support of the reading. Even if authors reported that it is risky to evaluate learning innovations using only students' feedback. The two papers from (Haataja et al., 2018) and (Hannula et al., 2019) are using eye-tracking to better understand the interactions between students in a group work or between teacher with his/her students; results showed that teacher’s gaze behavior is of situational nature. In the analysis of the events, the teacher either initiated eye contact without students’ response, where he did not seek eye contact at all, or where he established successful eye contact with students. The amount of eye contact carries with it high dwell times of face-targeted gazes. Nevertheless, the studies do not explain the reasons for the small amount of eye contact. However, we can suggest that it relates to an already established teacher-student relationship and/or the novelty brought about by the gaze tracking glasses on the teacher’s face.

In the comparison of solving a task with pen and pencils and with the help of a DGS, it appears that using technology influenced the duration of gaze fixations: slightly more short fixations, less medium length fixations, and clearly more long fixations. A more detailed analysis suggested that the long fixations are related both to instrument manipulation and cognitive processes. These results suggest that using a digital tool increases the amount of both automatic scanning fixations and long fixations related to more elaborated processing. However, the qualitative examination of the long gazes in context suggests that a significant amount of these long fixations is related to interacting with GeoGebra, for example when selecting an option from a drop-down menu or using a mouse to place an object in the coordinate system.

HD1 tasks mainly use the procedure in a way that maintains a deep level of understanding when students follow a suggested path to solve the task, either because it comes from their course or because it is natural at this level of teaching. Three articles have been selected in this category and are analyzed below.

In these three papers eye-tracking is used to better understand how learners can construct relations between objects or between representations of an object. In that sense the papers consider a semantic interpretation of eye movements based on mathematical understanding of objects, say the concept of function or the concept of multiple representation of a mathematical object. Authors indicate that eye-tracking cannot present the whole story but gives information that can be crossed with mathematical or semiotics reflections. Findings describe how learners behave but do not provide insight into the reasons for their behavior. The question is asked in Crips et al. (2011): “what determines what strategy a participant adopts when tackling such problems?” (p. 39).

Visual attention of learners is correlated with dialogues and gestural expressions (Shvarts 2018) which can be interpreted as a joint mental attention. Eye movements do not follow but rather anticipate the gesture along the side of the triangle thus joining visual and gestural expressions in anticipating perception. The two participants may acquire partial independence: joint mental attention may supersede joint visual attention thus freeing the visual system for other tasks and serving future independence of the tutor’s and the student’s activity.

When the input is text, dwell time and number of fixations have values that make text close to formulae (namely, quite low), but fixation duration is like graph (low). We can infer that text in the input is attended for a shorter time, both in terms of duration and in terms of the number of times the students come to see it. The degree of understanding of graphs or formulae is not the same which can indicate that students would prefer to consider a formula or a text instead of a graph to find information. It would also indicate that a necessary and deep teaching of reading a graph is important for a good understanding of mathematical concepts.

The main difference between tasks from low demand 1 (LD1) and low 2 (LD2) is that in LD2 the participants had the opportunity to explain or make comments about their answers. Beyond solving the task on the screen, the study provides other resources (interview, questionnaire, self-monitoring, audio, or small video) to better understand subjects’ comprehension.

The tasks captured in level 2 aim to explore procedures without connections or tasks based on visual perception and identification of shapes or statements on screen. We found the following mathematical topics: addition and subtraction, proofreading, placing numbers on a real line, calculation using money representation, algebraic manipulation, and some usual classroom problems.

Eye-tracking in these articles is used generally to highlight learners' understanding of a particular task. Some articles compare the behaviors of different learners monitoring activities and indicate that the willingness for monitoring is deeply anchored in a person (Cohors-Fresenborg et al., 2010); Soarès et al. (2021) compare eye-movements of low and high performers looking at the eye gaze interpreted in terms of difficulty or specific attention for students. Some other articles compare through eye-tracking, the behaviors of learners and experts, (Inglis & Alcock, 2012) who compared undergraduate students and mathematicians when looking at the validity of a proof; Soarès et al. (2021) also compare students' behavior with the teacher's predictions, and they highlight the benefits for teachers of observing pupils' behavior through the study of eye-movements. The relationship between eye-movements and fixation times or eye paths and the cognitive efforts being made is emphasized in most of the papers. (Espino et al., 2005) and (Ott et al., 2018) consider the understanding of logic sentences, the first part of the sentence show that eye-tracking technique confirmed the predictions of the model theory of reasoning, which posits that the figure (the way and the order one presents the possible solution, for instance, A-B or B-A) operates in the integration of information to construct the models; the second take profits of gaze behavior and gaze shifts to understand how multiple representations (text, formula, graphics) were prioritized. (Moutsios-Rentzos & Stamatis, 2015) are considering eye-movements of grade 1 students when they think and study the correlation of these eye-movements with activation of brain hemispheres; (Shayan et al., 2017) foster the development of proportional reasoning through eye and hand movements, considering the close relationship between mathematical thinking and embodiment. Which is also the purpose of(Werner & Raab, 2014) who consider eyes movements as a particular case of body movements in the process of solving a problem.

