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Moodle Stack Quiz Type 박종대 배재대학교
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Stack 이란 ? System for Teaching and Assessment using a Computer algebra Kernel Maxima 를 기반으로 함. Random 변수를 사용한 문제 출제 가능. Random 변수를 사용하는 경우 퀴즈 시도 할때 마다 문제가 달라짐. 다양한 답에 대해 세밀한 채점 가능. 그래프 출력가능.
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Maxima Maxima is based on a 1982 version of Macsyma, which was developed at MIT with funding from the United States Department of Energy and other government agencies. A version of Macsyma was maintained by Bill Schelter from 1982 until his death in 2001. In 1998, Schelter obtained permission from the Department of Energy to release his version under the GPL. That version, now called Maxima, is maintained by an independent group of users and developers.MacsymaMITUnited States Department of EnergyMacsymaBill Schelter Maxima does not include any of the many modifications and enhancements made to the commercial version of Macsyma during 1982–1999. Though the core functionality remains similar, code depending on these enhancements may not work on Maxima, and bugs which were fixed in Macsyma may still be present in Maxima, and vice-versa.Macsyma
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장점 Multi-part mathematical questions are possible: each question may have any number of inputs and any number of potential response trees. Partial credit is possible when an expression only satisfies some of the required properties. Plots can be dynamically generated and included within any part of the question.
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입력 matrix([1,2,3],[4,5,6]) enter α+β as alpha+beta, and 2π as 2*pi 1<x and x<5, not 1<x<5 for list 1,2,2,3 type [1,2,2,3] For set type {1,2,3} should be entered as exp(a*x)*sin(b*x) i is entered as either i or %i
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특수기호
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수식 입력
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@plot([x^4/(1+x^4),diff(x^4/(1+x^4),x)],[x,-3,3])@ @plot([sin(x),x,x^2,x^3],[x,-3,3],[y,-3,3])@
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Live Data Capture
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KeyVals key : value for example, p : (x-1)^3 Each key is the name of a variable local to the question Value is an expression in Maxima's languageMaxima's
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Potential Response Tree
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Question Variable x0 : -2; f0 : 1; x1 : 0; f1 : sin(x) /* Note, we should really use inf instead of 1000 here, but Maxima gives up plotting with the options used by STACK */ pg:if x<x0 then f0 else if x<x1 then 1000 else f1; CS:matrix([1,x0,x0^2,x0^3],[0,1,2*x0,3*x0^2],[1,x1,x1^2,x1^3],[0,1,2* x1,3*x1^2]); CT:transpose(matrix([ev(f0,x=x0),subst(x=x0,diff(f0,x)),ev(f1,x=x1),s ubst(x=x1,diff(f1,x))])); CV:transpose(matrix([a0,a1,a2,a3])); CS2:invert(CS).CT; ta : matrix([1,x,x^2,x^3]).CS2; tapt : if (x>x0 and x<x1) then ta else 1000;
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Answer Test : AlgEquiv This is the most commonly used test. The pseudo code If simplify(ex1-ex2) = 0 then true else false. This test will work with a variety of types of object of mathematical objects, including lists, sets, equations, inequalities and matrices. Exactly what it does depends on what objects are given to it.types of object This test disregards whether simplification is switched on, it always fully simplifies all its arguments.simplification
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Answer Test : CasEqual Are the parse trees of the two expressions equal?EqualComAssAre they equal up to commutativity and associativity of addition and multiplication, together with their inverses minus and division? For examplea+b=b+aEqualComAss
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Answer Test : EqualComAss Equality up to Associativity and Commutativity x+x≠2x. This is very useful in elementary algebra, where we want the form of the answer exactly. Simplification is automatically switched off when this test is applied, otherwise it makes no sense.
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Answer Test : NumRelative Tests whether abs(sa-ta) <= opt * abs(ta) Hence the opt is a tolerance.
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Answer Test : NumAbsolute Tests whether abs(sa-ta) < opt Hence the opt is a tolerance. The default tolerance is 0.05.
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Answer Test : SysEquiv The SysEquiv (system equivalence) test takes in two lists of polynomial equations in any number of variables and determines whether the two systems have the same set of solutions. This is done using the theory of Gröbner bases to determine whether the ideals generated by the two systems are equal. As the test allows for polynomials in several variables, it can cope with the intersections of the conic sections, as well as a large number of geometrically interesting curves. This test disregards whether simplification is switched on, it only simplifies its arguments where required. This allows the test to list equations in feedback that the student has erroneously included in their system.simplification
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결 론결 론 중학교에서 수학에 대해 흥미를 잃으면 고 등학교에서 복구가 어려운데, 무들 Stack 퀴즈를 사용하면 여러 번 시도 및 즉각 피드 백등으로 자기주도적 학습 환경 제공 가능. 중학교 수학문제를 체계적으로 입력하여 공유하면 좋을 것임. 거꾸로 교실등에 활용가능.
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