"iii. Professional Learning Communities (PLCs): PLCs are being established withdepartments to improve collaboration and identify tactics to improve student performance(DuFour, DuFour, Eaker, & Many, 2006).iv. Teacher Collaboration: Collaboration has been shown to contribute to school and studentsuccess in qualitative but not quantitative studies (Piccardi, 2005; Erkens, 2008; DuFour,2011).v. Teacher Collaboration (independent variable) can be measured using a tested andvalidated instrument (dependent variable) (Naughton, 2006);Student Achievement canbe measured using mathematics results on state test scoresvi. Methodology: Quantitative causal comparative design: The study will use a causalcomparative design to compare two groups as has been done in prior studiesd. Synthesis/Summaryi. Background: There is Need to Close the Mathematics Achievement Gapii. Gap/Problem: Demonstrate relationship between collaboration in PLC and mathematicsachievement in high minority low SES grade schoolsiii. PLCs: The Way to Implement Change is through Collaboration through PLCsiv. Collaboration: Collaboration is a mean to Impact Student Achievement v. Final Thoughts3. Problem statement - Explain the phenomena to study (qualitative) or variables/groups(quantitative) to study, in one sentence: It is unknown what differences exist, if any, in the levelsof perceived teacher collaboration within PLCs in schools identified as high performing versus thosereported at low performing schools, which serve both a high percentage of low SES students andHispanic students, on state math assessment.13 4. Sample and location – Identify sample, needed sample size, and location (study phenomenawith small numbers and variables/groups with large numbers): Need at least 30 grade schoolsthat are high performing and 30 that are low performing on state mathematics test scores in the stateof Texas. Schools need to have established PLCs for mathematics.a. Research questions – Provide research questions to collect data to answer the problemstatement:R : What differences exist, if any, between the levels of perceived teacher1 collaboration within PLCs in schools identified by the state of Texas as high performing versusthose perceived at low performing schools that serve both, a high percentage of low SES andHispanic students, on state math assessment?b. Hypothesis/variables or Phenomena - Develop Hypotheses with variables for each researchquestion (quantitative) or describe the phenomena to be better understood(qualitative)Compare high performing schools on their state test scores in mathematics (group1)to low performing schools (group 2)on their perceived level of collaboration in themathematics PLCs.c. H : There would be a significant difference betweenthe levels of perceived teacherA collaboration within PLCs in schools identified by the state of Texas as high performing versusthose perceived at low performing that serve both, a high percentage of low SES and Hispanicstudents, on state math assessment.d. H : There would be no significant difference between the levels of perceived teacher0 collaboration within PLCs in schools identified by the state of Texas as high performing versusthose perceived at low performing that serve both, a high percentage of low SES and Hispanicstudents, on state math assessment.14 5. Methodology and design - Describe the selected methodology and specific research design toaddress problem statement and research questions: Quantitative methodology with a causalcomparative research design6. Purpose statement – Provide one sentence statement of purpose including problem statement,sample, methodology, and design:The purpose of this causal comparative quantitative study is toexamine to what extent the level of teacher collaboration within Mathematics PLCs is a factor that may influence the mathematics achievement level on the Texas mathematics assessment ofelementary schools identified as 'high performing' or 'low performing', and serving a majority of lowSES and Hispanic students.7. Data collection – Describe primary instruments and sources of data to answer researchquestions:For the independent variable, this study will use the Mathematics Staff InteractionQuestionnaire (MSIQ) developed by Naughton (2006).To measure the dependent variable, theresearcher will use archival data (provided by the district’s Research Review Board office) for eachelementary school in one North Texan school district to differentiate schools based onachievementlevel as indicated by the 2011 Texas mathematics assessment.8. Data analysis – Describe the specific data analysis approaches to be used to address researchquestions:A priori analysis will be used to justify the sample size. Descriptive statistics will describethe sample characteristics and variable results. An independent t-test will test for difference betweenthe two groups of 30 schools (high performing versus low performing on mathematics) on level ofcollaboration. 15 "