Abstract:
A method for scoring constructed responses is provided. The method includes: establishing a question that requires a constructed response; determining at least one attribute parameter that defines the format of the constructed response; binding at least one variable to the at least one attribute parameter; defining at least one assertion rule, each setting forth a condition that the at least one variable will either satisfy or not satisfy; and creating a scoring system that includes at least full scoring credit if all of the at least one assertion rule is satisfied and partial scoring credit if some but not all of the at least one assertion rule is met; wherein when the question is presented and a constructed response received, the corresponding at least one variable is compared against the at least one assertion rule to identify which assertion rule is satisfied or not, and a score is provided based on the number and/or combination of satisfied at least one assertion rule.

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
       [0001]    This application claims priority to U.S. Provisional Application 61/265,305 filed on Nov. 30, 2009, entitled “Use and Definition of Scoring Rubrics,” the disclosure of which is hereby incorporated by reference in its entirely. The application also related to U.S. patent application Ser. No. 12/320,631 filed Jan. 30, 2009 and titled “Constructed Response Scoring Mechanism,” which itself claims priority to U.S. Provisional Application No. 61/193,252 filed Nov. 12, 2008 and titled “Constructed Response Scoring Mechanism,” each of which is hereby incorporated by reference in its entirety. 
     
    
     BACKGROUND 
       [0002]    1. Field of the Invention 
         [0003]    This application relates generally to the use and definition of scoring rubrics in assessment systems. 
         [0004]    2. Background Information 
         [0005]    Learning often happens incrementally. At first students may be able to recall, recognize or name concepts. As mastery increases, they may be able describe concepts, the properties of concepts, or relationships among concepts. Eventually, students may be able to apply concepts to novel situations, use learned material to generate new insights, or synthesize learned material. This learning sequence is often referred to as “depth of knowledge,” and refers to the depth with which students understand the material that they are taught. The specific stages and levels of depth vary across taxonomies, but the general idea is that knowledge becomes deeper and more internalized with additional mastery, and that in turn allows more robust application of the knowledge. 
         [0006]    When assessing student mastery, it is often desirable to evaluate their depth of knowledge. From the perspective of test developers it can be quite difficult to develop selected response items (test questions) that measure deeper levels of knowledge. A selected response item is a test question, such as a multiple choice question, in which the correct answer is selected from a collection of choices. 
         [0007]    Many testing programs use constructed response items to measure content at deeper levels of knowledge. A constructed response item is an item that does not offer the examinee answer options from which to choose, but rather the examinee must construct a response. In a typical system, each student&#39;s response is evaluated against a scoring rubric, which describes the characteristics of a response that should receive full credit. When partial credit is to be awarded, the characteristics of responses that receive some portion of the total overall score are also enumerated. For example, an item might award three points for full credit, and individually enumerate characteristics of imperfect responses that would warrant the award of two points, one point, and zero points. 
         [0008]    The scoring rubric usually goes through a refinement process called rangefinding. In this process, samples of student responses (usually from a field test) are evaluated by a committee of subject matter experts with the goal of selecting sample responses exemplifying each score point to be awarded. It is not uncommon for the scoring rubrics to be refined during this process. 
         [0009]    Using the refined rubric, human scorers apply the scoring criteria to score each examinee&#39;s response to the item. Typically, this process is monitored and managed, giving each scorer a number of pre-scored papers to evaluate whether they continue to apply the rubric correctly, and having a proportion of scored papers independently scored by a second scorer to monitor the reliability with which scorers apply the rubric. 
         [0010]    The current process has several limitations. First, it is very expensive to score constructed response items by hand, requiring that each response be read by one or more qualified scorers. Furthermore, the process by which scoring rubrics are refined does not offer an opportunity for large-scale evaluation of the consequences of the refinements, risking potential unintended consequences. Additionally, the process necessarily takes time, limiting the usefulness of constructed response items in online tests. For example, adaptive online tests use the scores on items administered early in the test to select the best items to administer later. Due to current limitations, human scoring prevents using constructed response items to support adaptive testing. 
