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Proof Blocks: Autogradable Scaffolding Activities for Learning to Write Proofs
Proof Blocks: Autogradable Scaffolding Activities for Learning to Write Proofs
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20260209102850
- ISBN
- 9798291564028
- DDC
- 510
- 저자명
- Poulsen, Seth.
- 서명/저자
- Proof Blocks: Autogradable Scaffolding Activities for Learning to Write Proofs
- 발행사항
- [Sl] : University of Illinois at Urbana-Champaign, 2023
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2023
- 형태사항
- 157 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 87-02, Section: B.
- 주기사항
- Advisor: Herman, Geoffrey;West, Matthew.
- 학위논문주기
- Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2023.
- 초록/해제
- 요약This dissertation introduces Proof Blocks, a tool which enables students to construct mathematical proofs by dragging and dropping prewritten proof lines into the correct order instead of needing to write them from scratch. First we present implementation details of the tool, as well as a rich reflection on our experiences using the tool in courses with hundreds of students. When writing a problem, the instructor specifies the dependency graph of the lines of the proof, so that any correct arrangement of the lines can receive full credit. We develop a novel algorithm which enables assigning students' partial credit on Proof Blocks problems based on the number of edits that their submission is from a correct solution, and give benchmarking results showing that this performance gives significant performance gains over the baseline algorithm, enabling large scale classroom deployment.Finally, we will present evaluations of Proof Blocks both in learning and assessment contexts. For assessment, we provide statistical evidence that Proof Blocks are easier than written proofs, which are typically very difficult. We also show that Proof Blocks problems provide about as much information about student knowledge as written proofs. Survey results show that students believe that the Proof Blocks user interface is easy to use, and that the questions accurately represent their ability to write proofs. Through our experiments targeted at measuring student learning, we provide evidence about various aspects of the process of students learning proof by induction. We give evidence that using Proof Blocks alone is not as effective for learning as using Proof Blocks after reading educational materials first. We also show that students who read a book chapter and complete a Proof Blocks activity perform marginally better than students who only read the book chapter, but it is not clear if the source of this improvement is the Proof Blocks or just exposure to more examples. Together with the evidence from out study showing that students who write proofs from scratch also learn no more than students just reading the book chapter, we conclude that though students can have clear learning gains very quickly when they have low knowledge of proof by induction, subsequent incremental learning gains are very difficult, and it is not well understood how to design a learning activity to help students experience these learning gains in a short period of time.
- 일반주제명
- Mathematics education
- 일반주제명
- Computer science
- 일반주제명
- Pedagogy
- 일반주제명
- Educational technology
- 키워드
- Graph algorithms
- 키워드
- Proof blocks
- 기타저자
- University of Illinois at Urbana-Champaign Computer Science
- 기본자료저록
- Dissertations Abstracts International. 87-02B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■020 ▼a9798291564028
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■035 ▼a(MiAaPQ)httphdlhandlenet2142121414
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a510
■1001 ▼aPoulsen, Seth.
■24510▼aProof Blocks: Autogradable Scaffolding Activities for Learning to Write Proofs
■260 ▼a[Sl]▼bUniversity of Illinois at Urbana-Champaign▼c2023
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2023
■300 ▼a157 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 87-02, Section: B.
■500 ▼aAdvisor: Herman, Geoffrey;West, Matthew.
■5021 ▼aThesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2023.
■520 ▼aThis dissertation introduces Proof Blocks, a tool which enables students to construct mathematical proofs by dragging and dropping prewritten proof lines into the correct order instead of needing to write them from scratch. First we present implementation details of the tool, as well as a rich reflection on our experiences using the tool in courses with hundreds of students. When writing a problem, the instructor specifies the dependency graph of the lines of the proof, so that any correct arrangement of the lines can receive full credit. We develop a novel algorithm which enables assigning students' partial credit on Proof Blocks problems based on the number of edits that their submission is from a correct solution, and give benchmarking results showing that this performance gives significant performance gains over the baseline algorithm, enabling large scale classroom deployment.Finally, we will present evaluations of Proof Blocks both in learning and assessment contexts. For assessment, we provide statistical evidence that Proof Blocks are easier than written proofs, which are typically very difficult. We also show that Proof Blocks problems provide about as much information about student knowledge as written proofs. Survey results show that students believe that the Proof Blocks user interface is easy to use, and that the questions accurately represent their ability to write proofs. Through our experiments targeted at measuring student learning, we provide evidence about various aspects of the process of students learning proof by induction. We give evidence that using Proof Blocks alone is not as effective for learning as using Proof Blocks after reading educational materials first. We also show that students who read a book chapter and complete a Proof Blocks activity perform marginally better than students who only read the book chapter, but it is not clear if the source of this improvement is the Proof Blocks or just exposure to more examples. Together with the evidence from out study showing that students who write proofs from scratch also learn no more than students just reading the book chapter, we conclude that though students can have clear learning gains very quickly when they have low knowledge of proof by induction, subsequent incremental learning gains are very difficult, and it is not well understood how to design a learning activity to help students experience these learning gains in a short period of time.
■590 ▼aSchool code: 0090.
■650 4▼aMathematics education
■650 4▼aComputer science
■650 4▼aPedagogy
■650 4▼aEducational technology
■653 ▼aEducational software
■653 ▼aMathematical proofs
■653 ▼aGraph algorithms
■653 ▼aProof blocks
■690 ▼a0984
■690 ▼a0280
■690 ▼a0456
■690 ▼a0710
■71020▼aUniversity of Illinois at Urbana-Champaign▼bComputer Science.
■7730 ▼tDissertations Abstracts International▼g87-02B.
■790 ▼a0090
■791 ▼aPh.D.
■792 ▼a2023
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17365895▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
