Spatial skills are correlated with young children’s success in mathematics

Like many experienced kindergarten educators, I eagerly immersed myself in the tide of instructional reform launched by the Ontario Ministry of Education’s 2004 Literacy and Numeracy Strategy. I became a Reading Specialist and took special education courses.

Somehow during that turbulent time I missed the news that spatial reasoning and geometry had been found to be highly predictive of later mathematics achievement in school as well as ‘a key predictor’ of success in reading and problem solving. I was taken aback in July of 2016 when I found this information staring up at me from page 75 of my new curriculum, The Kindergarten Program 2016.

Reading and problem solving aside, cognitive scientists G. Farmer, Brian Verdine, and five other researchers established in 2013 that spatial reasoning plays an important role in predicting overall mathematics success with even greater power than general mathematics scores. They demonstrated there is a relationship between spatial reasoning and student success in mathematics.

Further educational research offers more specific evidence of this connection. A 2014 study on the contribution of spatial skills and executive function to preschool mathematics achievement by Brian N. Verdine, Casey M. Irwin, Roberta Michnick Golinkoff, and Kathryn Hirsh-Pasek suggests that spatial skills uniquely predict 27 per cent of the variation in mathematics skills among four-year-old children from diverse social classes.

Spatial reasoning is a significant feature of our daily lives as we navigate through space in our world. It also figures prominently in 21st century STEAM careers (Science-Technology-Engineering-the Arts/Architecture-Math).

Spatial and geometric reasoning is not a single ability, skill, or process. It involves several concepts, processes, and tools for representing and communicating ideas about space and spatial relationships. Spatial Reasoning in the Early Years, edited by Brent Davis, researchers Yukari Okamoto, Donna Kotsopoulos, Lynn McGarvey, and David Hallowell explains that these skills include perspective taking, visualizing, locating, orienting, dimension shifting, path-finding, sliding, rotating, reflecting, diagramming, modelling, symmetrizing, composing, decomposing, scaling, map-making, and designing.

Pre-K and Kindergarten is an optimum time to teach spatial and geometric skills

When I mentioned my discovery about the importance of spatial reasoning education in kindergarten to a long-time friend of mine, an I.T. supply chain management specialist for a major national retailer, he quickly came back with a thought-provoking question: “Why do young children need to spend more time learning these particular skills?”

His probing question caused me to re-examine my unbridled enthusiasm for early spatial education. I asked myself, “Why this learning? Why at this age?”

As it turns out, there is a straightforward answer. During the past 25 years, educational researchers have confirmed that the period from pre-school (age two) to grade two (age seven) is an optimum time to improve and expand a child’s spatial skills. In their 2014 article, “Finding the missing piece: blocks, puzzles, and shapes fuel school readiness,” Brian Verdine and his three co-authors, Roberta Michnick Golinkoff, Kathryn Hirsh-Pasek, and Nora S. Newcombe, present convincing evidence that spatial skills and geometry deserve a substantial investment of time, effort, and resources in kindergarten and pre-school programs because:

• by 2 years of age children appear to have the tools necessary to begin to learn shape names and accurately apply them,
• spatial skills are malleable and can be improved with practice,
• improvements in spatial skills endure over time, and,
• improvements on one type of spatial reasoning task frequently transfer to other types of spatial tasks even at relatively young ages.

School is an ideal setting for improving spatial skills

Another compelling reason to give priority to spatial reasoning instruction in pre-k and kindergarten classrooms is that the school setting seems to be an ideal place for children to improve these skills. In their frequently quoted 1998 study, “Environmental Input and Cognitive Growth: A Study Using Time-Period Comparisons,” published in the August issue of Child Development, Janellen Huttenlocher, Susan Levine, and Jack Vevea, show that children’s spatial abilities grow during the school year but stall during the summer months.

A matter of gender and socio-economic equity

Improving spatial skills has also been shown to overcome gender and socio-economic barriers to success in mathematics at school and to lead students to gainful employment in the labour force – especially certain well paying careers in science, technology, engineering, art and architecture, and mathematics.

Important for all young learners

In their article, Verdine and his colleagues wrote that improving young children’s spatial education is more than a matter of leveling the playing field for certain students – it is an issue for all young learners: “… (A)lmost all children have relatively paltry access to formal spatial instruction, making it likely that the spatial and mathematical skills of most children would improve dramatically with good access to a “spatial education” delivered via goal-oriented activities and with awareness of the importance of spatial language and gestures.”

There are many techniques to improve spatial reasoning

The research literature indicates that it is relatively straightforward to improve the spatial reasoning abilities of children when they are young. It can be accomplished when adults interact with children during their play using a variety of playful, appealing, yet effective spatial toys and activities such as wooden unit blocks, puzzles, Duplo®, Magna Tiles®, pattern blocks, attribute blocks, and paper folding activities such as origami and paper airplane making. A key factor influencing spatial skills development in these examples are the spatial words, spatial gestures, questions and challenges that the toys and the play evoke from adults.

