Abstract:
An apparatus and method for teaching mathematics to children is disclosed. In one embodiment, the apparatus comprises a flat, ruler-like rod having expressed on one face a vertically arranged base-ten number line; lips at the ends of the rod; spaced-apart grooves on the back face of the rod; and an attached sleeve sized to snugly accommodate the rod and to slide thereon while indicating respective numerals on the number line. The sleeve is prevented from being separated from the rod by the lips on the rod. The sleeve has a transparent portion to frame individual numerals on the number line as the sleeve slides along the rod. On the inner portion of the reverse side of the sleeve a projection made of flexible material strikes the interior portion of individual grooves as the sleeve slides along the rod. In operation, the apparatus provides an audible and felt “click” as the sleeve passes over each numeral. A method is described for using the apparatus to teach elementary school children math concepts using a vertically oriented number line.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
   Not applicable. 
   BACKGROUND—FIELD OF INVENTION 
   This invention relates to tools and methods for teaching math concepts to young children and specifically to devices carrying number lines. 
   BACKGROUND 
   There is an unmet need for a simple device and method for teaching math to young children by utilizing their near-instinctive understanding that higher means “more” and lower means “less.” Currently, educators teach math to young children through the use of equations, inequalities, and number lines that are expressed horizontally and that are meant to be read left-to-right as one would read a sentence. At the same time, they use terms like “higher,” “bigger than,” “more” and “larger” even though none of the instructional tools appears to be any of those things. This method of teaching math is counter-intuitive to a very young child—who has barely learned to read (if at all), may or may not know left from right, and in any event has no experiences in the real world that would lead to the conclusion that relative placement of a numeral to the right means “higher” or that placement to the left means “lower.” 
   There is an unmet need for simple math instruction devices that provide visual, aural and tactile stimuli as the child uses the device to solve, and comprehend the meaning of, simple math problems. Generally, children learn best when information is presented through a combination of sight, hearing and touch. Many children have a particular affinity for a particular mode of learning, and they may be categorized as “visual learners, “aural learners” or “tactile learners”. Other children may have particular deficits (more or less serious) in visual, auditory or tactile processing. Still other children have physical disabilities, such as blindness, that may wholly or partially foreclose a mode of learning. If children are able to hold and manipulate a math instruction tool that provides visual, aural and tactile stimulation, mathematical information has a far better chance of being understood and retained. With the notable exception of the abacus, no simple math calculation tool combines sight, hearing and touch in one device. 
   There is an unmet need for a means to teach young children negative numbers. It is generally thought that kindergarten through third-grade children are not typically ready to grasp this concept. As a result, while a child is encouraged to subtract 3 from 5, or to add from zero to infinity, the child is discouraged—or even forbidden—from subtracting 5 from 3. By the time the negative number concept is taught in later grades, the child&#39;s sense of numbers is often so ingrained that the very notion of something less than zero seems alien. A device that provides an easy way for a young child to do simple problems that result in negative-number answers would allow for earlier introduction of an important math concept and may prevent the cognitive dissonance often generated when introduction occurs later in a child&#39;s development. 
   SUMMARY 
   My invention is an apparatus and method for teaching mathematics to children. In all of the embodiments discussed herein, a hand-held structure bears a base ten number line with vertically oriented numerals. 
   By “number line,” I mean the commonly understood meaning of the term. The American Heritage Dictionary (2000) defines a “number line” as “line that graphically expresses the real numbers as a series of points distributed about a point arbitrarily designated as zero and in which the magnitude of each number is represented by the distance of the corresponding point from zero”. For purposes of this application, I adopt this definition with the understanding that (a) the line may be drawn or formed by a physical element of a structure, such as a linear edge of a rod or a linear slit in a panel; (b) the “points” may be expressed on or in proximity to the line; and (c) the “points” may be expressed as marks, structural elements or as the numbers themselves. In other words, a “number line,” reduced to its essential elements, is a substantially visible, two-dimensional and linear line along which an evenly spaced and sequentially ordered series of real numbers extend from the number zero (e.g. 0, 1, 2, 3 . . . or −15, −10, −5, 0, 5, 10, 15 . . .) in such a way that the user can visually perceive the physical distance of a number from other numbers, and particularly from the number zero. 
