Mathematical Quality Of Instruction Research Articles

A Turkish adaptation of a framework for evaluating the mathematical quality of instruction

A structured assessment tool on the quality of mathematics instruction is considered to be important. It is believed that such a tool could play an important role in providing feedbacks to the preservice teachers during their trainings as well as in evaluating the quality of in-service teachers’ practices. From this point of view, firstly, it has been performed a comprehensive examination of the relevant frameworks developed to evaluate the quality of mathematics instruction. As a result, it was observed that the Mathematical Quality of Instruction (MQI) framework differed from the others with respect to both functional and structural features. Within the scope of this study, the adaptation of the MQI framework to Turkish language has been realized. In this study, the characteristics, usage, components and theoretical background of the MQI framework are shared with the reader. In addition, the adapted version of MQI framework was shared and the performance indicators to help potential users were elaborated. ​Extended English summary is in the end of Full Text PDF (TURKISH) file. Özet Matematik öğretiminin niteliğine ilişkin yapılandırılmış bir değerlendirme aracı oldukça önemlidir. Bu türden bir araç gerek öğretmen yetiştirme sürecinde öğretmen adaylarına geri dönüt vermek gerekse halen hizmet veren matematik öğretmenlerinin uygulamalarının niteliğini değerlendirerek uygulamaların geliştirilmesine katkıda bulunabilecektir. Bu düşüncelerle öncelikle matematik öğretiminin niteliğine ilişkin değerlendirme yapmak için kullanılabilecek çerçevelere ilişkin kapsamlı bir tarama yapılmıştır. Bu tarama neticesinde kullanışlılığı ve yapısal özellikleri nedeniyle Mathematical Quality of Instruction (MQI) çerçevesinin diğerlerinden ayrıldığı görülmüştür. Bu makale çalışması kapsamında matematik öğretiminin niteliğine ilişkin işlevsel bir değerlendirme yapmak amacıyla geliştirilen MQI çerçevesinin ülkemizde kullanılabilmesi amacıyla Türkçe’ye adaptasyonu gerçekleştirilmiştir. Bu çalışmada söz konusu çerçevenin özellikleri, kullanım şekli, bileşenleri ve kuramsal arka planı okuyucuyla paylaşılmıştır. Ayrıca adaptasyonu yapılan çerçeve paylaşılmış ve potansiyel kullanıcılara yardımcı olacak performans göstergeleri detaylandırılmıştır.

Two Replication Studies of the Relationships between Mathematical Knowledge for Teaching, Mathematical Quality of Instruction, and Student Achievement

Abstract In this paper, we share two conceptual replications of Hill et al.’s (2012c) study linking Mathematical Knowledge for Teaching (MKT), Mathematical Quality of Instruction (MQI), and student assessment scores. In study 1, we share data from 4th and 5th grade teachers in an urban school district. In study 2, we share data from middle school teachers in a school district with a relatively high proportion of emergent bilingual students. By varying contexts, we found that Hill et al.’s (2012c) suggested use of the MKT cutoff points was not warranted in our differing settings. Further, we found some significant relationships between MKT, MQI, and student assessments; however, we were not able to reproduce these consistently with our data. We suggest that the relationship between teaching practice and MKT may be quite sensitive to contextual factors including grade level, demographics, school effects, and assessments. We recommend that policymakers and researchers take caution when using such instruments to evaluate program initiatives and identify teachers for remediation or leadership positions. The impact sheet to this article can be accessed at 10.6084/m9.figshare.16610080.

A longitudinal study of novice primary school teachers’ knowledge and quality of mathematics instruction

Little is known about the relationship between knowledge and instructional quality of novice primary school teachers during their first 3 years of teaching mathematics. This study utilizes the Classroom video analysis and the Mathematical quality of instruction to examine changes in beginning teachers’ usable knowledge and instructional quality, respectively, and their relationship in each year. The analyses reveal positive associations between knowledge and instructional quality in the second and third year of teaching. Two case study teachers illustrate the tight link between knowledge and practice and how different school contexts provide contrasting opportunities to learn from practice, thus contributing to the different patterns of knowledge and instructional quality over time. The findings suggest that usable knowledge of student mathematical thinking at the beginning of the profession supports teacher improvement in both knowledge and practice over time if the vision of the school context is aligned with student-centered instruction.

