Equation-based assessment grading method and participant response system employing same

• US 9,117,375 B2
• Filed: 06/27/2011
• Issued: 08/25/2015
• Est. Priority Date: 06/25/2010
• Status: Active Grant

• Current Assignee: Smart Technologies ULC (Hon Hai Precision Industry Co., Ltd.)
• Original Assignee: Smart Technologies ULC (Hon Hai Precision Industry Co., Ltd.)
• Inventors: Labine, David, Wenzel, Lothar, Chu, Albert
• Primary Examiner(s): Yao, Sam
• Assistant Examiner(s): Fletcher, Jerry-Daryl
• Application Number:
  US13/169,550
• Publication Number:
  US 20110318724A1
• Time in Patent Office: 1,520 Days
• Field of Search: 434/188, 434/201, 434/322, 434/323, 434/350
• US Class Current: 1/1
• CPC Class Codes: G09B 19/02 Counting; Calculating abacus G06C1/00
• CPC Class Codes: G09B 7/08 characterised by modifying the teaching programme in response to a wrong answer, e.g. repeating the question, supplying further information

Abstract

A computerized assessment grading method comprises creating a syntax tree for a received equation-based response to at least one assessment question and a syntax tree for at least one solution to the at least one question, comparing the syntax trees, and grading the response based on the results of the comparison.

Claims

1. A computerized assessment grading method comprising:

receiving, by a processing device, an encoded equation-based response to at least one assessment question, said at least one assessment question comprising an equation;

decoding, by the processing device, said encoded equation-based response to yield a decoded equation-based response;

determining, by the processing device, a grading method selected from a plurality of different grading methods;

creating, by the processing device, (i) a syntax tree for the decoded equation-based response and (ii) a syntax tree for at least one solution to the at least one assessment question;

determining, by the processing device, whether the decoded equation-based response matches the equation of said at least one assessment question;

if the decoded equation-based response does not match the equation of said at least one assessment question, comparing, by the processing device, the syntax trees; and

grading, by the processing device, the response according to the determined grading method based on the results of the comparison;

wherein said grading comprises awarding a score based on the extent to which nodes of the syntax trees match.

2. The method of claim 1 wherein said grading method is selected from Order Equivalence, Formal Equivalence and Content Equivalence grading methods.

3. The method of claim 2 wherein said creating comprises parsing the decoded equation-based response and the at least one solution into tree-shaped hierarchies of operators and operands thereby to form the syntax trees.

4. The method of claim 3 wherein said creating further comprises normalizing the syntax trees.

5. The method of claim 4 wherein during said normalizing, the syntax trees are normalized into canonical form where common operators are simplified to a single n-ary operator.

6. The method of claim 3 wherein the tree-shaped hierarchies of operators and operands are generally based on orders of operation.

7. The method of claim 6 wherein operations to be performed first are placed at the bottom of the syntax trees and operations to be performed last are placed at the top of the syntax trees.

8. The method of claim 2 wherein said comparing comprises determining the similarity between nodes of the syntax trees.

9. The method of claim 2 wherein said comparing comprises determining if the syntax trees comprise the same nodes.

10. The method of claim 9 wherein when the syntax trees comprise the same nodes, said grading comprises grading the response as correct.

11. The method of claim 9 wherein said creating comprises parsing the decoded equation-based response and the at least one solution into tree-shaped hierarchies of operators and operands thereby to form the syntax trees.

12. The method of claim 11 wherein said creating further comprises normalizing the syntax trees.

13. The method of claim 12 wherein during said normalizing, the syntax trees are normalized into canonical form where common operators are simplified to a single n-ary operator.

14. The method of claim 11 wherein the tree-shaped hierarchies of operators and operands are generally based on orders of operation.

15. The method of claim 14 wherein operations to be performed first are placed at the bottom of the syntax trees and operations to be performed last are placed at the top of the syntax trees.

16. The method of claim 2 further comprising, prior to said comparing, determining if the syntax tree created for the decoded equation-based response is valid and when said syntax tree created for the decoded equation-based response is not valid, bypassing said comparing and grading said response as incorrect.

17. The method of claim 2 wherein said receiving comprises receiving the encoded equation-based response from a plurality of response devices.

18. The method of claim 2 wherein said decoding, by the processing device, comprises decoding the encoded equation-based response into a type-setting language.

