PLI Leadership Project

Overview

Rationale and Purpose

"Mathematics is a more powerful instrument of knowledge than any other that has been bequeathed to us by human agency."

-Descartes.

Students, especially marginalized students (students with an IEP, students with unstable homes, and ELLs), show a lack of mathematical knowledge in number sense and problem solving skills.  Since these mathematical skills form the foundation of Algebra, most marginalized students are not meeting high school graduation requirements and/or college admittance requirements in mathematics.  “Algebra is the key to the future of disenfranchised communities” because it the gatekeeper to higher mathematics as well as “the gatekeeper for citizenship; and people who don’t have it are like the people who couldn’t read and write in the industrial age” (Moses & Cobb, 2001). When students in disenfranchised communities are not passing courses that meet graduation requirements, they are not given access to the higher education track that other students have the opportunity to access.

The Graduate School of Education and Informational Studies at UCLA published a report, which showed “despite the demonstrated importance of students explaining their thinking, teacher-centered instruction continues to dominate elementary and secondary classrooms.  Moreover, the vast majority of teacher queries consist of short-answer, low-level questions that require students to recall facts, rules, and procedures, rather than high-level questions that require students to draw inferences and synthesize ideas” (Franke, Webb, Chan, Battey, Ing, Freund, & De, 2007).  The report goes on to recommend that, “teachers need to scaffold, monitor, and facilitate discourse around the mathematical ideas in ways that support student learning.  Teachers need to ask questions, engage students with one another, support students in articulating their mathematical thinking and find ways to engage students in comparing ideas or coming to consensus” (Franke, Webb, Chan, Battey, Ing, Freund, & De, 2007).

My research has found CGI to be able to improve students’ mathematical knowledge, especially students in an urban environment, by changing the way teachers teach mathematics.  By starting with what students already know and then guiding them to more complex mathematical ideas, all students are successful.  By actively engaging in peer teaching and mathematical discussions, students are able to learn higher-level mathematical concepts from others and solidify their mathematical knowledge.  My PLI Leadership Project will test out whether implementing Cognitively Guided Instruction (CGI), in mathematics, will improve marginalized and struggling students’ number sense and problem solving skills.  By improving number sense and problem solving skills in marginalized student groups, I am hoping that these groups will be successful in higher level math/algebra courses and therefore be able to graduate high school and/or go on to receive a higher level education.

Leadership Role

My leadership role within this project was to:

1. Attend and actively participate in ongoing training, over multiple days, in CGI pedagogy.  Attend Cotsen math conferences (where CGI was highlighted by Dr. Megan Franke) and CGI networking events.  Observe exemplary teaching at various school sites, where teachers have successfully implemented CGI strategies in their own classrooms.

2.  Implement a new mathematics teaching pedagogy, CGI, that places an emphasis on number sense, critical thinking, and problem solving skills.  This pedagogy also naturally lends itself to developing the Standards for Mathematical Practice (SMPs) within students. We have identified our restraints to be our district adopted math curriculum (Envision) and have been given permission, by the district, to abandon this curriculum if we feel it necessary to successfully implement CGI.

3. Support my first grade team in implementing CGI across our grade level.  Sharing Math Wall activities with my team members and explaining the thinking behind each one of the activities. Lead my team in planning CGI math instruction/activities and writing CGI word problem together. Facilitate a discussion around our findings, what our students did, and our next steps.

4.  Model CGI pedagogy by opening my classroom for other teachers to observe CGI through situated learning.

5. Conduct action-research that answers the question, “How can we better develop our students’ critical thinking and problem solving skills, as well as their understanding of key mathematical skills that are the foundation of algebra?”

6.  Facilitate a first grade presentation of how CGI has positively affected students' mathematical thinking and problem solving abilities.

Root Cause Analysis, Literature Review,  and PDSA Cycles

“Children who think relationally identify number relations and reason about which transformations make sense in a particular problem.  Students who lack opportunities to explore these ideas often fail to take advantage of the structure of the number system so that the learning of both arithmetic and algebra becomes harder than it needs to be” (Jacobs, Franke, Carpenter, Levi, & Battey, 2007).

