幾何估算能力對於幾何學習是一個重要的影響因素，但過去的研究很少探討其對幾何學習與空間能力的影響。除此之外，很少研究讓學習者將幾何概念應用在解決真實情境的幾何問題，並缺乏探討其對學習成效、空間能力與幾何估算能力的影響。因此，本研究針對國小學童的幾何數學開發了一套Ubiquitous Geometry(UG)學習系統，探討學習者在真實情境中使用UG來量測真實物體，進行幾何量測學習解題，並探討其對幾何估算能力、幾何學習成效、空間能力與Van Hiele幾何思考層次之影響，更進一步探討學習者的幾何量測學習行為與幾何估算能力、幾何學習成效、空間能力與Van Hiele幾何思考層次之相關。
研究對象為國小五年級學生共82位，分成實驗組(使用UG)、傳統量測組(使用量尺)與傳統教學組三組，為期約一個月的實驗時間。實驗結果顯示，在幾何估算能力中的Level2-估算自身到物體的「間距」與Level3-「遠距離」觀看物體的長與寬，實驗組皆顯著優於傳統量測組與傳統教學組。後測的幾何學習成效，實驗組皆顯著優於傳統量測組與傳統教學組。在空間能力中的類比推理，實驗組顯著優於傳統量測組與傳統教學組，而在空間能力的心像旋轉中，實驗組顯著優於傳統量測組。在Van Hiele幾何思考層次，實驗組顯著優於傳統量測組與傳統教學組。
在幾何量測學習行為的影響，結果發現在複合式形狀量測次數與幾何估算能力中Level2-估算自身到物體的「間距」及Level3-「遠距離」觀看物體的長與寬、後測幾何學習成效、空間能力皆呈現顯著正相關。此外，在複合式形狀解題策略中，發現實驗組比傳統量測組與傳統教學組的答對的人數多，而且實驗組會運用較簡單的解題策略計算出複合式面積。最後，多數實驗組的學習者皆認為透過實際量測並結合真實情境的幾何學習是非常有幫助的。

The geometry estimation ability is an extremely important fact for the geometry learning. However, there is few research that gave students opportunities to apply their geometry concept to solve geometry problems in authentic contexts. And the influence of the geometry concept on the learning achievement of geometry, spatial ability and geometry estimated ability is also ignored. Therefore, we developed an Ubiquitous geometry (UG) system for elementary school students to investigate whether their geometry estimation ability, geometry learning achievement, spatial ability and Van Hiele levels will be affected when they learned using UG. And we also further investigated the correlation between students’ geometry estimation ability, geometry learning achievement, spatial ability and van Hiele levels.
82 fifth grade elementary school students participated in this study for around one month, who were divided into three groups , experiment group (using UG), traditional measurement group (using ruler) and traditional teaching group. The result revealed that experiment group performed significantly better than traditional measurement group and traditional teaching group on Level2- 「distance estimation between students and objects」 and Level3-「long distance estimation the length and width of objects」of the geometry estimation ability. The experiment group also out performed significantly the traditional measurement group and the traditional teaching group in geometry learning achievement of post-test. As for spatial ability, in analogical reasoning, the experimental group performed better than the traditional measurement group and the traditional teaching group, and it also reached a significant level; while in mental rotation, the experimental group only performed significantly better than the traditional measurement group. In Van Hiele levels, the experimental group performed significantly better than the traditional measurement group and the traditional teaching group.
Regarding the influence of geometry measurement learning behavior using UG on learning achievement, it was demonstrated that there was a significant correlation between the amount of area measurement of compound shapes, and Level2-「distance estimation between students and objects」or Level3-「long distance estimation of the length and width of objects」of the geometry estimation ability. And the amount of area measurement of compound shapes also had a positive correlation with geometry learning achievement from post-test, spatial ability.
Besides, we found that the number of the experimental students who got correct answers is higher than those of the traditional measurement group and the traditional teaching group in solving compound area problems. And the experimental students usually employed easier strategies to solve compound area problems. Finally, most students of the experimental group thought that it is helpful geometry learning through the practical measurement in authentic contexts .

中文部分
林浚傑. (2007). 國小學童之平面視覺空間能力研究: 國立新竹教育大學應用數學系碩士班碩士論文, 未出版, 新竹市.
