Theoretical Framework

Research and Outreach

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Theoretical Framework and/Or Rationale

The Theoretical Framework describes your approach to the problems based on both the literature reviewed and your own professional experiences.

The Rationale is similar to a theoretical framework but usually not as comprehensive. It also specifies how your approach best addresses the needs outlined in the Needs Assessment.

Grant proposals require either a Theoretical Framework or Rationale.

Theoretical Framework and/or Rationale provide:

  • A framework for your approach based on key concepts
  • Why your approach best addresses the statements of your Needs Assessment and the project goal(s)

Sample #1 (Theoretical Framework)

Theoretical Framework for the Capacity Building Model for Mathematics Achievement

The roots of the XYZ  Systems Approach to mathematics reform are grounded in both the literature in the STEM education field and in the extensive experiences of the mathematics educators and mathematicians who will be involved in implementing and researching the proposed systems research. Based on our own experiences and supported by Cohen and Hill’s Learning Policy (2001), we believe that many educational reforms fail because teachers and the systems in which they work are not placed at the center of the reform.

As described earlier we found that variables affecting the success of lesson study included whether or not teachers had access to a quality standards-based curriculum, the school and district in which they worked had aligned teaching with the curriculum and the state standardized assessment, and the school and/or district had a system for supporting teacher collaboration. All of these factors were considered in designing the systems model used in the XYZ Systems Approach. Critical elements included: (1) A commitment to using one standards-based curriculum for all schools and students that was district-wide and both top-down and bottom-up (2) The selection of an NSF-developed curriculum, namely Investigations in Number, Data and Space and Connected Mathematics  (3) Alignment of the curriculum with teaching and assessment, including the use of formative assessments (4) Extensive professional development, including 130 hours for teachers in mathematics content and teaching (5) Professional development for all administrators in how to support the new curriculum (6) Extensive academic year follow-up support in schools for teachers (7) Mathematics specialists at each school who give teachers immediate help and model lessons (8) Support and time for teacher collaboration.

Sample #2 (Rationale)

The model was developed and over the last ten years and was implemented and  researched through the XYZ, a  National Science Foundation grant (2000-2006) which was a partnership between the “Your Town School District” (YTSD) and Desert State University (DSU). This initiative was grounded in previous work by the researchers, mathematicians, math educators and school leaders who make up the authors of this systems capacity building research proposal. In the 1990s our work, like many math reform programs during this period, focused on teachers and provided PD that was of high quality, but largely disconnected from district, school and classroom cultures and practices. During a Star Schools grant (U.S. Department of Education, 1999) we collaborated on a three-state project (California, Colorado and New Mexico) to assist teachers to use technology and expanded pedagogy to improve student achievement in mathematics. The NM staff led the professional development efforts. After highly rated summer institutes with teachers, the grant leaders were disappointed when in follow-up visits they found almost no change in classrooms.

In 2002, the decision was made to change our professional development (PD) approach and co-construct mathematics PD with teachers around the learning needs of their students. Around this time, Lesson Study was being introduced to the U.S. and with the help of Dr. “Red” and Dr. “Blue” we introduced a modified form of lesson study in NM (Green & Brown, 2007). We noticed that those teachers who working in districts with a common agreed-upon standards-based curriculum and had administrative support for collaboration had the most success in increasing student achievement.  We also found through this collaborative work that teachers wanted to know more about the mathematics content and thus we invited mathematicians to collaborate with us in our work.

Based on this prior work, Pink, Green, and Yellow in collaboration with the YTSD developed a Local Systemic Change Initiative, the Your Town Mathematics Initiative (YTMI), (Award #xxxxx, 2001-2006). The YTMI was a partnership with the university to improve teachers’ knowledge and skills in teaching mathematics using standards based resources, specifically Investigations in Number, Data and Space and Connected Mathematics (CMP). This mathematics partnership between DSU and the YTMI was remarkably successful and further contributed to the development of a research-based model for a systems-based approach to capacity building for math achievement. This restructuring effort for students in grades K-8 in a low-income (100% free and reduced lunch) district with 60% English Language Learners (ELLs) resulted in closing the achievement gap, and in some cases surpassing state averages. Figure 1 shows where student achievement scores were when we started the project.