Knowing that this problem exists in the field of education, and seeing how well my students do with mathematical concepts at the elementary level, I was curious to see where students start to “hit the bump in the road” to higher-level mathematics.  I decided to research my school’s CST scores in mathematics and compare it to my district’s high school CST scores in mathematics.  After gathering and analyzing all of the data, I was shocked to discover a downward spiral of mathematics scores on both Culver City High School’s CST test and exit exam (CAHSEE).  At my elementary school, Linwood E. Howe Elementary in the Culver City Unified School District, there were huge discrepancies in CST math scores between marginalized groups.  For the 2010-2011 school year, all marginalized subgroups underscored the White subgroup.  These subgroups underscored the White subgroup from 56%-20%.  I was curious to see if this trend would repeat itself at the high school level, or if the education debt would get larger or smaller over time and with more courses and choices of course being offered.

After seeing the CST mathematics scores for Culver High School, the only high school in the Culver City Unified School District, I was floored.  Scores on the mathematics portion of the CST drastically dropped across all subgroups.  The educational debt between the marginalized subgroups and the White subgroup, performing at the proficient/advanced level, ranged between 34%-19%.  In general, all students’ mathematical skills became worse as their knowledge of mathematics advanced due to higher-level math courses.  It seems as though the opposite should happen; as students’ mathematical knowledge advances, so do their skills.  Culver City High School's did not meet their percentage proficient rate for mathematics on the CST for the 2010-2011school year. The high school’s CAHSEE scores show that 86% of ELLs were not proficient in high school mathematics.  On top of everything, the mathematics text/instructional materials that were being used at the high school were over 13 years old (adopted in 2000).

When conducting my literature review, I discovered that early childhood researches (Clements & Sarama, 2011) found that young children have the potential to learn complex and sophisticated mathematics and that their knowledge of mathematics predicts their later school success. Clements and Sarama (2011) have also found that students from low-resource communities may have fewer opportunities to mathematize tacit knowledge; to reflect on and represent the situations with cognitive tools.  These children are also less able to explain mathematical ideas and processes.  Clements and Sarama  (2011) go on to warn “children must learn to mathematize their informal experiences by abstracting, representing, and elaborating them mathematically.  If they do not, they miss the opportunity to learn the language of mathematics.”  These early childhood researchers support CGI pedagogy because, “teachers need integrated knowledge of all three components of learning trajectories:  the mathematical content (goal), the developmental progressions of children’s thinking and learning, and instructional tasks and teaching strategies that help children move along those progressions” (Clements & Sarama, 2011).

I also learned that, “the transition from arithmetic to algebra has proven difficult for students, and it is now widely recognized that students need earlier opportunities to engage in algebraic reasoning” (Jacobs, Franke, Carpenter, Levi, & Battey, pg. 259).  Many researchers have found that students should be exposed to algebraic thinking as early as kindergarten, in order to “provide a foundation for smoothing the transition to algebra in later grades” (Jacobs, Franke, Carpenter, Levi, & Battey, pg. 260).   Mathematical researches from all over the country have found relational thinking to be a powerful and unifying idea that helps engage teachers in conversations that support the use of students’ algebraic reasoning.  Jacobs, Franke, Carpenter, Levi, and Battey (2007) define relational thinking as looking at expressions and equations in their entirety, noticing number relations among and within these expressions and equations.  Researchers have also found that “by focusing on relational thinking, teachers can effectively integrate the idea of relations into the learning of arithmetic so that the concepts and skills that students acquire during elementary school are both enhanced and better aligned with the concepts and skills that they need later to learn algebra” (Jacobs, Franke, Carpenter, Levi, & Battey, 2007. Mathematical scholars argue that the “fundamental goal of integrating relational thinking into the elementary curriculum is to facilitate students’ transition to the formal study of algebra in the later grades so that no distinct boundry exists between arithmetic and algebra” (Jacobs, Franke, Carpenter, Levi, & Battey, 2007). The findings of their research show that students in participating teachers’ (those who were trained in and taught relational thinking) classrooms scored significantly better than students in classrooms of nonparticipating teachers.

Based on my literature review I decided to implement CGI pedagogy when teaching mathematics.  Cognitively Guided Instruction (CGI) (Carpenter, Fennema, Franke, Levi, & Empson, 1999) is a professional development program based on the integrated program of research focused on four key components: the development of students’ mathematical thinking, instruction that influences that development, teachers’ knowledge and beliefs that influence their instructional practices, and the way that teacher’s knowledge, beliefs, and practices are influenced by their understanding of students’ mathematical thinking.  The model of children’s thinking, which is the basis for CGI, is built on an extensive research base.  In one study, (Peterson et al, 1989) researchers found that classes of teachers whose beliefs were more consistent with principals of CGI tended to have higher levels of student achievement than classes of teachers whose beliefs were less consistent with principals of CGI.  In another study, Villasenor and Kepner (1993) found that urban students in CGI classes performed significantly better than a matched sample of students in traditional classes.  All of these studies show that students having longer participation in CGI classes showed greater gains in the upper grades during the second and third years of study.  CGI is a great teaching tool for marginalized groups because it is, “particularly effective in ameliorating the negative effects of some educators’ low expectations for African American children’s’ learning of mathematics through providing learning trajectories that help teachers see what children can do and how they can be helped to progress to higher levels of mathematical thinking” (Clements & Sarama, 2011). All of the research articles that I have read on elementary mathematics have consistently demonstrated that CGI students show significant gains in problem solving.

