BOX 6.3
Thinking Inside the Box

As an example of a very effective and imaginative low-tech system for supporting spatial thinking, a class of 9-year-olds was presented with a box. The contents were unknown to them: their challenge was to find out what was inside the box through an ingenious adaptation of spatial sampling. The top of the box was perforated with 100 holes, arranged in a 10 × 10 grid. The two axes were labeled from 1 to 10 and from A to J, thus ensuring that each hole could be given a unique spatial identifier. Next to the box was a sheet of paper, also laid out with an identical 10 × 10 grid with the same axis identifiers. The children were given knitting needles and first had to calibrate them to provide “depth” readings below the surface of the box when the needle was inserted into a hole and it touched whatever object was in the box. They created summary tables of their data (in effect, x-y-z coordinates) and then transferred the coordinate data onto the paper using Lego blocks for the Z coordinate. When they finished creating a Lego shape and surface, they were allowed to open the box. Inside was a three-dimensional model of a mountain range which they had, much to their excitement, recreated through a classic example of spatial thinking.


In the K–12 educational context, the implementation of a support system for spatial thinking entails an awareness of a series of five interlocking components, all of which must be addressed for the system to be implemented successfully. There should be programs to provide

  1. material support in the form of computer hardware, software, high-speed network access, tools, and supplies (e.g., disks, paper, pencils);

  2. logistical support in the form of technical support for the installation, maintenance, and upgrading of hardware and software;

  3. instructional support in the form of pre-service and in-service training programs for teachers;

  4. curriculum support in the form of educational goals, knowledge and performance standards, assessment procedures, unit and lesson plans, and supporting materials; and

  5. community support in the form of the recognition of the educational value of the support system and, therefore, the collaboration by stakeholders in providing students with opportunities for problem solving in real-world contexts (e.g., requests for assistance, internships, access to data).

Designed and implemented appropriately, systems for supporting spatial thinking can have three major effects in the K–12 education context. First, they can change how things are taught, which is important in itself, but more importantly, they can change what can be taught. Second, they can offer students a critical awareness of a crucial thought process that is either unknown or poorly understood because it is largely hidden from view and insufficiently appreciated at present. Third, they can be mind-enhancing: students can learn to use a powerful way of thinking, one that can have lifelong implications for problem solving in life and career contexts. If we are successful in the design and implementation of support systems, we can help to foster a generation of students who will become spatially literate (see Chapter 11).

A support system facilitates the process of spatial thinking: it empowers students. However, we have to distinguish clearly between two goals: (1) that of learning to think spatially and (2) that of learning to use a support system for spatial thinking per se.

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