   By “vertically,” I mean that the numerals are oriented so that they can be read most easily when the relevant line of the number line is perpendicular to the ground or to the user. In contrast, the numerals of standard rulers, slide rules and number lines are expressed horizontally. 
   A slidable member capable of visually indicating respective numerals on the number line engages with the structure and slides thereon. In the preferred embodiment, the slidable portion includes a flexible projection that strikes the interior of grooves on the structure so that sound and vibrations are created as the slidable portion slides along the structure. The grooves are positioned so that a sound and vibration is made as each numeral on the number line is indicated by the slidable portion. Various simple math concepts, including number recognition, addition, subtraction, place value, inequality, negative numbers and simple algebra can be practiced with the invention. 
   Alternative embodiments include a ruler incorporating the invention, a structure with interchangeable panels carrying different number lines, and a manual calculator incorporating a plurality of number lines and slidable members. The invention and all of the embodiments may bear a drawn line and drawn points, but the need for such additional visual aids is not essential where a number line device includes a slidable member to physically travel the distance between numbers and/or a sound-making means can aurally emphasize the number of points on the line that a slidable member has traveled. 
   Also claimed is a method for teaching simple math concepts to children, which method comprises the steps of providing a vertically arranged number line, providing an indicator to show individual numerals on the number line, and positioning the indicator to show mathematical concepts by reference to the more intuitively appealing high-low relationships between numerals. 
   OBJECTS 
   It is an object of the invention to provide a vertically oriented number line for teaching children math concepts. It is a further object to provide a simple device for teaching children math concepts through the manipulation of an indicator over a vertically oriented number line. It is a further object of the invention to provide a simple device for teaching math concepts to children that produces a visual, aural and tactile stimulus as math problems are solved using the device. It is a further object of the invention to provide a simple device that allows children to practice math problems for longer periods because the tool provides positive aural and tactile stimulation that is fun for the child. It is a further object of the invention to provide a simple device for teaching negative number concepts to young children. It is a further object of the invention to provide a simple manual calculator for use by children. It is a further object of the invention to provide a device that reenforces a child&#39;s comprehension of number relationships. It is a further object of the invention to provide a method of math instruction that teaches young children math concepts through the use of vertically arranged numerals on a number line. Further objects and advantages of the invention will become apparent from a consideration of the drawings and ensuing description. 

   
     DRAWING FIGURES 
     In the drawings, closely related figures have the same number but different alphabetical suffixes. 
       FIG. 1A  shows a front view of the preferred embodiment. 
       FIG. 1B  shows a rear view of the preferred embodiment. 
       FIG. 1C  shows a side view of the preferred embodiment. 
       FIG. 1D  shows an exploded view of the preferred embodiment. 
       FIG. 2  shows a front view of a second embodiment 
       FIG. 3  shows a perspective, partially exploded view of a third embodiment. 
       FIG. 4A  shows a front view of a fourth embodiment. 
       FIG. 4B  shows a back view of a fourth embodiment. 
       FIG. 4C  shows an end view of a fourth embodiment. 
       FIG. 5  shows a perspective view of a fifth embodiment. 
       FIG. 6  shows a front view of a sixth embodiment. 
   

   DESCRIPTION 
   A preferred embodiment of the math instruction tool of the present invention is illustrated in  FIGS. 1A through 1D . The math instruction tool has a flat rod  10  approximately the size and shape of a ruler (12″×1″×0.2″), it being understood that many different sizes can be used. It is contemplated that rod  10  can be made of any durable material including wood, plastic or metal. A sleeve  26  encircles rod  10  and is sized to snugly fit and slide along rod  10 . At each end of rod  10  is an attached lip  14  sized to prevent sleeve  26  from becoming disengaged from rod  10 . 
