Abstract:
A computer-implemented method for teaching math is disclosed. The method comprises displaying a challenge for a learner to solve; displaying in first area a plurality of moveable pieces; displaying a second area defining a receptacle to which the learner can move the moveable pieces in attempting to solve the challenge; and evaluating the learner&#39;s response to the challenge.

Description:
[0001]    This application claims the benefit of priority of U.S. 61/321,843, filed Apr. 7, 2010, the entire specification of which is hereby incorporated herein by reference. 
     
    
     FIELD 
       [0002]    Embodiments of the present invention relate generally to software and systems designed for teaching purposes. 
       BACKGROUND OF THE INVENTION 
       [0003]    Concrete or physical manipulatives such as blocks, math racks, counter, etc., are used to facilitate learning, especially in the field of mathematics. Virtual manipulatives refer to digital “objects” that are the digital or virtual counterpart of concrete manipulatives. Virtual manipulatives may be manipulated, e.g., with a pointing device such as a mouse during learning activities. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0004]      FIGS. 1 to 5  show screenshots of a User Interface generated by the tile tool and system of the present invention. 
           [0005]      FIG. 6  shows an example of hardware for implementing the tile tool and system, in accordance with one embodiment of the invention. 
       
    
    
     SUMMARY 
       [0006]    Broadly, embodiments of the invention disclose a tile tool and a method for teaching math based on the tile tool. The tile tool may comprise a plurality of tiles, a tile receptacle, a tile bin, and a problem description. In particular, users are given a row of tiles that they can move to the tile receptacle to create multiplication representations. The multiplication representations may then either be described, with words (for example, “3 groups of 5 makes 15”) or symbolically (“3×5=15”) or the student may be asked to fill in a missing part of the description. Advantageously, the tile tool supports students as they begin to understand the concept of early multiplication. It allow students to work from a more concrete representation where all tiles are countable to a more symbolic representation where tiles are occluded to disallow counting individual items. 
       DETAILED DESCRIPTION 
       [0007]    In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the invention. It will be apparent, however, to one skilled in the art that the invention can be practiced without these specific details. In other instances, structures and devices are shown only in block diagram form in order to avoid obscuring the invention. 
         [0008]    Reference in this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment of the invention. The appearance of the phrases “in one embodiment” in various places in the specification are not necessarily all referring to the same embodiment, nor are separate or alternative embodiments mutually exclusive of other embodiments. Moreover, various features are described that may be exhibited by some embodiments and not by others. Similarly, various requirements are described that may be requirements for some embodiments but not other embodiments. 
         [0009]    Broadly, embodiments of the invention disclose a tile tool and a method for teaching math based on the tile tool. The tile tool may comprise a plurality of tiles, a tile receptacle, a tile bin, and a problem description. In particular, users are given a row of tiles that they can move to the tile receptacle to create multiplication representations. The multiplication representations may then either be described, with words (for example, “3 groups of 5 makes 15”) or symbolically (“3×5=15”) or the student may be asked to fill in a missing part of the description. Advantageously, the tile tool supports students as they begin to understand the concept of early multiplication. It allow students to work from a more concrete representation where all tiles are countable to a more symbolic representation where tiles are occluded to disallow counting individual items. 
         [0010]    Advantageously, in one embodiment the tile tool may be rendered as a virtual manipulative on a display screen so that a learner may interact with the virtual manipulative to solve math problems and to learn math problem solving techniques. 
         [0011]    The tile tool may be integrated in a system for teaching math. The system may be realized, in one, embodiment, as a general-purpose computer comprising suitable instructions for implementing the tile tool and associated method. 
         [0012]    Referring to  FIG. 1 , there is shown a user interface (UI)  100  generated by the tile tool, in accordance with one embodiment of the invention. As will be seen, the UI  100  comprises a problem box  102 , in which a problem to be presented. In accordance with various embodiments, problems may be presented as word descriptions (for example, “3 groups of 5 makes 15”) or symbolically (“3×5=15”). Alternatively, a student may be asked to fill in a missing part of the description, as is the case with the problem shown in the UI  100 . 
         [0013]    The user interface  100  also includes a tile bin  104 . A plurality of tiles  106  may initially be located within the tile bin  104 . In one embodiment, the user interface  100  includes a tile receptacle in the form of a tile mat or basket  108  located above the tile bin  104 . In use a student moves tiles  106  from the tile bin  104  into the tile mat  108  in order to solve problems. 
       Tile Bins: 
       [0014]    In one embodiment, students struggling with the early multiplication concept of grouping may be given a smaller number of tiles with smaller amounts. This allows them to start with numbers they may find easier to work with such as 1-5. 
         [0015]    In one embodiment tiles may show dots (numbergrams), numerals or animals. 
         [0016]    In one embodiment a user may be allowed to drag tiles to mat or back to bin. This enables a student to self-correct. 
         [0017]    In one embodiment, only specific tiles may be moveable. 
       Receptacle: 
       [0018]    The receptacle may take the form of a bucket, mat, or basket, in accordance with different embodiments. 
         [0019]    In one embodiment, a reset button (see  110  in  FIG. 1 ) may be provided value to allow a student to reset the receptacle to zero. 