英文部分
Baki, A., Kosa, T., & Guven, B. (2011). A comparative study of the effects of using dynamic geometry software and physical manipulatives on the spatial visualisation skills of pre‐service mathematics teachers. British Journal of Educational Technology, 42(2), 291-310.
Battista, M. T. (1990). Spatial visualization and gender differences in high school geometry. Journal for Research in Mathematics Education, 47-60.
Battista, M. T., Wheatley, G. H., & Talsma, G. (1982). The importance of spatial visualization and cognitive development for geometry learning in preservice elementary teachers. Journal for Research in Mathematics Education, 332-340.
BAYRAK, M. E. (2008). Investigation of effect of visual treatment on elementary school student’s spatial ability and attitude toward spatial ability problems. MIDDLE EAST TECHNICAL UNIVERSITY.
Bishop, A. J. (1980). Spatial abilities and mathematics education—A review. Educational Studies in Mathematics, 11(3), 257-269.
Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 31-48.
Cañadas, M. C., Molina, M., Gallardo, S., Martínez-Santaolalla, M. J., & Peñas, M. (2010). Let´ s teach geometry. Mathematics Teaching, 218, 32-37.
Casey, M. B., Nuttall, R., Pezaris, E., & Benbow, C. P. (1995). The influence of spatial ability on gender differences in mathematics college entrance test scores across diverse samples. Developmental Psychology, 31(4), 697.
Chiu-Pin, L., Shao, Y.-j., Lung-Hsiang, W., Yin-Jen, L., & Niramitranon, J. (2011). The impact of using synchronous collaborative virtual tangram in children's geometric. TOJET: The Turkish Online Journal of Educational Technology, 10(2).
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning.
Crompton, H. (2015). Using Context-Aware Ubiquitous Learning to Support Students’ Understanding of Geometry. Journal of Interactive Media in Education, 2015(1).
Davis, F. D. (1989). Perceived usefulness, perceived ease of use, and user acceptance of information technology. MIS quarterly, 319-340.
De Lisi, R., & Wolford, J. L. (2002). Improving children's mental rotation accuracy with computer game playing. The Journal of genetic psychology, 163(3), 272-282.
Dimakos, G., & Zaranis, N. (2010). The influence of the Geometer's Sketchpad on the geometry achievement of Greek school students. The Teaching of Mathematics, 13(2), 113-124.
Do, T. V., & Lee, J.-W. (2009). A multiple-level 3D-LEGO game in augmented reality for improving spatial ability Human-Computer Interaction. Interacting in Various Application Domains (pp. 296-303): Springer.
Eliasson, J., Nouri, J., Ramberg, R., & Cerratto Pargman, T. (2010). Design heuristics for balancing visual focus on devices in formal mobile learning activities. Paper presented at the Proceedings of the 4th World Conference on Mobile Learning, Valletta, Malta.
Erbas, A. K., & Yenmez, A. A. (2011). The effect of inquiry-based explorations in a dynamic geometry environment on sixth grade students’ achievements in polygons. Computers & Education, 57(4), 2462-2475.
Fennema, E. (1974). Mathematics learning and the sexes: A review. Journal for Research in Mathematics Education, 126-139.
Ferreira, J., Pedro, M., & Correia, N. (2015). Geometry in the Real World: Mobile Image Processing for Educational Games. Paper presented at the Proceedings of the 13th International Conference on Advances in Mobile Computing and Multimedia.
Frankosky, M., Wiebe, E., Buffum, P., & Boyer, K. E. (2015). Spatial Ability and Other Predictors of Gameplay Time: Understanding Barriers to Learning in Game-based Virtual Environments. Res. Immersive Environ. Learn. SIG.
Gardner, H. (1993). Multiple intelligences: The theory in practiceBasic Books. New York.
Gecü, Z., & Özdener, N. (2010). The effects of using geometry software supported by digital daily life photographs on geometry learning. Procedia-Social and Behavioral Sciences, 2(2), 2824-2828.
Guay, R. B., & McDaniel, E. D. (1977). The relationship between mathematics achievement and spatial abilities among elementary school children. Journal for Research in Mathematics Education, 211-215.
Gueven, B., & Temel, K. (2008). The effect of dynamic geometry software on student mathematics teachers' spatial visualization skills. TOJET: The Turkish Online Journal of Educational Technology, 7(4).
Guven, B. (2012). Using dynamic geometry software to improve eight grade students' understanding of transformation geometry. Australasian Journal of Educational Technology, 28(2).