   On the front face of rod  10  is a series of numerals  22  arranged vertically in relationship, to the linear lines formed by the edges of rod  10 , as shown in FIG.  1 A. It is contemplated that the numerals in series  22  may be imprinted, printed in relief, and/or expressed in symbols such as braille. As shown in  FIG. 1B , on the back face of rod  10  is a plurality of transverse elliptical grooves  18 , spaced apart to correspond to the spacing of numerals in series  22 , it being understood that holes, projections, riffles or teeth could be used instead of grooves  18 . It is further understood that such grooves, etc., can be positioned on the front face of rod  10  or along either or both sides of rod  10 . 
   On the face of sleeve  26  is a transparent portion  34  sized to accommodate one numeral in series  22 . Transparent portion  34  may comprise empty space or can be made of transparent material such as plastic or glass. On the interior wall of the back portion of sleeve  26  is a projection  30  made of flexible material such as thin metal or plastic and sized and positioned to strike the interior of grooves  18  with sound-making force as sleeve  26  slides along rod  10 . It is understood that various slidable elements (e.g., an element sliding on a groove or track, a magnetized element sliding along a flat metal surface, etc.) could be used instead of a sleeve. 
   In operation, the user slides sleeve  26  along rod  10  to solve simple math problems, experiencing an audible and felt “click” as sleeve  26  passes over a numeral in series  22  while, simultaneously, transparent portion  34  “lands on” a number and projection  30  strikes the interior wall of the corresponding groove  18 . It is understood that other sound-making means, including electronic, could be used to generate sound as sleeve  26  passes over a numeral in series  22 . The user thus can perceive the differences in magnitude between individual numbers by seeing their distance from zero, moving sleeve  26  along the number line formed by series  22  and the edge(s) of rod  10 , and counting the number of heard and felt “clicks.” 
   As contemplated, rod  10  is to be held vertically, or, alternatively, laid face up on a surface with the end corresponding to the lowest numeral pointing at the user. 
   When used to facilitate number recognition, the child simply views series  22  and learns the numerical symbols and the order in which they are normally arranged. 
   When solving simple addition and subtraction problems, sleeve  26  is first positioned so that transparent portion  34  covers the first numeral in series  22  specified in the equation, then made to slide (up for addition, down for subtraction) such that sleeve  26  “clicks” as many times as called for by the second specified number in the equation. For example, to solve 4+3, the user positions sleeve  26  so that transparent portion  34  frames the numeral  4 , then slides sleeve  26  up until he or she has seen transparent portion  34  land on three successive numerals, heard three audible “clicks”, and felt three sets of vibrations as projection  30  passes over three grooves  18 . The user would then see the numeral  7  framed in transparent portion  34 . 
   When used to solve equations resulting in negative numbers (e.g., 3−4), the user positions sleeve  26  so that transparent portion  34  frames the numeral  3 , then slides sleeve  26  along rod  10  such that sleeve  26  “clicks” the specified number of times called for by the second number in the equation, yielding, in the example, the number −1. 
   When used to determine an inequality, sleeve  26  is first positioned so that transparent portion  34  frames the comparing numeral, and the child is instructed that, if sleeve  26  must slide up to reach the compared numeral, the comparing numeral is less than the compared numeral, and vice versa. The device will also show the child that the number  7  is more than the numbers  6 ,  5 , etc., and that it is less than the numbers  8 ,  9 ,  10 , etc. 
   When solving simple algebra involving addition (e.g., 4+x=7), the device is used in one of two ways. The user could cover the numeral  4  with transparent portion  34 , then count the number of clicks needed to reach the numeral  7 . Or the user, if instructed to subtract the number  4  from both sides of the equation, yielding x=7−4, could cover the numeral  7  with transparent portion  34  and then “click” down to the numeral 4. For solving simple algebra problems involving inequalities (e.g., 7+x≦10), the user frames the numeral  7  with transparent portion  34  and slides sleeve  26  up to numeral  10 , determining that any number less than four solves the problem for x. Thus, the device can be used in a number of ways to introduce children to algebraic problem solving. 
