Abstract
Classroom observations have become an integral part of research related to mathematics education. In this qualitative study, we describe the current state of the mathematics education field with regard to the use of classroom observation. The research question was: How is classroom observation being used to measure instructional quality in mathematics education research? In all, 114 peer-reviewed manuscripts published between 2000 and 2015 that involved classroom observation as part of an empirical study were examined using a cross-comparative methodology. Seventy (61%) did not use a formalized classroom observation protocol (COP), 21 (18%) developed their own COP, and 23 (20%) used a previously developed COP. Of the implemented COPs, 44% have published validity evidence in a peer-reviewed journal. We perceive the great variety of research approaches for classroom observation as necessary and potentially challenging in moving mathematics education forward with respect to research on instructional contexts.
Similar content being viewed by others
References
American Educational Research Association, American Psychological Association, & National Council on Measurement in Education. (2014). Standards for educational and psychological testing. Washington, DC: American Educational Research Association.
American Educational Research Association, American Psychological Association, National Council on Measurement in Education, Joint Committee on Standards for Educational and Psychological Testing (US). (1999). Standards for educational and psychological testing. Washington, DC: American Educational Research Association.
Arbaugh, F., Lannin, J., Jones, D. L., & Park-Rogers, M. (2006). Examining instructional practices in Core-Plus lessons: Implications for professional development. Journal of Mathematics Teacher Education, 9(6), 517–550.
Baker, J. A. (1999). Teacher-student interaction in urban at-risk classrooms: Differential behavior, relationship quality, and student satisfaction with school. The Elementary School Journal, 100(1), 57–70.
Ball, D. L., & Rowan, B. (2004). Introduction: Measuring instruction. The Elementary School Journal, 105, 3–10.
Berry, III, R. Q., Rimm-Kaufman, S. E., Ottmar, E. M., Walkowiak, T. A., & Merritt, E. (2010). The Mathematics Scan (M-Scan): A measure of mathematics instructional quality. Unpublished measure, University of Virginia.
Blank, R. K., Porter, A., & Smithson, J. (2001). New tools for analyzing teaching, curriculum and standards in Mathematics & Science. Results from Survey of Enacted Curriculum Project. Final Report. Council of Chief State School Officers, Attn: Publications, One Massachusetts Avenue, NW, Suite 700, Washington, DC 20001-1431.
Borasi, R., Fonzi, J., Smith, C., & Rose, B. J. (1999). Beginning the process of rethinking mathematics instruction: A professional development program. Journal of Mathematics Teacher Education, 2, 49–78.
Bostic, J. (2017). Moving forward: Instruments and opportunities for aligning current practices with testing standards. Investigations in Mathematics Learning, 9(3), 109–110.
Bostic, J. (2018). Improving test development reporting practices. In L. Venenciano & A. Sanogo (Eds.), Proceedings of the 45th Annual Meeting of the Research Council on Mathematics Learning (pp. 57–64). Baton Rouge, LA.
Bostic, J., Lesseig, K., Sherman, M., & Boston, M. (2017). Classroom observation protocols: Choose your own tool. Research report presented at the National Council of Teachers of Mathematics Research Conference, San Antonio, TX.
Bostic, J., Matney, G., & Sondergeld, T. (2019). A lens on teachers’ promotion of the Standards for Mathematical Practice. Investigations in Mathematics Learning, 11(1), 69–82.
Boston, M. D. (2012a). Assessing the quality of mathematics instruction. Elementary School Journal, 113, 76–104.
Boston, M. (2012b). Assessing instructional quality in mathematics. The Elementary School Journal, 113(1), 76–104.
Boston, M., Bostic, J., Lesseig, K., & Sherman, M. (2015a). A comparison of mathematics classroom observation protocols. Mathematics Teacher Educator, 3, 154–175.
Boston, M., Bostic, J., Lesseig, K., & Sherman, M. (2015b). Classroom Observation tools to support the work of mathematics teacher educators. Invited Manuscript for Mathematics Teacher Educator, 3, 154–175.