Healy, L., & Hoyles, C. (2002). Software tools for geometrical problem solving: Potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6(3), 235-256.
Huang, S.-H., Wu, T.-T., Chen, H.-R., Yang, P.-C., & Huang, Y.-M. (2012). Mathematics Assisted Instruction System of M/U-Learning Environment. Paper presented at the Wireless, Mobile and Ubiquitous Technology in Education (WMUTE), 2012 IEEE Seventh International Conference on.
Hung, P.-H., Hwang, G.-J., Lee, Y.-H., & Su, I.-H. (2012). A cognitive component analysis approach for developing game-based spatial learning tools. Computers & Education, 59(2), 762-773.
Jones, G., Taylor, A., & Broadwell, B. (2009). Estimating linear size and scale: Body rulers. International Journal of Science Education, 31(11), 1495-1509.
Karaman, T., & Toğrol, A. Y. (2009). Relationship between gender, spatial visualization, spatial orientation, flexibility of closure abilities and performance related to plane geometry subject among sixth grade students. BOĞAZİÇİ ÜNİVERSİTESİ EĞİTİM DERGİSİ, 26(1).
Keller, J. M. (1987). Development and use of the ARCS model of instructional design. Journal of instructional development, 10(3), 2-10.
Kerr Jr, D. R. (1979). A Case for Geometry: Geometry Is Important, It Is There, Teach It. Arithmetic Teacher, 26(6), 14.
Ketamo, H. (2003). An adaptive geometry game for handheld devices. Educational Technology & Society, 6(1), 83-95.
Koedinger, K. R. (1998). Conjecturing and argumentation in high-school geometry students. Designing learning environments for developing understanding of geometry and space, 319-347.
Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schönmann, C., Plangger, F., . . . von Aster, M. (2011). Mental number line training in children with developmental dyscalculia. NeuroImage, 57(3), 782-795.
Large, A., Beheshti, J., Breuleux, A., & Renaud, A. (1996). Effect of animation in enhancing descriptive and procedural texts in a multimedia learning environment. Journal of the American Society for Information Science, 47(6), 437-448.
Lin, H.-C. K., Chen, M.-C., & Chang, C.-K. (2015). Assessing the effectiveness of learning solid geometry by using an augmented reality-assisted learning system. Interactive Learning Environments, 23(6), 799-810.
Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. Child development, 1479-1498.
Martin-Dorta, N., Sanchez-Berriel, I., Bravo, M., Hernandez, J., Saorin, J. L., & Contero, M. (2014). Virtual Blocks: a serious game for spatial ability improvement on mobile devices. Multimedia Tools and Applications, 73(3), 1575-1595.
Masendorf, F. (1995). Training learning-disabled children's spatial ability by computer games. European Education, 27(2), 49-58.
Merchant, Z., Goetz, E. T., Keeney-Kennicutt, W., Kwok, O.-m., Cifuentes, L., & Davis, T. J. (2012). The learner characteristics, features of desktop 3D virtual reality environments, and college chemistry instruction: A structural equation modeling analysis. Computers & Education, 59(2), 551-568.
Mistretta, R. M. (2000). Enhancing geometric reasoning. Adolescence, 35(138), 365.
Moreno, R., & Mayer, R. E. (1999). Cognitive principles of multimedia learning: The role of modality and contiguity. Journal of educational psychology, 91(2), 358.
Okagaki, L., & Frensch, P. A. (1994). Effects of video game playing on measures of spatial performance: Gender effects in late adolescence. Journal of applied developmental psychology, 15(1), 33-58.
Olkun, S. (2003). Comparing computer versus concrete manipulatives in learning 2D geometry. Journal of Computers in Mathematics and Science Teaching, 22(1), 43-46.
Olkun, S., Altun, A., & Smith, G. (2005). Computers and 2D geometric learning of Turkish fourth and fifth graders. British Journal of Educational Technology, 36(2), 317-326.
Panaoura, G., Gagatsis, A., & Lemonides, C. (2007). Spatial abilities in relation to performance in geometry tasks. WORKING GROUP 7. Geometrical Thinking 954, 1062.
Pittalis, M., Mousoulides, N., & Christou, C. (2007). Spatial ability as a predictor of students’ performance in geometry. Paper presented at the Proceedings of the Fifth Congress of the European Society for Research in Mathematics Educations (CERME 5).