Mathematical knowledge for teaching and the mathematical quality of instruction: a study of novice elementary school teachers

This study examines the association between mathematical knowledge for teaching and instructional quality in a sample of first-year elementary school teachers. Ten teachers completed the mathematical knowledge for teaching (MKT) survey at the end of teacher preparation. Three mathematics lessons taught during their first year of teaching were videotaped and scored using the Mathematical Quality of Instruction. Findings replicate prior studies that were conducted with more experienced teachers. A strong, positive and statistically significant association was found between teacher knowledge and the mathematics is clear and not distorted dimension of instructional quality. In addition, associations of moderate strength were found between MKT and other dimensions of instructional quality centered on the mathematics taught in the lesson. Analyses also revealed individual differences among teachers and raised the question of what other factors might impact instructional quality. Three cases studies highlight the role of lesson design, mathematics tasks, and participation structures that support or inhibit instructional quality and the use of knowledge during teaching. Conclusions suggest that preparation and induction programs should include a focus on individual teachers’ mathematical knowledge for teaching, the development of a student-centered vision of mathematics instruction, and tailored support during the first year of teaching.

On Classroom Observations

As STEM education matures, the field will profit from tools that support teacher growth and that support rich instruction. A central design issue concerns domain specificity. Can generic classroom observation tools suffice, or will the field need tools tailored to STEM content and processes? If the latter, how much will specifics matter? This article begins by proposing desiderata for frameworks and rubrics used for observations of classroom practice. It then addresses questions of domain specificity by focusing on the similarities, differences, and affordances of three observational frameworks widely used in mathematics classrooms: Framework for Teaching, Mathematical Quality of Instruction, and Teaching for Robust Understanding. It describes the ways that each framework assesses selected instances of mathematics instruction, documenting the ways in which the three frameworks agree and differ. Specifically, these widely used frameworks disagree on what counts as high quality instruction: questions of whether a framework valorizes orderly classrooms or the messiness that often accompanies inquiry, and which aspects of disciplinary thinking are credited, are consequential. This observation has significant implications for tool choice, given that these and other observation tools are widely used for professional development and for teacher evaluations.

The Mathematical Quality of Instruction (MQI) in Kindergarten: An Evaluation of the Stability of the MQI Using Generalizability Theory

ABSTRACTResearch Findings: We evaluated the score stability of the Mathematical Quality of Instruction (MQI), an observational measure of mathematics instruction. Three raters each scored, independently, 100 video-recorded lessons taught by 20 kindergarten teachers in the spring. Using generalizability theory analyses, we decomposed the MQI’s score stability into potential sources of variation (teachers, lessons, raters, and their interactions). The 13-item (3-domain) Ambitious Mathematics Instruction scale and the Whole Lesson scale each explained about one third of the variance attributed to differences in the main construct of interest (teachers’ instructional strategies). The MQI’s Errors and Imprecision scale was not relevant at the kindergarten level; there were virtually no errors and/or ambiguities observed across the 100 mathematics lessons. In a series of decision studies, we examined improvements in reliability with combinations of up to 6 raters and 8 lessons. Only the Richness of Mathematics domain scores and the Whole Lesson scores achieved acceptable reliabilities. Practice or Policy: The findings have important implications for the use of observation measures to document teachers’ mathematics practices in the early years of school.

