INTRODUCTION

The literature has identified differences by gender, with males scoring higher in performance on standardised tests measuring a command of mathematics (Hyde et al. 1990; Scheiber et al. 2015, among others) or spatial abilities (Halpern et al., 2007; Voyer & Saunders, 2004), mental rotation in particular (Hyde, 2014; Xu et al., 2016). Gender differences are less obvious when other measuring tools are used, however (Ganley & Vasilyeva, 2011; Gibbs, 2010). Some studies, assessing classroom learning or skills defined in the curriculum, have found girls to score higher than boys (Corbett et al. 2008; Liu & Wilson, 2009; Voyer & Voyer, 2014; Yarbrough et al., 2017). A number of authors have observed women to perform better as a rule in tests measuring numerical skills, and men in tasks calling for mathematical reasoning (Gibbs, 2010; Scheiber et al., 2015).

These differences have clear educational implications, as the practice with spatial tasks can bridge the gender gap in this type of reasoning (Rodán et al., 2022; Wu & Shah, 2004). As an example, evidence was found that mental rotation training can improve performance in mathematical tasks like calculation problems (Cheng & Mix, 2014). In this sense, visual-spatial abilities can condition success in STEM areas (Science, Technology, Engineering and Mathematics), where girls take advanced courses or related degrees to a lesser extent (Reinking & Martín, 2018). Research literature on gender differences documents the intertwined nature of spatial and mathematical development, suggesting that the activities aimed to increase spatial abilities can have positive effects on mathematics learning by students (Johnson et al., 2021). If the differences obtained stemmed from the implied mathematical contents, then the results would provide guidelines for the design of tasks and learning process, because those differences would need to be attended through proper diversity awareness instruction. This would also have consequences in the design of curricular programs, training of teachers and classroom planning, because the tasks presented would be more effective if the educational potential is maximized by bridging the differences (Rodán et al., 2022). However, recent meta-analysis showing that spatial training is effective to improve mathematical understanding and performance highlights a poor understanding of the mechanisms that support transfer and demands more theoretically-guided studies (Hawes et al., 2022).

The first stage in that endeavour is the establishment of relationships between spatial skills and mathematics. Some authors have contended that spatial abilities may determine mathematical performance, particularly as regards geometry ( Ganley & Vasilyeva, 2011). A possible explanation of the role of mental rotation in mathematical scores is related to problem-solving strategies (Delgado & Prieto, 2004). Geometric problem solving, unlike simple arithmetic or numerical tasks, may be impacted by factors other than mathematical ability, such as visuo-spatial aptitudes (Clements, 1980; Delgado & Prieto, 2004; Harris et al., 2021). The effect of spatial abilities might explain the differences in solving complex problems where they are required. Some authors have found men to be better at solving geometric problems requiring visualisation (González-Calero et al., 2018; Ramírez-Uclés et al., 2013). Others, in contrast, have reported that although gender differences can be found among secondary school students in spatial visualisation and performance in geometric tasks, no such differences were observed in the ability to reason or in the strategies used to solve geometric problems ( Battista, 1990). At the same time, several studies have shown that greater mathematical ability to solve problems translated into higher mental rotation test scores (Ramírez-Uclés et al., 2013) and in geometrical tasks involving visualization (for example, Rabab’h & Veloo, 2015; Ramírez & Flores, 2017; Rivera, 2011).

In an attempt to explain that variability, several reviews and meta-analyses have identified complexity as a factor with a bearing on gender differences in mathematics performance (Else-Quest, et al., 2010; Lindberg et al., 2010). Studies on gender differences that detected no significant variation in numerical errors, geometric notions or basic mathematical concepts and competence in addition, nonetheless reported men to solve complex mathematical problems more effectively than women (Stewart et al., 2017). In that same vein, other authors who observed no gender differences in simple tasks or spatial ability found boys significantly better able to deal with more difficult tasks (Manger & Eikeland, 1998). Such gender differences have also been identified in tests that measure mathematical talent (Benbow & Stanley, 1996).

In this research the tool at issue was broached from a descriptive perspective, given that a number of studies have detected evidence that the characteristics of a given task may explain the gender differences observed in mental rotation tests ( Lauer et al., 2019). The aim here focused on understanding gender-related differences in performance on a mental rotation test depending on the geometric complexity of the test item. More specifically, the question posed was: can the uneven performance between girls and boys be attributed to the geometric characteristics of the mental rotation test itself? The primary aim would be to ascertain whether gender differences are due to the geometric properties of mental rotation in terms of the presence of symmetries and different angles of rotation. No universally accepted indication supports the premise that such characteristics specifically determine gender differences. The processes carried out during the test determine the participants’ efficiency in solving a spatial task, so differences might well stem from factors identified in other studies, such as test scoring, response time limitations or the use of effective strategies ( Contreras et al., 2012).