Boston, M. D., & Smith, M. S. (2009). Transforming secondary mathematics teaching: Increasing the cognitive demands of instructional tasks used in teachers’ classrooms. Journal for Research in Mathematics Education, 40, 119–156.
Boston, M. D., & Wilhelm, A. G. (2015). Middle school mathematics instruction in instructionally-focused urban districts. Urban Education, 52(7), 829–861.
Briars, D. J., & Resnick, L. B. (2000). Standards, assessments… and what else? The essential elements of standards-based school improvement. Center for the Study of Evaluation, National Center for Research on Evaluation, Standards, and Student Testing, Graduate School of Education & Information Studies, University of California, Los Angeles.
Brigham Young University Department of Mathematics Education. (2008). Report on venue study. Retrieved from https://nctm.confex.com/nctm/…/BYU%20Study%20for%20Journal%20Rankings.pdf.
Brophy, J. (1986). Teacher influences on student achievement. American Psychologist, 41, 1069.
Brown, J. C., & Crippen, K. J. (2016). The growing awareness inventory: Building capacity for culturally responsive science and mathematics with a structured observation protocol. School Science and Mathematics, 116(3), 127–138.
Capobianco, B. M., & Rupp, M. (2014). STEM teachers’ planned and enacted attempts at implementing engineering design-based instruction. School Science and Mathematics, 114(6), 258–270.
Charalambous, C. Y., & Praetorius, A. K. (2018). Studying mathematics instruction through different lenses: Setting the ground for understanding instructional quality more comprehensively. ZDM Mathematics Education, 50, 355–366. https://doi.org/10.1007/s11858-018-0914-8.
Danielson, C. (2013). The framework for teaching: Evaluation instrument. Princeton, NJ: Danielson Group.
Doabler, C. T., Baker, S. K., Kosty, D. B., Smolkowski, K., Clarke, B., Miller, S. J., et al. (2015). Examining the association between explicit mathematics instruction and student mathematics achievement. The Elementary School Journal, 115(3), 303–333.
Donovan, M. S., & Bransford, J. D. (2005). How students learn: History, mathematics, and science in the classroom. Committee on How People Learn: A Targeted Report for Teachers National Research Council. Washington, DC: National Academies Press.
Farmer, J. D., Gerretston, H., & Lassak, M. (2003). What teachers take from professional development: Cases and implications. Journal of Mathematics Teacher Education, 6, 331–360.
Fraivillig, J. L., Murphy, L. A., & Fuson, K. C. (1999). Advancing children’s mathematical thinking in everyday mathematics classrooms. Journal for Research in Mathematics Education, 30, 148–170.
Franke, M. L., Carpenter, T. P., Levi, L., & Fennema, E. (2001). Capturing teachers’ generative change: A follow-up study of professional development in mathematics. American Educational Research Journal, 38, 653–689.
Franke, M., Kazemi, E., & Battey, D. (2007). Understanding teaching and classroom practice in mathematics. In F. Lester Jr. (Ed.), Second handbook of research on mathematics teaching and learning (pp. 225–256). Charlotte, NC: Information Age Publishing.
Good, T., & Brophy, J. (1994). Looking in classrooms (6th ed., pp. 209–262). New York: Harper Collins College Publishers.
Hall, A., & Miro, D. (2016). A study of student engagement in project-based learning across multiple approaches to STEM education programs. School Science and Mathematics, 116(6), 310–319.
Hamre, B., Pianta, R., Burchinal, M., Field, S., LoCasale-Crouch, J., Downer, J., et al. (2012). A course on effective teacher-child interactions: Effects on teacher beliefs, knowledge, and observed practice. American Educational Research Journal, 49(1), 88–123.
Hiebert, J., Stigler, J. W., Jacobs, J. K., Givvin, K. B., Garnier, H., Smith, M., et al. (2005). Mathematics teaching in the United States today (and tomorrow): Results from the TIMSS 1999 video study. Educational Evaluation and Policy Analysis, 27, 111–132.
