Responsiveness to Students’ Mathematical Thinking in Middle-Grades Classrooms

Responsiveness to students’ mathematical thinking is a characteristic of classroom discourse that reflects the extent to which students’ mathematical ideas are present, attended to, and taken up as the basis for instruction. Using the Mathematically Responsive Interaction (MRI) Framework and data from 11 middle-grades classrooms, we illustrate varied enactments of responsiveness and describe fluctuations in and relationships among different components of responsiveness. We found positive associations between different components of responsiveness, but they were not entirely predictive of one another. Individual classrooms appeared more or less responsive depending on which component was foregrounded. Our findings offer a more comprehensive characterization of responsiveness that documents the intertwined nature of teacher moves and student contributions during all whole-class instruction.

Implementation of solution-focused approach in teacher’s educational work

For many teachers working at school means solving problems of a various nature. These problems are often associated with teaching difficulties, and even more often with educational issues caused by students. When focussing on problems, teachers experience a sense of work overload, disappointment and stress, or a sense of helplessness and lack of empowerment. The paper presents an alternative, novel approach to teacher’s work. Instead of an in depth examination of problems, the solution-focussed approach redirects the teacher’s greater attention to searching for exceptions from existing problems and developing aspects which enable students to function effectively at school, to student’s achievements and resources. The article presents the theoretical assumptions of solution-based education and its possible use by the teacher in work with the student and the whole class.

Lifting the School Mat: An Investigation of Pedagogy and Children's Social Worlds at Mat Time

<p>Primary school teachers’ use of whole-class activity is a well-documented phenomenon. Typically, it is assumed that children’s active participation in group tasks is important for their academic learning and for developing self-concept. However, previous studies have found that children’s participation varies widely. The present research set out to investigate why individual children’s participation differs within the peer group during whole-class activity. Teachers’ pedagogy and children’s social worlds intersect during classroom interactions; it is in this intersecting space that this research is situated. One specific whole-class activity was chosen as a focus, namely mat time. This is a practice whereby the teacher calls the entire class to the mat typically for the purposes of instruction, discussion, or other similar activity. To understand mat time from the perspectives of the people who experience it, two studies were undertaken using a mixed strategy approach for data gathering. The first study investigated teachers’ perspectives (N=296) using a questionnaire. Participants were asked about a variety of themes relating to mat time including pedagogical uses, strategies, and outcomes. Principal components analyses confirmed the approximate uni-dimensionality of the data relating to each theme, which were then calibrated to a measurement variable using Samejima’s (1969, as cited in DeMars, 2010) graded response model. Various correlations and comparisons were conducted pertaining to the pedagogical factors influencing children’s participation, behaviour, and enjoyment. The second study used qualitative semi-structured interviews with children (n=49) from three year two classrooms situated in different schools. The data were analysed and discussed in relation to peer culture and peer-relations theories, which posit that children’s social groups consist of norms and interests that differ to those of adults’, and that such groups consist of internal social hierarchies. Taken together, the findings from the two studies indicated that teachers and children differ in their perception of the social climate at mat time. For instance, whereas teachers tended to report that mat time achieved prosocial objectives, children were more likely to describe socially divisive aspects. Such aspects included certain children’s desire to affiliate with specific peers while excluding others, or promoting their own participation over that of classmates. Seating position and opportunities to take active roles were sources of competition. Children’s differing participation was influenced by their individual strategic understandings of how to secure active roles, social support, and academic confidence. Furthermore, teachers generally reported that children were inattentive during mat time, suggesting that it may be an ineffective context for learning. Nevertheless, when teachers were cognisant of children’s interests, they tended to report better participation across the class. The implications for teaching practice include an onus for teachers to actively protect vulnerable children during mat time, socially and academically, and to ensure that opportunities to take part in activities are equitably distributed.</p>

Lifting the School Mat: An Investigation of Pedagogy and Children's Social Worlds at Mat Time