In this sense, attempts have also been made to understand the differences between boys and girls not only in their cognitive ability to solve complex problems requiring mathematical reasoning, but also in their approach to schoolwork and learning strategies, classroom behaviour or self-regulation, mathematical self efficacy and planning and attention strategies (Yarbrough et al., 2017). Gender differences have been detected in self-confidence, with women exhibiting less ( Preckel et al., 2008), for instance, in situations in which they scored lower if they were aware that the task at hand was intended to reveal gender differences (Spencer et al., 1999) or in competitive contexts where they proved to be more sensitive to pressure (Niederle & Vesterlund, 2010). Bench et al. (2015) provided helpful insight into self-confidence. When completing a mathematics test, men were observed to judge their success more highly than women, creating a positive bias. Nonetheless, women who had scored earlier success in mathematics likewise over-estimated their own performance (Bench et al, 2015). Consequently, in this study subjects’ mathematical ability was deemed of significance in understanding the gender differences associated with stereotypes in mathematics.

Gender differences were broached essentially from a psychometric perspective, analysing subjects’ performance on a standardised test (Steinmayr & Spinath, 2008; Wach et al., 2015). Some earlier studies have identified test administration or scoring procedures, such as limiting the time allowed (Maeda & Yoon, 2016; Peters, 2005) or using raw scores (Goldstein et al., 1990; Stumpf, 1993), that may condition such differences, whereas other authors have found no evidence of the effect of such factors (Voyer et al., 2004; Yoon & Mann, 2017). This research deployed the Primary Mental Abilities spatial relations tool (PMA SR, Thurstone & Thurstone, 1943), a mental rotation test in which men and subjects with complex problem-solving ability have been observed to perform better, although no interaction between those two variables has been detected ( Ramírez-Uclés & Ramírez Uclés, 2020).

Gender differences in the PMA-SR sub-test

Gender differences have been identified in PMA-SR performance (Campos, 2014; Lauer et al., 2019; Linn & Petersen, 1985; Stericker & LeVesconte, 1982). PMA-SR elements may be effectively analysed with both spatial strategies (differentiating among rotated reflection symmetries) and ‘analytical’ problem solving, which involves comparing the characteristics of the stimuli to identify matching features (shape, for instance). The latter procedure has been observed to be used more by women than by men (Linn & Petersen, 1985). Men may rely more on spatial strategies that entail visualising the rotation of objects or parts thereof, whereas women may rely more on strategies that involve comparing the characteristics of stimuli (such as size, shape and colour of the components and their inter-relationships) (Just & Carpenter, 1985; Pezaris & Casey, 1991). Although the reasons for gender differences in strategy use are unknown, the deployment of different strategies has been reported to be a source of inter-sex variation in mental rotation skills during child development ( Lauer et al., 2019). Investigations with tasks similar to PMA items, with rotated letters in mirrored form, showed that the strategy used comprised mental rotations of the images until being vertically oriented, and then another rotation out of the plane to return it to normal position (Núñez-Peña & Aznar-Casanova, 2009). When carrying out such process to identify the correct answers in the PMA test, items related to larger angles or presenting symmetries required more time for checking. This strategy, applied to the PMA test (see the example shown in Figure 1), could differentiate between the actions required in image A (rotate 90 degrees to compare with the sample) and B (rotate 45 degrees and apply a symmetry). However, another strategy could be to compare between the different alternatives, as when B is rotated 45 degrees to yield C, which is directly equal to the symmetrical of the sample. Although gender difference does not help in correctly solving the task, it can condition the selection of a certain process that can be more efficient in finding the solution (Contreras et al., 2007; Peña et al., 2008).

Some strategies can be rooted in geometric rationale, eschewing a strictly visual approach. When realising that a composition with two symmetries was tantamount to rotation, for instance, one of the students correctly identified the plane-rotated figures by applying symmetries to the incorrect answer. As an example, answer D (Figure 1) can be rotated to obtain a figure that is symmetrical to C, which is in turn symmetrical to the sample, and therefore D can be obtained as a rotation of the sample. A better spatial sense (National Council of Teachers of Mathematics, 2000) rather than spatial visualisation alone would infer higher potential performance in this test, for certain elements of background knowledge and geometric relationships could likewise be called into play.

That supports the utility of exploring items’ geometric characteristics, for several studies on spatial tests have shown the angle of rotation and presence of symmetries to affect scores. The time needed to find the correct answers varies depending on the angle of rotation and rises with the presence of reflections (Petrusic et al., 1978; Núñez-Peña & Aznar-Casanova, 2009). Wider angles of rotation have also been associated with a rise in complexity and a decline in performance (Alansari et al., 2008; Xu et al., 2016). Nonetheless, in some PMA items with a fairly high rate of erroneous replies a larger angle of rotation was not found to induce greater complexity (Cruz & Ramírez, 2018). As noted in earlier papers, that may have been because the impact of certain biased items on the total score was marginal only (Maeda & Yoon, 2016).