Hill, H. C., Charalambous, C. Y., & Kraft, M. A. (2012). When rater reliability is not enough: Teacher observation systems and a case for the generalizability study. Educational Researcher, 41(2), 56–64.
Hill, H., & Shih, J. (2009). Examining the quality of statistical mathematics education research. Journal of Research in Mathematics Education, 40(3), 241–250.
Jackson, K., Garrison, A., Wilson, J., Gibbons, L., & Shahan, E. (2013). Exploring relationships between setting up complex tasks and opportunities to learn in concluding whole-class discussions in middle-grades mathematics instruction. Journal for Research in Mathematics Education, 44(4), 646–682.
James, L. R., Demaree, R. G., & Wolf, G. (1993). Rwg: An assessment of within-group interrater agreement. Journal of Applied Psychology, 78, 306.
Jong, C., Pedulla, J. J., Reagan, E. M., Salomon-Fernandez, Y., & Cochran-Smith, M. (2010). Exploring the link between reformed teaching practices and pupil learning in elementary school mathematics. School Science and Mathematics, 110(6), 309–326.
Judson, E. (2013). Development of an instrument to assess and deliberate on the integration of mathematics into student-centered science learning. School Science and Mathematics, 113(2), 56–68.
Kane, M. T. (2006). Valildation. In R. L. Brennan, National Council on Measurement in Education, & American Council on Education (Eds.), Educational measurement. Westport, CT: Praeger Publishers.
Kane, M. T. (2016). Validation strategies: Delineating and validating proposed interpretations and uses of test scores. In S. Lane, M. Raymond, & T. M. Haladyna (Eds.), Handbook of test development (Vol. 2nd). New York, NY: Routledge.
Kane, T. J. & Staiger, D. O. (2012). Gathering Feedback for Teaching: Combining high-quality observations with student surveys and achievement gains. Research paper. MET Project. Bill and Melinda Gates Foundation.
Kapitula, L., & Umland, K. (2011). A validity argument approach to evaluating teacher value-added scores. American Educational Research Journal, 48(3), 794–831.
Kersting, N. B., Sutton, T., Kalinec-Craig, C., Stoehr, K. J., Heshmati, S., Lozano, G., et al. (2016). Further exploration of the classroom video analysis (CVA) instrument as a measure of usable knowledge for teaching mathematics: Taking a knowledge system perspective. ZDM Mathematics Education, 48(1–2), 97–109.
Khan, S., & VanWynsberghe, R. (2008). Cultivating the under-mined: Cross-case analysis as knowledge mobilization. Forum: Qualitative Social Research, 9, 1–21.
Le, V., Lockwood, J. R., Stecher, B. M., Hamilton, L. S., & Martinez, J. F. (2009). A longitudinal investigation of the relationship between teachers’ self-reports of reform-oriented instruction and mathematics and science achievement. Educational Evaluation and Policy Analysis, 31, 200–220.
Learning Mathematics for Teaching Project. (2011). Measuring the mathematical quality of instruction. Journal of Mathematics Teacher Education, 14, 25–47.
Lubienski, S. T. (2008). On” gap gazing” in mathematics education: The need for gaps analyses. Journal for Research in Mathematics Education, 39, 350–356.
Marshall, J., Smart, J., & Horton, R. (2010). The design and validation of EQUIP: An instrument to assess inquiry-based instruction. International Journal of Science & Mathematics Education, 8(2), 299–321.
Marshall, J. C., Smart, J., Lotter, C., & Sirbu, C. (2011). Comparative analysis of two inquiry observational protocols: Striving to better understand the quality of teacher-facilitated inquiry-based instruction. School Science and Mathematics, 111(6), 306–315.
Matsumura, L. C., Garnier, H., Slater, S. C., & Boston, M. (2008). Toward measuring instructional interactions ‘at-scale’. Educational Assessment, 13, 267–300.
