Abstract
Instructional research in German-speaking countries has conceptualized teaching quality recently according to three generic dimensions, namely, classroom management, student support and cognitive activation. However, as these dimensions are mainly regarded as generic, subject-specific aspects of mathematics instruction, e.g., the mathematical depth of argumentation or the adequacy of concept introductions, are not covered in depth. Therefore, a new instrument for the analysis of instructional quality was developed, which extended this three-dimensional framework by relevant subject-specific aspects of instructional quality. In this paper, the newly developed observational protocol is applied to three videotaped mathematics lessons from the NCTE video library of Harvard University to explore strengths and weaknesses of this instrument, and to examine in more detail how the instrument works in practice. Therefore, we used a mixed-methods design to extend the quantitative observer ratings, which enable high inference, by methods from qualitative content analysis. The results suggest the conclusion that the framework differentiates well between the lessons under a subject-specific perspective.
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Appendix: Items and indicators of the Observational instrument for TEDS-Instruct
Appendix: Items and indicators of the Observational instrument for TEDS-Instruct
Items | Indicators |
|---|---|
D1: classroom management (six items) | |
Effective use of lesson time | The lesson starts and ends on time Transitions between lesson phases run smoothly The lesson time is used for content-related instruction |
Clear rules and routines | Patterns for the organization of the lesson are apparent The students take part in organizing the lesson |
Preventing disturbances | The teacher successfully prevents emerging disturbances immediately The teacher is aware of everything that happens in the classroom |
Advance organization/structuring learning processes | The teacher informs the students about the lesson objectives The teacher’s expectations are apparent Tasks are given in precise language |
Productive atmosphere | The volume level is appropriate Students react to teacher’s signals The students and the teacher do not interrupt each other |
Lesson structure | A common thread is apparent in the lesson The lesson is separated clearly into sections The teacher ends the lesson in an appropriate manner |
D2: student support (seven items) | |
Students’ individual support | The teacher asks about students’ individual difficulties/individual progress The teacher takes time for individuals The teacher provides individual assistance for students |
Dealing with heterogeneity | Additional materials for subgroups of students exist Tasks address different types of students The teacher offers ad-hoc differentiation during lesson (e.g. by varying the cognitive level of questions) |
Self-directed learning | Students check their results independently with a sample solution The teacher encourages students to work independently Students may decide whether they would like to work in groups or not |
Teacher feedback to students | The teacher’s feedback is sophisticated The teacher’s feedback is constructive The teacher’s feedback is forward-looking |
Teacher appreciation of students | The teacher is patient The teacher positively enhances the students’ work The teacher encourages the students |
Student feedback | The teacher asks for feedback The teacher reacts to students’ feedback The teacher and students talk about issues in class |
Support of collaborative learning | The teacher initiates collaborative learning processes between students The teacher provides tasks that require agreement The teacher mediates interaction processes The students help each other |
D3: cognitive activation (five items) | |
Challenging questions and tasks | The teacher asks cognitively appropriate questions The teacher presents challenging tasks The teacher spontaneously encourages cognitive challenges |
Supporting metacognition | At least one metacognitive sub-process takes place The teacher provides time for metacognitive processes Students reflect on their learning processes |
Activation of prior knowledge/building on students’ ideas/co-construction | The teacher asks for students’ beliefs concerning the topic The students explain the task in their own words The teacher activates and explores students’ prior knowledge Knowledge is developed co-constructively in class |
Cognitively challenging teaching methods | Cognitively challenging teaching methods are used The teacher provides enough time to think about the tasks The teaching methods correspond to the content and the class |
Facilitating remembering and recalling | The teacher provides enough examples and helpful reminders The teacher provides enough repetitions Relevant steps are discussed with the whole class |
D4: subject-related quality (four items) | |
Dealing with mathematical errors of students | The teacher uses students’ errors as opportunities to learn The teacher analyzes students’ errors and misconceptions The teacher is tolerant towards students’ errors Students correct their errors on their own |
Teacher’s mathematical correctness | The teacher does not make any content-related or formal mistakes The teacher is precise concerning mathematical language and notation |
Teacher’s explanations | The teacher explains slowly, especially when difficulty arises The teacher focuses on the fundamental mathematical aspects Teacher’s explanations are suitable for the students Teacher’s explanations are well-structured and precise |
Mathematical depth of the lesson | Mathematical generalizations are developed The topic is related to other mathematical topics The content is embedded in a broader mathematical structure |
D5: teaching-related quality (four items) | |
Using multiple representations | Multiple representations are used during the lesson Relations between multiple representations are shown |
Deliberate practice | The teacher explains the importance of the exercises The exercises contain opportunities for exploring and reflection The exercises are self-differentiating |
Appropriate mathematical examples | The examples contain fundamental mathematical ideas The teacher provides an appropriate number of examples The examples are taken from students’ everyday life |
Relevance of mathematics for students | The teacher provides connections to students’ everyday life The teacher addresses the relevance of content Students may bring in their own experience and interests to class |
German national standards/Support of mathematical competencies (six items) | |
Mathematical language | The teacher provides time for building new concepts The teacher corrects language errors in an appropriate manner The teacher initiates the adequate use of mathematical language |
Mathematical modeling | The teacher encourages transition processes between the real world and maths The teacher encourages the validation of students’ results The teacher encourages connections between different subjects |
Problem solving | The teacher fosters the use of heuristic strategies The teacher poses mathematical problems The teacher encourages the development of new mathematical content |
Reasoning and proof | The teacher encourages mathematical reasoning The teacher demands mathematical explanations The teacher addresses mathematical proofs |
Calculations (using symbolic and formal aspects) | The teacher provides time for training the use of mathematical symbols The teacher provides time for training basic skills in mathematics |
Mathematical tools | The students use mathematical tools reasonably The teacher uses mathematical tools correctly |
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Schlesinger, L., Jentsch, A., Kaiser, G. et al. Subject-specific characteristics of instructional quality in mathematics education. ZDM Mathematics Education 50, 475–490 (2018). https://doi.org/10.1007/s11858-018-0917-5
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DOI: https://doi.org/10.1007/s11858-018-0917-5