The Impact of Reform: Challenges for Mathematics Teacher Preparation

The mathematics education community has been widely recognized as a leader in the standards-based reform movement. Despite the widespread interest and attention that reform documents such as the NCTM Standards have generated, what has yet to be fully understood is the impact of these types of reform documents on the preservice teacher preparation process. This paper examines the state of the standards-based reform effort in mathematics teacher education by presenting the results of a three-year study of six cohorts of secondary mathematics student teachers (n = 63). Examined in particular are the ways in which these student teachers' professed beliefs about and knowledge of the NCTM Standards contrast with their teaching practices. Possible explanations for the mismatch between belief and knowledge statements and teaching practices are examined, along with other implications for mathematics teacher preparation.     

Development and validation of Teacher Intentionality of Practice Scale (TIPS): A measure to evaluate and scaffold teacher effectiveness

Teacher evaluation instruments frequently fail to support teacher growth and improvement—particularly in critical constructs surrounding pedagogical content knowledge that promote student growth and achievement. The current study details the development and validation of the Teacher Intentionality of Practice Scale (TIPS), an observational protocol designed to measure intentional teaching practices and provide support for teacher growth over time. Findings suggest that TIPS provides a valid and highly reliable research-based teacher observational instrument that also serves as a professional development model to help scaffold the growth and improvement of K-12 educators. This paper details the theoretical foundations of TIPS, reports reliability and validity measures (including both Exploratory and Confirmatory Factor Analyses), and discusses applications and implications of TIPS for teacher evaluation and professional development.     

Identifying Early Numeracy Indicators for Kindergarten and First‐Grade Students

Recent studies have documented positive effects for early intervention in improving the mathematics performance of low‐achieving children. Consequently, educators need technically sound mathematics screening measures to identify children at risk and then intervene to improve achievement. In this article, we describe preliminary technical adequacy evidence for four early numeracy measures (number identification, quantity discrimination, quantity array, and missing number). We assessed over 300 kindergarten and first‐grade students in two states to evaluate the reliability and criterion validity of the four measures. Fall and spring administrations of the measures for one subgroup provided preliminary evidence of students' growth on the measures over time. The results supported three of the four measures as potential tools for screening in the early grades.     

初中生数学学习非智力因素调查问卷的编制

通过查阅文献资料与已有成熟问卷,征询专家意见,根据初中生数学学习特点,编制了"初中生数学学习非智力因素调查问卷".经过项目分析、探索性因素分析、验证性因素分析,对问卷进行相应修改,正式问卷包括动机、态度、意志、性格、情绪情感5个维度,以及对应的13个因子.所编问卷具有较好的信度(一致性系数,重测信度,分半信度)与效度(内容效度、结构效度、效标效度),可作为测量初中生数学学习非智力因素的有效工具.     

Designing Curriculum-Based Mathematics Professional Development for Kindergarten Teachers

This study examines the influence of a year-long mathematics professional development program on Kindergarten teachers’ beliefs, content knowledge, instructional practices, and their students’ achievement. The professional development program is grounded in the theoretical construct of learner-centered professional development and focuses on supporting teachers’ integration of standards-based pedagogies aligned with the Common Core State Standards in Mathematics. Data analysis included examining 15 Kindergarten teachers’ mathematics content knowledge, their beliefs about mathematics, their enactment of student-centered pedagogies, and student achievement on curriculum-based assessments. Findings indicated that teachers adopted more student-centered pedagogies and embraced more student-centered beliefs about mathematics teaching during their time in the project. Further, Kindergarten teachers also demonstrated gains in their mathematical content knowledge, and those content knowledge gains were linked to gains in student achievement.     

The Influence of Teachers’ Efficacy and Beliefs Regarding Mathematics Instruction in the Early Childhood Classroom

This was a correlational study conducted with a population of prekindergarten educators from a large, metropolitan school district. The purpose was to examine if there were relationships between and among early childhood teachers’ sense of self-efficacy, their beliefs about the importance of mathematics, and their mathematics instructional practices. Examining teachers’ efficacy and beliefs can inform educational practice and help to differentiate between more and less successful instructional practices when teaching mathematics in the early childhood classroom. Data were collected on teacher efficacy and teacher beliefs about the importance of mathematics with two self-report questionnaires. The hypothesis that the teachers higher in efficacy will rate the importance of mathematics higher on the teacher-belief scale than the teachers with lower efficacy was found to be true with this sample, but the correlation was weak. The level of efficacy of the early childhood teachers in this sample confirmed that in assessing their capabilities, they rate themselves high in instructional strategies, classroom management, and student engagement. The early childhood teachers did not rate their belief in mathematics as high as their efficacy. Observations of mathematics instructional practices were conducted with twenty teachers. It was hypothesized that the combination of high teacher efficacy and high teacher mathematics beliefs would show alignment with the presence of standards-based mathematics instructional practices. The results were not statistically significant. No correlation signals a need for more research to explore what other personal or external factors relate to mathematics instructional practices in the early childhood classroom. The research may inform pre kindergarten teachers and teacher educators about effective instructional strategies and knowledge needed to launch early childhood students on a developmentally appropriate pathway to mathematical literacy.     

