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Classroom observation and mathematics education research

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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.

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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.

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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

Schlesinger and Jentsch (2016), Schoenfeld (2013)

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

Morrell et al. (2004), Wainwright et al. (2004)

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)

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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

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