McCaffrey, D. F., Hamilton, L. S., Stecher, B. M., Klein, S. P., Bugliari, D., & Robyn, A. (2001). Interactions among instructional, practices, curriculum, and student achievement: The case of Standards-based high school mathematics. Journal for Research in Mathematics Education, 32, 493–517.
McCaslin, M., Good, T. L., Nichols, S., Zhang, J., Wiley, C. R., Bozack, A. R., et al. (2006). Comprehensive school reform: An observational study of teaching in grades 3 through 5. The Elementary School Journal, 106(4), 313–331.
Mendez, E. P., Sherin, M. G., & Louis, D. A. (2007). Multiple perspectives on the development of an eighth-grade mathematical discourse community. The Elementary School Journal, 108(1), 41–61.
Morrell, P. D., Wainwright, C., & Flick, L. (2004). Reform teaching strategies used by student teachers. School Science and Mathematics, 104(5), 199–213.
Morrone, A. S., Harkness, S. S., D’ambrosio, B., & Caulfield, R. (2004). Patterns of instructional discourse that promote the perception of mastery goals in a social constructivist mathematics course. Educational Studies in Mathematics, 56(1), 19–38.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.
Newton, K. J. (2009). Instructional practices related to prospective elementary school teachers’ motivation for fractions. Journal of Mathematics Teacher Education, 12(2), 89–109.
Ottmar, E. R., Rimm-Kaufman, S. E., Berry, R. Q., & Larsen, R. A. (2013). Does the responsive classroom approach affect the use of standards-based mathematics teaching practices? Results from a randomized controlled trial. The Elementary School Journal, 113(3), 434–457.
Peters Burton, E., Kaminsky, S. E., Lynch, S., Behrend, T., Han, E., Ross, K., et al. (2014). Wayne School of Engineering: Case study of a rural inclusive STEM-Focused High School. School Science and Mathematics, 114(6), 280–290.
Pianta, R. C., Belsky, J., Vandergrift, N., Houts, R., & Morrison, F. J. (2008). Classroom effects on children’s achievement trajectories in elementary school. American Educational Research Journal, 45(2), 365–397.
Ross, S. M., Smith, L. J., & Alberg, M. (1998). The school observation measure (SOM VC). Memphis: Center for Research in Educational Policy, The University of Memphis.
Rubel, L. H., & Chu, H. (2012). Reinscribing urban: Teaching high school mathematics in low income, urban communities of color. Journal of Mathematics Teacher Education, 15(1), 39–52.
Santagata, R., & Barbieri, A. (2005). Mathematics teaching in Italy: A cross-cultural video analysis. Mathematical Thinking and Learning, 7(4), 291–312.
Sawada, D., Piburn, M. D., Judson, E., Turley, J., Falconer, K., Benford, R., et al. (2002). Measuring reform practices in science and mathematics classrooms: The reformed teaching observation protocol. School Science and Mathematics, 102, 245–253.
Saxe, G. B., Gearhart, M., & Seltzer, M. (1999). Relations between classroom practices and student learning in the domain of fractions. Cognition and instruction, 17, 1–24.
Schifter, D. A., & Simon, M. (1992). Assessing teachers’ development of a constructivist view of mathematics learning. Teacher and Teacher Education, 8, 187–197.
Schlesinger, L., & Jentsch, A. (2016). Theoretical and methodological challenges in measuring instructional quality in mathematics education using classroom observations. ZDM Mathematics Education, 48(1–2), 29–40.
Schoen, H. L., Cebulla, K. J., Finn, K. F., & Fi, C. (2003). Teacher variables that relate to student achievement when using a standards-based curriculum. Journal for Research in Mathematics Education, 34, 228–259.
Schoenfeld, A. H. (2013). Classroom observations in theory and practice. ZDM Mathematics Education, 45(4), 607–621.
Sears, R., & Chavez, O. (2014). Opportunities to engage with proof: the nature of proof tasks in two geometry textbooks and its influence on enacted lessons. ZDM Mathematics Education, 46, 767–780.
