Available online at www.sciencedirect.com ScienceDirect Procedia - Social and Behavioral Sciences 237 ( 207 ) 260 264 7th International Conference on Intercultural Education Education, Health and ICT for a Transcultural World, EDUHEM 206, 5-7 June 206, Almeria, Spain Spatial thinking and memory in Russian high school students with different levels of mathematical fluency Tatiana Tikhomirova* Psychological Institute of Russian Academy of Education, 9, 4, Mokhovaya str., Moscow 25009, Russia Abstract In the current study Russian high school students with different levels of mathematical fluency were asked to complete the Mental Rotation Task and the Corsi Block-Tapping Task. We found significant differences between the groups with different levels of mathematical fluency in efficiency of spatial thinking and the level of visuo-spatial memory. Also, we revealed differences in the number and density of the relationships within the structure of spatial memory and thinking between the groups with different levels of mathematical fluency. Gender had a minor effect on the number of correct answers. 207 206 The Authors. Published by by Elsevier Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EDUHEM 206. Peer-review under responsibility of the organizing committee of EDUHEM 206. Keywords: spatial thinking; mental rotation; spatial memory; mathematical fluency; gender differences; high school age.. Introduction Research on mathematical fluency, the ability to perform basic mathematical operations quickly and accurately (Haughton, 980), is of great social and practical importance due to the requirements of state educational standards. It has been shown that individual differences in mathematical fluency at school age are associated with success in mathematical disciplines (Singer-Dudek & Greer, 2005). At the same time, it is necessary to focus on cognitive functioning of students with different levels of mathematical fluency. The existing studies emphasize the importance of spatial thinking and spatial memory (Bull, Espy, & Wiebe, 2008). The most informative indicator of spatial thinking in the context of the relationship with mathematical success is * Corresponding author. Tel.: +7-903-4-28-0. E-mail address: tikho@mail.ru 877-0428 207 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of EDUHEM 206. doi:0.06/j.sbspro.207.02.204
Tatiana Tikhomirova / Procedia - Social and Behavioral Sciences 237 ( 207 ) 260 264 26 mental rotation (Shepard & Metzler, 97). It was found that mental rotation performance predicts success in many mathematical disciplines, for example geometry (Delgado & Prieto, 2004). In the context of the relationship with mathematical success, spatial memory has traditionally been considered as a component of the working memory associated with the processing of shapes of stimuli and their location in space; it can be measured with tasks, in which a participant is asked to recall a particular sequence of objects (Baddeley & Hitch, 994). A number of studies have indicated that low success rates in solving mathematical tasks correlate with the low scores on spatial memory in the Corsi Block task (e.g., Bull, Johnston, & Roy, 999). It was also shown that the spatial memory performance can be associated with various aspects of mathematical knowledge from understanding arithmetic operations to assessing non-symbolic quantities (e.g., Zorzi, Priftis, & Umilta, 2002). It should be noted that the studies of sex differences in spatial thinking consistently ascertain the superiority of men in the Mental Rotation task with the effect size of one standard deviation (Halpern, 2000). It is also noted that the gender effect on the Mental Rotation scores is the most significant among various cognitive measures. Thus, the theoretical analysis showed ) the importance of studying spatial thinking and memory and their relationship with speed indicators of mathematical success; 2) the relevance of the study on an extended sample of high school students; 3) the need to assess the effect of gender on the performance on the Mental Rotation task and the Corsi Block task. Accordingly, the main purpose of our study was to examine the structure of the relationships between spatial thinking and memory in groups of students of the senior school age with different levels of mathematical fluency. 