Figure 1
2000- Achievement Scores for YTSD Students as Compared to the State

graph1Figure 2 shows the proficiency levels for students in the district at the end of the five year program. Of special interest is the effect of the program on subgroups, especially ELLs who are now scoring far above all ELLs in the state. The students are above the state scores in grades 3 and 8. Students in those grades had spent the most time learning math in the XYZ. There is a drop in 11th grade. The initiative was aimed at K-8 students and the effects seem to be maintained in grade 9 but drop off as students move further into high school. The XYZ is fully sustainable by the district which is using operational funds to improve student achievement by continuing to have a math specialist at each school to support the mathematics PD.



graph2Figure 2 – 2006- Achievement Scores for YTSD Students as Compared to the State


A summary of scores by sub-groups is provided in Table I below. A Student Outcomes Study was begun in 2003 to look for the effect of the XYZ on student achievement. The final study showed that PD, level of implementation of the PD in the classroom, and teacher’s collaborative work using modified lesson study all had a significant positive effect on student achievement. A mixed effect statistical model was used to show that variance decreased in student test scores during the initiative which lead to higher achievement for all students. The study also found changes in classroom instructional behaviors which included increased use of teacher questioning, more problem-modeling, increased student engagement and increased classroom discourse (Green, Orange, Grey, White & Black, 2007).


Table I: Percent of Students Proficient or Above (2005-2006) New Mexico Standards Based Assessments
Grade 3 Grade 8
All Students 56% 44% 28% 26%
Hispanic Students 55% 39% 27% 19%
English Language Learners 57% 33% 21% 8%
Economically Disadvantaged 56% 36% 28% 14%
Students With Disabilities 27% 20% 4% 3%

Research on this initiative as well as related research in the field provides the basis for a systems-based capacity building model to support district-based mathematics achievement. The components in the capacity building model will provide the groundwork for the XYZ research study which will study the use of this model in a larger and more heterogeneous district.


Sample #3 (Rationale)



Folded Corner: Teacher Leaders help teachers improve classroom practice and build an infrastructure for continued professional learning.Rising expectations of classroom teachers to increase student learning coupled with the lack of capacity that school districts have to support teacher growth have created fault lines in education in which teachers and students are falling through the cracks. Principals are held accountable for increasing student achievement, yet they often lack the content knowledge and instructional expertise to support effective teaching practices.  We see Teacher Leaders as the bridge to create a support system for teachers and serve as a partner to school administrators in order to improve instruction for all students learning at the classroom level. A nation which is searching for ways to improve students’ Science learning is looking to classroom teaching for the answers (Cohen & Ball, 2001; Hiebert, Gallimore, & Stigler, 2002; Lampert, 1985; Stigler & Hiebert, 1999, 2004; National Council of Teachers of Science [NCTS], 1989, 1991, 2000; National Research Council [NRC], 2000). Teachers are asked to embrace ideas about teaching and learning that may be distinctly different from the ways in which they were taught (Cohen & Ball, 2001; Ma, 1999; NCTS, 1991).  Standards and curricula materials reflect different views about the nature of science, the role of the teachers in the science classroom, the way in which students learn mathematics, and the sources of scientific authority (Hiebert et al., 1997). Studies have shown that the teacher is the most important factor in realizing these changes (Darling-Hammond & Sykes; Sanders & Horn, 1998; Wenglinsky, 2000).  Teachers’ content knowledge is often a limiting factor in teaching science.  Ball’s work (1997, 2003, 2004) demonstrated that curriculum is mediated by the teacher’s knowledge of the subject.

Professional learning opportunities in science content and pedagogy are essential to the support of support teachers as they encounter these rising expectations (Darling-Hammond & Sykes, 1999; NCTL, 2000; Rand Corporation, 2003).  In addition, there is a need for new leadership models including science coaches and Teacher Leaders to support teachers in gaining the required new skills for teaching mathematics deeply and effectively. The literature on science teacher leadership highlights the need for the Teacher Leaders’ knowledge of science, science pedagogy, and students’ scientific thinking (Langbort, 2001, Friel & Bright, 2001). In her list of Who are Teacher Leaders? Langbort (2001) lists eighteen attributes of a science Teacher Leader, including being a spokesperson for science education, an active member of the science education community, and a mentor to other science teachers. According to Friel and Bright (2001), Teacher Leaders play two vital roles in their schools: 1) they can model quality instruction in their own classrooms and 2) facilitate reflection with colleagues.