Simon, M. A., & Shifter, D. (1991). Towards a constructivist perspective: An intervention study of mathematics teacher development. Educational Studies in Mathematics, 22, 309–331.
Slavin, R. E., Lake, C., & Groff, C. (2009). Effective programs in middle and high school mathematics: A best evidence synthesis. Review of Educational Research, 79, 839–911.
Smith, M. (2014). Tools as a catalyst for practitioners’ thinking. Mathematics Teacher Educator, 3, 3–7.
Steenbergen-Hu, S., & Cooper, H. (2013). A meta-analysis of the effectiveness of intelligent tutoring systems on K–12 students’ mathematical learning. Journal of Educational Psychology, 105, 970–987.
Swafford, J. O., Jones, G. A., & Thornton, C. A. (1997). Increased knowledge in geometry and instructional practice. Journal for Research in Mathematics Education, 28, 467–483.
Tarr, J. E., Reys, R. E., Reys, B. J., Chavez, O., Shih, J., & Osterlind, S. (2008). The impact of middle grades mathematics curricula on student achievement and the classroom learning environment. Journal for Research in Mathematics Education, 39, 247–280.
Toerner, G., & Arzarello, F. (2012). Grading mathematics education research journals. Newletter of the European Mathematical Society, 86, 52–54.
U.S. Department of Education, Institute of Education Sciences, What Works Clearinghouse. (2012, February). High School Math intervention report: I CAN Learn®. Retrieved from http://whatworks.ed.gov.
U.S. Department of Education, Institute of Education Sciences, What Works Clearinghouse. (2013, January). High School Mathematics intervention report: Carnegie Learning Curricula and Cognitive Tutor®. Retrieved from http://whatworks.ed.gov.
Valli, L., & Croninger, R. (2002). High quality teaching of foundational skills in mathematics and reading (# 0115389). Washington: National Science Foundation Interdisciplinary Educational Research Initiative.
Wainwright, C., Morrell, P. D., Flick, L., & Schepige, A. (2004). Observation of reform teaching in undergraduate level mathematics and science courses. School Science and Mathematics, 104(7), 322–335.
Walkington, C., Arora, P., Ihorn, S., Gordon, J., Walker, M., Abraham, L., & Marder, M. (2012). Development of the UTeach observation protocol: A classroom observation instrument to evaluate mathematics and science teachers from the UTeach preparation program. Unpublished paper. Southern Methodist University.
Walkowiak, T., Berry, R., Meyer, J., Rimm-Kaufman, S., & Ottmar, E. (2014). Introducing an observational measure of standards-based mathematics teaching practices: Evidence of validity and score reliability. Educational Studies in Mathematics, 85, 109–128.
Wasserman, N., & Walkington, C. (2014). Exploring links between beginning UTeachers’ beliefs and observed classroom practices. Teacher Education & Practice, 27(2/3), 376–401.
Wilhelm, A. G., & Kim, S. (2015). Generalizing from observations of mathematics teachers’ instructional practice using the instructional quality assessment. Journal for Research in Mathematics Education, 46(3), 270–279.
Williams, S., & Leatham, K. (2017). Journal quality in mathematics education. Journal for Research in Mathematics Education, 48(4), 369–396.