Studying instructional quality by using a content-specific lens: the case of the Mathematical Quality of Instruction framework

In this study, we use Mathematical Quality of Instruction (MQI), a content-specific observation framework, to examine the mathematical quality of instruction of three focal lessons in order to examine the instructional aspects illuminated by this framework as well as discuss those aspects not captured by MQI. While prior work provides evidence on the validity and reliability of the MQI measures, no prior work systematically explores the strengths and limitations of MQI in capturing instructional quality. Our analysis points to the affordances of MQI for highlighting differences within lessons across instructional dimensions related to the mathematics of the lesson, as well as for comparing across lessons with respect to the depth and quality of the mathematics instruction provided to students. We discuss how the depth of information provided by MQI may guide instructional improvement efforts. In addition, we explore three categories of instructional aspects not highlighted when examining instruction through the lens of MQI, addressing areas in which MQI in particular, and observation instruments in general, might be limited in their capacity to support teachers in instructional improvement efforts.

Attending to General and Mathematics-Specific Dimensions of Teaching: Exploring Factors Across Two Observation Instruments

ABSTRACTNew systems that seek to evaluate teachers with regard to their classroom quality often rely on observation instruments that capture general instructional pedagogies. However, decades of research suggest that content-specific dimensions of instruction also are important to differentiate teachers and improve student outcomes. We explore the degree of overlap between a general and a content-specific instrument when capturing upper elementary teachers’ mathematics instruction. To do so, we conducted exploratory and confirmatory factor analyses on data from more than 2,000 videotaped lessons scored using both the Classroom Assessment Scoring System, a general instrument, and the Mathematical Quality of Instruction, a content-specific instrument. Findings indicate that there is some overlap between instruments but that preferred factor structures include both general and content-specific practices.

MQI를 이용한 예비교사와 현직교사의 수학수업의 질 분석

This study analyzed the quality of mathematics classes with observations using the instrument, MQI(Mathematical Quality of Instruction). Class recordings and interviews were conducted on 2 pre-service teachers and 4 in-service teachers. This study recorded and analyzed 3 or 4 classes for each mathematics teacher by using revised MQI. There were a total of 8 raters: 2 or 3 raters analyzed each class. MQI has four dimensions: Richness of the Mathematics, Working with Students and Mathematic, Errors and Imprecision, Student Participation in Meaning-Making and Reasoning. In the dimension of 'Richness of Mathematics', all teachers had good scores of 'explanations of teacher' but had lower scores of 'linking and connections', 'multiple procedures or solution methods' and 'developing mathematical generalizations.' In the dimension of 'Working with Students and Mathematics', two in-service teachers who have worked and having more experience had higher scores than others. In the dimension of 'Errors and Imprecision', all teachers had high scores. In the dimension of 'Student Participation in Meaning-Making and Reasoning', two pre-service teachers had contrast and also two in-service teachers who hadn't worked not long had contrast. Implications were deducted from finding to improving quality of mathematics classes.

A Comparison of Mathematics Classroom Observation Protocols

In this article, we provide information to assist mathematics teacher educators in selecting classroom observation tools. We review three classroom observation tools: (1) the Reform-Oriented Teaching Observation Protocol (RTOP); (2) the Instructional Quality Assessment (IQA) in Mathematics; and (3) the Mathematical Quality of Instruction (MQI). We begin by describing each tool and providing examples of research studies or program evaluations using each tool. We then look across tools to identify each tool's specific focus, and we discuss how the features of each tool (and the protocol for its use) might serve as affordances or constraints in relation to the goals, purposes, and resources of a specific investigation. We close the article with suggestions for how each tool might be used by mathematics teacher educators to support teachers' learning and instructional change.

Examining the use of a structured analysis framework to support prospective teacher noticing

The ability to notice important events in a teaching situation and make decisions about these events is a key component of teaching well. Prospective teachers tend to notice more superficial aspects of classroom practice, such as class management. This article examines a video club in which four student teachers utilized the Mathematical Quality of Instruction (MQI) analysis framework to code each other’s lessons and to discuss their coding in facilitated group sessions. We found that participants became better able to notice important aspect of mathematics more generally and MQI components more specifically. They also adopted a less evaluative stance toward what they noticed. Finally, their self-reported beliefs and practices altered; they credited their participation in the video club for their attempts to incorporate more opportunities for students to engage with mathematical content and ideas.