<p>Primary school teachers’ use of whole-class activity is a well-documented phenomenon. Typically, it is assumed that children’s active participation in group tasks is important for their academic learning and for developing self-concept. However, previous studies have found that children’s participation varies widely. The present research set out to investigate why individual children’s participation differs within the peer group during whole-class activity. Teachers’ pedagogy and children’s social worlds intersect during classroom interactions; it is in this intersecting space that this research is situated. One specific whole-class activity was chosen as a focus, namely mat time. This is a practice whereby the teacher calls the entire class to the mat typically for the purposes of instruction, discussion, or other similar activity. To understand mat time from the perspectives of the people who experience it, two studies were undertaken using a mixed strategy approach for data gathering. The first study investigated teachers’ perspectives (N=296) using a questionnaire. Participants were asked about a variety of themes relating to mat time including pedagogical uses, strategies, and outcomes. Principal components analyses confirmed the approximate uni-dimensionality of the data relating to each theme, which were then calibrated to a measurement variable using Samejima’s (1969, as cited in DeMars, 2010) graded response model. Various correlations and comparisons were conducted pertaining to the pedagogical factors influencing children’s participation, behaviour, and enjoyment. The second study used qualitative semi-structured interviews with children (n=49) from three year two classrooms situated in different schools. The data were analysed and discussed in relation to peer culture and peer-relations theories, which posit that children’s social groups consist of norms and interests that differ to those of adults’, and that such groups consist of internal social hierarchies. Taken together, the findings from the two studies indicated that teachers and children differ in their perception of the social climate at mat time. For instance, whereas teachers tended to report that mat time achieved prosocial objectives, children were more likely to describe socially divisive aspects. Such aspects included certain children’s desire to affiliate with specific peers while excluding others, or promoting their own participation over that of classmates. Seating position and opportunities to take active roles were sources of competition. Children’s differing participation was influenced by their individual strategic understandings of how to secure active roles, social support, and academic confidence. Furthermore, teachers generally reported that children were inattentive during mat time, suggesting that it may be an ineffective context for learning. Nevertheless, when teachers were cognisant of children’s interests, they tended to report better participation across the class. The implications for teaching practice include an onus for teachers to actively protect vulnerable children during mat time, socially and academically, and to ensure that opportunities to take part in activities are equitably distributed.</p>

Organisation and Self-Concept in Year 6 and Year 7 Mathematics

<p>In New Zealand, schools use the term "tracking", "ability grouping", “setting” or “streaming” to define their class grouping and organisation for mathematics. This organisation of grouping may hinder students’ development of mathematical concepts in their primary and secondary school years. To group or not to group seems to be an important question facing many mathematical educators today. The aim of this study was to investigate if class organisation in regards to grouping affects female students’ mathematical self-concept. The research looks at possible factors affecting mathematical self-concept of students in a comparative study of their Year 6 and Year 7 mathematics learning by focusing on their attitudes to grouping in mathematics over a one-year period spanning two year levels. The Year 6 class organisation was mixed ability (within-class ability grouping for number strategies). The same cohort of girls was followed into Year 7 where three classes were taught using whole class teaching, with a cross-class ability grouping approach. This research draws from data collected from a purposive sample of one school in the Wellington area. Qualitative and quantitative methods were used in order to explore whether class organisation (cross-class or mixed ability grouping) affected students’ self-concept in relation to their mathematical learning. The underlying research paradigm was social constructivist, chosen in order to gain knowledge from students’ experiences and perceptions. Thirty-one questionnaires and nine one-to-one semi-structured interviews were used. The questionnaire answers were put into three categories of strategy groupings based on the expectations for Number from the New Zealand Curriculum (Ministry of Education, 2003a) in order to explore the responses from students of a broad range of abilities. Each semi-structured interview was recorded and transcribed in full for analysis. This study indicates that students are aware of their mathematical ability whether being taught in a small group or whole class situation. Year 6 students preferred learning within a small group ability approach. They felt that this way of organisation fostered an inclusive environment which allowed for individual differentiation, encouraged risk taking, collaboration, helping of others, and feeling confident to discuss ideas, strategies, and ask questions without feeling judged by their peers. Whole class contribution, test scores, and assessment was found to affect the Year 7 students’ mathematical self-concept negatively and positively. The students felt that learning within a whole class approach which was broadly ability grouped was a positive experience as all students could hear everyone’s questions, ideas, strategies, and points of view. Implications from this research include that more exploration is needed in New Zealand schools into the effects of class organisation on students’ mathematical self-concept in order to inform teacher practices of differentiation in relation to the organisation of small group and whole class situations. This and other such research can also inform professional development for teachers on effective ways to create inclusive mathematics learning community environments.</p>

