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Culturally Sustaining Practices In Middle Schools, Chandra Diaz, Rebecca M. Nelson, Laurie A. Ramirez, Nancy B. Ruppert
Culturally Sustaining Practices In Middle Schools, Chandra Diaz, Rebecca M. Nelson, Laurie A. Ramirez, Nancy B. Ruppert
Current Issues in Middle Level Education
The social unrest during the summer of 2020 in the United States has produced a renewed sense of urgency and agency for the interrogation of curriculum in K-12 education and the development of culturally sustaining practices. This urgency has encouraged more teacher preparation programs to be intentional in developing culturally sustaining teachers. This paper offers four pillars to frame classroom practices to be integrated holistically and support middle level preservice teachers’ development of their culturally sustaining practices. Pillar one focuses on understanding self. The ability to honestly self-reflect and to understand personal practice deeply and continually is critical. Pillar two …
Unmasking Microaggressions On The Homefront: Exploring Faculty And Staff Perceptions After Attending An Online Workshop On Microaggressions In Higher Education, Andrea N. Crenshaw, Natasha N. Ramsay-Jordan, Allyson Deskins
Unmasking Microaggressions On The Homefront: Exploring Faculty And Staff Perceptions After Attending An Online Workshop On Microaggressions In Higher Education, Andrea N. Crenshaw, Natasha N. Ramsay-Jordan, Allyson Deskins
Georgia Educational Researcher
Microaggressions are brief and everyday slights, insults, indignities, and denigrating messages sent to people of color and/or marginalized groups (women, LGBTQ+, etc.) by well-intentioned [people] who are unaware of the hidden messages being communicated (Sue et al., 2007). Microaggressions are connected to broader conceptualizations of the impact of implicit bias and systems of inequity. Specifically, in K-12 and higher education, microaggressions impact the physical, social, and emotional well-being of those who experience them. Growing research posits the need for more discussions in education about racism, sexism, and other bias prevalent in the field of education (Bergerson, 2003). As such, some …
Securing Global Health: Global Citizenship And Covid-19 Awareness, Birol Bulut, Muhammed Kursat Oksuzoglu
Securing Global Health: Global Citizenship And Covid-19 Awareness, Birol Bulut, Muhammed Kursat Oksuzoglu
Georgia Educational Researcher
The aim of this study was to investigate the relationship between prospective social studies teachers' global citizenship levels and their COVID-19 awareness levels. To do that, Relational survey model, one of the quantitative research methods, was used. The sample consisted of 409 prospective social studies teachers selected by simple random sampling method from six universities in Turkey. Global Citizenship Scale (GCS), The Coronavirus (COVID-19) Awareness Scale (CAS), and the Personal Information Form developed by the researchers were used in data collection. The t-test, Pearson Correlation Analysis and Multiple Regression Analysis were per-formed to analyze data. A positive and significant relationship …
Arts-Based Interdisciplinary Music And Mathematics Tasks: Exploring Conceptualizations Of Equitable Creative Learning In Teacher Education, Alesia Mickle Moldavan, Graham Johnson
Arts-Based Interdisciplinary Music And Mathematics Tasks: Exploring Conceptualizations Of Equitable Creative Learning In Teacher Education, Alesia Mickle Moldavan, Graham Johnson
Georgia Educational Researcher
Preservice teachers need opportunities in teacher education courses to explore arts-based interdisciplinary learning that can inspire connections between communities of practice and allow learners to integrate concepts and imagine creative possibilities. This study reports on preservice teachers engaged in a workshop on arts-based interdisciplinary music and mathematics tasks. Data included surveys, task-related artifacts, and participant observations to examine how preservice teachers conceptualize and engage in such tasks. Three resonating themes were identified, revealing that preservice teachers generally thought (a) music and mathematics are more engaging and relatable in interdisciplinary contexts than when taught alone, (b) interdisciplinary music and mathematics tasks …
Reflection On Best Practices In Designing Online Middle Level Learning, Holly J. Thornton
Reflection On Best Practices In Designing Online Middle Level Learning, Holly J. Thornton
Current Issues in Middle Level Education