       SUMMARY 
       [0011]    In one general aspect, systems and methods are provided for using and defining scoring rubrics in assessment systems. In some implementations, a tool is provided to facilitate the definition of scoring rubrics for use with constructed response items in testing applications. This tool may reduce the level of knowledge and expertise required to define scoring rubrics, and speed the development of test items. This allows development of machine-scored constructed response items to fit into the standard workflow for test item development, in which items are drafted by content experts, and sequentially reviewed by editors and other content experts. Furthermore, this tool allows a scoring rubric to be refined during the review process. 
         [0012]    According to an embodiment of the invention, a method for scoring constructed responses is provided. The method includes: establishing a question that requires a constructed response; determining at least one attribute parameter that defines the format of the constructed response; binding at least one variable to the at least one attribute parameter; defining at least one assertion rule, each setting forth a condition that the at least one variable will either satisfy or not satisfy; and creating a scoring system that includes at least full scoring credit if all of the at least one assertion rule is satisfied and partial scoring credit if some but not all of the at least one assertion rule is met; wherein when the question is presented and a constructed response received, the corresponding at least one variable is compared against the at least one assertion rule to identify which assertion rule is satisfied or not, and a score is provided based on the number and/or combination of satisfied at least one assertion rule. 
         [0013]    The above embodiment may have various optional features. The method may include: testing the scoring system by entering at least one constructive response to the question and analyzing the results of the scoring system for accuracy in the scoring of the at least one constructive response; and modifying, in response to erroneous scoring determined by the analyzing, at least one of the at least one attribute parameter, at least one variable, at least one assertion rule, and/or scoring system. After the testing and before the modifying, there may be identifying, in response to erroneous scoring determined by the analyzing, at least one of the at least one attribute parameter, at least one variable, at least one assertion rule, and/or scoring system that is responsible for any error in scoring. The question may be a mathematically based question, and the at least one attribute parameter may comprises a geometric object or geometric object set. The geometric object may be one of a point, a line, an arrow, a connected collection of lines, and/or a preset image. The method may be embodied in a non-transitory computer-readable medium. 
         [0014]    According to another embodiment of the invention, a computer program for scoring constructed response is provided. The program is embodied in a non-transitory computer readable medium and configured for operation in cooperation with electronic computer hardware. The program: establishes a question that requires a constructed response; determines at least one attribute parameter that defines what can be provided in the constructed response; binds at least one variable to the at least one attribute parameter; defines at least one assertion rule, each setting forth a condition that the at least one variable will either satisfy or not satisfy; and creates a scoring system that includes at least full scoring credit if all of the at least one assertion rule is satisfied and partial scoring credit if some but not all of the at least one assertion rule is met; wherein when the question is presented and a constructed response received, the corresponding at least one variable is compared against the at least one assertion rule to identify which assertion rule is satisfied or not, and a score is provided based on the number and/or combination of satisfied at least one assertion rule. 
         [0015]    The above embodiment may have various optional features. The program may: test the scoring system by entering at least one constructive response to the question and analyzing the results of the scoring system for accuracy in the scoring of the at least one constructive response; and modifying, in response to erroneous scoring determined by the analyzing, at least one of the at least one attribute parameter, at least one variable, at least one assertion rule, and/or scoring system. After the testing and before the modifying, the program may identify, in response to erroneous scoring determined by the analyzing, at least one of the at least one attribute parameter, at least one variable, at least one assertion rule, and/or scoring system that is responsible for any error in scoring. The question may be a mathematically based question, and the at least one attribute parameter may be a geometric object or geometric object set. The geometric object may be one of a point, a line, an arrow, a connected collection of lines, and/or a preset image. 