2. Methods 2.. Participants The sample included 426 students (48.8% male) of 9th grades of Russian educational institutions aged from 4.50 to 7.75 years (mean = 5.77, SD = 0.38). Data collection was conducted in educational institutions strictly following the protocol under the constant supervision of a researcher. Analysis of the results was carried out on the basis of anonymized personal data. 2.2. Procedure The participants were administered a Russian-language online version of the test battery Spatial Abilities developed by InLab (Goldsmiths, University of London) and adapted at the Russian-British laboratory of behavior genetics at the Psychological Institute of Russian Academy of Education. The test battery includes a number of tasks aimed at measuring the level of cognitive performance and mathematical fluency (Tosto et al., 203). Problem Verification Task (PVT), mathematical fluency. The test includes two training tasks and 48 test tasks involving solved arithmetic examples. The participants had to decide whether the answer was correct or not and press the appropriate key on the keyboard within 0 seconds. If no response is given in time, the program automatically goes to the next task, and the answer is defined as incorrect. The computer program records the number of correct answers. Corsi Block-Tapping Task, visuo-spatial memory. The participants were presented a set of square blocks lighting up one after another. The test begins with a sequence of 4 blocks; the maximum possible number of elements in a sequence 9. During the presentation the blocks light up for second at intervals of second. The participants were asked to repeat the presented sequence by clicking the blocks with a computer mouse. The test is automatically discontinued if a participant does not correctly reproduce the sequences at a particular level of difficulty. The program records the number of correct answers. Mental Rotation Task, spatial thinking. In this test the participants were asked to decide which of the pictures at the bottom of the screen is a replica of the target at the top of the screen. The participants were asked to solve as many tasks as possible within 3 minutes. The test consisted of 7 training tasks with feedback and 8 test tasks presented with an interval of second. It is assumed that not all the tasks can be completed within this limited time period. The program records the total number of completed tasks and the number of correct answers.
262 Tatiana Tikhomirova / Procedia - Social and Behavioral Sciences 237 ( 207 ) 260 264 3. Results and discussion 3.. Descriptive statistics Table shows the average number of correct answers given with a time limit of 0 seconds for each task of the PVT; the average number of correct answers for the Corsi Block-Tapping Task. For the Mental Rotation Task two measures were calculated: ) the number of correct answers within 3 minutes, and 2) the difference between the number of correct answers and the total number of tasks efficiency. The minimum and the maximum possible scores are as follows: PVT from 0 to 48; the Corsi Block-Tapping task from 0 to 2; the Mental Rotation task from 0 to 8. Table. Means and standard deviations Mean SD Problem Verification Task, correct answers 38. 5.97 Corsi Block, correct answers 5.55.97 Mental Rotation Task, correct answers 33.87.08 Mental Rotation Task, efficiency 4. 5.89 3.2. Formation of groups with different levels of mathematical fluency Based on the descriptive statistics three groups of participants were formed depending on the level of mathematical fluency. The medium-level group included 38 students (47.2% male) with scores ranging from to + SDs (mathematical fluency scores ranging from 32.4 to 44.08). Accordingly, a high-level group had values greater than 44.08 (42 students, 66.7% male) and the low-level group included students with scores below 33.4 (66 students, 45.5% male). Table 2 shows the average values for the tests for groups with differing levels of mathematical fluency; in parentheses are the standard deviations. Negative values in spatial thinking efficiency are due to the calculation algorithm the difference between the number of correct answers and the total number of attempts. The closer the value is to 0, the higher is the efficiency of spatial thinking. Table 2. Descriptive statistics for groups with different levels of mathematical fluency High level (N=42) Medium level (N=38) Low level (N=66) Corsi Block-Tapping Task, correct answers 6.3 (2.26) 5.67 (.85) 4.50 (.95) Mental Rotation Task, correct answers 35.33 (.78) 33.65 (0.44) 33.98 (3.54) Mental Rotation Task, efficiency 8.00 (2.80) 3.29 (5.2) 2.98 (8.2) An increase in the average values is observed in the high-level group in comparison to the low-level group for spatial memory and spatial reasoning efficiency. An exception is the number of correct answers on the Mental Rotation task: in the low-level group the average value was higher than in the medium-level group. The Bonferroni multiple comparison test showed significant differences between the groups. However, the fact of the increase in the average values in the low-level group might be due to the choice of strategy. Perhaps, in this group the preferred strategy was to accomplish more tasks without careful consideration. Probably with the increase in the total number of attempts the number of correct answers also increased. This assumption is also confirmed by the low (-2.98) efficiency score for this test in the low-level group. For further analysis the two measures on the Mental Rotation task were used to analyze the strategies. 3.3. ANOVA The effect of the level of mathematical fluency and the gender effect were evaluated using a bivariate ANOVA. Dependent variables were indicators of spatial thinking and memory.