An increase in online learning during the pandemic has led to new thinking about online instruction that will last far beyond the pandemic. The hurried nature of instructional design as the pandemic shifted teaching and learning from the classroom to the computer may have neglected the need to design lessons using best practices online instead of focusing on content delivery and grading. Practices that are part of successful middle level education including cultivating depth of student understanding, developmental responsiveness, social emotional learning and differentiation to meet young adolescent student needs may have been neglected in pandemic online lesson design. This …
Examining Teaching And Learning Environments Among Kentucky Schools To Watch And Non-Schools To Watch Schools Using Tell Survey Data, Michael Dicicco, Ryan Alverson
Examining Teaching And Learning Environments Among Kentucky Schools To Watch And Non-Schools To Watch Schools Using Tell Survey Data, Michael Dicicco, Ryan Alverson
Current Issues in Middle Level Education
In 2017, the state of Kentucky distributed the Teaching, Empowerment, Leading, and Learning (TELL) survey to gain an understating of the learning environments in Kentucky schools. Many of the items on the TELL survey addressed key components of the School to Watch criteria and rubric. Researchers were interested in the teaching and learning conditions in Kentucky middle schools that contributed to successful school environments as defined by the Schools to Watch criteria, and to use results from the TELL survey to see what high scoring schools were doing well according to the teachers and principals that completed the survey. Researchers …
Differentiated Instruction And Kindergarten Through 5th Grade Teachers, Aslihan Unal, Zafer Unal, Yasar Bodur
Differentiated Instruction And Kindergarten Through 5th Grade Teachers, Aslihan Unal, Zafer Unal, Yasar Bodur
Georgia Educational Researcher
The purpose of this article is to examine Kindergarten through 5th-grade teachers’ understanding of differentiated instruction and perception of their ability to implement differentiated instruction in their classrooms. Differentiated instruction is a critical factor for children’s success. Thirty-one K-5 teachers from the state of Georgia participated in this study. The teacher survey on differentiated instruction developed by Tomlinson (2001) and modified by Page (2007) was used in this study. The researchers also included two open-ended, differentiated instruction questions and seven demographic questions. Study results suggested that while teachers mostly agree that differentiation is an important instructional strategy, they are faced …
Making Connections To Address Mathematics Anxiety: A Case Study Of The Instructional Triangle And Remedial College Instructors, Njeri M. Pringle, Jamie L. Workman, Meagan C. Arrastia-Chisholm
Making Connections To Address Mathematics Anxiety: A Case Study Of The Instructional Triangle And Remedial College Instructors, Njeri M. Pringle, Jamie L. Workman, Meagan C. Arrastia-Chisholm
Georgia Educational Researcher
Mathematics anxiety is a reality for many students as a number of community college and four-year university students feel disconnected from math and struggle to pass mathematics courses. Using a case study and grounded theory approach, six remedial mathematics instructors were interviewed and observed to examine their instructional strategies and practices. During the interviews, participants expounded upon the changes in strategies and practices implemented when aiding students struggling with anxiety. The Instructional Triangle was applied across participants to compare and contrast their experiences. The analysis focused on environmental factors that could increase or exacerbate mathematics anxiety. In particular, a theme …
“A Brave Group Of People”: Teacher Candidates’ Perceptions Of Teaching In Middle School, Bettie Perry, Jori S. Beck, Kaavonia Hinton
“A Brave Group Of People”: Teacher Candidates’ Perceptions Of Teaching In Middle School, Bettie Perry, Jori S. Beck, Kaavonia Hinton
Current Issues in Middle Level Education
We set out to create a middle grades program and to inform the field about the perceptions of our teacher candidates on teaching middle school. To accomplish these twin goals, we sought to better understand our teacher candidates’ perceptions of teaching middle school and how these perceptions might be changed if necessary. Our review of research included three themes to frame this work: (a) middle school philosophy, (b) motivations to teach, and (c) middle school teacher preparation. We chose an emergent, qualitative research design to cull rich data from diverse stakeholders including open-ended survey data. We found an overarching deficit …
