Is It DAP? American Preschool Teachers’ Views on the Developmental Appropriateness of a Preschool Math Lesson from China

Planned instruction is an important teaching form in early childhood mathematics education, but some educators are concerned about its developmental appropriateness. The present study was undertaken to address this issue. One hundred and seven American preschool teachers participated in the study: They watched a video-taped math lesson that was conducted in a 4-year-olds’ classroom in China and answered video-cued questions in a questionnaire. A mix of qualitative and quantitative methods was used in analyzing the data. Research Findings: Results show that on average, participants rated the quality and developmental appropriateness of the lesson as high. They acknowledged children’s active learning, teacher’s careful preparation, and use of different learning methods. But, they also identified inadequate elements such as lack of peer interactions and lesson differentiation. Practice or Policy: A relief of American preschool teachers’ current beliefs regarding the developmental appropriateness of math lessons provides critical reference for professional preparation/development programs. American preschool teachers’ high value of children’s active learning in a planned math lesson and their appreciation of teacher’s skillful guidance imply an imperative need to promote American preschool teachers’ pedagogical knowledge and skills in teaching mathematics to young children.     

Promoting equity in mathematics teacher preparation: a framework for advancing teacher learning of children’s multiple mathematics knowledge bases

Research repeatedly documents that teachers are underprepared to teach mathematics effectively in diverse classrooms. A critical aspect of learning to be an effective mathematics teacher for diverse learners is developing knowledge, dispositions, and practices that support building on children’s mathematical thinking, as well as their cultural, linguistic, and community-based knowledge. This article presents a conjectured learning trajectory for prospective teachers’ (PSTs’) development related to integrating children’s multiple mathematical knowledge bases (i.e., the understandings and experiences that have the potential to shape and support children’s mathematics learning—including children’s mathematical thinking, and children’s cultural, home, and community-based knowledge), in mathematics instruction. Data were collected from 200 PSTs enrolled in mathematics methods courses at six United States universities. Data sources included beginning and end-of-semester surveys, interviews, and PSTs’ written work. Our conjectured learning trajectory can serve as a tool for mathematics teacher educators and researchers as they focus on PSTs’ development of equitable mathematics instruction.     

Using video-based anchored instruction to enhance learning: Taiwan's experience

The purpose of this study is to investigate the effects of computer-assisted videodisc-based anchored instruction on attitudes toward mathematics and instruction as well as problem-solving skills among Taiwanese elementary students. Results from a t-test indicate a significant main effect on student attitudes toward mathematics. Results from a two-way Repeated Measures ANOVA show that students' problem-solving skills improve significantly with anchored instruction. Results also indicate that all the students benefit from the effects of anchored instruction on their problem-solving performance regardless of their mathematics and science abilities. The findings suggest that video-based anchored instruction provide a more motivating environment that enhanced students' problem-solving skills. This study is significant because it establishes an example of video-based anchored instruction for Taiwanese students and also provides empirical evidence of its effects on affective and cognitive responses among fifth graders in learning mathematics. This study is helpful to educators who want to help students learn to think and learn throughout technology.     

Promotion of self-regulated learning in classrooms: investigating frequency, quality, and consequences for student performance

An implication of the current research on self-regulation is to implement the promotion of self-regulated learning in schools. Teachers can promote self-regulated learning either directly by teaching learning strategies or indirectly by arranging a learning environment that enables students to practise self-regulation. This study investigates teachers’ direct and indirect promotion of self-regulated learning and its relation to the development of students’ performance. Twenty German mathematics teachers with their overall 538 students (grade 9) were videotaped for a three-lesson unit on the Pythagorean Theorem. Students’ mathematics performance was tested several times before and after the observed lessons. A low-inferent coding system was applied to assess the teachers’ implicit or explicit instruction of cognitive strategies (e.g., organisation), metacognitive strategies (e.g., planning), and motivational strategies (e.g., resource management). High-inferent ratings were used to assess features of the learning environment that foster self-regulation. Results reveal that a great amount of strategy teaching takes place in an implicit way, whereas explicit strategy teaching and supportive learning environment are rare. The instruction of organisation strategies and some features of the learning environment (constructivism, transfer) relate positively to students’ performance development. In contrast to implicit strategy instruction, explicit strategy instruction was associated with a gain in performance. These results reveal a discrepancy between the usefulness of explicit strategy instruction and its rare occurrence in classrooms.     