Acknowledgements
We would like to share our sincere appreciation to Timothy Folger, Maria Nielsen, and Davis Gerber at Bowling Green State University, and Dan Chibnall at Drake University for their assistance throughout this project.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Appendices
Appendix 1
Classroom observation protocol | Construct measured | Indicators | Typical study population | Validity evidence | References |
---|---|---|---|---|---|
Instructional Quality Assessment (IQA) | Academic rigor and accountable talk | Instructional tasks, task implementation, explanations of mathematical thinking and reasoning | K-12 mathematics instruction | Content, response processes, internal structure | Boston (2012a, b), Boston et al. (2015a, b), Boston and Smith (2009), Jackson et al. (2013), Schlesinger and Jentsch (2016), Schoenfeld (2013), Wilhelm and Kim (2015) |
Reformed Teaching Observation Protocol (RTOP) | Reform-oriented mathematics and science teaching (i.e., standards-based teaching, inquiry orientation, student-centered teaching practices) | Lesson design; lesson implementation; content; classroom culture | K-12 mathematics instruction | Content, response processes, internal structure | Boston et al. (2015a, b), Jong et al. (2010), Marshall et al. (2011), Peters Burton et al. (2014), Sawada et al. (2002), Schlesinger and Jentsch (2016) |
Mathematical Quality of Instruction (MQI) | Rigor and richness of mathematics present | Common core-aligned student practices; working with students and mathematics; richness of mathematics; errors and imprecision; classroom work is connected to mathematics | K-9 mathematics instruction | Content, response processes, internal structure, relationship to other variables | Boston et al. (2015a, b), Hill et al. (2012), Kapitula and Umland (2011), Schlesinger and Jentsch (2016), Schoenfeld (2013) |
UTeach Observation Protocol (UTOP) | Effective STEM teaching | Designing lessons that are inquiry based, Use real-world connections and involve active participation; Modifying instruction (using questioning, responding to student needs and classroom contexts); content knowledge in the work of teaching | K-12 mathematics instruction | Internal structure | Schlesinger and Jentsch (2016), Schoenfeld (2013), Wasserman and Walkington (2014) |
Teaching for Robust Understanding (TRU) Framework | Attributes of equitable and robust learning environments | Content; cognitive demand; equitable access to content; agency; ownership and identity; formative assessment | K-12 mathematics instruction | Content | |
Oregon Teacher Observation Protocol | Reform-oriented teaching | Habits of mind; metacognition; student discourse; challenged ideas; student misconceptions; conceptual thinking; divergent thinking; interdisciplinary connections; pedagogical content knowledge; multiple representations | K-16 mathematics instruction | Content |
Appendix 2
Classroom observation protocols | Construct measured | Indicators | Sample in the cited study | Validity evidence | References | |
---|---|---|---|---|---|---|
1 | Dyadic teacher–student contact observational system (Good and Brophy 1994) | Student–teacher interactions (negative and positive) | Interactions around academic work classroom procedures & behavior | 61 at-risk youth grade 3–5 | Internal structure | Baker (1999) |
2 | Classroom Assessment Scoring System (CLASS) | High quality teacher–student interactions | Classroom organization, instructional and emotional support | 440 preschool teachers | Content, response processes, and internal structure | Hamre et al. (2012) |
3 | Classroom Observation of Student–Teacher Interactions-Mathematics (COSTI-M) | Explicit Instructional Interactions | Teacher demonstration, student independent practice, student errors, and teacher feedback | 129 kindergarten classrooms | Internal structure | Doabler et al. (2015) |
4 | Levels of Engagement with Children’s Mathematical Thinking from CGI | Teachers’ attention to student thinking | Extent to which student thinking is elicited and used in instructional (decisions) | 26 elementary teachers (grades 1–5) who had participated in CGI PD | None provided | Franke et al. (2001). |
5 | High Quality-Teaching of Foundational Skills in Math and Reading (Valli and Croninger 2002) | High quality-teaching in upper elementary schools | Small group work and high-level questions | Three instructors of elementary education course | None provided | Newton (2009) |
6 | Robust Mathematical Discussion (RMD) protocol | Quality of mathematical discussion | Mathematical and discursive strength of discourse | Two 8th-grade math classes | None provided | Mendez et al. (2007) |