Observation Of Field Practice Rubric: Establishing Content Validity And Reliability, Ruchi Bhatnagar, Carla L. Tanguay, Caroline Sullivan, Joyce E. Many
Observation Of Field Practice Rubric: Establishing Content Validity And Reliability, Ruchi Bhatnagar, Carla L. Tanguay, Caroline Sullivan, Joyce E. Many
Georgia Educational Researcher
Most teacher education assessments are criticized for lacking validity and reliability. This study describes the process of developing the Observation of Field Performance rubric to assess initial teacher candidates’ classroom performance and establishing the content validity as well as reliability of the rubric. A panel of content area experts determined that 10 out of 12 items of the rubric were essential and the CVR was above the acceptable range for all 12 items, indicating that the rubric had a strong content validity. Additionally, the analysis of instructors’ ratings on the rubric showed that the rubric had good level of internal …
Teacher Awareness Of Trauma Informed Practice: Raising Awareness In Southeast Georgia, Regina Rahimi, Delores D. Liston, Amee Adkins, Jamie Nourzad
Teacher Awareness Of Trauma Informed Practice: Raising Awareness In Southeast Georgia, Regina Rahimi, Delores D. Liston, Amee Adkins, Jamie Nourzad
Georgia Educational Researcher
While the concept of trauma-informed care has been developed in other fields, its development within the field of Education is relatively new (Thomas, Crosby, & Vanderhaar, 2019), However, as the educational field is becoming more and more aware of this approach, we recognize there is a critical need for teachers and other educational professionals to recognize the symptoms of trauma in students, the associated behaviors of trauma-affected students, and instructional and environmental strategies for addressing these to support student success (trauma informed pedagogy). This paper outlines a study examining the extent to which teachers in the region of southeast Georgia …
Teaching Candidates To Assess Student Learning: A Covid Collaboration With Arts And Sciences Faculty, Nancy B. Ruppert, Jessica Pisano
Teaching Candidates To Assess Student Learning: A Covid Collaboration With Arts And Sciences Faculty, Nancy B. Ruppert, Jessica Pisano
Current Issues in Middle Level Education
In the fall of 2020, due to COVID, our candidates did not have access to student work samples early in the semester. In order to learn how to assess student learning I reached out to an Arts and Sciences faculty who teaches a freshman course. The Arts and Science faculty was a former middle school teacher who was scheduled to talk about the teaching of writing in our methods class. We decided to add using work samples from her current students to provide an assessment experience. This exercise allowed candidates to create a one-point rubric, analyze student work, give feedback, …
Georgia Management Students’ Perceptions Of Faculty Academic Qualifications And Professional Experiences, Juliann Sergi Mcbrayer, Gregory Quinet, Steven Tolman, Katherine Fallon
Georgia Management Students’ Perceptions Of Faculty Academic Qualifications And Professional Experiences, Juliann Sergi Mcbrayer, Gregory Quinet, Steven Tolman, Katherine Fallon
Georgia Educational Researcher
The purpose of this study was to explore perceptions of undergraduate management students at one Georgia institution of higher education regarding the importance of academic qualifications and professional experiences possessed by their management faculty. The study addressed the importance of these attributes to include relevant practical experience, traditional academic training, scholarly productivity, higher education institutions attended, and level of engagement with the business community. This quantitative study surveyed 70 upper-level management students using Likert categories to provide an exploratory view of attributes that today’s students view as important in faculty. The findings ranked attributes of relevant professional experience more important …
Interpersonal Dynamics Of The Supervisory Triad Of Pre-Service Teacher Education: Lessons Learned From 15 Years Of Research, Anna Hart
Georgia Educational Researcher