Reading between the lines: Teaching linear algebra

This paper compares lessons on linear equations from the same curriculum materials taught by two teachers of different levels of mathematical knowledge for teaching (MKT). The analysis indicates that the mathematical quality of instruction in these two classrooms appears to be a function of differences in MKT. Although the two teachers were teaching from the same curriculum materials, the teacher with higher MKT had more complete and concise ways to describe key concepts, had multiple ways to represent ideas about linear equations, could move nimbly among different mathematical expressions of linear relationships, and gave students a larger role in articulating the mathematical ideas of the lesson. However, curriculum materials seem to have moderated what would otherwise have been larger disparities in the quality of instruction between the two teachers. The lower-MKT teacher made minor mathematical errors, stayed on topic, and defined concepts in reasonably accurate ways when he followed the curriculum materials closely.

MKT and curriculum materials are only part of the story: Insights from a lesson on fractions

This paper investigates the contribution of mathematical knowledge for teaching (MKT) and curriculum materials to the mathematical quality of instruction by comparing the enactment of a fractions problem taught by two teachers with differing MKT. It was found that MKT seem to support teachers' precise use of mathematical language and to prevent errors; the curriculum materials provided a rich representational context for mathematical work. However, teachers' orientations toward mathematics and mathematics teaching and their goals for student learning also seemed to contribute to their use of curriculum materials to engage students with rich mathematics and to support students' participation in the development of the mathematics. Although orientations and goals made it more likely for a teacher to use multiple representations and elicit multiple solution methods, MKT was needed to productively use these elements in instruction. Based on this analysis, it is argued that there are aspects of developing orientations and goals that are related to MKT.

A validation study of the use of mathematical knowledge for teaching measures in Ireland

Researchers who study mathematical knowledge for teaching (MKT) are interested in how teachers deploy their mathematical knowledge in the classroom to enhance instruction and student learning. However, little data exists on how teachers’ scores on the US-developed measures relate to classroom instruction in other countries. This article documents a validation study of Irish teachers’ scores on measures of MKT that were adapted for use in Ireland. A validity argument is made identifying elemental, structural and ecological assumptions. The argument is evaluated using qualitative and quantitative data to analyse inferences related to the three assumptions. The data confirmed the elemental assumption but confirming the structural and ecological assumptions was more difficult. Only a weak association was found between teachers’ MKT scores and the mathematical quality of instruction. Possible reasons for this are outlined and challenges in validating the use of measures are identified.

Measuring the mathematical quality of instruction

Measuring the mathematical quality of instruction

Mathematical Knowledge for Teaching and the Mathematical Quality of Instruction: An Exploratory Study

This study illuminates claims that teachers' mathematical knowledge plays an important role in their teaching of this subject matter. In particular, we focus on teachers' mathematical knowledge for teaching (MKT), which includes both the mathematical knowledge that is common to individuals working in diverse professions and the mathematical knowledge that is specialized to teaching. We use a series of five case studies and associated quantitative data to detail how MKT is associated with the mathematical quality of instruction. Although there is a significant, strong, and positive association between levels of MKT and the mathematical quality of instruction, we also find that there are a number of important factors that mediate this relationship, either supporting or hindering teachers' use of knowledge in practice.

The Contribution of Training and Subject Matter Knowledge to Teaching Effectiveness: A Multilevel Analysis of Longitudinal Evidence from Belize

Differentes recherches ont etabli l'influence des enseignants sur la qualite de l'apprentissage des enfants. La question est de savoir ce qui rend un enseignant plus performant qu'un autre. Quatre indicateurs, etudies par les AA., peuvent etre utilises dans ce but : les acquisitions pedagogiques des enseignants, leurs participations dans les programmes d'etudes, leurs connaissances des matieres enseignees et leurs strategies pedagogiques