Abstract: In a computer-implemented educational environment, four particular features are provided, which may be used separately or in combination, to drive the instruction of a particular curriculum, e.g. the instruction of fractions. In another implementation, educators and authors may use permutations and combinations of such features to construct in a graphical user interface a progression of interactive elements which help guide a student from visual concepts to procedures, such as equations and formulas. In a particular implementation, by using these features carefully, a curriculum author may design instructional sequences that provide careful, step-by-step sequences that help students progress from understanding the visual concepts, e.g. of fractions, to mastering procedures, e.g. fractions equations.

Abstract: Introduced herein is a technique that includes digital opening math discussions (“openers”) and digital dosing math discussions (“closers”) through the use of manipulative models in combination with well-authored and strategically placed sticky notes that can contain teacher instructions (“teacher ‘i’s”) and through the user of strategic feedback. This technique allows teachers to gain confidence while delivering research-based instruction.

Abstract: In a computer-implemented educational environment, four particular features are provided, which may be used separately or in combination, to drive the instruction of a particular curriculum, e.g. the instruction of fractions. In another implementation, educators and authors may use permutations and combinations of such features to construct in a graphical user interface a progression of interactive elements which help guide a student from visual concepts to procedures, such as equations and formulas. In a particular implementation, by using these features carefully, a curriculum author may design instructional sequences that provide careful, step-by-step sequences that help students progress from understanding the visual concepts, e.g. of fractions, to mastering procedures, e.g. fractions equations.

Abstract: In a computer-implemented educational environment, four particular features are provided, which may be used separately or in combination, to drive the instruction of a particular curriculum, e.g. the instruction of fractions. In another implementation, educators and authors may use permutations and combinations of such features to construct in a graphical user interface a progression of interactive elements which help guide a student from visual concepts to procedures, such as equations and formulas. In a particular implementation, by using these features carefully, a curriculum author may design instructional sequences that provide careful, step-by-step sequences that help students progress from understanding the visual concepts, e.g. of fractions, to mastering procedures, e.g. fractions equations.