Organisation and Self-Concept in Year 6 and Year 7 Mathematics

<p>In New Zealand, schools use the term "tracking", "ability grouping", “setting” or “streaming” to define their class grouping and organisation for mathematics. This organisation of grouping may hinder students’ development of mathematical concepts in their primary and secondary school years. To group or not to group seems to be an important question facing many mathematical educators today. The aim of this study was to investigate if class organisation in regards to grouping affects female students’ mathematical self-concept. The research looks at possible factors affecting mathematical self-concept of students in a comparative study of their Year 6 and Year 7 mathematics learning by focusing on their attitudes to grouping in mathematics over a one-year period spanning two year levels. The Year 6 class organisation was mixed ability (within-class ability grouping for number strategies). The same cohort of girls was followed into Year 7 where three classes were taught using whole class teaching, with a cross-class ability grouping approach. This research draws from data collected from a purposive sample of one school in the Wellington area. Qualitative and quantitative methods were used in order to explore whether class organisation (cross-class or mixed ability grouping) affected students’ self-concept in relation to their mathematical learning. The underlying research paradigm was social constructivist, chosen in order to gain knowledge from students’ experiences and perceptions. Thirty-one questionnaires and nine one-to-one semi-structured interviews were used. The questionnaire answers were put into three categories of strategy groupings based on the expectations for Number from the New Zealand Curriculum (Ministry of Education, 2003a) in order to explore the responses from students of a broad range of abilities. Each semi-structured interview was recorded and transcribed in full for analysis. This study indicates that students are aware of their mathematical ability whether being taught in a small group or whole class situation. Year 6 students preferred learning within a small group ability approach. They felt that this way of organisation fostered an inclusive environment which allowed for individual differentiation, encouraged risk taking, collaboration, helping of others, and feeling confident to discuss ideas, strategies, and ask questions without feeling judged by their peers. Whole class contribution, test scores, and assessment was found to affect the Year 7 students’ mathematical self-concept negatively and positively. The students felt that learning within a whole class approach which was broadly ability grouped was a positive experience as all students could hear everyone’s questions, ideas, strategies, and points of view. Implications from this research include that more exploration is needed in New Zealand schools into the effects of class organisation on students’ mathematical self-concept in order to inform teacher practices of differentiation in relation to the organisation of small group and whole class situations. This and other such research can also inform professional development for teachers on effective ways to create inclusive mathematics learning community environments.</p>

Using dyadic observation to explore equitable learning opportunities in classroom instruction

Because of poverty, many children do not receive adequate prenatal care, nutrition, or early childhood education. These inequities combine to ensure that many students enter school with considerably less academic content knowledge and skills for learning than their peers. Teachers and schools did not create these gaps, but they must address them. The impact of schools in reducing gaps has been explored for decades only to yield inconsistent findings. One possible reason for these contradictory results is because these studies ignore classroom process. We argue for the inclusion of process in research on opportunity and achievement gaps to better articulate if schools provide inequitable learning opportunities. Further, we argue for dyadic (teacher to individual student) measurement of classroom process because commonly-used observation instruments only measure teachers’ interactions with the whole class. These instruments obscure differential teacher treatment that may exist in some classrooms. To improve policy and practice, we call for supplementing extant measures of teachers’ whole-class interactions (process) and student outcome (product) measures with those that measure dyadic interactions to learn how opportunities to learn in classrooms and schools are distributed among students to reduce, sustain, or enhance learning gaps.