A unique dichotomy exists in the Land of Enchantment known as New Mexico. While extensive collaborations around the state show that New Mexico has great potential to improve science learning, it is still a high-needs state in which almost all of its districts are designated as high-needs LEAs. On the one hand, two national labs and a significant presence of science- and technology-based industry mean that we have some of the world’s finest scientists. On the other hand, our remoteness and low population density limit us to a very small tax base, which has significant repercussions in the public schools. New Mexico personifies a cultural diversity that is also reflected in our schools, with a majority of our students (K-12) being Hispanic, second language learners. Therefore, as the first minority-as-majority-state (42%Caucasian, 47% Hispanic, 9% Native American, 1% African-American),  New Mexico has the unprecedented potential and consequent responsibility to educate traditionally underrepresented groups in the STEM (Science, Technology, Engineering, and Mathematics) fields to be the next generation of scientists, mathematicians, and engineers.

New Mexico is also well positioned to increase the quality, quantity, and diversity of Teacher Leaders. Over 50% of the students in DSU’s teacher education program are Hispanic students, and we have a growing number of Native American students studying to be teachers or participating in graduate programs in education. DSU has a solid record of increasing the successful participation and graduation of Hispanic students and students with disabilities in the STEM fields as demonstrated in NSF and Department of Education-supported programs throughout the university. We anticipate that at least half of our teachers for the institute will represent ethnically and linguistically diverse students.

Moreover, New Mexico is a reflection of the complex educational, cultural, and demographic changes occurring throughout the nation, but it is facing them sooner than the rest of the country. Consequently, we have a unique laboratory setting that is rich in ethnic, cultural, linguistic, socioeconomic, and geographic diversity.  Since students in classrooms across our nation are becoming more culturally and linguistically diverse, the successful strategies that promote student success that are implemented and documented in New Mexico can be replicated in the future in districts across our nation.

Students living in New Mexico desperately need improved science education. Our students rank very low on standardized tests in both science and math; 87% of 8th graders are below proficient levels in science, while 82% of 8th graders are below proficient levels in science. Being from the fourth poorest area of the United States, the majority of our students are on free or reduced lunches and come from homes where the median income for a family of four is $20,000. Twice as many children in New Mexico (24%) live in poverty as those throughout the U.S. (11.8%) (U.S. Census Bureau, 2005). New Mexico is one of the poorest states in the nation, and the repeating cycles of intergenerational poverty continue (Santos & Tiano, 2002; SW Hispanic Research Institutes, 2003).

In the 2003 Report Card on American Education, New Mexico ranked 48th in student achievement; in the 2003, 2005, and 2007 National Assessment in Educational Progress (NAEP) reports, New Mexico ranked 49th in terms of math and science achievement.

riverOther factors that have hindered the educational achievement of New Mexico students include: a high student drop-out rate; high teacher turnover; and a low high school graduation rate. We liken the flow of our students through the education system to an “acequia” (traditional Hispanic community irrigation system) analogy. New Mexico is ranked 50th in terms of the national matriculation rates (Kids Count, 2008). We start with a large flow of 9th graders, which is drained by a high school drop-out rate of almost 44%, with the drop-out rate increasing over the past five years. Of high school seniors, 62% are diverted from entering New Mexico colleges owing to many factors including the cost of higher education and the lack of prerequisite skills.

Looking at the U.S. Census Bureau for the poverty percent for all ages, we find that only Louisiana is poorer than New Mexico. In the poverty percent for all population members under 18, only three other states have a higher poverty rate than New Mexico.  Looking directly at some of our larger partner school districts, we see that in Las Cruces Public Schools over 25% of children age 5-17 are living in poverty, while in “Some-Town School District” almost 50% of children age 5-17 are living in poverty.