This is the second of a two-part series about enhancing spatial reasoning among kindergarten students. The first appeared in the April/May 2017 issue of Canadian Teacher Magazine.
More than two decades of research has demonstrated that spatial ability is connected to understanding numeric quantities (i.e., subitizing) and to early numeracy performance, and that better spatial reasoning improves the quality of children’s early mathematics performance.
Spatial reasoning is not a single ability, skill or process. It incorporates numerous concepts, processes and tools to represent and communicate ideas about space and spatial relationships. In the 2015 publication Spatial Reasoning in the Early Years edited by Brent Davis, researchers Yukari Okamoto, Donna Kotsopoulos, Lynn McGarvey and David Hallowell identify four key components of spatial skills. They are:
- visualization and representation i.e., maps and models (being able to “see” the relationship among stationary objects in reality and/or in graphic representations);
- navigation i.e., perspective taking and self-locomotion (being able to see the changing relationships among moving objects);
- mental rotation and transformation of static and dynamic (moving) objects;
- recognizing, composing, and decomposing stationary geometric shapes and figures.
Several researchers have investigated the use of video programs, software, games and tablet and phone apps for the spatial training of young children. In their 2014 article “Finding the Missing Piece: Blocks, Puzzles, and Shapes Fuel School Readiness,” author-researchers Verdine, Golinkoff, Hirsh-Pasek and Newcombe explore current research on spatial and geometric instruction for three- to six-year-olds.
Verdine and his co-authors urge caution about the use of video games, computer programs and apps for children aged two to six because of the importance of adult interaction, which is what precipitates the development of spatial language and gestures. They write: “In general, electronic toys tend to cut interactions with adults out of the equation, which may have ramifications for learning beyond language…. People are powerful for young children and their actual physical presence and involvement seems to promote children’s learning, possibly because of their contingent responses to children.”
According to those four scholars, aspects of electronic and digital technology must be designed carefully for use with preschoolers and kindergarten students. The technology must provide age-appropriate content as well as respond to the learner’s input contingently, adjusting the level of instruction to scaffold the experience. It goes without saying these days, but the authors also point out that the digital resource must have an intuitive interface. They also assert that few toys and apps appear to have been constructed with these principles in mind.
Faced with an ever increasing number of children’s mathematics apps and software and advertiser hyperbole about the benefits of such educational technology, how can educators select the best instructional aids from among them? We should turn to the experts. The Ontario Mathematics Gazette is one source of intelligent information on the subject. Markus Wolski, Agnes Grafton, Ross Isenegger and Greg Clarke are experienced teachers who are developing interactive electronic learning tools for desktop as well as iOS and Android devices for the Ontario Ministry of Education. The ministry offers them at www.mathies.ca. One of their digital resources is a virtual pattern block device, similar to the physical ones commonly available in classrooms. It’s made up of an unlimited number of triangles, hexagons and other shapes that can be placed, rotated and manipulated in a workspace to model patterns, show number operations or represent fractions. You can find out about the latest digital tool developments in the “mathies” project by signing up for email updates at http://mathclips.ca/WhatsNewEmailList.html.
There are other good sources of information. In its 2015 publication, Inspiring Your Child to Learn and Love Math: Module Two Fact Sheet – Kindergarten Count Together, the Council of Ontario Directors of Education (CODE) recommends the TVOntario online video game Marigold’s Shapeville. It can be found at www.tvokids.com/games/shapeville. At the same site one can also find Sandy Math Shapes, and Melvin’s Gather and Guess. In a similar vein, educators can also find another 33 geometric and spatial online games hosted by the US-based PBS (Public Broadcasting Service) at http://pbskids.org/games/shapes/, as well as numerous mapping and spatial games which can be found among 139 other PBS online games at http://pbskids.org/games/problem-solving/.
Another reputable site is Simon Fraser University’s Geometry for Young Learners (G4YL) at http://www.sfu.ca/geometry4yl/triangles.html. Led by Dr. Nathalie Sinclair, Geometry for Young Learners is a group of mathematics educators working together to improve student learning. One of the group’s goals is to identify effective ways of allowing young children to develop sophisticated mathematical ideas while drawing on their powerful visual and kinesthetic capacities. This site features access to Web Sketchpad, a type of dynamic geometry software (DGS) considered as a powerful tool for improving student learning. Incorporating an engaging visual component, it allows learners to explore, test conjectures, discover patterns and think creatively. The basic tools of DGS are more than appropriate for the primary school mathematics curriculum. Students are excited to interact with the software and it offers many opportunities for collaboration and discussion. The group has also developed and posted a few lessons at the primary level on their site.