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

Research 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.     

Examining the Relationship Between Teacher Evaluation and Student Assessment Results in Washoe County

In this article, we describe findings from an analysis of the relationship between scores on a standards-based teacher evaluation system modeled on the Framework for Teaching (Danielson, 1996) and student achievement measures in a large Western school district. We apply multilevel statistical modeling to study the relationship between the evaluation scores and state and district tests of reading, mathematics, and a composite measure of reading and mathematics. Using a value-added framework, the teacher evaluation scores were included at the 2nd level, or teacher level, of the model when other student and teacher-level characteristics were controlled. This study provided some initial evidence of a positive association between teacher performance, as measured by the evaluation system, and student achievement. The coefficients representing the effects of teacher performance on student achievement were positive and were statistically significant in 4 of 9 grade-test combinations studied.     

Measuring Mathematical Competences of Engineering Students at the Beginning of Their Studies

This article reports about our efforts to determine engineering students' competence in mathematics. Our research is embedded in a larger project, KoM@ING–Modeling and developing competence: Integrated IRT based and qualitative studies with a focus on mathematics and its usage in engineering studies, within the program Modeling and Measuring Competencies in Higher Education (KoKoHS). KoKoHS provides the umbrella organization of several research projects addressing the modeling and measuring of competences at the college level. KoM@ING aims to model the role of engineering students' mathematical competences for their studies from both a quantitative and a qualitative perspective.

Here, we report the development of a large-scale instrument assessing engineering freshmen's competence in mathematics by applying Rasch analysis to determine measures for item difficulties and student abilities. Several analyses were performed to provide insights into the measures' reliability and validity. In particular, to examine cognitive validity, we scrutinized students' think-aloud protocols when solving the items to investigate their problem solving abilities as a proxy for item difficulty. Overall, we found first evidence that our instrument is suitable to assess engineering freshmen's competence in mathematics. This instrument may be helpful to conduct further research and to inform those concerned with college organization and policy.     

Coach learning to help teachers learn to enact conceptually rich,student-focused mathematics lessons

The past decade has witnessed a strong, standards-based call for improving what mathematics is taught and how it is taught. In the USA, districts have hired instructional coaches to help teachers shift their teaching from algorithm-based instruction to instruction that is more student-centered and conceptually focused. The purpose of this study was to contribute to the field’s understanding of (a) the specific coaching practices that help teachers enact more conceptual-based forms of instruction; and (b) how coaches learn to enact those practices. Using a design-based implementation research approach, we trained coaches using a particular model for one-on-one coaching (Content-Focused Coaching); the coaches then worked with teachers to plan lessons aligned with the coaching model. Data consisted of videotapes of pre-lesson conferences that were transcribed and coded according to the model. Analyses of 32 coaches’ practice over a 2-year period suggest that each of the three components of our coaching model (attention to student thinking, pedagogy, and mathematics) demonstrated statistically significant improvement over time. An illustrative analysis of five coaching sessions of one coach revealed a progression over five sessions from planning discussions that stayed at the level of general strategies to more specific conversations about teaching a particular task and then to deeper discussions that integrate attention to mathematical concepts, student thinking, and pedagogical moves. We view this delineation of coach learning as an important first step in laying the groundwork for the design of future coach training.

     

Approaches to measuring use of research evidence in K-12 settings: A systematic review

An increased focus on the use of research evidence (URE) in K-12 education has led to a proliferation of instruments measuring URE in K-12 education settings. However, to date, there has been no review of these measures to inform education researchers’ assessment of URE. Here, we systematically review published quantitative measurement instruments in K-12 education. Findings suggest that instruments broadly assess user characteristics, environmental characteristics, and implementation and practices. In reviewing instrument quality, we found that studies infrequently report reliability, validity, and demographics about the instruments they develop or use. Future work evaluating and developing instruments should explore environmental characteristics that affect URE, generate items that match up with URE theory, and follow standards for establishing instrument reliability and validity.     

Validity Evidence Supporting Use of Anchoring Vignettes to Measure Teaching Practice

High-quality measures of instructional practice are essential for research and evaluation of innovative instructional policies and programs. However, existing measures have generally proven inadequate because of cost and validity issues. This paper addresses two potential drawbacks of survey self-report measures: variation in teachers’ interpretation of response scales and their interpretation of survey questions. To address these drawbacks, researchers tested out use of “anchoring vignettes“ in teacher surveys to capture information about teaching practice, and they gathered validity evidence in regard to their use as a tool for adjusting teachers’ survey self-reports about their instructional practices for research purposes, or potentially to inform professional development. Data from 65 teachers in grades 4-9 responding to our survey suggested that vignette adjustments were reliable and valid for some instructional practices more than others. For some instructional practices, researchers found significant and high correlations between teachers’ adjusted survey self-rating, through use of anchoring vignettes, and previous observation ratings of teachers’ instruction, including ratings from several widely-used observation rubrics. These results suggest that anchoring vignettes may provide an efficient, cost-effective method for gathering data on teachers’ instruction.     