My PDSA Cycle outlines the problem I am trying to address, assumptions, activities, and anticipated results of the action-resaerch project.

Challenges and Changes

During the course of the leadership project, several challenges were posed that required changes to be made to the original implementation plan, as described below:

• Fidelity of Implementation: Teachers were afraid to stray from teaching EnVision Math curriculum, not following the district pacing guides, and not using district summative math assessments.  The key to the success of CGI implementation, was giving teachers the freedom to meet their students where they were at and then to bring them up from there.  To address this problem, I spoke with my principal and got her approval for teachers to use CGI math pedagogy instead of district approved curriculum.  When I went back to teachers with this good news, several still feared what would happen if the district caught them teaching math using CGI.  I then went to the Assistant Superintendent of Curriculum and Instruction and asked her for permission to teach using CGI pedagogy.  She gave her approval, but the same few teachers were still uneasy about teaching mathematics using CGI.
• K-2 CGI Implementation: By facilitating three of my first grade students through a very powerful school board presentation (of how CGI math has positively affected their mathematical skills) parents started advocating for their children to be instructed using CGI math techniques, instead of traditional teaching pedagogy.  After listening to parents and seeing how CGI had impacted student learning, the principal at my school site mandated that kindergarten through second grade teachers implement CGI pedagogy for the 2014-2015 school year.  My principal told teachers that they would be formally trained in CGI, so that they felt comfortable teaching mathematics using CGI.
• Addressing Negative Attitudes: After the district gave our school permission to use our current district adopted EnVision math curriculum as a resource (and not as what teachers have to teach) and the principal mandated CGI for the upcoming 2014-2015 school year, teachers still had negative attitudes towards implementing CGI.  A few teachers, and I, got together to try to address this issue and we decided to host a CGI Lab Day at our school site.  All K-2 teachers form our school site were invited, as well as teachers from both inside and outside of the district.

Data

I conducted a pre-assessment and a post-assessment to see the effects CGI pedagogy has had on my students' understanding of mathematical skills, critical thinking, and problem solving.

Upon analyzing the pre-assessment and post-assessment data that I collected, I found that all of my student groups (English Language Learners, Students with Disabilities, and Non EL/Non SDC) improved in their mathematic explanations, strategies and approaches, recording of thinking, and accuracy.  I also showed my students their pre and post-assessments, so they could compare how they have grown as mathematicians through the year.  All of my students stated that they think they are better mathematicians now (in May) and that they loved doing CGI number stories to learn math.

Modifications and Improvements

Upon reflection on the implementation of CGI pedagogy to teach mathematics, there are a few modifications that could be integrated for even better student outcome, including:

• Student and Family Centered Mathematics Projects:  These projects would be done at home with the student and his/her family.  They would extend the current classroom learning of mathematics skills and concepts.  They would also provide choice for students based on what interests them.  This would be more meaningful and purposeful than the current workbook style homework.
• Number Talks and Number Strands:  These whole class talks revolve around a number or a set of numbers.  They also focus on different mathematical skills and concepts.  They are teacher lead, and are used to help students understand foundational mathematical concepts by seeing the relationships between numbers.  These talks can also use Rekenreks and quick images.
• Math Workshop:  Students practice math skills through small group or individual activities while the teacher pulls small groups of students to work on math strategies, recording skills, mathematical concepts, and extend/stretch student leaning.
• Parental Involvement:  Provide parents with an informational CGI night at the beginning of the school year.  Discuss what CGI is, and what CGI is not.  Address any concerns parents have toward the CGI teaching pedagogy (since it is not the traditional way to teach mathematics).

Reflection

Through my action-research leadership project, I have improved how I teach mathematics.  My project has not only had a positive impact on my class, it also had an impact on all of the first grade students.  The impact my project has had will continue into the next academic school year (2014-2015) when all kindergarten through second grade students will receive mathematics instruction through CGI.  My students have a passion for mathematics and they view it as both fun and challenging.  I know where my students are at, in relation to the mathematical standards they are expected to learn, and where they are still developing their understandings of mathematical skills and concepts.