Tatiana Tikhomirova / Procedia - Social and Behavioral Sciences 237 ( 207 ) 260 264 263 Table 3. Assessment of the group effect and the gender effect on the analyzed measures. Factor Measure SS F p-value ƞ2 Level of mathematical fluency Gender Gender x Level of mathematical fluency Corsi Block-Tapping Task, correct answers 86.33 2.04 0.00 0.06 Mental Rotation Task, correct answers 26.62 0. 0.90 0.00 Mental Rotation Task, efficiency 5669.22.9 0.00 0.06 Corsi Block-Tapping Task, correct answers 6.53 4.6 0.03 0.0 Mental Rotation Task, correct answers 368.30.4 0.00 0.03 Mental Rotation Task, efficiency 20.3 0.09 0.77 0.00 Corsi Block-Tapping Task, correct answers 5.86 0.82 0.44 0.00 Mental Rotation Task, correct answers 233.93 0.98 0.38 0.0 Mental Rotation Task, efficiency 322.66 2.78 0.06 0.0 The Levene s test showed that the variances of the test scores are not equal (p < 0.05) and it will be taken into account when interpreting the results. Table 3 shows that the level of mathematical fluency was significant for all measures except for the number of correct answers in Mental Rotation. The same size of the group effect was found for mental rotation efficiency and the number of correct answers in the Corsi Block task (ƞ 2 = 0.06; p < 0.00). The results of multiple comparisons with the Bonferroni correction showed significant differences in the number of correct answers for the Corsi Block task and Mental Rotation efficiency for the low-level group compared to the medium-level and high-level groups (p < 0.0), but not between the latter (p > 0.05). Students with higher scores for spatial memory and spatial thinking efficiency on average show higher levels of mathematical fluency, compared with students with low levels of mathematical fluency (see Table 2). The gender effect was significant for the number of correct answers on Corsi Block (p <0.00; ƞ 2 = 0.0) and Mental Rotation (p < 0.00; ƞ 2 = 0.03). Boys showed better results in Corsi Block (mean = 5.87, SD = 2.02) than girls (mean = 5.3, SD =.87), as well as in Mental Rotation (boys: mean = 35.90, SD =.42; girls: mean = 3.89, SD = 0.42). Taking into account the small effect sizes and the Levene s test significance, this result may be due to variances inequality. However, these results are consistent with previous studies (e.g., Bull, Davidson, & Nordmann, 200). No interaction between the factors was found. 3.4. Correlation analysis The analysis did not show significant correlations between the number of correct answers for Corsi Block and Mental Rotation in any of the groups (see Table 4). The main differences in the structure of the relationship of cognitive characteristics were observed for the mental rotation efficiency. In particular, it correlated with the number of correct answers for Corsi Block in the medium-level and low-level groups. Also, the relationship of two indicators of spatial thinking was different across groups: the number of correct answers and efficiency only correlated in the medium-level and low-level groups (r = 0.53 and r = 0.70, p < 0.0). Considering the negative nature of the relationship and the negative values of the indicators, the higher was the number of correct answers, the higher was the mental rotation efficiency in these groups. Interestingly, in the high-level group no relationship between the two parameters of spatial thinking was found. This might be due to the differences in strategies among students with different levels of mathematical fluency: in the low-level and medium-level groups efficiency increases with the number of correct answers. In the high-level group an increase in efficiency happens not at the expense of quantity, but due to other indicators, such as the quality of the solution of each test task. Table 4. Correlations between test scores in groups with different levels of mathematical fluency () (2) (3) Corsi Block-Tapping Task, correct answers () Mental Rotation Task, correct answers (2) 0,5 0,09 0,06 Mental Rotation Task, efficiency (3) 0,22-0,