         [0016]    According to yet another embodiment of the invention, a method for scoring constructed responses is provided. The method includes establishing a question that requires a constructed response; creating object sets that define the nature of the constructed response; binding the object sets to variables; defining assertion rules each setting forth a premise that the variables will either satisfy or not satisfy; and creating a scoring system that is configured to score the constructed response based on at least how many assertion rules are satisfied, including at least full scoring credit if all of assertion rules are satisfied and partial scoring credit if some but not all of the assertion rules are met; wherein when the question is presented and a constructed response received, the corresponding variables are compared against the assertion rules to identify which assertion rules are satisfied or not, and a score is provided based on the number and/or combination of satisfied assertion rules. 
         [0017]    The above embodiment may have various optional features. The method may: test the scoring system by entering at least one constructive response to the question and analyzing the results of the scoring system for accuracy in the scoring of the constructive response; and modifying, in response to erroneous scoring determined by the analyzing, at least one of the object sets, variables, assertion rules, and/or scoring system. After the testing and before the modifying, the method may identify, in response to erroneous scoring determined by the analyzing object sets, variables, assertion rules, and/or scoring system that is responsible for any error in scoring. The question may be a mathematically based question, and the object sets may be a geometric object or object set. The geometric object may be one of a point, a line, an arrow, a connected collection of lines, and/or a preset image. The method may be embodied in a non-transitory computer-readable medium. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0018]      FIG. 1  is a block diagram of an embodiment of an exemplary system for implementing the invention. 
           [0019]      FIG. 2  is a screenshot of an exemplary user interface (UI) for collecting student responses according to an embodiment of the invention. 
           [0020]      FIG. 3  illustrates exemplary binding statements used in the binding stage according to an embodiment of the invention. 
           [0021]      FIG. 4  illustrates exemplary assertions according to an embodiment of the invention. 
           [0022]      FIG. 5  illustrates an exemplary snippet from a scoring specification for a three-point item according to an embodiment of the invention. 
           [0023]      FIG. 6  is a block diagram of an exemplary method for scoring user responses according to an embodiment of the invention. 
           [0024]      FIG. 7  is a flow chart of a method for modifying scoring rubrics. 
           [0025]      FIG. 8  is a flow chart of a method for using scoring rubrics. 
       
    
    
     DETAILED DESCRIPTION 
       [0026]    As one skilled in the art will appreciate, embodiments of the present invention may be embodied as, among other things: a method, system, or computer-program product. Accordingly, the embodiments may take the form of a hardware embodiment, a software embodiment, or an embodiment combining software and hardware. In one embodiment, the present invention takes the form of a computer-program product that includes computer-useable instructions embodied on one or more computer-readable media. 
         [0027]    Computer-readable media include both volatile and nonvolatile media, removable and nonremovable media, and contemplates media readable by a database, a switch, and various other network devices. Network switches, routers, and related components are conventional in nature, as are means of communicating with the same. By way of example, and not limitation, computer-readable media comprise computer-storage media and communications media. 
         [0028]    Computer-storage media, or machine-readable media, include media implemented in any method or technology for storing information. Examples of stored information include computer-useable instructions, data structures, program modules, and other data representations. Computer-storage media include, but are not limited to RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile discs (DVD), holographic media or other optical disc storage, magnetic cassettes, magnetic tape, magnetic disk storage, and other magnetic storage devices. These memory components can store data momentarily, temporarily, or permanently. 
         [0029]    Communications media typically store computer-useable instructions—including data structures and program modules—in a modulated data signal. The term “modulated data signal” refers to a propagated signal that has one or more of its characteristics set or changed to encode information in the signal. An exemplary modulated data signal includes a carrier wave or other transport mechanism. Communications media include any information-delivery media. By way of example but not limitation, communications media include wired media, such as a wired network or direct-wired connection, and wireless media such as acoustic, infrared, radio, microwave, spread-spectrum, and other wireless media technologies. Combinations of the above are included within the scope of computer-readable media. 