This leadership project has forced me to become a leader on campus and has allowed me to further my love of mathematics.  My concept of leadership has also changed through this project. Before I started this project, I thought leadership was the principal, but now I know that a school is comprised of teacher leaders.  I have become a leader of mathematics both at my school site and at the district level.  Teachers come into my classroom to watch me teach mathematics through CGI and they ask me for advice when choosing number sets for their CGI problems. I have also learned that leaders need to get more than the support of their teaching staff if they want to implement a change, they also need to get the support of their parent community.  This might mean that they need to hold parent meetings and/or present to the school board. The experiences and skills that I have utilized during this leadership project will help guide me through my future leadership roles.

CPSEL Connection

Standard 1 Facilitating the development, articulation, implementation, and stewardship of a vision of learning that is shared and supported by the school community.

1.1 Facilitate the development of a shared vision for the achievement of all students based upon data from multiple measures of student learning and relevant qualitative indicators.

1.2  Communicate the shared vision so the entire school community understands and acts on the school’s mission to become a standards-based education system.

1.3  Use the influence of diversity to improve teaching and learning.

1.4  Identify and address any barriers to accomplishing the vision.

1.5  Shape school programs, plans, and activities to ensure that they are integrated, articulated through the grades, and consistent with the vision.

1.6  Leverage and marshal sufficient resources, including technology, to implement and attain the vision for all students and all subgroups of students.

Standard 2 Advocating, nurturing, and sustaining a school culture and instructional program conducive to student learning and staff professional growth.

2.1  Shape a culture in which high expectations are the norm for each student as evident in rigorous academic work.

2.2  Promote equity, fairness, and respect among all members of the school community.

2.3  Facilitate the use of a variety of appropriate content-based learning materials and learning strategies that recognize students as active learners, value reflection and inquiry, emphasize the quality versus the amount of student application and performance, and utilize appropriate and effective technology.

2.4  Guide and support the long-term professional development of all staff consistent with the ongoing effort to improve the learning of all students relative to the content standards.

2.5  Provide opportunities for all members of the school community to develop and use skills in collaboration, distributed leadership, and shared responsibility.

2.6  Utilize multiple assessments to evaluate student learning in an ongoing process focused on improving the academic performance of each student.

Standard 3 Ensuring management of the organization, operations, and resources for a safe, efficient, and effective learning environment.

3.1  Sustain safe, efficient, clean, well-maintained, and productive school environment that nurtures student learning and supports the professional growth of teachers and support staff.

3.3  Establish school structures and processes that support student learning.

3.4  Utilize effective systems management, organizational development, and problem-solving and decision-making techniques.

3.5  Align fiscal, human, and material resources to support the learning of all subgroups of students.

3.6  Monitor and evaluate the program and staff.

Standard 4 Collaborating with families and community members, responding to diverse community interests and needs, and mobilizing community resources.

4.4  Communicate information about the school on a regular and predictable basis through a variety of media.

Standard 5 Modeling a personal code of ethics and developing professional leadership capacity.

5.1  Model personal and professional ethics, integrity, justice, and fairness, and expect the same behaviors from others.

5.3  Use the influence of office to enhance the educational program, not personal gain.

5.4  Make and communicate decisions based upon relevant data and research about effective teaching and learning, leadership, management practices, and equity.

5.5  Demonstrate knowledge of the standards-based curriculum and the ability to integrate and articulate programs throughout the grades.

5.6  Demonstrate skills in decision-making, problem solving, change management, planning, conflict management, and evaluation.

5.7  Reflect on personal leadership practices and recognize their impact and influence on the performance of others.

5.8  Engage in professional and personal development.

5.9  Encourage and inspire others to higher levels of performance, commitment, and motivation.

Standard 6 Understanding, responding to, and influencing the larger political, social, economic, legal, and cultural context.

6.1  Work with the governing board and district and local leaders to influence policies that benefit students and support the improvement of teaching and learning.

6.2  Influence and support public policies that ensure the equitable distribution of resources and support for all subgroups of students.

6.4  Generate support for the school by two-way communication with key decision-makers in the school community.

6.6  View oneself as a leader of a team and also as a member of a larger team.

Documentation

• CGI School Board Presentation
• PLI Project Prezi on Implementing CGI
• Math Partnership with Middle and High schools
• Madison's (Non EL/Non SDC) CGI Assessments
• Angelica's (EL) CGI Assessments
• Angel's (EL & SDC) CGI Assessments