7 | Comprehensive School Reform Classroom Observation System (CSRCOS) | Instructional practice at scale | Instructional opportunity, student activities, and teacher–student relationships | 145 3rd through 5th-grade classrooms | None provided | McCaslin et al. (2006) |
8 | COS-1, 3, and 5 (Classroom Observation System for First, Third, and Fifth Grade) | Quality of classroom supports | Quality of emotional and instructional interactions and amount of exposure to literacy and math activities | 791 children at grades 1, 3, and 5 | None provided | Pianta et al. (2008) |
9 | Observing Patterns of Adaptive Learning (OPAL) | Promoting mastery goals in the classroom | Task, authority, recognition, grouping, evaluation, and time | 28 elementary education majors | None provided | Morrone et al. (2004) |
10 | Classroom Implementation Framework | Lesson quality | Tasks, role of teacher, social culture, mathematical tools, and equity | 26 in-service secondary mathematics teachers | None provided | Arbaugh et al. (2006) |
11 | Growing Awareness Inventory: (GAIn) protocol ** derived from Culturally Responsive Instruction Observation Protocol (CRIOP) | Culturally responsive pedagogy | Classroom relationships, discourse, and sociopolitical consciousness | 19 secondary math and science preservice teachers (PSTs used GAIn to code cooperating teachers lessons, i.e., it was an instructional tool) | None provided | Brown and Crippen (2016) |
12 | TIMSS 1995/1999 Video Study procedure | Mathematics lesson structure and presentation | Organization of classroom interaction, instructional activities, and organization of math content | 39 8th-grade classrooms in Italy | None provided | Santagata and Barbieri (2005) |
13 | Science Learning through Engineering Design (SLED) ** derived from Inquiring into Science Instruction Observation Protocol (ISIOP) | Design-informed pedagogical methods for STEM instruction | Engineering design-informed pedagogical methods | 35 Grades 5 and 6 STEM teachers | None provided | Capobianco and Rupp (2014) |
14 | Mathematics Integrated into Science: Classroom Observation Protocol (MISCOP) | Quality of science lesson when math is integrated | The degree to which mathematics is integrated into student-centered learning of science | 54 secondary STEM teachers | Content validity, Response processes, Internal structure | Judson (2013) |
15 | Classroom Video Analysis (CVA) | Usable knowledge for teaching mathematics | Teachers’ ability to analyze authentic teaching events | Nationally recruited sample of 676 elementary and middle school teachers | None provided | Kersting et al. (2016) |
16 | Electronic Quality of Inquiry Protocol (EQUIP) | Quality of inquiry-based instruction in math and science | Categories include instruction, discourse, assessment, and curriculum | 52 classrooms (35 teachers) middle school science teachers | Internal structure | Marshall et al. (2011) |
17 | School Observation Method (SOM) and Rubric for Student-Centered Activities (RSCA) (Ross et al. 1998) | Student-centered classroom instruction | Instructional orientation, classroom organization, instructional strategies, student activities, technology use, and assessment | 45 observations across 4 different STEM education programs | None provided | Hall and Miro (2016) |
18 | Cases of Reasoning and Proving (CORP) | How teachers use the proof tasks during a lesson | Context and nature of the lesson, cognitive demand of the tasks, and proof schemes | Three geometry teachers | None provided | Sears and Chavez (2014) |
19 | Classroom Observation Instrument (COI) | Advancing student thinking | Teacher lesson planning, Classroom practices, and “on-the-fly” decision making | 18 first grade teachers using Everyday Mathematics curriculum | None provided | Fraivillig et al. (1999) |
20 | Classroom Observation Inventory (COI) | Culturally relevant pedagogy | Dimensions of CureMap: teaching mathematics for understanding; centering instruction on students’ experiences; developing students’ critical consciousness about or with mathematics | 14 high school teachers | None provided | Rubel and Chu (2012) |
21 | Mathematics Scan (M-SCAN) | Standards-based mathematics teaching practices | Structure of lesson, multiple representations, students’ use of tools, cognitive depth, discourse community, explanation & justification, problem solving, and connections & applications | 88 3rd grade teachers—43 of whom taught at schools receiving Responsive Classroom (RC) training | Content, response processes, relationship to other variables, and internal structure | Ottmar et al. (2013) |
Rights and permissions
About this article
Cite this article
Bostic, J., Lesseig, K., Sherman, M. et al. Classroom observation and mathematics education research. J Math Teacher Educ 24, 5–31 (2021). https://doi.org/10.1007/s10857-019-09445-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10857-019-09445-0