         [0020]    In one embodiment a counter for the total in the receptacle (see  112  in  FIG. 2 ) may be selectively turned on or off. Students working to find a factor for a specific number are supported by showing the total as they build the number with tiles. 
         [0021]    In one embodiment, the tile tool may allow a student to highlight and count off tiles in the receptacle. This gives students a visual and auditory model for skip counting. 
         [0022]    In one embodiment, tile tool may arrange tiles on mat in arrays with rows of e.g. 5 for easier skip counting. This reinforces using multiples of 5 and 10 to help skip count. 
         [0023]    In one embodiment, tile tool may allow students to choose placement of tiles on the mat. This allows students to group tiles in ways that support the development of multiplicative thinking. 
         [0024]    Referring now to  FIG. 2 , UI  200  students are given a group of tiles and asked to choose a group that will make a target number. Once a tile is placed on the mat, the student may add more tiles to build the target number or type in the answer to the problem. 
         [0025]      FIG. 3  shows an embodiment of the receptacle in the form of a basket  300 . A counter  302  shows the number of tiles in the basket and a recycle/empty button  304  may be used to return the tiles in the basket  300  back to the tile bin (not shown). 
         [0026]      FIG. 4  shows a UI  400  in which tiles in the tile bin have values indicated by numbergrams. The correspondence between the equation in the problem box and the tiles in the basket is clearly highlighted. 
         [0027]      FIG. 5  shows a top view of a tile basket showing how a student has organized three groups of 2 sixes each. 
         [0028]      FIG. 6  of the drawings shows an example of hardware  600  that may be used to implement the tile tool in accordance with one embodiment. The hardware  600  may include at least one processor  602  coupled to a memory  604 . The processor  602  may represent one or more processors (e.g., microprocessors), and the memory  604  may represent random access memory (RAM) devices comprising a main storage of the system  600 , as well as any supplemental levels of memory e.g., cache memories, non-volatile or back-up memories (e.g. programmable or flash memories), read-only memories, etc. In addition, the memory  604  may be considered to include memory storage physically located elsewhere in the system  600 , e.g. any cache memory in the processor  602  as well as any storage capacity used as a virtual memory, e.g., as stored on a mass storage device  600 . 
         [0029]    The system  600  also typically receives a number of inputs and outputs for communicating information externally. For interface with a user or operator, the system  600  may include one or more user input devices  606  (e.g., a keyboard, a mouse, imaging device, etc.) and one or more output devices  608  (e.g., a Liquid Crystal Display (LCD) panel, a sound playback device (speaker, etc.). 
         [0030]    For additional storage, the system  600  may also include one or more mass storage devices  610 , e.g., a floppy or other removable disk drive, a hard disk drive, a Direct Access Storage Device (DASD), an optical drive (e.g. a Compact Disk (CD) drive, a Digital Versatile Disk (DVD) drive, etc.) and/or a tape drive, among others. Furthermore, the system  600  may include an interface with one or more networks  612  (e.g., a local area network (LAN), a wide area network (WAN), a wireless network, and/or the Internet among others) to permit the communication of information with other computers coupled to the networks. It should be appreciated that the system  600  typically includes suitable analog and/or digital interfaces between the processor  602  and each of the components  604 ,  606 ,  608 , and  612  as is well known in the art. 
         [0031]    The system  600  operates under the control of an operating system  614 , and executes various computer software applications, components, programs, objects, modules, etc. to implement the techniques described above. Moreover, various applications, components, programs, objects, etc., collectively indicated by reference  616  in  FIG. 6 , may also execute on one or more processors in another computer coupled to the system  600  via a network  612 , e.g. in a distributed computing environment, whereby the processing required to implement the functions of a computer program may be allocated to multiple computers over a network. The application software  616  may include a set of instructions which, when executed by the processor  612 , causes the system  610  to generate the tile tool described. 
         [0032]    In general, the routines executed to implement the embodiments of the invention may be implemented as part of an operating system or a specific application, component, program, object, module or sequence of instructions referred to as “computer programs.” The computer programs typically comprise one or more instructions set at various times in various memory and storage devices in a computer, and that, when read and executed by one or more processors in a computer, cause the computer to perform operations necessary to execute elements involving the various aspects of the invention. Moreover, while the invention has been described in the context of fully functioning computers and computer systems, those skilled in the art will appreciate that the various embodiments of the invention are capable of being distributed as a program product in a variety of forms, and that the invention applies equally regardless of the particular type of computer-readable media used to actually effect the distribution. Examples of computer-readable media include but are not limited to recordable type media such as volatile and non-volatile memory devices, floppy and other removable disks, hard disk drives, optical disks (e.g., Compact Disk Read-Only Memory (CD ROMS), Digital Versatile Disks, (DVDs), etc.), among others. 
         [0033]    Although the present invention has been described with reference to specific example embodiments, it will be evident that various modifications and changes can be made to these embodiments without departing from the broader spirit of the invention. Accordingly, the specification and drawings are to be regarded in an illustrative sense rather than in a restrictive sense.