Rafi, A., Anuar, K., Samad, A., Hayati, M., & Mahadzir, M. (2005). Improving spatial ability using a Web-based Virtual Environment (WbVE). Automation in construction, 14(6), 707-715.
Roberts, M. L., & Wortzel, L. H. (1979). New life-style determinants of women's food shopping behavior. The Journal of Marketing, 28-39.
Shih, S.-C., Kuo, B.-C., & Liu, Y.-L. (2012). Adaptively Ubiquitous Learning in Campus Math Path. Educational Technology & Society, 15(2), 298-308.
Smith, I. M. (1964). Spatial ability: University of London Press.
Thom, R. (2002). Measurement? It's Fun! Didn't You Guess? Australian Primary Mathematics Classroom, 7(2), 26.
Van Hiele, P. M. (1959). The child’s thought and geometry: Brooklyn, NY: City University of New.
Waller, D. (2000). Individual differences in spatial learning from computer-simulated environments. Journal of Experimental Psychology: Applied, 6(4), 307.
Wallner, G., & Kriglstein, S. (2012). DOG eometry: teaching geometry through play. Paper presented at the Proceedings of the 4th International Conference on Fun and Games.
Wijers, M., Jonker, V., & Drijvers, P. (2010). MobileMath: exploring mathematics outside the classroom. ZDM, 42(7), 789-799.
Yang, J. C., & Chen, S. Y. (2010). Effects of gender differences and spatial abilities within a digital pentominoes game. Computers & Education, 55(3), 1220-1233.
Baki, A., Kosa, T., & Guven, B. (2011). A comparative study of the effects of using dynamic geometry software and physical manipulatives on the spatial visualisation skills of pre‐service mathematics teachers. British Journal of Educational Technology, 42(2), 291-310.
Battista, M. T. (1990). Spatial visualization and gender differences in high school geometry. Journal for Research in Mathematics Education, 47-60.
Battista, M. T., Wheatley, G. H., & Talsma, G. (1982). The importance of spatial visualization and cognitive development for geometry learning in preservice elementary teachers. Journal for Research in Mathematics Education, 332-340.
BAYRAK, M. E. (2008). Investigation of effect of visual treatment on elementary school student’s spatial ability and attitude toward spatial ability problems. MIDDLE EAST TECHNICAL UNIVERSITY.
Bishop, A. J. (1980). Spatial abilities and mathematics education—A review. Educational Studies in Mathematics, 11(3), 257-269.
Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in geometry. Journal for Research in Mathematics Education, 31-48.
Cañadas, M. C., Molina, M., Gallardo, S., Martínez-Santaolalla, M. J., & Peñas, M. (2010). Let´ s teach geometry. Mathematics Teaching, 218, 32-37.
Casey, M. B., Nuttall, R., Pezaris, E., & Benbow, C. P. (1995). The influence of spatial ability on gender differences in mathematics college entrance test scores across diverse samples. Developmental Psychology, 31(4), 697.
Chiu-Pin, L., Shao, Y.-j., Lung-Hsiang, W., Yin-Jen, L., & Niramitranon, J. (2011). The impact of using synchronous collaborative virtual tangram in children's geometric. TOJET: The Turkish Online Journal of Educational Technology, 10(2).
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning.
Crompton, H. (2015). Using Context-Aware Ubiquitous Learning to Support Students’ Understanding of Geometry. Journal of Interactive Media in Education, 2015(1).
Davis, F. D. (1989). Perceived usefulness, perceived ease of use, and user acceptance of information technology. MIS quarterly, 319-340.
De Lisi, R., & Wolford, J. L. (2002). Improving children's mental rotation accuracy with computer game playing. The Journal of genetic psychology, 163(3), 272-282.
Dimakos, G., & Zaranis, N. (2010). The influence of the Geometer's Sketchpad on the geometry achievement of Greek school students. The Teaching of Mathematics, 13(2), 113-124.
Eliasson, J., Nouri, J., Ramberg, R., & Cerratto Pargman, T. (2010). Design heuristics for balancing visual focus on devices in formal mobile learning activities. Paper presented at the Proceedings of the 4th World Conference on Mobile Learning, Valletta, Malta.
Erbas, A. K., & Yenmez, A. A. (2011). The effect of inquiry-based explorations in a dynamic geometry environment on sixth grade students’ achievements in polygons. Computers & Education, 57(4), 2462-2475.
