| NSF Org: |
DRL Division of Research on Learning in Formal and Informal Settings (DRL) |
| Recipient: |
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| Initial Amendment Date: | August 9, 2012 |
| Latest Amendment Date: | July 16, 2015 |
| Award Number: | 1222340 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Ferdinand Rivera
DRL Division of Research on Learning in Formal and Informal Settings (DRL) EDU Directorate for STEM Education |
| Start Date: | August 15, 2012 |
| End Date: | July 31, 2018 (Estimated) |
| Total Intended Award Amount: | $147,243.00 |
| Total Awarded Amount to Date: | $147,243.00 |
| Funds Obligated to Date: |
FY 2014 = $37,260.00 FY 2015 = $38,438.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
1520 SAINT OLAF AVE NORTHFIELD MN US 55057-1574 (507)786-3000 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
1520 St. Olaf Avenue Northfield MN US 55057-1574 |
| 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): | Discovery Research K-12 |
| Primary Program Source: |
04001415DB NSF Education & Human Resource 04001516DB 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
Boston University, Education Development Center, Inc., and St. Olaf College are collaborating on Assessing Secondary Teachers' Algebraic Habits of Mind (ASTAHM) to develop instruments to assess secondary teachers' Mathematical Habits of Mind (MHoM). These habits bring parsimony, focus, and coherence to teachers' mathematical thinking and, in turn, to their work with students. MHoM is a critical component of mathematical knowledge for teaching at the secondary level. Recognizing the need for a scientific approach to investigate the ways in which MHoM is an indicator of teacher effectiveness, the partnership is researching the following questions:
1. How do teachers who engage MHoM when doing mathematics for themselves also bring MHoM to their teaching practice?
2. How are teachers' engagement with MHoM and their use of these habits in teaching related to student understanding and achievement?
To investigate these questions, ASTAHM is developing two instruments: a paper and pencil (P&P) assessment and an observation protocol that measure teachers' knowledge and classroom use, respectively, of MHoM.
The work is being conducted in two phases: (1) an instrument-refinement and learning phase, and (2) an instrument-testing and research phase. Objectives of Phase 1 are to gather data to refine the project's existing instruments and to learn about the bridge factors that impact the relationship between teachers' knowledge and classroom use of MHoM. Specific research activities include: administering the pilot P&P assessment to 40 teachers, videotaping Algebra instructions of 8 teachers, performing initial testing and refinement of the instruments, and using the data to analyze the bridge factors. Phase 2 is a large-scale study involving field-testing the P&P assessment with 200 teachers, videotaping 20 teachers and studying them using the observation protocol, collecting achievement data from 3000 students, and checking P&P content validity with 200 mathematicians. With these validated instruments in hand, the project will then conduct an investigation into the above research questions. Lesley University's Program Evaluation and Research Group (PERG) is the external evaluator. PERG is assessing ASTAHM's overall success in developing valid and reliable instruments to investigate the extent to which a relationship exists between teachers' MHoM and their classroom practice, as well as student achievement. Evaluators are also investigating whether users' coding guides for both instruments enable field-testers to effectively use and adequately score them.
This work fits into a larger research agenda with the ultimate goal of understanding the connections between secondary teachers' mathematical knowledge for teaching and secondary students' mathematical understanding and achievement. The MHoM construct is closely aligned with the Common Core State Standards-Mathematics (CCSS-M); especially its Standards for Mathematical Practice. For example, both place importance on seeking and using mathematical structure. Thus the instruments this project produces can act as pre- and post-measures of the effectiveness of professional development programs in preparing teachers to implement the CCSS-M. Mathematics teacher knowledge at the secondary level is an understudied field. Through analyses of the practices and habits of mind that teachers bring to their work, ASTAHM is developing instruments that can be used to shed light on effective secondary teaching.
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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.
School districts have limited funds for professional development for secondary teachers. They have to make wise choices about how to use those funds to have the greatest impact on students. However, the field does not have good answers to questions about what kinds of knowledge teachers need to most effectively serve students’ mathematical needs. Furthermore, the field has not had tools to investigate these questions. Districts are thus making decisions about professional development with limited information.
Mathematics teachers are expected to know their content well, but research in mathematics education has revealed that these teachers need much more. In particular, they need content knowledge that is specific to the work of teaching. This notion of mathematical knowledge for teaching (MKT) has been researched extensively in elementary education, but MKT has been understudied at the secondary school level. This project investigated mathematical habits of mind as critical components of MKT at the secondary level. These mathematical habits of mind are the specialized ways of approaching mathematical problems and thinking about mathematical concepts that resemble the ways employed by mathematicians. Our work over the past decade has convinced us of the importance of these habits for students and for teachers of mathematics. They bring focus and coherence to teachers’ mathematical thinking and, in turn, to their work with students.
What students need to learn to be successful in secondary school mathematics also goes beyond traditional content. New standards recognize this: for example, the Common Core State Standards for Mathematical Practice address this with a set of habits and practices — to be taught as part of the standard mathematics curriculum — that will equip students to be lifelong learners of whatever mathematics content they need. So teachers also need to be adept at using these habits and practices so that they can fosters these habits in their students. However, the field does not yet know how to measure the extent to which secondary teachers have these habits themselves.
The Assessing Secondary Teachers’ Algebraic Habits of Mind (ASTAHM) project made inroads in these issues in the following ways:
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The project identified several mathematical habits of mind that are particularly useful in the work of secondary mathematics teachers.
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The project created a paper and pencil assessment to measure secondary teachers’ mathematical habits of mind. The project conducted statistical analyses on the assessment to ensure that it is statistically valid and reliable, so that it can be used by research projects, school districts, and professional developers.
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The project created an observation tool to capture the mathematical habits that are used by secondary teachers in their classroom work with students.
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The project analyzed and identified relationships between teacher outcomes on the assessment and student achievement data.
Federal and foundation funded projects have used ASTAHM tools to measure their impact on teachers’ knowledge and practice. Researchers on the ASTAHM team and others have also used the tools to find a collection of valuable insights:
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Growth in mathematical habits of mind in the context of mathematics and equity oriented PD was linked to better measures of instructional quality as measured by the Instructional Quality Assessment (Boston, 2012).
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Growth in mathematical habits of mind has been linked to student outcomes on the Tripod survey (Tripod Education Partners), a measure of students’ classroom experiences. In particular, students with teachers whose scores on the ASTAHM assessment rose reported feeling more cared for in class. (Sword, Matsuura, Cuoco, Stevens, 2018)
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Relationships between teacher mathematical habits of mind and student achievement are complex; however, analyzing data in a small sample suggests that better mathematical habits of mind for teachers are correlated with better outcomes for students. (See figure below.)
More research is needed to better unpack the complex relationships between secondary teacher knowledge and student achievement in mathematics. ASTAHM has provided tools to conduct that research.
Last Modified: 10/05/2018
Modified by: Ryota Matsuura
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