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Pedagogically and research-based intelligent adaptive learning technology accesses and stays in the Zone of Proximal Development (ZPD) for each learner. That means it provides the right next lesson at the right level of difficulty at the right time. When work is easy, learners can do the work on their own without any help. It’s in their "comfort zone." If all the work a learner is asked to do is always in the comfort zone, no real learning will take place and the learner will eventually lose interest. Conversely, when the work is too hard, the learner becomes frustrated and will likely give up. The area between the comfort zone and the frustration zone is the one where true learning will take place – the optimal learning zone. It’s the area where a learner will need some help or will need to work hard to understand a concept or complete a task. By keeping the challenge appropriate, the learner is guided to be a mathematical ‘doer’ — someone who thinks and strategizes in ways they can apply in school and in their real life experience. This is optimal teaching and optimal learning.

The cognitive transformations triggered by tools have two sides, paralleling the kinds of effects discussed above. One side is learning effects with the tool. This recognizes the changed functioning and expanded capability that takes place as the user uses and gets used to particular tools. Impact occurs through the redistribution of a task‰s cognitive load between persons and devices (e.g. Pea, 1993; Perkins, 1993), including symbol-handling devices (e.g,. a spell checker) or across persons, mediated by devices and symbol systems (telephones, fax machines). As these examples suggest, such tools are all around us, but their possibility also invites the design of special-purpose tools for supporting various cognitive functions. For instance, experiments have shown that a computerized Reading Partner that provides ongoing metacognitive-like guidance improves students‰ comprehension of texts while they read with the tool (Salomon, Globerson, & Guterman, 1991).

Social Mediation by Cultural Artifacts

The role of tools and symbol systems as both reflecting and affecting the human psyche has long been recognized. But it is mainly due to the Russian sociocultural tradition of Vygotsky (e.g., 1978), Luria (1981), and Leont‰ev (1981), and their Western interpreters (e.g,. Cole & Wertch, 1996), that scholarly attention has focused on tools as social mediators of learning. Here we use ‹toolsŠ in a broad sense, including not only physical implements but technical procedures like the algorithms of arithmetic and symbolic resources such as those of natural languages and mathematical and musical notation.