   For vision-impaired children, raised or braille numerals would be expressed on rod  10 , it being understood that a device in accordance with the embodiment may be larger to enable the child to more easily identify the numeral located in transparent portion  34 . By feeling the numerals, and by hearing and feeling the “clicks” as the sleeve  26  slides along rod  10 , the child can perform and practice all of the calculations set forth above. 
   ALTERNATIVE EMBODIMENTS 
   Alternative Embodiment—Pointers 
     FIG. 2  shows a second embodiment having the same elements as the preferred embodiment except that sleeve  38  only partially encircles rod  10 . Centered on the visible edges of the front portion of sleeve  38  are projections  39  and  40  in the form of pointers. In operation, this embodiment is used as discussed above except that sleeve  38  indicates a specified numeral with projections  39 - 40  rather than transparent portion  34 . It is understood that various indicators could be used, such as arrow symbols expressed on the sliding element. Or the visible portion of the sliding element may be roughly the same size of a numeral, and placement of the visible portion next to a numeral would serve to visually specify it. Or a transparent portion could include a horizontally disposed line that partially covers a numeral, thus visually indicating it. 
   Alternative Embodiment—Other Shapes 
     FIG. 3  shows a third embodiment comprising a triangle-shaped rod  42  with an interior channel  46  running lengthwise along rod  42 , as shown. Channel  46  includes spaced-apart openings  48 . Rod  42  with triangle-shaped caps  43  and  44  accommodates a first number line (not shown) comprising a distinct set of numerals, a second number line (not shown) comprising a distinct set of numerals, and a third number line (not shown) comprising a distinct set of numerals. A triangle-shaped sleeve  50  with windows  51  and  52  and a third window (not shown) is sized to snugly fit and slide along rod  42 . On one interior fold of sleeve  50  is a flexible projection (not shown) in accordance with the invention that strikes openings  48  as sleeve  50  slides along rod  42 . Other polygonal-shaped rods, irregular polygonal-shaped rods or irregularly shaped rods can be similarly accommodated to the invention. It is understood that multiple channels  46  could be used. It is further understood that rod  42  could be made so that multiple sleeves, one for each face of the rod, may be used. 
   Alternative Embodiment—Improved Ruler 
     FIGS. 4A through 4C  show a fourth embodiment including a rod  70  having parallel slits  74  and  78 . Rod  70  has an arch  71 . Along front face edges  72  and  73  are expressed markings comprising a system of linear measurement so that rod  70  can function as a standard ruler. Expressed vertically along rod  70  and between slits  74  and  78  is a series of numerals  90 . Sleeve  98  passes through slits  74  and  78 . A transparent portion  102  of sleeve  98  is sized and positioned to frame respective numerals in series  90  as sleeve  98  slides along slits  74  and  78 . On the interior rear wall of sleeve  98  is a projection (not shown) in accordance with the invention that strikes the interior portion of grooves  94  with sound-making force as sleeve  98  slides along slits  74  and  78 . 
   Arch  71  is common in standard rulers, and this structure provides the added value of accommodating a sleeve in accordance with the invention without interfering with ruler functions. It is understood that any longitudinal groove, channel or linear indention could be used rather than an arch. 
   Alternative Embodiment—Interchangeable Panels 
   A fifth embodiment, shown in  FIG. 5 , is a 1″×12″×⅛″ rod  118  with a ½″×12″×{fraction (1/16)}″-deep channel  122  running lengthwise along the front face, it being understood that various sizes of rods and channels may be used. At the bottom end of rod  118  is fixed cap  126 , and, at the top end, detachable cap  130 . Sleeve  26 , with window  34 , encircles rod  118 . A ½″×12″×{fraction (1/16)}″ panel  134  is detachably inserted into channel  122 . Panel  134  has expressed thereon a vertically arranged series of numerals  138  in accordance with the invention. Panel  134  may be made of cardboard, paper or more durable material such as wood, metal or plastic. Optionally, rod  118  may include a transparent portion (not shown) covering channel  122 , which protects panel  134  and helps hold it in place. Additional panels (not shown) have expressed thereon a variety of number lines or other teaching aids. 