In light of the lack of research on the properties of spatial tests, specific research is demanded on the geometric characteristics of the direction and angle of rotation contained in items associated with gender differences (Maeda & Yoon, 2016) and on the complexity of the geometric shapes used in such tests (Arendasy & Sommer, 2012). This study is a response to such calls for research to determine whether cognitive processes may differ depending on the characteristics of the stimuli (such as object shape, rotation direction and angle, rotational task complexity) and whether the way some of those features are deployed is sex-related (Maeda & Yoon, 2016). This article addresses two types of mistakes made on the PMA spatial relations sub-test, characterised in terms of two geometric properties, angle of rotation and presence of symmetries. The aim is to analyse differences between boys and girls and between more and less mathematically skilled students. From the above premises, the study stems from the following hypothesis: 1) subjects with better mathematical abilities obtain better results in the analyzed test; 2) boys get higher scores in tests tan girls, but no gender differences are observed derived from the geometrical properties; and 3) there could be an interaction between the independent variables gender and mathematical ability in relation to the dependent variable test score.

METHODOLOGY

Participants

The sample comprised 328 secondary school students between the ages of 13 and 16 (mean: 15; standard deviation: 0.97), 143 of whom (sub-sample Complex Problem, CP) were participating in a mathematics talent enhancement programme underway in two Spanish regions, specifically Andalucía and Castilla-León. The uneven distribution by gender in this sub-sample was the result of the smaller number of girls in the programme, an issue faced in earlier studies as well (Hyde, 2014). The 184 subjects in the control sub-sample (No Complex Problem, NCP) were enrolled in different secondary schools in the same regions as the CP students, none of whom had been identified by their teacher as having complex mathematical problem-solving abilities (Table 1).

Instruments

The Spanish language version of the Thurstone (Thurstone & Thurstone, 1976) Primary Mental Abilities Test - Spatial Relations published by TEA Ediciones was used in this study. The Cronbach’s alpha index calculated for this sample was 0.89, which compares to 0.93, the value indicative of reliability or internal consistency. This test measures the ability to interpret and recognise objects that change their position in space while retaining their internal structure. It is a tool often used in classroom evaluations, it is administered in five minutes and can be administered to a whole group with a few simple instructions. Each of its 20 items depicts a sample figure and six others, some of which were the result of rotating the sample around a central point (plane rotation). The remaining options were images involving symmetries and plane rotations. Each correctly identified plane-rotated figure scored as a correct answer whereas defining symmetries as plane rotations constituted an incorrect answer.

No geometric terminology (rotation, angles, symmetries) was used in the instructions for taking the test, which referred to the correct options as the figures ‘that are exactly the same as the sample but in a different position’. For the incorrect answers the instructions were ‘None of the others is identical to the sample, for even if you set them upright, they are backwards or upside-down’.

Allusion was made to visual strategies to identify them: ‘You only need to set them up straight to see they’re exactly the same’; ‘Don’t turn the test sheet around. Leave it flat without lifting it off the desk. You have to turn [the figures] around mentally to see what they would look like’. Three examples with the respective answers were given, noting that ‘the total number of identical figures may vary from row to row’. In Figure 1, for instance the correct answers were identified as A, D and F.

One of the particulars of the tool is that as subjects have no way of knowing the number of correct options in each item or the scoring criteria, they cannot determine the possible advantage of omitting or responding to an item when in doubt. The total score was computed as the number of correct less the number of incorrect choices, whilst two types of errors were possible: excluding a rotation or including a symmetry.

Procedure

The 143 subjects participating in the mathematics enhancement programme (sub-sample CP) were assumed to have complex mathematical problem-solving ability. To be eligible for the programme they had to pass an entrance exam based on solving complex, non-routine problems involving logic, arithmetic or geometry. The following is an example:

“A magic square is a 3x3 matrix such that adding the numbers in all the rows, columns and diagonals gives us the same sum. That value is the square’s ‘magic sum’. Could there be a magic square with nine consecutive odd numbers, seven of which are prime numbers? What would those numbers be?”

The tests were administered to each group collectively, with examinees answering on paper and within the 5 min allowed. Participation in the test, administered by the researchers in the programme classroom for sub-sample CP and the standard classrooms for sub-sample NCP, was voluntary.

