| NSF Org: |
DUE Division Of Undergraduate Education |
| Recipient: |
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| Initial Amendment Date: | July 24, 2015 |
| Latest Amendment Date: | August 15, 2018 |
| Award Number: | 1523898 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Patrice Waller
DUE Division Of Undergraduate Education EDU Directorate for STEM Education |
| Start Date: | August 1, 2015 |
| End Date: | July 31, 2022 (Estimated) |
| Total Intended Award Amount: | $343,998.00 |
| Total Awarded Amount to Date: | $412,773.00 |
| Funds Obligated to Date: |
FY 2018 = $68,775.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
1380 LAWRENCE ST STE 300 DENVER CO US 80204-2055 (303)724-0090 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
1201 Larimer Street, Suite 4000 Denver CO US 80217-3364 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): |
Robert Noyce Scholarship Pgm, IUSE |
| Primary Program Source: |
04001819DB NSF Education & Human Resource |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.076 |
ABSTRACT
Mathematics faculty members and educational researchers are increasingly recognizing the value of the history of mathematics as a support to student learning. This collaborative project, involving seven diverse institutions, will help students learn and develop a deeper interest in, and appreciation and understanding of, fundamental mathematical concepts and ideas by utilizing primary sources - original historical writings by mathematicians on topics in mathematics. Educational materials for students will be developed at all levels of undergraduate mathematics courses, and will be designed to capture the spark of discovery and to motivate subsequent lines of inquiry. In particular, the student projects to be developed will be built around primary source material to guide students, including pre-service teachers, mathematics majors, and other STEM discipline majors, to explore the mathematics of the original discovery in order to develop their own understanding of that discovery. Mathematics faculty and graduate students from over forty (40) institutions will participate in the development and testing process, thereby ensuring a large national network of faculty with expertise on the use of these educational materials. The impacts of the materials and approaches to implementing them will be investigated in terms of teaching, student learning, and departmental and institutional change.
The TRIUMPHS project will employ an integrated training and development process to create and test approximately fifty (50) student projects, which will include (1) twenty (20) primary source projects (PSPs) designed to cover its topic in about the same number of course days as classes would otherwise and (2) thirty (30) one-day mini-PSPs. In addition to the well-researched benefits of engaging students in active learning, particular advantages of this historical approach will involve providing context and direction for the subject matter. Important goals of the TRIUMPHS project are to (a) hone students' verbal and deductive skills through studying the work of some of the greatest minds in history and (b) invigorate undergraduate mathematics courses by identifying the problems and pioneering solutions that have since been subsumed into standard curricular topics. Through intensive, research-based professional development workshops, the TRIUMPHS project will also provide training in various aspects of developing and implementing PSPs to approximately seventy (70) faculty and doctoral students. By working collaboratively to develop PSPs while training faculty across the country in their use, the investigators will ensure that these educational materials are robustly adaptable and proactively disseminated to a wide variety of institutional settings, while simultaneously developing an ongoing professional community of mathematics faculty interested in teaching with primary sources. An evaluation-with-research study will provide formative and summative evaluation of the project, as well as contribute to the general knowledge base of (i) how student perceptions of the nature of mathematics evolve, (ii) how students' ability to write mathematical arguments changes over time, and (iii) how to support faculty in developing and implementing this research-based, active learning approach.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
The TRIUMPHS (TRansforming Instruction in Undergraduate Mathematics via Primary Historical Sources) project was a multi-year, seven-institution collaboration aimed at improving instruction in undergraduate mathematics by providing high-quality curricular resources and related professional development opportunities. Additional project goals include studying the effects of teaching and learning with these resources and the related professional development opportunities on instructors and their students, and strengthening the training of graduate students as future mathematics instructors and education researchers.
The foundation of this initiative has been the development, testing, and dissemination of Primary Source Projects (PSPs) designed to teach core topics in today's undergraduate mathematics curriculum through engagement with primary sources. Two key features distinguish PSPs from standard mathematics textbooks. First, PSPs place students in direct contact with the writings of the individuals who created and shaped the mathematics they are expected to learn, thereby exposing important mathematical ideas, the motivations behind those ideas, and the ways in which experts think about them. The second distinguishing feature of PSPs is a carefully crafted series of tasks that are closely intertwined with primary source passages to help students explore, interpret, and engage with the mathematics in those passages. This "guided reading" approach maintains the benefits of learning from primary sources by providing context, motivation, and direction to undergraduate mathematics learning, and addresses challenges associated with reading primary sources by incorporating inquiry-based learning principles that encourage instructors to use more student-centered teaching strategies than the typical lecture approach.
TRIUMPHS's significant accomplishments include:
Expanding the base of high-quality classroom materials available to undergraduate mathematics instructors.
The TRIUMPHS collection includes 99 PSPs on core topics taught in courses ranging across the entire undergraduate mathematics curriculum. To ensure the collection's quality while providing instructors a "hands-on" training experience, an integrated development cycle was employed in which PSPs were first vetted via a rigorous two-stage peer-review process before being made freely available for classroom use by site testers. Site testers then received implementation support via communication with project authors and a set of "Notes to Instructors" accompanying each PSP that offers concrete suggestions for classroom use. Afterwards, site testers provided feedback in the form of Implementation Reports which allowed authors a chance to revise their PSPs to further enhance quality.
Strengthening the ability of the undergraduate mathematics teaching community to meet the needs of a diverse student population through effective use of instructional strategies that actively engage students in learning and provide context for their mathematical studies.
133 faculty served as official Site Testers, with projects used in over 240 classrooms at more than 100 different institutions. Because PSPs are freely available by download from the TRIUMPHS website [https://blogs.ursinus.edu/triumphs/], an unknown additional number of instructors used PSPs in their classrooms. TRIUMPHS's extensive program of workshops and minicourses on the instructional use of PSPs further strengthened the development of human resources by providing participants with training related to the use of student-centered instructional practices in undergraduate mathematics.
Strengthening future undergraduate mathematics instruction by providing graduate students with co-teaching and mentoring opportunities under the direction of experienced PSP instructors.
TRIUMPHS provided six mathematics doctoral students and three mathematics education doctoral students with co-teaching experiences that involved the teaching of ten different courses in which PSPs were used. A workshop specifically designed for graduate students also provided 24 future mathematics faculty members with a unique training experience in the pedagogy of PSPs.
Strengthening the discipline of mathematics education through the addition of strong mathematics education researchers to the professoriate.
Four mathematics education doctoral students received mentoring in qualitative research methodology over the course of the grant, with one of these four producing the only PhD in the History and Pedagogy of Mathematics / Research in Undergraduate Mathematics Education domain in the US for many years, for his dissertation investigating aspects of instructor growth resulting from teaching with PSPs.
Extending the STEM education knowledge base regarding the effects on students and instructors of innovative teaching approaches and faculty training supporting the adoption of more student-centered classroom instruction.
Using data provided by our official site testers and the students enrolled in their courses, TRIUMPHS's ongoing Evaluation-with-Research study is contributing to a general understanding of:
* how to best support faculty in developing and implementing an active learning approach such as that represented by PSPs;
* the effects of studying mathematics from PSPs on students' worldviews, or perceptions about the nature of mathematics, as well as their learning of "meta-discursive rules," or the overarching standards that govern the ways in which experts carry out the practice of mathematics; and
* students' challenges with a PSP learning experience and the contribution of those challenging experiences to their mathematical growth (e.g., increased confidence in doing mathematics) using theoretical lenses from psychology that have application in mathematics education research.
Last Modified: 01/06/2025
Modified by: Diana White
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