A Framework for Conceptualizing and Evaluating the Validity of Instructionally Relevant Assessments

Assessments that function close to classroom teaching and learning can play a powerful role in fostering academic achievement. Unfortunately, however, relatively little attention has been given to discussion of the design and validation of such assessments. The present article presents a framework for conceptualizing and organizing the multiple components of validity applicable to assessments intended for use in the classroom to support ongoing processes of teaching and learning. The conceptual framework builds on existing validity concepts and focuses attention on three components: cognitive validity, instructional validity, and inferential validity. The goal in presenting the framework is to clarify the concept of validity, including key components of the interpretive argument, while considering the types and forms of evidence needed to construct a validity argument for classroom assessments. The framework's utility is illustrated by presenting an application to the analysis of the validity of assessments embedded within an elementary mathematics curriculum.     

The standards for academics’ standards-based assessment practices

The use of standards-based assessment (SBA) has gained prominence in higher education due to a wide range of research evidence that supports its effectiveness in improving learning and teaching. Although the concept is widely used in academic discourse and practice, it has multiple interpretations which have led to diverse assessment practices to the extent that some of these depart from the principles of SBA. To help build a common understanding of what constitutes SBA practices, we explored the construct of academic SBA practices using both theoretical and empirical approaches. We developed a tool, based on the principles of SBA emerging from practices noted in the literature and identified from focus groups. We used factor analysis to extract the dimensions of the construct and to establish empirical evidence for the utilisation of the tool using a data set of 410 academics who engaged in self-assessment. Results showed that a six-factor model is the most parsimonious among other models. We used these dimensions to develop a framework for describing academic SBA practices. The use of the framework and tool has critical implications for curriculum design, professional practice and development, and policy articulation.     

An investigation of the validity and reliability of the adapted mathematics anxiety rating scale-short version (MARS-SV) among Turkish students

This study adapted the Mathematics Anxiety Rating Scale-Short Version (MARS-SV) into Turkish and investigated the validity and reliability of the adapted instrument. Twenty-five bilingual experts agreed on the language validity, and 49 Turkish language experts agreed on the conformity and understandability of the scale’s items. Thirty-two subject matter experts’ responses provided evidence for content validity. Finally, 475 college students (51.58% men) responded to the adapted scale. Based on the existing literature, several models were specified and estimated. Confirmatory factor analyses showed that only five-factor model provided fit to the data (all fit indices exceeded 0.90). Standardized factor loadings were found all positive, significant, and ranged from 0.40 to 0.78. Factors are named as the Mathematics Test Anxiety, Course Anxiety, Computation Anxiety, Application Anxiety, and Social Anxiety. All subscales were significantly correlated with the total scale score as well as among themselves. It was concluded that the adapted scale measures the construct of mathematics anxiety in Turkish college student populations.     

以生活情境为导向的小学数学教学微视频探析

最近几年,在小学数学课堂教学中逐步渗入互联网微视频,要实现其有效的意义与价值,离不开以生活情境为导向的明灯来指引小学数学教学走向更有效的方法和路径。本文主要从以下几方面着手,探析以生活情境为导向的小学数学教学微视频的核心概念、存在意义及使用措施。     

A Note on the Problem Solving Style Questionnaire: An alternative to Kolb's Learning Style Inventory?

Given the psychometric limitations of existing measures of Kolb's experiential learning model (ELM), two new scales of learning styles have been developed. The validity of these scales has been supported in samples of undergraduate and MBA students in the USA. This paper provides evidence of some psychometric properties of scores yielded by these scales using samples of undergraduate students in the UK. Only limited support is found for the internal consistency reliability and construct validity of scores produced by the scales. However, an item attrition exercise identifies a two‐factor solution providing an acceptable fit to the data. The scales are reported as being positively correlated with academic performance and prior academic achievement. Despite the mixed evidence, we suggest further development of the scales is warranted to create a psychometrically sound measure of the ELM.     

MATHEMATICS EDUCATION VALUES QUESTIONNAIRE FOR TURKISH PRESERVICE MATHEMATICS TEACHERS: DESIGN, VALIDATION, AND RESULTS

The purpose of this study was to develop a questionnaire that could measure preservice mathematics teachers' mathematics educational values. Development and validation of the questionnaire involved a sequential inquiry in which design principles were established from the existing literature and a pool of items was constructed then submitted to experts for consideration of the construct validity. Alterations to the items based on their suggestions were made to produce a trial version of the questionnaire. A pilot study involving preservice mathematics teachers explored the validity and usefulness of the questionnaire. The pilot results were used to revise the questionnaire that was administered to a sample of preservice mathematics teachers attending Cumhuriyet University, Sivas, Turkey. Further explorations of the construct and structural validity, item contributions, and reliability were achieved by using a factor analysis and two different item analysis methods. Results revealed that the questionnaire included four factors, satisfactory item contributions, and acceptable internal consistency. One result obtained in this study suggested that some mathematics education values based on Western culture (e.g., accessibility–special) have not been accepted by Turkish preservice mathematics teachers.