Design and variables

The independent variables in the 2x2 bifactorial intergroup design were (boy or girl) and mathematical ability (CP, in possession of complex mathematical problem solving ability; or NCP, control sub-sample). The dependent variables were the total score in PMA test, the sets of error indicators and the types of error (described below).

Type of error

Imperfect performance in an item was the result of failing to checkmark all the identical options or incorrectly labelling one or more of the non-identical figures as identical. Since the identical figures were rotations and the non-identical figures symmetries, two types of errors were defined: exclusion of rotations and inclusion of symmetries. The geometric characterisation of those errors entailed envisioning the re-positioning needed to convert the initial sample figure into the figure shown in each proposed answer. An analysis of the items revealed that rotations could have acute angles ranging approximately from 30º to 60º, obtuse angles from around 120º to 150º and perpendicular directions forming right angles (Cruz & Ramírez, 2018). Given those characteristics, rotations were classified under four headings: 0º to 90º; 90º; 90º to 180º; and 180º (which in some figures could be interpreted as 0º if composed with the respective symmetry). Counter-clockwise rotation was defined as positive, while the first seven types of error were associated with excluding rotations. Including a symmetry as one of the four types of rotations led to a further seven types of errors (Table 2). Error type 6, for instance, was made when students failed to identify a correct choice in which the figure was rotated 90º relative to the sample. Students making error type 14, in contrast, incorrectly identified a figure obtained with a -90º rotation symmetry as a rotation. One additional type of error consisted in the failure to identify any figure as identical to the sample (type 0 = no answer).

Grouping the error types associated with rotations and symmetries yielded the error sets defined in Table 3.

RESULTS

The data were analysed with 2 x 2 ANOVAs, with the dependent and independent variables as described in the methodology. Partial eta squared (η²_p ) was adopted to compute effect size. Statistical significance was set at a confidence interval of 95 %, with p < .05 as the criterion. Analyses were run on SPSS software (v. 19 for Windows).

Further to the findings for the total scores in PMA, students with complex problem-solving ability (CP) performed better than the controls (NCP) [F(1, 324) = 59.43, p = .000; η²_p = .155] and girls (F) obtain lower scores than boys (M) [F(1,324) = 6.20, p = .013, η²_p = .019]. Nor the interaction between the two independent variables was observed to have any significant effect on subjects’ performance.

Error sets

As Table 4 shows, the CP students made significantly fewer errors than the NCP controls in all the error indicator sets. They excluded fewer rotations: on the whole (R) [ η²_p = .110]; and whether positive (PR) [η²_p = .107]; or negative (NR) [η²_p = .085]. They also included fewer symmetries (S): [η²_p = .076], whether positive (PS) [η²_p = .065]; or negative (NS) [ η²_p = .075]. No significant gender-based differences were observed for any of the error sets. Nor was any significant effect found for the possible interaction between independent variables.

Type of error

The findings likewise attested to the significantly fewer errors recorded for the CP students than for the NCP controls in all the error types analysed (see Table 5): Type 0 [η²_p = .039]; Type 1 [η²_p = .074]; Type 2 [η²_p = .040]; Type 3 [η²_p = .099]; Type 4 [η²_p = .079]; Type 5 [η²_p = .023]; Type 6 [ η²_p = .033]; Type 7 [η²_p = .107];Type 9 [η²_p = .046]; Type 10 [ η²_p= .030]; Type 11 [η²_p = .038]; Type 12 [η²_p = .027]; Type 13 [ η²_p = .041]; Type 14 [η²_p = .037] and Type 15 [η²_p = .078]. As in the error sets, no significant differences were observed in the interaction between the two independent variables for any of the error types analysed. No significant gender based differences were observed either for any of the error sets.

In relation to the gender differences found in error Type 0, table 6 shows the percentage of unanswered options by item.

DISCUSSION AND CONCLUSIONS

In light of the present findings, the analysis of two types of errors identified in the PMA test can be said to introduce a nuance in the gender- and mathematical ability-based differences observed in earlier studies.

In this study significant differences were found between students with and without the ability required to solve complex mathematical problems. The former made significantly fewer mistakes of all the types analysed, more effectively differentiating between rotation and symmetry irrespective of the angle of rotation. That finding was consistent with earlier reports that associated greater mathematical competence with higher performance in this type of assessment tools (Ramírez-Uclés et al., 2013)

Gender was not found to have a significant effect on any of the errors or error sets derived from the geometrical properties. No gender differences in performance were detected in connection with angles of rotation or symmetries. In other words, being a boy or a girl did not affect the presence of errors consisting in omitting correct answers for a given angle of rotation or incorrectly including a symmetry. That finding would afford an initial response to one of the issues identified in the literature to be in need of attention (Maeda & Yoon, 2016), inferring that the gender differences found in test performance must be due to other factors. Such factors appear to be related to the fact that boys answer more items (Goldstein et al., 1990; Maeda & Yoon, 2016; Peters, 2005). Contrary to earlier reports (Alansari et al., 2008; Petrusic et al., 1978; Xu et al., 2016), no greater complexity was perceived with wider angles of rotation or the presence of symmetries.