According to Temple University researcher Nora Newcombe, parents and kindergarten educators can also support young children’s spatial reasoning skills by reading them “spatially challenging picture books” such as Zoom by Istvan Banyai, Actual Size by Steven Jenkins and Shrinking Mouse by Pat Hutchins. These books examine scenes from various angles or perspectives, include maps and spatial language, or feature illustrations that require close spatial attention to decipher their meaning.

Digital apps, programs, games, and videos for spatial training

Some researchers have investigated the use of video programs, video games, and apps for the spatial training of young children. In their 2014 article mentioned earlier, Verdine, Golinkoff, Hirsh-Pasek, and Newcombe urge caution about using video games, programs, and apps with children aged two to six because of the importance of adult interaction and feedback in developing spatial language and gestures. “In general,” they write, “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 the aforementioned quartet of author-researchers, electronic and digital technology must be designed carefully for use with preschoolers and kindergarteners. Besides providing age-appropriate content, the technology must respond to the learner’s input contingently, adjust the level of instruction to scaffold the experience, and have an intuitive interface. Verdine and his colleagues have found that few toys and apps seem to have been constructed with these principles in mind. They also point out that the educational benefits claimed by such technology are often unsubstantiated, and that parents and educators may not be getting the information they need to make the best choices when purchasing and using these products.

How can we determine the best digital activities for spatial training?

Faced with a rapidly increasing number of children’s mathematics apps and software, how can educators and parents select the best instructional tools from among them? Like anyone else, we should turn to the experts. A good starting point is the U.S.-based National Council of Teachers of Mathematics (NCTM) and their creation of “illuminations.” The K-2 searchable data base is located at https://illuminations.nctm.org/Search.aspx?view=search&type=ac&gr=Pre-K-2.

The Ontario Mathematics Gazette is another source of sound 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 Association for Mathematics Education and the Ontario Ministry of Education. The ministry offers them at www.mathies.ca. 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 .

The Ontario Educational Resource Bank (OERB), meanwhile, provides educators with three digital kindergarten interactive learning resources: Build Shapes, Grocery Store, and Positional Language. Each is designed to develop understanding of 2D shapes, 3D figures, and spatial language. The OERB web site can be found at https://resources.elearningontario.ca/. You can also find the zip files for these three digital resources on the kindergartenspatialreasoning.wikispaces.com site located at: https://kindergartenspatialreasoning.wikispaces.com/Digital+apps+and+software+resources# .

Next steps for pre-Kindergarten and Kindergarten educators

Given the importance of spatial reasoning and geometry to success in mathematics and in life, and the ease of improving these skills, it seems to me that pre-K and Kindergarten educators like me owe it to our young students to learn as much as possible about spatial reasoning and geometry, children’s typical learning trajectories in these areas, high yield strategies that improve learning in this area, and about how to incorporate spatial learning opportunities in our mathematics programs.

There are several great places to start this journey. One is the site M4YC (mathematics for young children), which offers free lesson packages. Two others are the EduGAINS — Mathematics site and a kindergarten educators’ collaborative inquiry knowledge building wiki, kindergartenspatialreasoning, and their Twitter feed. Each hosts a variety of spatial activity suggestions. One of the two best resources in my opinion, however, is the comprehensive 2014 book, Learning and Teaching Early Math: The Learning Trajectories Approach by Douglas H. Clements and Julie Sarama. Teachers who have studied the learning trajectories approach and used it in their classrooms found the learning trajectories “a great approach to teaching math” in Kindergarten: “It allowed us to understand early childhood mathematical development and provided us with engaging activities to incorporate into the classroom.” The second is the 2016 publication by Joan Moss, Catherine D. Bruce, Bev Caswell, Tara Flynn, and Zachary Hawes, Taking Shape: Activities to Develop Geometric and Spatial Thinking Grades K-2. It contains 32 well designed spatial activities which are well explained and easy for busy classroom teachers to implement.

Edward Schroeter, B.J., B.Ed., OCT, is a Reading Specialist, Kindergarten Specialist, with Special Education, French as a Second Language, and Library Resource Teacher qualifications. He was trained and worked as an newspaper reporter and documentary video producer. He is a four-time national award-winning playwright and former producer of historical theatre for young audiences. During the past 25 years that he has taught Grade 4, Core French, French Immersion SK, Grade 3 French Immersion, and Kindergarten for the Kawartha Pine Ridge District School Board and one of its predecessor boards, the Peterborough County Board of Education.

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