The second aspect corresponds to the methods used, which are all laboratory methods, in which selected learners are observed solving problems. Quantitative methods measure fixation times, gazes, dwell times when qualitative ones focus on describing the eye-movements, but both interpret the data in terms of cognitive engagement and compare results with complementary perspective to didactic or psychological analyses.

The tasks captured in this level are mainly focused on memorization, verification of some result, computation using numbers and without context, finding known results, identification or perception concerning some geometric object or shape. Tasks captured on this level include previously learned facts, rules or definitions or the process of committing facts, rules, or definitions to memory. In this set of studies, the ways to explore subject answers by the task, their explanations, or ways to solve the impasses are not clearly presented or discussed on paper. Most of the provided mathematical tasks are based on visual stimuli.

Numerous papers in this category address issues of psychological nature, linking mathematics performance and anxiety (Hunt et al., 2015), or mathematics perceptions and skills ((Knoblich et al., 2001), (Campbell et al., 2009)) or mental effort and task difficulty (Andrzejewska & Stolińska, 2016). But (Kosko et al., 2023) are focusing on teacher’s gaze on specific students. Eye tracking is used as a medium allowing to better understand the links (links between two sensibilities or links supporting interactions), but with rather little interest in the mathematical tasks themselves; for example, in (Kosko et al., 2023) the task is barely mentioned, and we must refer to another article to understand what it's all about (Kosko, 2022). (Knoblich et al., 2001) show that elements of a mathematical sentence are not considered in the same way, which leads to indications about the possible difficulties of students in problem-solving. (Campbell et al., 2009) focus on identifying physiological manifestation of perceptual shift which allows researchers to gain knowledge of the neural correlates of additional subjective cognitive experiences that are relevant for image-based reasoning in geometry-shifts of attention, for example, or conceptual-verbal identification of a figure. (Hunt et al., 2015) as well as (Şimşek et al., 2020) take profit of measurements of fixation duration, fixation dispersion, saccade duration and blink duration to conclude that eye-tracking can provide information and serve as an indicator to interpret the students’ difficulty in problem-solving or in image-based reasoning in geometry shifts of attention or conceptual-verbal identification of a figure. (Andrzejewska & Stolińska, 2016) argue that longer fixation times can be linked either to a confrontation to a difficulty or a greater involvement in the exploration of a problem. (Kim et al., 2018) through the study of mathematical symbolism and the way students at different levels and with different knowledge can tackle it, show that eye-tracking can give important feedback to conceive and design mathematical software. The study of (Nazaruk & Marchel, 2019) concerns acquisition of mathematical skills for preschools’ pupils using different representations of geometric figures and everyday life objects such as a house, a dog, etc. Eye tracking benefits are considered in terms of method of catching the children’s behavior in front of these figures. There is also in numerous papers an attempt of correlation between the time of task completion, the accuracy of the answers and the dwell time. And, even if, "tracking eye movements does not actually give direct knowledge of thought processes (and problem-solving technique)." (Kim et al., 2018), the method appears in the papers of this category to interpret the psychological state of learners faced with solving a problem.

To answer RQ2 we have drawn up the table of Appendix 5 which gives summarized indications as to 1) the level of the students concerned, 2) whether the article is aimed more at the study of teaching or learning (from the pupil's or the teacher's point of view) and 3) in which area of mathematics the proposed task appears. We summarize our findings concerning the papers in eye-tracking studies as following:

Educational level and subjects

Mathematics domain

Task design

In our sample of papers, only seven directly involve teachers ((Haataja et al., 2019), (Maatta et al., 2021), (Hannula et al., 2022),(Soares et al., 2021),(Kosko, 2022)(Kosko et al., 2023)); some are also considering the contribution of the study for teacher development even if the main target of the study is students’ behavior (Şimşek et al., 2020) or school curriculum (Nazaruk & Marchel, 2019). On the other hand, Professional Content Knowledge appears in the result of students’ devoted studies (Kosko et al., 2023).