Fennema, E. (1974). Mathematics learning and the sexes: A review. Journal for Research in Mathematics Education, 126-139.
Ferreira, J., Pedro, M., & Correia, N. (2015). Geometry in the Real World: Mobile Image Processing for Educational Games. Paper presented at the Proceedings of the 13th International Conference on Advances in Mobile Computing and Multimedia.
Frankosky, M., Wiebe, E., Buffum, P., & Boyer, K. E. (2015). Spatial Ability and Other Predictors of Gameplay Time: Understanding Barriers to Learning in Game-based Virtual Environments. Res. Immersive Environ. Learn. SIG.
Gardner, H. (1993). Multiple intelligences: The theory in practiceBasic Books. New York.
Gecü, Z., & Özdener, N. (2010). The effects of using geometry software supported by digital daily life photographs on geometry learning. Procedia-Social and Behavioral Sciences, 2(2), 2824-2828.
Guay, R. B., & McDaniel, E. D. (1977). The relationship between mathematics achievement and spatial abilities among elementary school children. Journal for Research in Mathematics Education, 211-215.
Gueven, B., & Temel, K. (2008). The effect of dynamic geometry software on student mathematics teachers' spatial visualization skills. TOJET: The Turkish Online Journal of Educational Technology, 7(4).
Guven, B. (2012). Using dynamic geometry software to improve eight grade students' understanding of transformation geometry. Australasian Journal of Educational Technology, 28(2).
Healy, L., & Hoyles, C. (2002). Software tools for geometrical problem solving: Potentials and pitfalls. International Journal of Computers for Mathematical Learning, 6(3), 235-256.
Hogan, T. P., & Brezinski, K. L. (2003). Quantitative estimation: One, two, or three abilities? Mathematical Thinking and Learning, 5(4), 259-280.
Huang, S.-H., Wu, T.-T., Chen, H.-R., Yang, P.-C., & Huang, Y.-M. (2012). Mathematics Assisted Instruction System of M/U-Learning Environment. Paper presented at the Wireless, Mobile and Ubiquitous Technology in Education (WMUTE), 2012 IEEE Seventh International Conference on.
Hung, P.-H., Hwang, G.-J., Lee, Y.-H., & Su, I.-H. (2012). A cognitive component analysis approach for developing game-based spatial learning tools. Computers & Education, 59(2), 762-773.
Jones, G., Taylor, A., & Broadwell, B. (2009). Estimating linear size and scale: Body rulers. International Journal of Science Education, 31(11), 1495-1509.
Jones, M. G., Gardner, G. E., Taylor, A. R., Forrester, J. H., & Andre, T. (2012). Students' accuracy of measurement estimation: Context, units, and logical thinking. School Science and Mathematics, 112(3), 171-178.
Karaman, T., & Toğrol, A. Y. (2009). Relationship between gender, spatial visualization, spatial orientation, flexibility of closure abilities and performance related to plane geometry subject among sixth grade students. BOĞAZİÇİ ÜNİVERSİTESİ EĞİTİM DERGİSİ, 26(1).
Keller, J. M. (1987). Development and use of the ARCS model of instructional design. Journal of instructional development, 10(3), 2-10.
Kerr Jr, D. R. (1979). A Case for Geometry: Geometry Is Important, It Is There, Teach It. Arithmetic Teacher, 26(6), 14.
Ketamo, H. (2003). An adaptive geometry game for handheld devices. Educational Technology & Society, 6(1), 83-95.
Koedinger, K. R. (1998). Conjecturing and argumentation in high-school geometry students. Designing learning environments for developing understanding of geometry and space, 319-347.
Kucian, K., Grond, U., Rotzer, S., Henzi, B., Schönmann, C., Plangger, F., . . . von Aster, M. (2011). Mental number line training in children with developmental dyscalculia. NeuroImage, 57(3), 782-795.
Large, A., Beheshti, J., Breuleux, A., & Renaud, A. (1996). Effect of animation in enhancing descriptive and procedural texts in a multimedia learning environment. Journal of the American Society for Information Science, 47(6), 437-448.
Levine, D. R. (1982). Strategy use and estimation ability of college students. Journal for Research in Mathematics Education, 350-359.