However, significant gender differences were observed in the test score and the number of non-answered items, especially those resulting from lack of time (Ramírez-Uclés & Ramírez Uclés, 2020). Table 6 shows that, from item 11 onwards, more than 50% of girls do not answer thus pointing to the use of strategies that demand more time in the response. Given the specific characteristics of the test and the fact that the subjects are unaware of the number of correct options, we find it interesting to study in future works whether differences stem from personality traits related with poor self-confidence or the need to constantly check the results. Nor was the interaction between the two independent variables (gender and complex mathematical problem-solving ability) observed to have any significant effect. In the items analysed, a command of complex problem-solving was the feature that determined higher test performance, with no gender-based differences observed. These findings introduce considerable nuance in the understanding of the gender differences traditionally identified in visuo-spatial aptitudes and more specifically in mental rotation. Here more mathematically skilled subjects exhibited higher performance on the test, irrespective of gender. Higher performance may be attributable to other factors forming part of geometric rationale, such as an understanding of properties unaltered by isometry (parallelism, perpendicularity and relative position are all retained), order 2 compositions (a composition with two symmetries is a rotation; one with two rotations a third rotation; one with a rotation and a symmetry, a second symmetry) or analytical strategies (Linn & Petersen, 1985).

Mathematics educators have long stressed the importance of drawing connections between visuo-spatial ability and problem solving (Arcavi, 2003; Clements & Battista, 1992). In addition to visualisation, the classroom development of a sense of space (National Council of Teachers of Mathematics, 2000) entails other features of geometric knowledge, such as movements in a plane and in space. Mental rotation items could be performed more efficiently by subjects with a more highly developed sense of space. Nonetheless, tasks associated with that sense such as those requiring physical construction, mental conversion of foldable or non-rigid objects; or the identification of simple shapes embedded in more complex shapes, not usually deemed mental rotation tasks, are excluded from certain meta-analyses (Lauer et al. 2019). The gender differences detected in mental rotation tests might be more fully understood if research focused at the same time on the geometric rationale involved in performing the tasks in an attempt to address the controversy identified in a number of studies (such as Battista, 1990; and González-Calero et al., 2018). Boys’ ability to work faster on this test led to higher performance, for instance. Another area worthy of study would be personality traits, above and beyond cognitive factors, that might affect the deployment of more effective and efficient strategies (Preckel et al., 2008; Yarbrough et al., 2017). Factors such as self-confidence may be an outcome not only of a subject’s gender, but also of their mathematical ability (Bench et al., 2015). Given that mental rotation abilities are reportedly improved by fostering motivational beliefs and improving self-competence perceptions, motivational aspects get relevance in the educational processes to improve mental rotation abilities (Moè, 2021).

Among the limitations of this study, we can highlight that no general intelligence test is included that relates the ability to solve complex problems with the intellectual G factor. In future studies it would be interesting to include both variables to observe the potential relationship between the corresponding constructs. Another limitation of the work is given by the study of a concrete test and a particular sample in which there were different numbers of boys and girls. However, we consider that the results provide interesting educational information in relation to the gender differences found in STEM. In a test traditionally showing gender differences it wasn’t proved that such differences stemmed from the geometrical characteristics analyzed.

The fact that the mathematical contents did not cause the differences could shift the focus of the educational process towards saving the differences in emotional and behavioral aspects, such as self-confidence.

Acknowledgments

This publication is part of the R+D+I project PID2020-117395RB-I00, funded by MCIN/AEI/10.13039/501100011033.

REFERENCES

Alansari, B. M., DerEgowski, J. B., & McGeorge, P. (2008). Sex differences in spatial visualization of Kuwaiti school children. Social Behavior and Personality, 36(6), 811-824. https://doi.org/10.2224/sbp.2008.36.6.811

Arendasy, M. E., & Sommer, M. (2012). Gender differences in figural matrices: The moderating role of item design features. Intelligence, 40(6), 584-597. https://doi.org/10.1016/j.intell.2012.08.003

Arcavi, A. (2003). The role of visual representations in the learning of mathematics. Educational Studies in Mathematics, 52(3), 215-241. https://doi.org/10.1023/A:1024312321077

Battista, M. T. (1990). Spatial visualization and gender differences in high school geometry. Journal for Research in Mathematics Education, 21(1), 47-60. https://doi.org/10.2307/749456

