| NSF Org: |
DUE Division Of Undergraduate Education |
| Recipient: |
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| Initial Amendment Date: | July 4, 2013 |
| Latest Amendment Date: | June 3, 2019 |
| Award Number: | 1246094 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Karen Keene
DUE Division Of Undergraduate Education EDU Directorate for STEM Education |
| Start Date: | July 1, 2013 |
| End Date: | September 30, 2019 (Estimated) |
| Total Intended Award Amount: | $225,261.00 |
| Total Awarded Amount to Date: | $257,237.00 |
| Funds Obligated to Date: |
FY 2017 = $31,976.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
175 W MARK ST WINONA MN US 55987-3384 (507)457-5519 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
MN US 55987-5838 |
| 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): |
S-STEM-Schlr Sci Tech Eng&Math, IUSE, TUES-Type 1 Project |
| Primary Program Source: |
04001718DB NSF Education & Human Resource 1300XXXXDB H-1B FUND, EDU, NSF |
| 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
This project team is investigating a new method for teaching and learning multivariable calculus in which students actively explore central ideas through measurement and conjecture. The intellectual merit of this approach rests on the use of physical models of multivariable functions with a dry-erase surface and accompanying instruments that allow students to draw, measure, and grasp concepts geometrically. Through a marriage of the "flipped classroom" and collaborative learning, student teams work through activity sheets to investigate key ideas and relationships before a formal introduction in lecture. The project team conjectures that discovery learning with the physical models builds geometric understanding of multivariable calculus, imbues meaning in the algebraic formulas, improves performance and attitudes, and improves understanding of scientific applications. To disseminate its findings and exercise the project's broader impact, the PI team is conducting summer workshops with dozens of faculty, previously recruited from high schools, two- and four-year colleges and universities. Participants learn how about effective use of the surfaces and during the subsequent academic year all participants teach multivariable calculus using the surfaces, as well as arrange a control class at their respective institutions for comparison. Written assessments and clinical interviews are being used to compare learning outcomes between students using the surfaces and students receiving traditional instruction.
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 Raising Calculus to the Surface project was designed to help students extend simple calculus ideas into the world of multivariable calculus and discover new multivariable calculus concepts prior to lecture. The project created small group activities, surface manipulatives, and measurement tools which let students draw, measure, and make connections between various representations of multivariable functions prior to formal lecture. The activities were designed to support both small group and whole class discussion, providing space for students to make discoveries in small groups and engage in mathematical debate at the whole class level. These discussions are often used to feed upcoming content in the course.
The manipulatives and measurement tools serve several purposes within the classroom. First, the surface and contour map manipulatives serve as a common work space for students within the small groups, as all of the manipulatives have a dry erase finish. Second, as students are free to rotate and turn the manipulatives in any direction, they explore calculus concepts which are coordinate-independent. Third, as there are six different surface models, student groups are able to investigate mathematics in their specific case and provide their evidence during whole class discussion. Students are able to point, draw upon, and refer to the surface or contour representations and relationships between them even before they've mastered formal definitions, enabling more student to participate in discussion and helping instructors engage students in authentic mathematic discourse. Lastly, the project helps instructors utilize student ideas and concepts to drive new course content.
The project has been shared among mathematics and physics instructors. The project has hosted nine workshop with more than 100 attendees. More than 50 instructors have used the materials in their classrooms. The project has produced more than 10 peer-reviewed publications and provided more than 40 presentations at regional, national, and international conferences.
Last Modified: 08/12/2020
Modified by: Aaron Wangberg
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