Clinical field experience is recognized by many as the most influential and beneficial component of pre-service teacher education. The present article represents part of a larger qualitative meta-synthesis, the purpose of which was to explore the influence of the interpersonal dynamics of the supervisory triad—comprised of the pre-service teacher candidate, the mentor teacher, and the university supervisor—on pre-service candidates’ clinical experiences. Positioning theory was chosen to frame this investigation, as it employs distinct definitions for role and position, the delineation of which is of critical importance in the context of pre-service clinical relationships. Findings of the larger study reveal …
Do Advanced Degrees Matter? A Multiphase Mixed-Methods Study To Examine Teachers’ Obtainment Of Advanced Degrees And The Impact On Student And School Growth, Mei-Lin Chang Dr., Ivan M. Jorrín Abellán, Jim Wright, Jihye Kim, Rachel E. Gaines
Do Advanced Degrees Matter? A Multiphase Mixed-Methods Study To Examine Teachers’ Obtainment Of Advanced Degrees And The Impact On Student And School Growth, Mei-Lin Chang Dr., Ivan M. Jorrín Abellán, Jim Wright, Jihye Kim, Rachel E. Gaines
Georgia Educational Researcher
Teacher quality has been found to offset the adverse effect of racial and socioeconomic differences in academic achievement; and teacher quality is often thought to be the product of a quality education. However, existing literature has produced mixed results regarding the relationship between student achievement and teachers’ possession of advanced degrees (ADs). Despite these mixed results, ADs are often the most efficient (if not the only) way for teachers to earn certification and salary upgrades. A longitudinal, multiphase mixed-methods explanatory study aimed to bridge shortcomings of existing research on the effects of teachers obtaining ADs. Associations between teacher credentials and …
Reliability Analysis Of Complementary Assessment Tools For Measuring Teacher Candidate Dispositions, Winifred C. Nweke, Tasha P. Perkins, Comfort Y. Afolabi
Reliability Analysis Of Complementary Assessment Tools For Measuring Teacher Candidate Dispositions, Winifred C. Nweke, Tasha P. Perkins, Comfort Y. Afolabi
Georgia Educational Researcher
Assessing the dispositions of teacher candidates remains a challenge for many Educator Preparation Providers (EPPs). This article details the process and results of establishing the reliability of two complementary instruments, the Candidate Beliefs Self-Assessment Survey (SAS) and the Candidate Dispositions Performance Assessment Rubric (CDPA). The instruments are linked through the same dispositional themes that undergird the indicators in the CDPA and belief statements in the SAS. Internal consistency reliability coefficients were determined using Cronbach’s alpha for SAS (0.81) and the CDPA (0.96). In addition, inter-rater reliability coefficient of 0.80 was determined for CDPA using Intraclass correlation (ICC) method based on …
An Alternative Approach To The Traditional Internship, Basil M. Conway, David Erikson, Christopher Parrish, Marilyn Strutchens, Jennifer Whitfield
An Alternative Approach To The Traditional Internship, Basil M. Conway, David Erikson, Christopher Parrish, Marilyn Strutchens, Jennifer Whitfield
Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators
This paper reports the benefits and challenges of incorporating a paired-placement model at four different post-secondary teacher preparation programs in secondary mathematics education. The paired-placement model places two secondary mathematics clinical teachers with one mentor (or cooperating) teacher during their internship experience. Benefits exhibited were increased collaboration, more knowledgeable cooperating teachers, increased sense of community, teaming, pedagogical risk-taking, increased reflective practice, established natural professional learning communities, Plan-Do-Study-Act Cycle (PDSA), and increased accountability. Challenges found through the PDSA cycle include personnel issues, number of days teaching, perceived classroom management preparation, preparing university supervisors, mentors, and teacher candidates, and support for collaboration …
An Examination Of K-12 Teachers’ Assessment Beliefs And Practices In Relation To Years Of Teaching Experience., Aslihan Unal, Zafer Unal
An Examination Of K-12 Teachers’ Assessment Beliefs And Practices In Relation To Years Of Teaching Experience., Aslihan Unal, Zafer Unal
Georgia Educational Researcher
This study compared K-12 teachers’ assessment beliefs and practices in relation to their years of teaching experience. The data for this study was collected from 87 public school teachers. The findings suggest that as the teachers’ years of experience increases, the value they place in assessment increases as well.
