Geocaching is an activity that uses the GPS technology on your mobile device to allow for some real-life treasure hunting. Members of this community are invited to hide small boxes—”geocaches”—and log their location on a free, downloadable app. Once the geocache is logged, it will show up as a blip on the map of other users of the app, who can then find it for themselves.
There is almost always a “logbook” inside the geocache, where people can write their names and the date of discovery. Depending on the size of the box, users also may leave other items—notes, trinkets, stickers, etc.—with the assumption that other discoverers can exchange items.
Making it a point to find geocaches during a vacation, or depending on your location, a trip to the corner store, can mathematize an otherwise ordinary situation. Using maps is a superb way to strengthen children’s spatial reasoning skills. Letting them take the lead in navigating the way to a geocache is a great way to get kids practicing their math in a way is both fun and practical.
Children inherently have strong spatial reasoning skills. In his presentation at Erikson Institute’s International Symposium, researcher Jan de Lange makes this point succinctly.
“Imagine you have a house with forty rooms. I can bet you that your three year old will know exactly where the sweets or his favorite toys are after you show him once–in three dimensions!”
In Walk with Rosie, a part of our Focus on the Lesson video series, preschool students were able to draw accurate maps of the route they took through an obstacle course set up in their classroom. Bolstering these inherent strengths with real-world map use, therefore, can start very young.
According to the official website, there are 548 geocaches hidden within a 5-mile radius of Erikson Institute in Chicago, and millions more hidden worldwide. On the app, each geocache is given a rating on how difficult it is to find, so users can challenge themselves accordingly.
Do note that geocaches and their contents are produced entirely by users of the app; therefore, upon discovering a geocache, adult supervision is suggested (although hopefully not needed!).
From recognizing octagonal stop signs to remembering where the cookies are stored, children encounter geometry early and often. Regularly engaging children with some of the names, rules, and applications involved in geometry will allow them to make the most of their natural skills in this area. There are plenty of children’s books that kids love to further pique their interest. We’ve listed a few of our favorites here.
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Shapes, Shapes, Shapes by Tana Hoban
Tana Hoban has a number of children’s books featuring eye-catching photos centered around a single theme. In this case, you guessed it, she focuses on shapes and the various ways they appear in everyday life. With no text and not even a story to follow, this book is great for inspiring children to think and talk about the shapes they encounter in their own lives.
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Changes, Changes by Pat Hutchins
Changes, Changes tells the story of a wooden family living in a house of blocks. Whenever a problem occurs, they must come up with a shape-based solution. When their house catches fire, for instance, they engineer a fire engine out of blocks. Kids can “play along” with the blocks in the classroom or come up with their own geometric solutions to the various calamities the family encounters.
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Me on the Map by Joan Sweeney
Map-reading can be a challenging concept for children (and adults!) to grasp, but Me on the Map presents the topic in a kid-friendly, step-by-step manner. Starting with a map of a young girl’s room, the book “zooms out” to display maps of increasing complexity: a map of her house leads to a map of her street; a map of her continent leads to a map of the world. After reading Me on the Map, children may be eager to construct their own maps of their bedroom, classroom, house or school.
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We’re Going on a Bear Hunt by Michael Rosen and Helen Oxenbury
A family sets out to catch sight of a bear but encounters several obstacles on the way in this classic children’s chant story. The descriptions of how they handle these hurdles (walking through a snowstorm, for example) is great practice for positional prepositions, which can be especially difficult for children to master. The sounds that accompany the family’s escapade (splashing through water, squelching through mud), keeps youngsters entertained and involved throughout the book.
This article from NPR’s ongoing education blog discusses the strength of a familiar low-tech toy: the block.
Even amid a technological revolution in teaching, which is bringing tablets, apps, and smartboards into more and more early learning classrooms, the block maintains its place as a time-tested learning tool.
Part of its strength in this regard is its ability to bring out multiple math ideas at once. Students will strengthen spatial reasoning skills as they try to avoid making their structures topple over. Students will also reinforce their geometric knowledge, as they pick out all of the squares or make a rectangle out of two triangle-shaped blocks.
Even ideas like fractions and algebra can be introduced on a basic level with this low-tech toy.
“Essentially they’re solving for X,” says Todd Erickson of Standford University’s Bing Nursery School. “They’ve got one piece on one side and one piece on the other and a distance to fill. So what is that amount going to be?”
Research suggests that finding a healthy mix of low- and high-tech learning tools is probably best for young learners overall. High-tech toys allow for flexibility and experimentation but can easily become a distraction for children. Low-tech toys, while potentially more limited in application, provide engaging, kinesthetic experiences.
A preschool student puts together shape blocks to make larger, more complicated shapes from memory. In doing so, she makes connections between the various configurations she is constructing.
Focus on the Child videos are taken from one-on-one interviews with individual children. The interviews are designed to elicit evidence of children’s mathematical thinking. They are not teaching episodes or formal assessments.
This link jumps into books that give children a chance to explore spatial reasoning. Over and under, going that direction or going the other direction, mapping, perspective. There are plenty of ways to get young children to think dynamically about the mathematical world around them. And when using picture books to support math and spatial thinking, teachers and parents can entice children with creative storytelling.
This third grade teacher leads a gallery walk with her students with the purpose of having children explain their thinking with peers. She discusses the importance of such a strategy and the opportunities that a gallery walk can have with children who are wrestling with math concepts.
The lesson explores geometry, measurement, and children’s abilities to grapple with different geometrical shapes filling an area.
To view the set-up for this kind of classroom activity, this video features a Gallery Walk from another classroom.