   The user operates the device as discussed above. To change panels, the user removes detachable cap  130 , removes panel  134  by sliding it out of channel  122 , slides a replacement panel (not shown) into channel  122 , and re-attaches cap  130 . 
   Alternative Embodiments—Manual Calculator 
   A sixth embodiment, shown in  FIG. 6 , is a manual calculator. In this embodiment, flat panel  160  has four vertically oriented series of numerals  164 - 167  having expressed thereon the numerals  0  through  9 . Running on each side of each series  164 - 167  are slits  168 - 172 . Sleeve  176  passes through slits  168  and  169 , and a projection on the back interior portion of sleeve  176  (not shown) engages with grooves (not shown) on the back face of panel  160  in accordance with the preferred embodiment. In like manner, sleeve  177  passes through slits  169  and  170 , sleeve  178  passes through slits  170  and  171 , and sleeve  179  passes through slits  171  and  172 . Above series  164 - 167  appear expressions of mathematical place value (e.g., “THOUSANDS,” “HUNDREDS,” “TENS, ” “ONES”). 
   In operation, the user solves various math problems by moving sleeves  176 - 179  along series  164 - 167 . Thus, for example, to solve the equation 42+17=x, the user positions sleeve  179  to frame the numeral  2  and positions sleeve  178  to frame the numeral  4 . Moving sleeve  179  seven “clicks” upward and sleeve  178  one “click” upward yields the answer  59 . To solve the equation 777+555=x, the user positions sleeves  177 - 79  to frame the numeral  7  on series of numerals  165 - 67  and positions sleeve  176  to frame the numeral zero on series  164 . The user then moves sleeve  179  up two clicks, drop to zero, up two clicks (for a total of five movements) to the numeral  2  on series  167 . “Carrying the one,” the user then moves sleeve  178  up two clicks, drop to zero, up three clicks (for a total of six movements) to the numeral  3  on series  166 . Carrying the one, the user then moves sleeve  177  up two clicks, drop to zero, then up three clicks to the numeral  3  on series  165 . Carrying the one, the user then moves sleeve  176  up one click to the numeral  1  on series  164 . Reading left to right, the user then sees that the numerals  1 ,  3 ,  3 , and  2  are indicated. This corresponds to the answer to the equation (i.e., 777+555=1,332). It is understood that panel  160  may form the face of another structure, such as a case or notebook. 
   An eighth embodiment (not shown) is identical to the seventh embodiment except that panel  160  has been folded to form a four-sided rod, capped at the ends, with a number line-sleeve assembly on each face of the rod, and the place value designations changed to “1s”, “10s”, “100s” and “1000s.” 
   ADVANTAGES 
   As described and illustrated, the invention provides a tool and method for teaching young children math concepts through the use of a more understandable number line device that, in the embodiments discussed, simultaneously engage multiple senses. This is a marked improvement over all prior number line devices because young children understand math in vertical terms, and because learning and memory are enhanced dramatically when information is taken in through more than one sense. It is believed that all children, including children with a special abilities, processing deficits or physical handicaps, may greatly benefit from the various embodiments. Further, the invention allows more complicated math concepts, such as negative numbers, to be presented in a manner that is better adapted to the cognitive ability of young children. Still further, the invention provides a math instruction tool for visually impaired children that emphasizes learning through aural and tactile stimuli. Another advantage is that it is likely to be perceived as far more fin than a typical number line, making it more likely that the child will learn more, remember more, and practice more. Other advantages are revealed in the description and drawings. 
   SCOPE 
   Although the description above contains many specifications, these should not be construed as limiting the scope of the invention but as merely providing illustrations of some of the presently preferred embodiments of the invention. For example, the structure could be substantially larger for use by an instructor. Various means can be contemplated for allowing the invention to be kept in a child&#39;s notebook (e.g., projections with openings to accommodate a ring binder). Thus, the scope of the invention should be determined by the appended claims and their legal equivalents, rather than by the examples given.