Alternative Seating And Students' Perceptions: Implications For The Learning Environment, Alicia Stapp
Alternative Seating And Students' Perceptions: Implications For The Learning Environment, Alicia Stapp
Georgia Educational Researcher
Expectations placed on educators to improve academic performance continue to increase across the United States. One reason for this rise in expectancy is the enactment of The Every Student Succeeds Act (ESSA) of 2015. Replacing the No Child Left Behind (NCLB) Act of 2002, the ESSA mandates that “all students are taught to high academic standards” (ESSA, 2015). Subsequently, educators constantly seek best practices that foster effective learning environments. A component of the learning environment oftentimes excluded from research is the physical structure of a classroom, such as the type of seating in a classroom. Research suggests that students who …
Pre-Service Teachers’ Perceptions About The Effectiveness Of The Toon Comic Books In Their Guided Reading Instruction, Ewa Mcgrail, Alicja Rieger, Gina M. Doepker
Pre-Service Teachers’ Perceptions About The Effectiveness Of The Toon Comic Books In Their Guided Reading Instruction, Ewa Mcgrail, Alicja Rieger, Gina M. Doepker
Georgia Educational Researcher
Recently, education and literacy researchers have acknowledged educational merit in guided reading that incorporates interactive and authentic reading texts, such as graphic novels, which meet the needs of today’s predominantly multimodal learners (Jennings, Rule, & Zanden, 2014; Kist & Pytash, 2015). This qualitative study explores through interviews and a questionnaire the perceptions of pre-service teachers about the effectiveness of the comic book series known as TOON comics in guided reading with struggling readers and writers, from kindergarten through fifth grade. Pre-service teachers have expressed positive views concerning the use of these comic books in guided reading instruction with their struggling …
Voices From The Field, Lina B. Soares
Voices From The Field, Lina B. Soares
Georgia Educational Researcher
This research study sought to determine the impact from participation in a practicum field experience on teacher candidates’ perceived professional dispositions for effective teaching. A further intent was to describe what teacher candidates perceived to be the necessary professional dispositions for effective teaching as they reflected on their experiences in their particular preparation contexts. A mixed-methods sequential explanatory design was used to examine and understand the development of dispositions from pre-service teachers’ perspectives. The participants consisted of seventeen middle grade undergraduate students who completed over 200 hours of field experience while attending a mid-size university in the Southeastern region of …
Making Your Traditional Text Work: Input, Scaffolding And Communication, Andrew J. Demil
Making Your Traditional Text Work: Input, Scaffolding And Communication, Andrew J. Demil
The Coastal Review: An Online Peer-reviewed Journal
Second Language Acquisition (SLA) studies provide evidence that comprehension activities that involve meaningful language production and communication promote language acquisition more effectively than mechanical drills. Recent studies review the state of foreign language textbooks and demonstrate that the majority of foreign language textbooks do not follow SLA research. This article provides ways that a second language instructor can use a traditional text to help lead to meaningful language instruction.
Perceptions Of Preservice Teachers’ E-Portfolios For Hiring Decisions, Molly Zhou, Marilyn M. Helms
Perceptions Of Preservice Teachers’ E-Portfolios For Hiring Decisions, Molly Zhou, Marilyn M. Helms
Georgia Educational Researcher
Preservice teachers often build E-portfolios of their work prior to graduation, but their use beyond the college classroom is not clear. To identify if E-portfolios are used during the teacher hiring process, 170 administrators from 84 (K-12) schools in eight North Georgia districts were surveyed regarding their use of E-portfolio materials. Based on the mixed methods used, E-portfolios were not strongly favored for use in decision-making. To increase their usefulness, preservice teachers should actively provide access to artifacts valued by potential employers including certification documents, classroom management plans, evidence of work with Individualized Educational Plan (IEP) students, ability to work …
The Continuing Professional Development Of School Psychologists In Georgia: A Comparison To National Practices And Preferences, P. Dawn Tysinger, Jeffrey A. Tysinger, Terry D. Diamanduros, Rebecca Smith
The Continuing Professional Development Of School Psychologists In Georgia: A Comparison To National Practices And Preferences, P. Dawn Tysinger, Jeffrey A. Tysinger, Terry D. Diamanduros, Rebecca Smith
Georgia Educational Researcher
The current study investigated Georgia school psychologists’ continuing professional development (CPD) practices and preferences for comparison to a national study of school psychology professional development by Armistead, Castillo, Curtis, Chappel, and Cunningham (2013). Utilizing the same instrument as Armistead et al., a survey was emailed to 442 members of the Georgia Association of School Psychologists (GASP). Ninety-five surveys were completed at a 21.5% response rate. Both Georgia school psychologists and national school psychologists reported receiving a median of approximately 40 hours of professional development in the previous year. Georgia school psychologists differed from the national sample with a higher percentage …
Engaging In Lesson Study At Georgia College, Angel R. Abney, Brandon Samples, Doris Santarone
Engaging In Lesson Study At Georgia College, Angel R. Abney, Brandon Samples, Doris Santarone
Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators
A lesson study cycle is a professional development process that integrates research and reflection through collaboration. The cycle allows a group to refine a lesson based on these collaboration efforts such as interaction with students and the post-lesson discussion. Secondary pre-service teachers in a mathematics methods course engaged in a lesson study cycle through collaboration between in-service teachers, Georgia College professors, and students in a local high school classroom. We systematically investigated this process to determine that through preparing, enacting and reflecting on their practice, Pre-service Teachers (PST) developed insight, reasoning, and understanding of the mathematics that they taught.