Fifteen over thirty-eight papers concern students at a university level (undergraduate) when twelve concern students of secondary classes (3 of high school, grade 10-13, seven of low secondary grades (grade 6 to 9) and three of primary and preschool level, some straddle the line between low secondary and primary or low and high secondary. The nine others do not give information about the learners’ grade. Twenty-nine of the papers address students’ issues and seven are more focused on teachers. The two last addresses both viewpoints.

Concerning mathematics domains and topics our findings coincide with Strohmaier et al. (2020); many of the papers we analyzed relate mainly to numbers and arithmetic, and we identified a variety of other topics: Algebra (2 papers), Function (2), Geometry (3), Logics (3), Number (7), Probability (1), Proportionality (3), Proof (5), Pre-algebra (1).

Contrarily to (Strohmaier et al., 2020) we identified methodological details in eye-tracking studies. Although the researchers make clear the data collection setting and the reason why the proposed task is used according to research goals, it was curious to find just one paper author's comment about challenging and cognitive demands of the proposed task (Moutsios-Rentzos & Stamatis, 2015), our interest in this article. However, in some of them the cognitive singularities and relevance of the proposed situation was presented ((Andrá et al., 2015); (Campbell et al., 2009); (Salminen-Saari et al., 2021); Shvarts, 2018 ).

Many of the studies provided multiple-choice tasks. Since eye tracking seemed particularly beneficial for studying processes rather than outcomes (Strohmaier et al., 2020) we classify most of multiple-choice tasks as low cognitive demand because we had no detailed information concerning subjects’ improvements on mathematical reasoning, development of emerged procedures or other different kinds of revealed mental representation.

We know ET data collection settings need many technologies and human sources, including ethics and non-invasive ways of using devices. In most of the papers, it seems that identification tasks on the screen (multiple choice) take an important role in task design in eye-tracking studies; it could be due to equipment and the possibility to gather data with the gaze, reading and identification tasks could be easier to observe shifts and stimuli in brain record with eye-tracking equipment (Campbell et al., 2009), or the idea of changing geometry approach using task mainly based on identification process.

Since eye-tracking has a more visual input, it is understandable that tasks mainly based on observation or identification on screen take more place in the task design of such research. On the other hand, it’s curious because this type of visualization task is not often used in dynamic geometric environment research, which usually provides task-design exploring and constructing geometric procedures (Assis & Bairral, 2022), or justifying and proving processes (Mariotti, 2000). In proving analyzed studies three of them provided tasks mainly based on numbers filed (integer, prime, rational, divisibility etc.) and two exploring function topics ((Roy et al., 2017); (Panse et al., 2018)). The five captured studies focusing on reading and comprehension of proofs approach: proof validation (Inglis & Alcock, 2012), explanation and self-explanation training (Hodds et al., 2014), distribution of attention and inferred processing demand(Roy et al., 2017), reading behavior and skimming (Panse et al., 2018), and attention allocation (Panse et al., 2018).

Since ET studies involve many digital technologies and nowadays the integration of technological resources is demanding on mathematics content, we decided also to analyze whether the studies integrate technology on the provided tasks. We assume integration as protagonist, as a process to think and solve the task differently. Only five studies integrated digital technology on the provided tasks; two of them focused on geometric content ((Hannula et al., 2019); (Shayan et al., 2017)). (Roy et al., 2017) provided e-Proof with audiovisual attempts to consider the dimensions of proof discussed in their theoretical framework and making explicit how they define learning to investigate the effects of e-Proofs on students’ reading behaviors. (Crisp et al., 2011) provided tasks related with research based on students’ strategy to deriving a function, Shvarts (2018) elaborated a computer-based interactive activity for disclosing a parabola, and (Hannula et al., 2019) inserts GeoGebra in a task adapted from Steiner point.(Shayan et al., 2017) implemented tasks to foster proportional reasoning in a tablet of bimanual interaction problems in which the user must place a left-hand finger and a right-hand finger on the screen at the same time and move both fingers simultaneously to receive a particular visual feedback goal, a green coloration either of the background or of objects they are manipulating.

In an ecological system (e.g. a class), the provided task is an essential point that needs to be carefully considered. The task design and the subject's performance are not neutral and form part - among other things - of semiotic mediation and have an influence on cognitive requirements, data collection and results. This mean that teachers and students, and even researchers, play an important role in the quality of teaching-learning processes and not only in metacognitive monitoring activities (Cohors-Fresenborg et al., 2010).