         [0030]      FIG. 1  is a block diagram of a system  100  that includes components such as client  102 , scoring manager  104 , scoring engine  106 , and primitive library  108 . Each component includes a communication interface. The communication interface may be an interface that can allow a component to be directly connected to any other component or allows the component to be connected to another component over network  110 . Network  110  can include, for example, a local area network (LAN), a wide area network (WAN), cable system, telco system, or the Internet. In an embodiment, a component can be connected to another device via a wireless communication interface through the network  110 . Client  102  may be or can include a desktop computer, a laptop computer or other mobile computing device, a network-enabled cellular telephone (with or without media capturing/playback capabilities), a server, a wireless email client, or other client, machine or device, or any combination of the above, to perform various tasks including Web browsing, search, electronic mail (email) and other tasks, applications and functions. Client  102  may additionally be any portable media device such as digital still camera devices, digital video cameras (with or without still image capture functionality), media players such as personal music players and personal video players, and any other portable media device, or any combination of the above. 
         [0031]    Scoring manager  104  is utilized for administering and scoring constructed response items for a user. The scoring manager  104  may also be utilized to generate individual expert systems to represent the scoring knowledge for a single constructed response item. The scoring manager  104  additionally may be configured to refine each expert system and test it against a broad range of student responses. In an embodiment, scoring manager  104  is a server external to client  102 . In another embodiment, scoring manger  104  may be an application that resides and is executable within client  102 . 
         [0032]    As shown, scoring engine  106  and primitive library  108  are components that reside within scoring manager  104 . In other embodiments, one or more of the scoring engine  106  and primitive library  108  may be external to the scoring manager  104 . The scoring engine  106  is a component that receives a user&#39;s response to a question and evaluates the response against a scoring rubric. The scoring engine  106  may include or have access to the library of primitives  108 . In an embodiment, the primitive library  108  may include the calculation of distances, slopes, comparisons of strings and numbers, and other basic operations. In order to make the scoring engine  106  general so that it can support a very large range of items, the primitive library  108  may be low-level and higher order predicates may be created from the primitive library  108 . In other embodiments, complex predicates may be added to the primitive library. In an embodiment, in using the primitive library  108 , the language for representing a scoring rubric may enable the library functions to reference elements including, but not limited to, object sets, objects, attributes of objects, as well as transformations of any of these elements. 
         [0033]      FIG. 2  is a screenshot of an exemplary user interface (UI)  200  for collecting student responses. The UI  200  may be presented through an application that is part of the client  102  and/or the scoring manager  104 . In an embodiment, through the UI  200 , the invention uses items developed for user responses collected on a Cartesian grid to illustrate points. In other embodiments, the invention can be applied to user responses to other types of items using other response modes. In an embodiment, the UI  200  is referred to as an Interactive Grid (IG). A broad range of different item types can be presented in the IG. 
         [0034]    The UI  200  may be used to ensure that user responses are collected with a consistent mechanism that creates and transmits a data structure to a scoring engine. A user response may comprise a set of objects, each of which may have one or more attributes. For example, the UI can produce a collection of objects that may include points, line segments connecting points, geometric objects comprised of connected line segments, and user-defined atomic objects, such as the weights  202  on the left palette in  FIG. 200 . Each object may be characterized by an ordered set of points. For example, the lines on the bottom-center of the weights  202  may be an example of an ordered set of points. In an embodiment, the UI  200  can return a data structure containing these objects to the scoring engine  106 . In an embodiment, objects have properties that include, but are not limited to, locations, names, labels, and values. 
         [0035]    In another embodiment, the UI  200  can be configured to capture natural language where the object set may include elements of a semantic network derived from a parse of the text provided by the user. Alternatively, the UI  200  can be configured to capture input from an equation editor representing sequences of symbols as the initial set of objects. Moreover, in other embodiments, an application to test proficiency with a computer program may capture menu commands, keyboard input, or mouse events as the set of objects. However, this list is intended to be exemplary rather than exhaustive. 
         [0036]    In an embodiment, a scoring rubric may be defined in three sequential stages: a binding stage, in which references to elements are established; an assertion stage, in which assertions about elements are evaluated and stored; and a scoring stage, in which a score is assigned based on the values of the results of the assertions. XML-based language may be used for implementing these stages for the UI responses. 