19. The method of claim 18 wherein said type-setting language is LaTex.

20. A computerized assessment grading method comprising:

upon receipt of an encoded equation-based response to an assessment question, said assessment question comprising an equation, decoding, by a processing device, the encoded equation-based response and processing the decoded equation-based response to determine a hierarchy of operators and operands and a grading method selected from a plurality of different grading methods;

determining, by the processing device, if the response comprises an equation that matches the equation of the assessment question;

if the response does not comprises an equation that matches the equation of the assessment question, comparing, by the processing device, (i) the response hierarchy of operators and operands with (ii) a solution hierarchy of operators and operands; and

grading, by the processing device, the response according to the determined grading method based on the comparison;

wherein said grading comprises awarding a score based on the extent to which nodes of the syntax trees match.

21. The method of claim 20 wherein said grading method is selected from Order Equivalence, Formal Equivalence and Content Equivalence grading methods.

22. The method of claim 21 wherein said decoding, by the processing device, comprises decoding the encoded equation-based response into a type-setting language.

23. The method of claim 22 wherein the response and solution hierarchies of operators and operands are generally based on orders of operation.

24. The method of claim 22 wherein said comparing comprises determining if the hierarchies of operators and operands match.

25. The method of claim 22 further comprising, prior to said comparing, determining if the hierarchy of operators and operands determined from processing the decoded equation-based response is valid and when said hierarchy of operators and operands determined from processing the decoded equation-based response is not valid, bypassing said comparing and grading said response as incorrect.

26. The method of claim 22 further comprising, prior to said creating, receiving the encoded equation-based response from one or more response devices.

27. The method of claim 22 wherein said type-setting language is LaTex.

29. A participant response system comprising:

at least one response device, each response device having an input interface permitting a user to input an equation-based response to a question, said question comprising an equation; and

processing structure communicating with each response device, said processing structure, in response to a received encoded equation-based response, carrying out the method according to claim 20.

28. A participant response system comprising:

at least one response device, each response device having an input interface permitting a user to input an equation-based response to a question, said question comprising an equation; and

processing structure communicating with each response device, said processing structure, in response to an encoded equation-based response received from a response device, decoding the encoded equation-based response to yield a decoded equation-based response, determining from the decoded equation-based response a grading method selected from a plurality of different grading methods and executing the determined grading method that causes said processing structure to create a syntax tree for the decoded equation-based response, determine whether the decoded equation-based response matches the equation of the question, if the decoded equation-based response does not match the equation of the question compare (i) the syntax tree created for the decoded equation-based response with (ii) a solution syntax tree, and grade the response according to the grading method based on the results of the comparison;

wherein said grading comprises awarding a score based on the extent to which nodes of the syntax trees match.

30. An apparatus comprising:

a processing device; and

memory storing computer program code, the processing device communicating with the memory and executing the computer program code causing the apparatus at least to, in response to a received encoded equation-based response to an assessment question, wherein said assessment question comprises an equation;

decode, by the processing device, said encoded equation-based response to yield a decoded equation-based response;

determine, by the processing device, a grading method selected from a plurality of different grading methods;

create a syntax tree for the decoded equation-based response;

determine whether the decoded equation-based response matches the equation of the assessment question;

if the decoded equation-based response does not match the equation of the assessment question compare (i) the syntax tree created for the decoded equation-based response with (ii) a solution syntax tree; and

grade the response according to the grading method based on the results of the comparison;

wherein said grading comprises awarding a score based on the extent to which nodes of the syntax trees match.

31. The apparatus of claim 30 wherein said grading method is selected from Order Equivalence, Formal Equivalence and Content Equivalence grading methods.

32. The apparatus of claim 31 wherein said processing device is caused to decode the encoded equation-based response into a type-setting language.

33. The apparatus of claim 32 wherein said type-setting language is LaTex.

34. A non-transitory computer readable medium embodying computer program code, which when executed causes a processing device to, in response to a received equation-based response to an assessment question, said assessment question comprising an equation:

decode, by the processing device, said encoded equation-based response to yield a decoded equation-based response;

determine, by the processing device, a grading method selected from a plurality of different grading methods;

create a syntax tree for the decoded equation-based response;

determine whether the decoded equation-based response matches the equation of the assessment question;

if the decoded equation-based response does not match the equation of the assessment question, compare (i) the syntax tree created for the decoded equation-based response with (ii) a solution syntax tree; and

grade the response according to the grading method based on the results of the comparison;

wherein said grading comprises awarding a score based on the extent to which nodes of the syntax trees match.