264 Tatiana Tikhomirova / Procedia - Social and Behavioral Sciences 237 ( 207 ) 260 264 4. Conclusion 0,7** 0,26** -0,53** -0,70** *p<0.05;** p<0.0. Upper row high-level group, middle row medium-level group, bottom row low-level group. Overall, the results of this study showed differences in the structure of the relationship of spatial thinking and memory in groups of high school students with low, medium and high levels of mathematical fluency. Thus, the results of ANOVA showed a statistically significant effect of the factor Level of mathematical fluency on spatial memory and efficiency of spatial thinking with the same size effect. At the same time, the high-level group showed higher scores for spatial memory and spatial thinking efficiency, compared with the low-level group. Gender showed significant effect on the number of correct answers for both spatial memory and thinking tests, but with a negligible effect size. There were no sex differences in the efficiency of spatial thinking. The correlation analysis showed similar structures of the relationships between spatial memory and thinking in the groups of students with low and medium levels of mathematical fluency. In these groups spatial memory performance (Corsi Block) showed positive correlations with mental rotation efficiency and negative with the number of correct answers on the Mental Rotation task. In the group of students with a high level of mathematical fluency no significant correlations were found. Of particular note is the lack of correlation between mental rotation efficiency and the number of correct answers. It seems that the differences in the structure of relationships found in groups with different levels of mathematical fluency might be due to the use of different cognitive strategies for solving mathematical tasks within limited time. Thus, the future direction of research in this field should focus on the mechanisms underlying the relationships between cognitive characteristics and success in various academic disciplines. Acknowledgements This study was supported by the grant from the Russian Science Foundation [grant RSF 5-8-30055]. References Baddeley, A.D. & Hitch, G.J. (994). Developments in the concept of working memory. Neuropsychology, 8(4), 485. Bull, R., Espy, K.A., & Wiebe, S.A. (2008). Short-term memory, working memory, and executive functioning in preschoolers: Longitudinal predictors of mathematical achievement at age 7 years. Developmental neuropsychology, 33, 205 228. Bull, R., Johnston, R.S., & Roy, J.A. (999). Exploring the roles of the visual-spatial sketch pad and central executive in children's arithmetical skills: Views from cognition and developmental neuropsychology. Developmental neuropsychology, 5, 42 442. Bull, R., Davidson, W.A., Nordmann, E. (200). Prenatal testosterone, visual-spatial memory, and numerical skills in young children. Learning and Individual Differences, 20, 246 250. Delgado A.R., Prieto G. (2004). Cognitive mediators and sex-related differences in mathematics. Intelligence, 32, 25 32. Halpern, D.F. (2000). Sex differences in cognitive abilities (3rd ed.). London: LEA. Haughton, E.C. (980). Practicing practices: Learning by activity. Journal of Precision Teaching,, 2 30. Shepard, R.N. & Metzler, J. (97). Mental rotation of three-dimensional objects. Science, 7, 70 703 Singer-Dudek, J. & Greer, R.D. (2005). A long-term analysis of the relationship between fluency and the training and maintenance of complex math skills. The Psychological Record, 55, 36 376. Tosto, M.G., Tikhomirova, T., Galajinsky, E., Akimova, K., Kovas, Y. (203). Development and Validation of a Mathematics-number sense Web-based Test Battery. Procedia Social and Behavioral Sciences, 86, 423 428. Zorzi, M., Priftis, K., & Umiltà, C. (2002). Brain damage: neglect disrupts the mental number line. Nature, 47, 38 39.