Lin, H.-C. K., Chen, M.-C., & Chang, C.-K. (2015). Assessing the effectiveness of learning solid geometry by using an augmented reality-assisted learning system. Interactive Learning Environments, 23(6), 799-810.
Linn, M. C., & Petersen, A. C. (1985). Emergence and characterization of sex differences in spatial ability: A meta-analysis. Child development, 1479-1498.
Maguire, E. A., Gadian, D. G., Johnsrude, I. S., Good, C. D., Ashburner, J., Frackowiak, R. S., & Frith, C. D. (2000). Navigation-related structural change in the hippocampi of taxi drivers. Proceedings of the National Academy of Sciences, 97(8), 4398-4403.
Martin-Dorta, N., Sanchez-Berriel, I., Bravo, M., Hernandez, J., Saorin, J. L., & Contero, M. (2014). Virtual Blocks: a serious game for spatial ability improvement on mobile devices. Multimedia Tools and Applications, 73(3), 1575-1595.
Masendorf, F. (1995). Training learning-disabled children's spatial ability by computer games. European Education, 27(2), 49-58.
Merchant, Z., Goetz, E. T., Keeney-Kennicutt, W., Kwok, O.-m., Cifuentes, L., & Davis, T. J. (2012). The learner characteristics, features of desktop 3D virtual reality environments, and college chemistry instruction: A structural equation modeling analysis. Computers & Education, 59(2), 551-568.
Mistretta, R. M. (2000). Enhancing geometric reasoning. Adolescence, 35(138), 365.
Montague, M., & van Garderen, D. (2003). A cross-sectional study of mathematics achievement, estimation skills, and academic self-perception in students of varying ability. Journal of Learning Disabilities, 36(5), 437-448.
Moreno, R., & Mayer, R. E. (1999). Cognitive principles of multimedia learning: The role of modality and contiguity. Journal of educational psychology, 91(2), 358.
Okagaki, L., & Frensch, P. A. (1994). Effects of video game playing on measures of spatial performance: Gender effects in late adolescence. Journal of applied developmental psychology, 15(1), 33-58.
Olkun, S. (2003). Comparing computer versus concrete manipulatives in learning 2D geometry. Journal of Computers in Mathematics and Science Teaching, 22(1), 43-46.
Olkun, S., Altun, A., & Smith, G. (2005). Computers and 2D geometric learning of Turkish fourth and fifth graders. British Journal of Educational Technology, 36(2), 317-326.
Panaoura, G., Gagatsis, A., & Lemonides, C. (2007). Spatial abilities in relation to performance in geometry tasks. WORKING GROUP 7. Geometrical Thinking 954, 1062.
Pittalis, M., Mousoulides, N., & Christou, C. (2007). Spatial ability as a predictor of students’ performance in geometry. Paper presented at the Proceedings of the Fifth Congress of the European Society for Research in Mathematics Educations (CERME 5).
Rafi, A., Anuar, K., Samad, A., Hayati, M., & Mahadzir, M. (2005). Improving spatial ability using a Web-based Virtual Environment (WbVE). Automation in construction, 14(6), 707-715.
Roberts, M. L., & Wortzel, L. H. (1979). New life-style determinants of women's food shopping behavior. The Journal of Marketing, 28-39.
Shih, S.-C., Kuo, B.-C., & Liu, Y.-L. (2012). Adaptively Ubiquitous Learning in Campus Math Path. Educational Technology & Society, 15(2), 298-308.
Siegler, R. S., & Booth, J. L. (2005). Development of numerical estimation. Handbook of mathematical cognition, 197-212.
Smith, I. M. (1964). Spatial ability: University of London Press.
Sowder, J. T. (1992). Estimation and number sense.
Thom, R. (2002). Measurement? It's Fun! Didn't You Guess? Australian Primary Mathematics Classroom, 7(2), 26.
Van Hiele, P. M. (1959). The child’s thought and geometry: Brooklyn, NY: City University of New.
Waller, D. (2000). Individual differences in spatial learning from computer-simulated environments. Journal of Experimental Psychology: Applied, 6(4), 307.
Wallner, G., & Kriglstein, S. (2012). DOG eometry: teaching geometry through play. Paper presented at the Proceedings of the 4th International Conference on Fun and Games.
Wijers, M., Jonker, V., & Drijvers, P. (2010). MobileMath: exploring mathematics outside the classroom. ZDM, 42(7), 789-799.