Reducing the typology to two levels (low or high) is probably not fine enough, even if it is already a challenge to determine the boundaries between cognitive task requirements. We rely on Stein’s framework to categorize the tasks provided in the selected papers. Difficulty in solving certain tasks could not be related only to prior knowledge, but rather to the dynamics of data production and the uncomfortable or intrusive use of eye vision equipment.

Since ET captured papers didn’t relate task design with cognitive load, we are aware it could be a limitation of our analysis. The cognitive task demand framework ((Stein & Lane, 1996); (Stein & Smith, 1998); (Stein et al., 2000)) was neither based on ET studies nor even included digital technologies on the criteria of task identification. For future research we suggest the possibility of creating a typology of task demand with description including technological issues. In this sense this paper can contribute with such view.

Another point of questioning is that such a framework mixing gaze observation and problem-solving does not contain many tasks based on reasoning and proof processes, particularly in geometry. When we decided to create the fourth stage by considering reasoning and proof studies, we thought, given that this is a subject with a high cognitive load, that we would find more tasks with high cognitive demand, but this is not the case. In addition to observing that the geometry program needs even more attention from professional developers and researchers, we assert that the content of our paper and the provision of such analysis could enrich this model.

In some papers we have the idea that technology resources are only added in data collection settings without reflection about cognitive changes and so on. On the other hand, in some studies we can observe how researchers are improving their way of gathering data (Roy et al., 2017), for instance, designing tasks using digital resources. Although we identified detailed information regarding data collection setting, we think that studies could provide details (aims, affordances, constraints etc.) of the proposal tasks relating with the analysis and learning gains etc.

If we are interested in promoting other learning aspects (besides identification, observation etc.) we must pay attention to the type of the designed task. Hence, results of study are not separated from this didactical decision. We're not saying we can't provide undemanding tasks, but we need to be aware of the situation in which they may or may not be more appropriate. As eye tracking is a multidisciplinary field, we need to consider the focus of study between psychology, neuroscience, mathematics education and so on. But it is necessary to cross-analyze with other frameworks (didactic, psychological, pedagogical, etc.) to establish the link between ET parameters and cognitive functions. Another important point is to consider tasks in a digital environment which considers more than the effective task but also the technology as a tool which changes the task-design and the mathematics content and related procedures.

In terms of methodology, numerous papers are using both quantitative and qualitative analysis which participate in this cross analysis which brings to eye-tracking research a more cognitive insight highlighting different ways of learning within the whole research.

Educational contributions and future analysis

Cognitive and meta-cognitive strategies (Cohors-Fresenborg et al., 2010) are linked with eye-tracking parameters (Shayan et al., 2017). Most of the papers are considering eye-tracking as an individual tool, allowing to describe and understand the glance when a learner is confronted with a task. But some of them consider eye-tracking as a meaning to better describe and understand the non-verbal interactions between students and between students and teacher. These remarks lean authors to consider as possible a statistical treatment of data (duration of gaze, number of blinks etc.) which leads to a quantitative methodology based on parameters of eye-tracking. Papers coming from mathematics education crossed this quantitative analysis with a qualitative one, mostly using tools of task analysis and record of dialog and gestures. So far, we could classify the use of eye tracking:

Appendixes – Example of analyzed tasks.

Appendix 1 (High demand – Level 2)

(Salminen-Saari et al., 2021)

The students were asked to find the shortest possible way to connect four cities located at the vertices of a square (Fig. 5).

Appendix 2 (High demand – Level 1)

Crisp, Inglis, Mason & Watson (2011, p. 1).

Example of a generalisation task used.

Appendix 3 (Low demand – Level 2)

Espino, Santamaría, Meseguer & Carreiras (2005, p. B1-B2, Table 1 - B4)

This paper examines the time-course of processing during syllogistic reasoning. This

kind of reasoning is produced from pairs of categorical premises such as:

All Athletes are Brokers

All Brokers are Catalans

where a valid conclusion is “All Athletes are Catalans”. Depending on the quantifier used,

there are four kinds of premise and conclusion:

— All A are B (A)

— Some A are B (I)

— No A are B (E)

— Some A are not B (O)

The letters in parentheses are the traditional abbreviations for each kind of proposition.

The arrangement of terms in the pair of premises determines the figure of the syllogism.

There are four figures:

1 2 3 4

B-A A-B B-A A-B

C-B C-B B-C B-C

A is the extreme-term in the first premise (e.g. Athletes); B is the middle-term, that appears repeated in both premises (e.g. Brokers), and C is the extreme-term in the second premise (e.g. Catalans).

Appendix 4 (Low demand – Level 1)

Knoblich, Ohlsson, and Raney (2001, p. 1002)