Recasts Used with Preschoolers Learning English as their Second Language

This study examined linguistic recasts provided by 16 early childhood educators to preschool children learning English as a second language (EL2). Recasts are semantic and syntactic revisions of children’s utterances. The educator–child interactions were filmed during book reading and play dough activities with small groups of four children, one of whom was EL2. The EL2 children were rated by their educators as having less well-developed expressive language skills than their unilingual peers. However, despite this finding, educators provided similar rates of recasts to both groups of children. Eight EL2 children with the lowest expressive language skills demonstrated fewer uptakes of their educator’s recasts in comparison to EL2 children with higher expressive language skills. The implications of this study include increasing the rate of recasts and reducing their complexity to provide language-learning opportunities for all preschool children, especially for those learning English as a second language.     

Teaching Preschoolers to Count: Effective Strategies for Achieving Early Mathematics Milestones

Attention to early childhood mathematics instructional strategies has sharpened due to the relatively poor mathematics performance of U.S. students in comparison to students from other countries and research evidence that early mathematics skills impact later achievement. Early Childhood counting skills form the foundation for subsequent mathematics learning. In this article, we discuss the milestones of counting development and examine preschool classroom mathematics observations through the lenses of two CLASS Dimensions, Concept Development and Instructional Learning Formats. Recommendations for effective instructional strategies around counting and suggestions for incorporating mathematics instruction into storybook reading are provided.     

What Is the Long‐Run Impact of Learning Mathematics During Preschool?

The current study estimated the causal links between preschool mathematics learning and late elementary school mathematics achievement using variation in treatment assignment to an early mathematics intervention as an instrument for preschool mathematics change. Estimates indicate (n = 410) that a standard deviation of intervention‐produced change at age 4 is associated with a 0.24‐SD gain in achievement in late elementary school. This impact is approximately half the size of the association produced by correlational models relating later achievement to preschool math change, and is approximately 35% smaller than the effect reported by highly controlled ordinary least squares (OLS) regression models (Claessens et al., 2009; Watts et al., 2014 ) using national data sets. Implications for developmental theory and practice are discussed.     

The meaning of mathematics instruction in multilingual classrooms: analyzing the importance of responsibility for learning

In the multilingual mathematics classroom, the assignment for teachers to scaffold students by means of instruction and guidance in order to facilitate language progress and learning for all is often emphasized. In Sweden, where mathematics education is characterized by a low level of teacher responsibility for students’ performance, this responsibility is in part passed on to students. However, research investigating the complexity of relations between mathematics teaching and learning in multilingual classrooms, as well as effect studies of mathematics teaching, often take the existence of teachers’ responsibility for offering specific content activities for granted. This study investigates the relations between different aspects of responsibility in mathematics teaching and students’ performance in the multilingual mathematics classroom. The relationship between different group compositions and how the responsibility is expressed is also investigated. Multilevel structural equation models using TIMSS 2003 data identified a substantial positive influence on mathematics achievement of teachers taking responsibility for students’ learning processes by organizing and offering a learning environment where the teacher actively and openly supports the students in their mathematics learning, and where the students also are active and learn mathematics themselves. A correlation was also revealed between group composition, in terms of students’ social and linguistic background, and how mathematics teaching was performed. This relationship indicates pedagogical segregation in Swedish mathematics education by teachers taking less responsibility for students’ learning processes in classes with a high proportion of students born abroad or a high proportion of students with low socio-economic status.     

