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EP-3759702-B1 - BEAD-ON-TILE APPARATUS AND METHODS

EP3759702B1EP 3759702 B1EP3759702 B1EP 3759702B1EP-3759702-B1

Inventors

  • RANKINE, Anthony, John

Dates

Publication Date
20260506
Application Date
20190224

Claims (15)

  1. An apparatus for providing instruction in at least one of mathematics and quantifiable sciences, the apparatus comprising: an instruction board formed from a plurality of instruction tiles (27), each of the instruction tiles (27) having predetermined plateau region instruction locations (11) thereon located within an instruction location plateau region framed by edges (14A, 15A, 16A) of two horizontal channels and one vertical channel (14, 15, 16), and a predetermined saturation state instruction location (17) thereon located outside the instruction location plateau region; and instruction pieces (24) configured to be received on the instruction tiles (27) at the predetermined plateau region instruction locations (11) and the predetermined saturation state instruction location (17).
  2. The apparatus of claim 1, wherein the predetermined saturation state instruction location (17) is located at the junction of the upper horizontal channel (15) and the vertical channel (16).
  3. The apparatus of claim 1, wherein the predetermined plateau region instruction locations (11) are arranged in a three-by-three zoned matrix.
  4. The apparatus of one of the preceding claims, wherein each instruction tile (27) has an edge and wherein edges of adjacent instruction tiles (27) adjoin to form the instruction board.
  5. The apparatus of one of the preceding claims, wherein said two horizontal channels (14, 15) and said one vertical channel (16) provide instruction piece sliding pathways.
  6. The apparatus of any one of the preceding claims, wherein the predetermined saturation state instruction location (17) is located outside the instruction location plateau region, in the top left corner.
  7. The apparatus of any one of the preceding claims, wherein the predetermined plateau region instruction locations (11) and the predetermined saturation state instruction location (17) are recessed into the instruction tile (27).
  8. The apparatus of any one of the preceding claims, wherein the predetermined plateau region instruction locations (11) and the predetermined saturation state instruction location (17) are bearing printed indicia (10).
  9. The apparatus of any one of the preceding claims, wherein the plurality of instruction tiles (27) are assembled into a unified tessellation.
  10. The apparatus of any one of the preceding claims, wherein the plurality of instruction tiles (27) have at least one edge and wherein the edges of adjacent instruction tiles (27) abut one another and are adjoined to form a tessellation that defines the instruction board.
  11. The apparatus of any one of the preceding claims, including at least one stencil (30-39) with an optional opening or cutout (40-49), wherein the stencil is a means for enforcing the setup of the correct stencil-specific instruction piece count and instruction piece pattern.
  12. The apparatus of any one of the preceding claims, including a plurality of stencils (39-39) wherein each of the stencils has an opening or cutout (40-49) that permits an underlying one of the predetermined plateau region instruction locations (11) or an underlying one of the predetermined saturation state instruction location (17) to be visible through the opening or cutout (40-49) when the stencil (30-39) is positioned on the instruction tile (27).
  13. A method for providing instruction in at least one of mathematics and quantifiable sciences, the method comprising: providing an apparatus according to any one of the preceding claims; and manipulating the instruction pieces (24) to the predetermined plateau region instruction locations (11) and the predetermined saturation state instruction location (17) in a predetermined order to perform a change of state operation relating to the at least one of mathematics and quantifiable sciences.
  14. The method of claim 13, wherein the instruction pieces are placed on the predetermined plateau region instruction locations (11) from left to right and in ascending rows.
  15. The method of claim 13 or 14 for performing 632M multiplication or 632M division, wherein M designates a multiplicand or divisor value for the 632M multiplication or 632M division, comprising: setting up an instruction board, designated 632M-Board, comprising a column of four instruction tiles for S-values, and an adjoining column of four rows of instruction tiles, a rank of the column of the four rows being one higher than the M value, followed by the steps of: (A) setting up a series of S-values 6, 3, 2, 1 from top to bottom rows in the S-value column of the 632M-Board; (B) setting up the 1M value in the adjoining column on both the bottom, next row up and top row; (C) adding the bottom row into the next row up, which yields 2M in the S=2 row; (D) duplicating the 2M value into the row above it (S=3 row); (E) adding the topmost row (S=6) downwards into the row beneath, which yields 3M in the S=3 row; and (F) duplicating the 3M value into the topmost row and the bottom row (S=1 and 6 rows), and (G) adding the bottom row into the topmost row, which yields 6M in the topmost row; or (F') duplicating the 3M value into the topmost row, and (G') doubling the topmost row in-situ; (H) setting up the 1M value in the bottom row (S=1); and (I) replicating on an instruction board detached from the 632-Board the add-shift process for multiplication or the subtract-shift process for division using the 632M-Board as the template for setting up values on the instruction board.