         [0037]      FIG. 3  illustrates exemplary binding statements used in the binding stage.  FIG. 3  presents two exemplary binding statements. The first, “SelectObjectSet” binds a subset of the input set to the variable “S1.” The first binding statement collects all of the objects that have at least one side (NUMBEROFSIDES GT 0). The symbol “@” is bound sequentially to each object in the input set. The second statement in  FIG. 3 , “Bind,” creates an additional binding, associating the symbol “S1Count” with the number of elements contained in set “S1.” The symbol “$” dereferences the previously bound variable “S1.” 
         [0038]    An assertion is a predicate that is either true or false. The assertion further is an atomic unit from which scoring rubrics can be built. Each assertion can be named for later reference in the scoring stage.  FIG. 4  illustrates exemplary assertions according to an embodiment of the invention. In  FIG. 4 , the first two assertions dereference the previously bound integer “S1Count” and assert that it is (respectively) equal to four and less than four. These assertions are named by the user, for example, “FourObjects” and “FewerObjects.” The third assertion references another previously bound integer, which is the count of objects in another set meeting some other set of conditions. In this example, the third assertion is named “FourGood” and is true if the value of “S3Count” is 4. 
         [0039]    In the scoring stage, named assertions are collected in a set of And-Or trees, one tree for each numeric score point. An exemplary snippet from a scoring specification for a three-point item appears in  FIG. 5  according to an embodiment of the invention. In this case, full credit is assigned if there are four objects represented and all four meet whatever criteria was used to construct set “S3,” and thus leading to the bound variable “S3Count” above. 
         [0040]    The representation of annotated And-Or trees is well known in the computer science art. In an embodiment, the internal representation used is a set of nodes, in which each node has a list of children, each of which can be an And node, an Or node, or an assertion node. The resulting internal representation of the binding, assertion, and scoring trees comprises an Answer Set that includes an expert system embodying the knowledge of the scoring rubric for a particular item. The scoring rubric may be written directly in the specification language or authoring tools may be developed to help test developers specify the rubrics. In some embodiments, tools may be domain specific. 
         [0041]      FIG. 6  is a block diagram of an exemplary method  600  for scoring user responses. In an embodiment, the three-stage Answer Set is applied to the set of elements returned by the UI. One practical value of method  600  is that this process facilitates the use of a low-level library of primitives which can reduce or eliminate the need for any programming when defining a very broad range of new items or item types. In an embodiment, method  600  can integrate the assertion and scoring stage into one stage. 
         [0042]    At operation  602 , a user response is captured as a collection of objects with attributes. In an embodiment, the response is captured through a UI such as UI  200  ( FIG. 2 ). At operation  604 , a component binds the variables identified in a binding tree. In an embodiment, the component is a scoring engine such as scoring engine  106  ( FIG. 1 ). At operation  606 , results (true or false) are stored for each named assertion. At operation  608 , starting with the highest possible score, a scoring tree is evaluated, stopping when the subtree associated with a score evaluates to true. 
         [0043]    Various implementations also provide an enhanced method of “rangefinding” which refines expert systems and tests them against a broad range of student responses. Rangefinding is a committee process in which subject-matter experts agree on appropriate scores for sample examinee responses. During rangefinding, a small sample of items, often in the range of 25-100, are reviewed by committees to test the application of the scoring rubrics. During this process, refinements are made to the rubric, and sample papers are selected to train scoring staff on the accurate scoring of responses to the item. 
         [0044]    However, improvements are needed for enhancing the rangefinding process. The invention provides such improvements. For example, decisions of the rangefinding committee can be expressed formally as assertions in the language used to define the scoring rubrics. Formalizing the committee results as a series of explicit rules improves the accuracy of scoring, and would likely lead to more reliable scoring even when scoring is done by human scorers. Furthermore, committee decisions can be systematically tested against the full set of field-test data to locate unintended consequences of the proposed new rules. 