Mathematics in Early Childhood: Research-Based Rationale and Practical Strategies

Mathematics education is a critical part of the curriculum for students worldwide. The foundation for understanding mathematical concepts related to number sense begins early in life, and early childhood classrooms can provide the seeds for mathematical skills that will be needed later in life. In this article, the authors make a case for meaningful and developmentally appropriate mathematics experiences for young children in diverse early learning settings. Instructional and curricular methods inspired by the Reggio Emilia Approach are described as effective ways to teach number concepts to young children from preschool through primary age. Strategies for teachers of young learners are presented in order to strengthen the mathematics curriculum in contemporary early learning settings. The authors’ analysis and recommendations are informed by their extensive experiences including studies in Reggio Emilia early childhood settings (infant toddler, preschool, and primary schools) and their work in early childhood teacher education at their respective universities.     

Mathematics and Science Learning Opportunities in Preschool Classrooms

Research Findings: The present study observed and coded instruction in 65 preschool classrooms to examine (a) overall amounts and (b) types of mathematics and science learning opportunities experienced by preschool children as well as (c) the extent to which these opportunities were associated with classroom and program characteristics. Results indicated that children were afforded an average of 24 and 26 min of mathematics and science learning opportunities, respectively, corresponding to spending approximately 25% of total instructional time in each domain. Considerable variability existed, however, in the amounts and types of mathematics and science opportunities provided to children in their classrooms; to some extent, this variability was associated with teachers' years of experience, teachers' levels of education, and the socioeconomic status of children served in the program. Practice or Policy: Although results suggest greater integration of mathematics and science in preschool classrooms than previously established, there was considerable diversity in the amounts and types of learning opportunities provided in the preschool classrooms. Affording mathematics and science experiences to all preschool children as outlined in professional and state standards may require additional professional development aimed at increasing preschool teachers' understanding and implementation of learning opportunities in these 2 domains in their classrooms.     

Blending Effective Behavior Management and Literacy Strategies for Preschoolers Exhibiting Negative Behavior

Sometimes students will exhibit various aggressive behaviors in the preschool classroom. Early childhood educators need to have behavior management strategies to manage the students’ negative behaviors within the classroom setting. This article will provide a rationale for embedding literacy instruction within behavior management strategies to assist preschool age students with negative behaviors. Three widely used classroom management strategies will be explained: group contingencies, anger management, and individualized behavior plans with differential reinforcement of other behaviors. Each strategy will have developmentally appropriate literacy skills infused into it. In conclusion, a suggestion will be given to early childhood educators on how to implement these blended management techniques.     

Mapping beliefs about teaching to patterns of instruction within science,technology, engineering,and mathematics

In this paper, we identify beliefs about teaching and patterns of instruction valued and emphasized by science, technology, engineering, and mathematics faculty in higher education in the USA. Drawing on the notion that effective teaching is student-centered rather than teacher-centered and must include a balance of knowledge-, learner-, community-, and assessment-centered learning environments; we use qualitative interview data to explore how faculty's reported beliefs about teaching are associated with their consideration of these four types of environments. Findings indicated that although a range of beliefs about teaching emerged, most were firmly located in knowledge-centered learning environments, with little or no focus on the remaining three learning environments. Furthermore, even patterns of instruction that were heavily student-centered were situated within a knowledge-centered learning framework. We argue that for student-centered instruction to be truly successful, faculty must consider all four learning environments in crafting and facilitating the classroom environment.     

Content area reading pedagogy and domain knowledge: a Bourdieusian analysis

The twofold purpose of this study was to trace prospective and practicing mathematics teachers’ understandings of content area reading instruction in relation to domain knowledge in mathematics, and to examine the extent to which online pedagogical mentoring supported the integration of such instruction and knowledge. The design called for two pairs of prospective and practicing mathematics teachers to develop, implement, and reflectively evaluate four lessons. A multilevel mentoring approach was used to leverage the valuing of domain knowledge in mathematics. Course materials, lesson plans, teacher reflections, mentors’ feedback, interviews, and case reports were analysed using Bourdieu’s concepts of cultural capital, field, and misrecognition. Results indicate that despite the study’s focus on prioritising domain knowledge through pedagogical mentoring, the instances in which such knowledge were integrated effectively with reading instruction varied in relation to a mentor’s expertise in mathematics. If reading teacher educators are to support prospective and practicing mathematics teachers in content area reading instruction, additional sources of mathematics cultural capital are needed.     