Benbow, C. P., & Stanley, J. C. (1996). Inequity in equity: How ‘‘equity” can lead to inequity for high potential students. Psychology, Public Policy and Law, 2, 249 292. https://doi.org/10.1037/1076-8971.2.2.249

Bench, S. W., Lench, H. C., Liew, J., Miner, K., & Flores, S. A. (2015). Gender gaps in overestimation of math performance. Sex Roles, 72, 536-546. https://doi.org/10.1007/s11199-015-0486-9

Campos, A. (2014). Gender differences in imagery. Personality and Individual Differences, 59, 107–111. https://doi.org/10.1016/j.paid.2013.12.010

Cheng, Y., & Mix, K. S. (2014). Spatial training improves children´s mathematics ability. Journal of Cognition and Development, 15(1), 2-11. https://doi.org/10.1080/15248372.2012.725186

Clements, M. K. (1980). Analyzing children’s errors on written mathematical tasks. Educational Studies in Mathematics, 11, 1-21. https://doi.org/doi:10.1007/BF00369157

Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. En D.A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 420-464). MacMillan.

Contreras, M. J., Martínez-Molina, A., & Santacreu, J. (2012). Do the sex differences play such an important role in explaining performance in spatial tasks? Personality and Individual Differences, 52(6), 659-663. https://doi.org/10.1016/j.paid.2011.12.010

Contreras, M. J., Rubio, V., Peña, D., Colom, R., & Santacreu, J. (2007). Sex differences in dynamic spatial ability: The unsolved question of performance factors. Memory & Cognition, 35(2), 297-303. https://doi.org/10.3758/BF03193450

Corbett, C., Hill, C., & St. Rose, A. (2008). Where the girls are: The facts about gender equity in education-executive summary. Educational Foundation, American Association of University Women.

Cruz, A., & Ramírez, R. (2018). Componentes del sentido espacial en un test de capacidad espacial. En L. J. Rodríguez-Muñiz, L. Muñiz-Rodríguez, A. Aguilar González, P. Alonso, F. J. García-García, & A. Bruno (Eds.), Investigación en Educación Matemática XXII (pp. 211-220). SEIEM.

Delgado, A., & Prieto, G. (2004). Cognitive mediators and sex-related differences in mathematics. Intelligence, 32, 25-32. https://doi.org/10.1016/S0160-2896(03)00061-8

Else-Quest, N. M., Hyde, J. S., & Linn, M. C. (2010). Cross-national patterns of gender differences in mathematics: A meta-analysis. Psychological Bulletin, 136(1), 103-127. https://doi.org/10.1037/a0018053

Ganley, C. M., & Vasilyeva, M. (2011). Sex differences in the relation between math performance, spatial skills and attitudes. Journal of Applied Developmental Psychology, 32(4), 235-242. https://doi.org/10.1016/j.appdev.2011.04.001

Gibbs, B. G. (2010). Reversing fortunes or content change? Gender gaps in math related skill throughout childhood. Social Science Research, 39(4), 540-569. https://doi.org/10.1016/j.ssresearch.2010.02.005

Goldstein, D., Haldane, D., & Mitchell, C. (1990). Sex differences in visual-spatial ability: The role of performance factors. Memory & Cognition, 18(5), 546-550. https://doi.org/10.3758/BF03198487

González-Calero, J. A., Cózar, R., Villena, R., & Merino, J. M. (2018). The development of mental rotation abilities through robotics-based instruction: An experience mediated by gender. British Journal of Educational Technology, 50(6), 3198 3213. https://doi.org/10.1111/bjet.12726

Halpern, D. F., Benbow, C. P., Geary, D. C., Gur, R. C., Shibley, J. S., & Gernsbacher, M. A. (2007). The science of sex differences in science and mathematics. Psychological Science in the Public Interest, 8(1), 1-51. https://doi.org/10.1111/j.1529-1006.2007.00032.x

Harris, D., Lowrie, T., Logan, T., & Hegarty, M. (2021). Spatial reasoning, mathematics, and gender: Do spatial constructs differ in their contribution to performance? British Journal of Educational Psychology, 91(1), 409–441. https://doi.org/10.1111/bjep.12371

Hawes, Z., Gilligan-Lee, K., & Mix, K. (2022). Effects of spatial training on mathematics performance: A meta-analysis. Development Psychology, 58(1), 112-137. https://doi.org/10.1037/dev0001281

Hyde, J. S. (2014). Gender similarities and differences . Annual Review of Psychology, 65, 373-398. https://doi.org/10.1146/annurev-psych-010213-115057

Hyde, J. S., Fennema, E., & Lamon, S. (1990). Gender differences in mathematics performance: A meta-analysis. Psychological Bulletin, 107, 139–55. https://doi.org/10.1037/0033-2909.107.2.139