Using Ti-Nspire To Engage Preservice Mathematics Teachers In An Exploratory Geometry Module, Alesia D. Mickle, Pier A. Junor Clarke
Using Ti-Nspire To Engage Preservice Mathematics Teachers In An Exploratory Geometry Module, Alesia D. Mickle, Pier A. Junor Clarke
Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators
In the mathematics classroom, most preservice mathematics teachers possess basic skills to use technology as an instructional strategy in communicating content standards. However, today’s demands for preservice teachers to engage in a variety of “best teaching practices” in their preservice teaching and edTPA requirements can oftentimes place the acquisition of technical skills and integration of new technology in content curriculum far from the forefront of their minds. Ertmer, Conklin, Lewandowski, Osika, Selo, and Wignall (2003) acknowledged preservice teachers’ desires to gain the adequate technical skills necessary to use technology in teachers’ daily tasks of facilitating and managing their classrooms. They …
Teachers’ And Parents’ Perceptions Of Parental Involvement On Inner City Children’S Academic Success, Molly Zhou
Teachers’ And Parents’ Perceptions Of Parental Involvement On Inner City Children’S Academic Success, Molly Zhou
Georgia Educational Researcher
Parental involvement (PI) is an important factor in children’s academic learning. In this study, teachers’ and parents’ perceptions of parental involvement on inner city children’s academic success were examined. The setting of the study was in an inner city Tittle I elementary school with a 90% African American student population. A purposeful random sampling method was used in the study. Fifty five parents and 14 teachers participated in the study. The Parental Involvement Survey was used to collect data from the 69 participants. Collected data were analyzed with SPSS. The findings revealed that parents and teachers perceived that family, extended …
Impediments To Using Or Sharing What Is “Known”, Winifred Nweke, Virginia Elliott
Impediments To Using Or Sharing What Is “Known”, Winifred Nweke, Virginia Elliott
Georgia Educational Researcher
The purpose of this mixed methods study was to investigate variables that impede the utilization of research findings in, or the transfer of learning from professional development workshops into, classroom best practices. Participants comprised 202 Georgia Master Teachers who attended Leadership Institutes. Participants were taught strategies for differentiating assessment. A 21-item online survey was used to collect data two months after the institute. Eighty-six teachers (42.6%) completed the survey. Fifty-five (64%) respondents had implemented, at least, one strategy. The strategies they found most useful were allowing students redo assignments for full credit, isolating and retesting specific standards rather than a …
Differences In Beliefs Across A Series Of Four Mathematics Content Courses, Susanna Molitoris Miller, Caitlin Walkey
Differences In Beliefs Across A Series Of Four Mathematics Content Courses, Susanna Molitoris Miller, Caitlin Walkey
Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators
College students often ask questions such as, “Why do I have to take this class? Is there a point to it?” For Early Childhood Education (ECE) majors these questions may often take on a slightly different form, wondering, “How can I incorporate this information into my classroom?” or “Do I understand this well enough to teach this to my students?” It is especially important for pre- service teachers to feel confident working with the mathematical content that they are learning and for them to believe that they can successfully teach that same information to a group of students. Swackhamer, Koellner, …
Analysis Of Achievement For Understanding Geometry, Annita W. Hunt
Analysis Of Achievement For Understanding Geometry, Annita W. Hunt
Proceedings of the Annual Meeting of the Georgia Association of Mathematics Teacher Educators
The purpose of this study was to investigate the effectiveness of a mathematics professional development course. More specifically, in this study we examine whether geometric experiences have an impact on level of performance in mathematics. The van Hiele (Fuys, D., Geddes, D., & Tischler, R., 1988) model of geometric understanding provided a research framework from which to view geometric understanding. This model suggests five levels of understanding that should be taken into consideration when examining levels of geometric thinking: Visual, Descriptive/Analytic, Abstract/Relational, Formal Deduction/Proof, and Rigor. The sample under study was three cohorts of practicing elementary teachers and mathematics coaches …