The role of technology in supporting classroom assessment in play-based kindergarten

There has been a rapid increase in the integration of new technologies in early education. While research has examined how technology can benefit classroom instruction, few studies have looked specifically at how technology is used by early educators to enhance their classroom assessment practices. The current study examined educators’ approaches towards the integration of technology in assessment in 20 play-based kindergarten classrooms. The majority of educators described technology as improving the efficiency of their assessment practices, while a minority of educators described technology as meaningfully extending student learning in assessment. Implications of different uses of assessment technology are discussed.     

Video Modeling and Explicit Instruction: A Comparison of Strategies for Teaching Mathematics to Students with Learning Disabilities

As classrooms begin to adopt a greater number of digital technologies such as computers and tablets, it is important for educators to understand how effective such tools can be in aiding in the delivery of instruction to students who struggle in mathematics, such as those identified with a learning disability in mathematics. One digital‐based instructional strategy with a limited research base for students with a learning disability is video modeling. Through a single subject alternating treatments design, this study compared the use of video modeling to face‐to‐face explicit instruction for teaching geometry word problems to three secondary students with a learning disability in mathematics. Across 10 sessions of intervention, all three students demonstrated improved performance on all dependent variables with both interventions, while the explicit instruction condition produced slightly greater accuracy scores for two of the three students. The results and their implications for the field of mathematics are discussed.     

The Dialectic Relationship between Research and Practice in Mathematics Teacher Education

This paper addresses issues linking research in student teacher learning with reflection on practice in mathematics teacher education. From a situated perspective on learning and practice, we explore our own practice as teacher educators while researching student teacher learning in our classrooms. We describe a study on student teacher learning, considering student teacher learning as a “process of becoming”, and how the results of this research have affected our development as mathematics teacher educators and members of a community of inquiry. Our work shows how in the mathematics teacher education context the relationship between theory and practice becomes an element of both teacher educator and researcher development.     

The Role of Preschools and Preschool Teachers: Icelandic preschool educators' discourses

The purpose of the study was to investigate how preschool teachers in Iceland view early childhood education and the professional preschool teacher. Focus groups consisting of early childhood educators in Iceland were interviewed. Each of four focus groups comprised educators who held similar positions. They were: (1) preschool teachers; (2) preschool directors; (3) preschool consultants; and (4) educators of preschool teachers. Data were analyzed using strategies of qualitative inquiry. The analysis revealed dilemmas concerning the use of concepts such as teaching and care, cooperation with the primary schools, the organization of the preschool day, and the role of preschool teachers in children's learning. The results were interpreted in the light of postmodern perspectives of the child and early childhood institutions.     

Learning to Teach Mathematics: Questioning, Listening, and Responding

This paper reports a study designed to explore prospective teachers' learning to teach mathematics in the complex context of a university-based curriculum and instruction course. The course, taught with a focus on inquiry, used prospective teachers' weekly interactions with students as springboards for investigations of mathematics, teaching, and learning. A framework of questioning, listening, and responding is used to analyze prospective teachers' understandings and the tensions they experienced. The difficulties and tensions prospective teachers face in turn pose challenges and tensions for teacher educators. This revised version was published online in July 2006 with corrections to the Cover Date.     

Learning environment,self-efficacy for teaching mathematics,and beliefs about mathematics

Learning environment research has a long history of significant relationships between the learning environment and student outcomes. This study investigated relationships between the learning environments of mathematics courses in a teacher education program and two outcomes, mathematics teaching self-efficacy and beliefs about mathematics. These two outcomes have been repeatedly shown to influence the future teaching practices of preservice teachers but, to date, their relationships with learning environment have been investigated neither with preservice teachers nor at all in the United Arab Emirates or wider Gulf region. The learning environment was found to be significantly related to preservice teachers’ mathematics teaching self-efficacy and beliefs about mathematics. Learning environments perceived more favourably by preservice teachers were associated with higher self-efficacy for teaching mathematics, but also with more-traditional beliefs, making these findings important for higher education institutes and teacher educators.