Johnson, T., Burgoyne, A., Mix, K., & Young, C. (2021). Spatial and mathematics skills: Similarities and differences related to age, SES, and gender. Cognition, 218(2), Artículo 104918. https://doi.org/10.1016/j.cognition.2021.104918

Just, M. A., & Carpenter, P. A. (1985). Cognitive coordinate systems: Accounts of mental rotation and individual differences in spatial ability. Psychological Review, 92(2), 137–172. https://doi.org/10.1037/0033-295X.92.2.137

Lauer, J. E., Yhang, E., & Lourenco, S. F. (2019). The development of gender differences in spatial reasoning: A meta-analytic review. Psychological Bulletin, 145(6), 537 565. https://doi.org/10.1037/bul0000191

Lindberg, S. M., Hyde, J. S., Petersen, J., & Linn, M. C. (2010). New trends in gender and mathematics performance: A meta-analysis. Psychological Bulletin, 136, 1123-1135. https://doi.org/10.1037/a0021276

Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. Child Development, 56(6), 1479– 1498. https://doi.org/10.2307/1130467

Liu, O. L., & Wilson, M. (2009). Gender differences and similarities in PISA 2003 mathematics: A comparison between the United States and Hong Kong. International Journal of Testing, 9(1), 20-40. https://doi.org/10.1080/15305050902733547

Maeda, Y., & Yoon, S. Y. (2016). Are gender differences in spatial ability real or an artifact? Evaluation of measurement invariance on the Revised PSVT. Journal of Psychoeducational Assessment, 34(4), 397-403. https://doi.org/10.1177/0734282915609843

Manger, T., & Eikeland, O. (1998). The effects of spatial visualization and students’ sex on mathematical achievement. British Journal of Psychology, 89, 17-25. https://doi.org/10.1111/j.2044-8295.1998.tb02670.x

Moè, A. (2021). Doubling mental rotation scores in high school students: Effects of motivational and strategic trainings. Learning and Instruction, 74, 101461. https://doi.org/10.1016/j.learninstruc.2021.101461

National Council of Teachers of Mathematics (2000). Principles and standards for school mathematics. NCTM.

Niederle, M., & Vesterlud, L. (2010). Explaining the gender gap in math test scores: The role of competition. Journal of Economic Perspectives, 24(2), 129-44. https://doi.org/10.1257/jep.24.2.129

Núñez-Peña, M. I., & Aznar-Casanova, J. A. (2009). Rotación mental: Cómo la mente rota las imágenes hasta colocarlas en su posición normal. Ciencia Cognitiva: Revista Electrónica de Divulgación, 3(2), 58-61.

Peña, D., Contreras, M. J., Shih, P. C., & Santacreu, J. (2008). Solution strategies as possible explanations of individual and sex differences in a dynamic spatial task. Acta Psychological, 128(1), 1-14. https://doi.org/10.1016/j.actpsy.2007.09.005

Peters, M. (2005). Sex differences and the factor of time in solving Vandenberg and Kuse mental rotation problems. Brain and Cognition, 57(2), 176-184. https://doi.org/10.1016/j.bandc.2004.08.052

Petrusic, W. M., Varro, L., & Jamieson, D. G. (1978). Mental rotation validation of two spatial ability tests. Psychological Research, 40(2), 139-148. https://doi.org/10.1007/BF00308409

Pezaris, E., & Casey, M. B. (1991). Girls who use “masculine” problem-solving strategies on a spatial task: Proposed genetic and environmental factors. Brain and Cognition, 17(1), 1–22. https://doi.org/10.1016/0278-2626(91)90062-D

Preckel, F., Goetz, T., Pekrun, R., & Kleine, M. (2008). Gender differences in gifted and average-ability students: Comparing girls’ and boys’ achievement, self concept, interest, and motivation in mathematics. Gifted Child Quarterly, 52(2), 146-159. https://doi.org/10.1177/0016986208315834

Rabab’h, B., & Veloo, A. (2015). Spatial visualization as mediating between mathematics learning strategy and mathematics achievement among 8th grade students. International Education Studies. 8(5), 1-11. https://doi.org/10.5539/ies.v8n5p1

Ramírez, R., & Flores, P. (2017). Habilidades de visualización de estudiantes con talento matemático: Comparativa entre los test psicométricos y las habilidades de visualización manifestadas en tareas geométricas. Enseñanza de las Ciencias, 35(2), 179-196. https://doi.org/10.5565/rev/ensciencias.2152

Ramírez-Uclés, R., Ramírez-Uclés, I., Flores, P., & Castro, E. (2013). Analysis of spatial visualization and intellectual capabilities in mathematically gifted students. Revista Mexicana de Psicología, 30, 24-31.