         [0045]      FIG. 7  is a block diagram of an exemplary method  700  for refining a scoring rubric. At operation  702 , items are field tested and are scored either in real time or after data collection. At operation  704 , a sample of responses are identified for transmission to a rangefinding committee. In an embodiment, the sample of responses may be selected by combing a small random sample with student responses selected to represent the work of otherwise high- or low-performing students. This may be done because otherwise high-performing students may score poorly on the item, or otherwise low-performing students may score well on the item. 
         [0046]    At operation  706 , items and corresponding scores are provided to the rangefinding committee. In an embodiment, the rangefinding committee is trained in the formal specifications of the scoring rubric. In instances where the committee reaches a consensus that a score is incorrect, at operation  708 , one or more piles or principles are identified that differentiates the correct score from the incorrect scores. At operation  710 , a modification to the scoring rubric, corresponding to the indentified rules, is provided. 
         [0047]    At operation  712 , the identified rules for modifying the scoring rubric are applied to field test responses in order to identify any unintended consequences of the new rules. In an embodiment, this may be done by identifying scores that changed under the new rules and evaluating those changes. At operation  714 , a consensus on whether to fully implement the new rules is achieved based on the modification to the formal scoring rubric. In an embodiment, the consensus is achieved after the committee reviews a new sample of responses for which the revision resulted in a change of scores and determines that the changes are limited to those intended. 
         [0048]    Referring to  FIG. 8 , a method for use in defining a scoring rubric that may be used, by way of example and not by way of limitation, with the various systems described above includes five steps. The first step allows the user to create sets of items by specifying their properties. In one implementation, this is accomplished through a series of menu selections. In one instance, the user selects properties or functions from categories of functions or properties (e.g., location, geometric properties, etc.). Properties might be specified in response to questions or by visually drawing (locations for example) on a representation of the answer grid. 
         [0049]    In the second step, the user names sets, properties of sets, elements of the created sets, and/or properties of the elements. Again, the properties may be arranged according to their type or functions and accessed through menus, icons, or hand-entered. 
         [0050]    Users may want to create sets based on properties of other sets or their elements. For example, a rubric may require information about all objects within a given distance of another object (say, Object A). Users might first select all Object A as in the first step (Set A), then bind the location of the desired element of Set A to a variable or set of variables. Those variables could then be used to create another set (say, Set B), which consists of all objects within a certain radius of Object A. 
         [0051]    The process then allows users to make assertions about sets or bound variables (Step 4). These true/false assertions might be selected from a menu or categorized tree or other interface. Individual assertions may be combined using Boolean logic to create complex assertions. Each assertion must evaluate to either true or false. For example, an assertion might assert that a single object is within the prescribed radius of Object A, or that single Object A is found in Set A, or that both conditions are true. 
         [0052]    In Step 4 scores are associated with sets of assertions. An interface might represent the set of assertions as a tree, with nodes representing basic logical operators and leaves representing previously defined assertions. For example, if Assertion  1  is true and Assertion  2  is true, then the student receives a 1. Various interfaces might facilitate this specification. 
         [0053]    In the final step, the system allows the user to test the rubric and refine it. In a good implementation, this provides information about all bound variables and sets, and provides a mechanism for the user to go back and refine the rubric. 
         [0054]    One implementation of a tool for defining constructed responses is described on pages 11 through 35 below. Furthermore, the attached Appendix describes an implementation of a tool for defining constructed responses. 
         [0055]    While particular embodiments of the invention have been illustrated and described in detail herein, it should be understood that various changes and modifications might be made to the invention without departing from the scope and intent of the invention. The embodiments described herein are intended in all respects to be illustrative rather than restrictive. Alternate embodiments will become apparent to those skilled in the art to which the present invention pertains without departing from its scope. 
         [0056]    From the foregoing it will be seen that this invention is one well adapted to attain all the ends and objects set forth above, together with other advantages, which are obvious and inherent to the system and method. It will be understood that certain features and sub-combinations are of utility and may be employed without reference to other features and sub-combinations.