Description

Field of the Invention The present invention relates to apparatus and methods designed to provide children grounding, insights, and self-directed instruction in mathematics and the quantifiable sciences. Background of the Invention and Related Art Subitization is about the power of three. Every animal is innately equipped to make three field of view distinctions, namely right, center and left. The present invention taps into this power to subitize. Additionally, in humans there are vertical strata, namely, ground level, eye level and overhead. This overall creates a three-by-three zoned matrix totaling nine zones of alertness. Hence, radix-10 numericity is a natural fit for super-subitized perception in humans. Fingers and finger counting is irrelevant. Using modular components, the present invention has broad scope of application to all quantifiable science. However, radix-10 mathematics will be the focus of this disclosure because radix-10 mathematics is the first quantitative science children experience. As long as the invention taps into their subitization arsenal, children are innately equipped to auto-acquire the principles behind mathematics and other quantifiable sciences. The apparatus, on which they play and learn, must reinforce correctness and minimize the potential for goof-ups and self-doubt. Apparatus according to the invention, such as depicted in Fig. 1B in one of its many adaptable multi-register forms, in this case a three row/register, five rank, one tray setup, has no prior art. The closest facsimile, merely in terms of possessing a planar layout, was postulated from a hand sketch in the archives of the Royal Danish Library in 1908. Within a solitary, hand-written manuscript dating to 1615 titled "El Primera Nueva Coronica y Buen Gobierno" by its author, Felipe Guaman Poma de Ayala, is a sketch of what modern historians call the Ayala Yupana, an Incan abacus. Ayala's hand sketch is reproduced in Fig. 1A, rotated 90° counterclockwise. No other sketch like it exists and no physical embodiment of it has ever been unearthed. Nor does anyone know what tokens were used on the Ayala Yupana. Despite the fact that it is naturally designed for a radix-12 number system, several western-centric radix-10 numerical models have been force-fit so the Ayala Yupana functions as a planar, single register, radix-10 abacus. In 2001, Nicolino de Pasquale proposed a radix-40 model. Summary of the Invention The invention and preferred embodiments are defined in the appended claims. In one aspect of the invention, the preferred instruction site for radix-10 numeric state representations is a compact, super-subitized, square tile, on which instruction pieces are moved into instruction locations on an instruction board. In exemplary embodiments, the instruction site is referred to as a "Digit-Square," the instruction pieces are referred to as "beads," the instruction locations are referred to as "bead sites" and the instruction board is referred to as a "Candy Board." Sculpted into the design of the tile is a subitize-informed bead site layout that breathes life into the super-subitization perceptiveness capability of the human brain. A tenth bead site, representing a saturation state, comparable to all ten fingers outstretched, is located in the top left corner of each Digit-Square. Preferably, the appropriate cultural and language glyph is printed within the bounds of each bead site and on the tile. For example, the bead site layout of Fig. 2A depicts a right to left magnitude sequence (left is greater) with ascending row/echelons (above is greater), imprinted with conventional Hindu-Arabic digit glyphs, namely "0" through "9". Typographic glyphs act as stepping stones so that, in due course, children self-acquire adult symbol usage. As Figs. 6AA through 6JJ make clear, when beads occupy bead sites on a Digit-Square, the bead count, the bead pattern, and numeric value/state is reinforced by the numeric glyph in the next higher bead site. Fig. 6KK depicts the "TEN" saturation state. The invention applies the golden rule: without relatability, learning is imposition not acquisition. On the Digit-Square, starting at "0" incrementing to "TEN" involves eleven states and ten changes of state, as depicted in the eleven Figs. 6AA through 6KK. What children see visually are eleven states. What children don't see visually are the ten changes of state because those are mental constructs called counting, i.e. changes of state via incrementing. Another form of instruction site is the "Tray" tile. Compatible with the Digit-Square tile, the Tray tile is depicted in Fig. 3A in a plan view and in section views in Fig. 3B and Fig. 3C, also showing the preferred bead. Tray tiles serve as bead repository adjuncts to adjoining Digit-Squares. One or more tiles, such as Digit-Squares and Trays, may be assembled into a unified tessellation in an embodiment of an instruction board referred to as a "Candy Board" for the parlance of chil