An excellent and very large US site (similar to the SFU and mathies.ca site above) is Illuminations, a project of the US National Council of Teachers of Mathematics (NCTM). The site, which services each of the conventional math strands from Pre-K to grade 12, features many spatial and geometric online activities, lists its mission as helping teachers access quality standards-based resources for teaching and learning mathematics, including interactive tools for students and instructional support for teachers. Located at https://illuminations.nctm.org/Content.aspx?id=58, the site offers 17 online geometric and spatial reasoning digital games or activities suitable for pre-K to kindergarten students optimized for tablet and desktop, though I found they ran consistently best on Internet Explorer. You can find games and activities such as Concentration with shapes, Shape Cutter, Shape Tool, Making Triangles, Geometric Solids, Lady Bug Mazes, Tangram Puzzles, Making Rectangles, and Turtle Pond at https://illuminations.nctm.org/Search.aspx?view=search&type=ac&st=g&gr=Pre-K-2 or search the site with the following search criteria: Interactive, NCTM Standards, Pre-K-2, Geometry.
The above mentioned geometry activities are only a small fraction of the material you can find on Illuminations. It is a vast site, containing more than 700 mathematics lesson plans and 100 mathematics activities, which consist of virtual manipulatives, applets and games. With some help from adults, children can use the online math activities, play math strategy games against a computer or players from around the world. The site also offers seven free mobile apps for iOS and Android and thirteen Calculation Nation® games. All of the material—the lessons and interactives—are searchable by either NCTM’s Principles and Standards or by the United States Common Core State Standards, both of which strongly resemble Canadian curriculum standards.
Although arguably less engaging for young children than some of its competitors’ newer, visually and aurally stimulating games, another good interactive online option for developing spatial skills is IXL Math. Its kindergarten math section is well organized and businesslike and conforms to the criteria for high quality digital resources outlined by Verdine, Golinkoff, Hirsh-Pasek and Newcombe in their article. The guided activities allow children to discover the defining features of definition-focused shape categories, focusing on their properties such as the number of sides, vertices and edges, and asking them to classify and sort and count them. The IXL site contains approximately forty spatial and geometric activities for kindergarten organized into five mathematics sections: sorting/ordering/classifying, two-dimensional shapes, three-dimensional shapes, patterning, positions. Unfortunately, the site provides only ten free practices per day per computer unless you are willing to pay a $12.95 per child per month fee. It is located at https://ca.ixl.com/math/.
When choosing sites and apps for young children, the most important features are their ability to adapt to a child’s current level of spatial skills and its focus on positional language, geometric properties (e.g., number of sides, vertices and edges), and the classification and sorting of shapes—at least according to the experts.
Despite the excitement conjured by electronic and digital apps and programs and their seeming ubiquitous nature, the jury on them is still out. Author-researchers Verdine, Golinkoff, Hirsh-Pasek and Newcombe along with Jennifer Zosh and Andrew Filipowicz have compared the quantity and quality of the language children hear during play with a traditional (nonelectronic) and an electronic shape sorter designed to teach children about geometric shapes. In their 2015 article, “Talking Shape: Parental Language With Electronic Versus Traditional Shape Sorters” they write that traditional toys prompt more parental spatial language and more varied overall language than electronic toys: “This finding is troublesome in light of the many studies showing that early language exposure is important. The quantity and quality of language addressed to children is a key predictor of children’s later vocabulary and school success, and spatial language has important impacts on spatial skills.”
Age-appropriate content, the ability to adapt to a child’s learning trajectory, and their judicious use so as not to substantially limit interactions with adults are the keys to using digital resources for spatial instruction in the prekindergarten and kindergarten age group.
Verdine, B.N., Golinkoff, R.M., Hirsh-Pasek, K., & Newcombe, N.S. (2014, March). Finding the missing piece: Blocks, puzzles, and shapes fuel school readiness. Trends in Neuroscience and Education 3(1), 7–13. Retrieved from http://kathyhirshpasek.com/wp-content/uploads/2015/08/Verdine-et-al-2014TINE-Final.pdf.
Zosh, J., Verdine, B., Filipowicz, A., Golinkoff, R. M., Hirsh-Pasek, K., & Newcombe, N. S. (2015). Talking shape: Parental language with electronic versus traditional shape sorters. Mind, Brain and Education, 136-144. Retrieved from http://9cb.375.myftpupload.com/wp-content/uploads/2016/06/Talking-shape-Parental-language-with-electronic-versus-traditional-shape-sorters.pdf.
Verdine, B. N., Irwin, C. M., Golinkoff, R. M., & Hirsh-Pasek, K. (2014). Contributions of executive function and spatial skills to preschool mathematics achievement. Journal of experimental child psychology, 126, 37-51. Retrieved from http://9cb.375.myftpupload.com/wp-content/uploads/2016/06/Contributions-of-executive-function-and-spatial-skills-to-preschool-mathematics-achievement.pdf
ABOUT THE AUTHOR
Edward Schroeter, B.J., B. Ed., OCT, Reading Specialist, Kindergarten Specialist, Special Education Part 2, FSL-1, Library Resource-1, was trained and worked as a newspaper reporter and documentary video producer. He is a six-time national award-winning playwright and producer of theatre for young audiences. He has taught Core French, French Immersion SK, Grade 3 French Immersion, Grade 4 and kindergarten for the Kawartha Pine Ridge District School Board and the Peterborough County Board of Education, for the past 24 years. He has been published in educational magazines and blogs across Canada and currently reviews and writes math curriculum materials for young children for Nelson Canada.
This article is from Canadian Teacher Magazine’s Sept/Oct 2017 issue.