| NSF Org: |
DUE Division Of Undergraduate Education |
| Recipient: |
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| Initial Amendment Date: | September 19, 2016 |
| Latest Amendment Date: | August 15, 2018 |
| Award Number: | 1625678 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Karen Keene
DUE Division Of Undergraduate Education EDU Directorate for STEM Education |
| Start Date: | September 15, 2016 |
| End Date: | August 31, 2019 (Estimated) |
| Total Intended Award Amount: | $735,947.00 |
| Total Awarded Amount to Date: | $810,939.00 |
| Funds Obligated to Date: |
FY 2018 = $74,992.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
660 S MILL AVENUE STE 204 TEMPE AZ US 85281-3670 (480)965-5479 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
P.O.Box 871804 Tempe AZ US 85287-1804 |
| 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): | 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
Calculus is an essential tool, and provides a conceptual foundation, in each of the STEM disciplines. Acquiring deep conceptual understandings when first learning calculus poses many difficulties for students and creates many challenges for teachers. As a consequence, many concerted efforts in calculus reform appear to have failed to make educationally significant differences in student understanding that their proponents predicted. Project DIRACC: Developing and Investigating a Rigorous Approach to Conceptual Calculus will build on the documented success at Arizona State University's already-redesigned and already-deployed Calculus I to redesign and implement Calculus II, and will research students' learning in both the redesigned and traditional calculus sequences. In addition, Project DIRACC will develop short-answer assessment tools (also known as concept inventories) for Calculus I and Calculus II that other institutions can use to assess, compare and contrast their students' progress in understanding central ideas of the calculus. Students taking this redesigned calculus sequence will be better prepared for, and will be more likely to apply, their comprehension of rate-of-change functions and accumulation functions in other STEM courses and to learn calculus-dependent material in subsequent mathematics courses. The textbook produced by this project will be made available as an open resource for others to use or build upon. Finally, the results on students' calculus learning, and the calculus concept inventories built to investigate students' learning, will inform future research in these areas. Results from Project DIRACC will be disseminated widely at regional, national and international conferences and published in peer reviewed mathematics education journals and conference proceedings.
One possible reason for the lack of effectiveness of calculus reform is that the fundamental structure of the underlying curriculum has remained unchanged in the vast majority of contexts where the subject is taught. Specifically, reform projects have not focused on students' development of richly connected meanings for rate-of-change functions and accumulation functions, which are essential to any introductory calculus. The Project DIRACC courses are highly conceptual because they are based upon students' development of coherent meanings for ideas applicable throughout calculus and that also facilitate the learning of mathematical ideas beyond calculus. The first course addresses this challenge by making the fundamental theorem of calculus central to every aspect of students' experience of calculus in the course. At the same time, the Project DIRACC calculus sequence will be explicitly computational because, as in the existing first course, students will use computers to represent processes that define functions as models of dynamic situations, which then become objects of study themselves. The courses will also acknowledge and address known weaknesses in students' preparation for calculus. The calculus concept inventories will be developed using standard instrument-development techniques, given at the beginning and end of their respective courses, and their psychometric properties will be established with approximately 600 students per course.
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.
Project DIRACC’s impact is in two areas:
- Impact of DIRACC curricular approach to conceptual development for ideas of calculus
- Impact of Calculus 1 and Calculus 2 concept inventories
Impact of DIRACC’s Conceptual Development of Calculus
At ASU, DIRACC calculus is the standard curriculum for mathematics and science majors, with occasional exceptions due to unavailability of instructors familiar with DIRACC.
Locally, the ASU team is working with colleges in the Maricopa County Community College system to align calculus taught in the MCCC system and DIRACC math/science calculus at ASU.
The DIRACC curriculum is discussed widely in national and international circles. The PI regularly receives emails from people attending conferences of the Mathematical Association of America, American Mathematical Association of Two Year Colleges; Congress of the European Society for Research in Mathematics Education, International Group for the Psychology of Mathematics Education, and the MAA Special Interest Group for Research in Undergraduate Mathematics Education who heard about DIRACC and wish to learn more. The PI was invited to an international conference in Norway to speak about the DIRACC curriculum—its motive, design, and impact on student learning.
Regarding DIRACC’s impact on curricular efforts, Steve Boyce (Portland State University) is adapting portions of the DIRACC curriculum under its Creative Commons license for use in the Knewton calculus curriculum. The Israeli high school curriculum committee included variation, covariation, and accumulation functions as key concepts in its new 5-point high school mathematics curriculum as a result of members learning of the PI’s research and the DIRACC curriculum.
Impact of Calculus 1 and Calculus 2 concept inventories
The DIRACC Calculus Concept Inventories have had both a national and international impact. Texas A & M University received an NSF grant to build from the C1CI (and other instruments) to create an assessment that can be used as both a pretest and a posttest. The C1CI is used most appropriately as an end-of-semester assessment. A working group of the MAA Special Interest Group for Research in Undergraduate Mathematics is also using the C1CI in its effort to assess students’ understanding of core concepts of calculus. Finally, The Israel Science Foundation funded a grant led by Tommy Dreyfus in which the DIRACC C1CI is mentioned specifically in terms of its methodology and as inspiration for a high school calculus concept inventory. The PI is a consultant on the Dreyfus grant.
Last Modified: 01/09/2020
Modified by: Patrick Thompson
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