Ramírez-Uclés, I., & Ramírez Uclés, R. (2020). Gender differences in visuospatial abilities and complex mathematical problem solving. Frontiers Psychology, 11(191), 1-10. https://doi.org/10.3389/fpsyg.2020.00191

Reinking, A., & Martín, B. (2018). La brecha de género en los campos STEM: Teorías, movimientos e ideas para involucrar a las chicas en entornos STEM. Journal of New Approaches in Educational Research, 70(2), 160-166. https://doi.org/10.7821/naer.2018.7.271

Rivera, F. D. (2011). Towards a visually-oriented school mathematics curriculum. Springer. https://doi.org/10.1007/978-94-007-0014-7

Rodán, A., Montoro, P. R., Martínez-Molina, A., & Contreras, M. J. (2022). Effectiveness of spatial training in elementary and secondary school: everyone learns. Educación XX1, 25(1), 381-406. https://doi.org/10.5944/educXX1.30100

Scheiber, C., Reynolds, M. R., Hajovsky, D. B., & Kaufman, A. S. (2015). Gender differences in achievement in a large, nationally representative sample of children and adolescents. Psychology in the Schools, 52, 335-348. https://doi.org/doi:10.1002/pits.21827

Spencer, S. J., Steele, C. M., & Quinn, D. M. (1999). Stereotype threat and women’s math performance. Journal of Experimental Social Psychology, 35, 4-28. https://doi.org/10.1006/jesp.1998.1373

Steinmayr, R., & Spinath, B. (2008). Sex differences in school achievement: What are the roles of personality and achievement motivation? European Journal of Personality, 22, 185–209. http://dx.doi.org/10.1002/per.676

Stericker, A., & LeVesconte, S. (1982). Effect of brief training on sex-related differences in visual-spatial skill. Journal of Personality and Social Psychology, 43(5), 1018–1029. https://doi.org/10.1037/0022-3514.43.5.1018

Stewart, C., Root, M. M., Koriakin, T., Choi, D., Luria, S. R., Bray, M. A., Sassu, K. Maykel, C., O´Rourke, P., & Courville, T. (2017). Biological gender differences in students’ errors on mathematics achievement tests. Journal of Psychoeducational Assessment, 35(1-2), 47-56. https://doi.org/10.1177/0734282916669231

Stumpf, H. (1993). Performance factors and gender-related differences in spatial ability: Another assessment. Memory & Cognition, 21(6), 828-836. https://doi.org/10.3758/BF03202750

Thurstone, L. L., & Thurstone, T. G. (1943). Chicago tests of primary mental abilities: Manual of instructions. Science Research Association.

Thurstone, L. L., & Thurstone, T. G. (1976). P.M.A.: Aptitudes Mentales Primarias. TEA.

Voyer, D., Rodgers, M. A., & McCormick, P. A. (2004). Timing conditions and the magnitude of gender differences on the Mental Rotations Test. Memory & Cognition, 32(1), 72-82. https://doi.org/10.3758/BF03195821

Voyer, D., & Saunders, K. A. (2004). Gender differences on the mental rotations test: A factor analysis. Acta Psychologica, 117(1), 79-94. https://doi.org/10.1016/j.actpsy.2004.05.003

Voyer, D., & Voyer, S.D. (2014). Gender differences in scholastic achievement: A meta analysis. Psychological Bulletin, 140(4), 1174-1204. https://doi.org/10.1037/a0036620

Wach, F. S., Spengler, M., Gottschling, J., & Spinath, F. M. (2015). Sex differences in secondary school achievement — The contribution of self-perceived abilities and fear of failure. Learning and Instruction, 36, 104–112. http://dx.doi.org/10.1016/j.learninstruc.2015.01.005

Wu, H., & Shah, P. (2004). Exploring visuospatial thinking in chemistry learning. Science Education, 88, 465-492. https://doi.org/10.1002/sce.10126

Xu, X., Kim, E. S., & Lewis, J. E. (2016). Sex difference in spatial ability for college students and exploration of measurement invariance. Learning and Individual Differences, 45, 176-184. https://doi.org/10.1016/j.lindif.2015.11.015

Yarbrough, J. L., Cannon, L., Bergman, S., Kidder-Ashley, P., & McCane-Bowling, S. (2017). Let the data speak: Gender differences in math curriculum-based measurement. Journal of Psychoeducational Assessment, 35(6), 568-580. https://doi.org/10.1177/0734282916649122

Yoon, S. Y., & Mann, E. L. (2017). Exploring the spatial ability of undergraduate students: Association with gender, STEM majors, and gifted program membership. Gifted Child Quarterly, 61(4), 313-327. https://doi.org/10.1177/0016986217722614

---

Received: 15 February 2022
Accepted: 22 July 2022
Published: 13 June 2023