Patterning activities, specifically those related to repeating patterns, may encourage young chil... more Patterning activities, specifically those related to repeating patterns, may encourage young children’s appreciation for underlying structures. This paper investigates preschool teachers’ knowledge and self-efficacy for defining, drawing, and continuing repeating patterns. Results indicated that teachers were able to draw and continue various repeating patterns but had difficulties defining repeating patterns. In general, teachers had a high self-efficacy for all tasks. However, teachers’ had a significantly lower self-efficacy for defining repeating patterns than for drawing and continuing repeating patterns.
The aim of this study is to investigate the geometrical knowledge as well as the geometrical self... more The aim of this study is to investigate the geometrical knowledge as well as the geometrical self-efficacy of kindergarten children, including abused and neglected kindergarten children. Individual interviews were conducted with 141 kindergarten children, ages 5–6 years old, of which 69 children were labeled as abused and neglected by the social welfare department of their municipality. Results indicated that both groups of kindergarten children had high self-efficacy beliefs related to identifying geometrical figures which were not significantly related to knowledge. In addition, significant differences in knowledge were found between the two groups.
Patterning activities, specifically those related to repeating patterns, may encourage young chil... more Patterning activities, specifically those related to repeating patterns, may encourage young children’s appreciation for underlying structures. This paper investigates preschool teachers’ knowledge and self-efficacy for defining, drawing, and continuing repeating patterns. Results indicated that teachers were able to draw and continue various repeating patterns but had difficulties defining repeating patterns. In general, teachers had a high self-efficacy for all tasks. However, teachers’ had a significantly lower self-efficacy for defining repeating patterns than for drawing and continuing repeating patterns.
Qualitative research on classroom-based mathematics learning in inquiry-oriented classrooms is sc... more Qualitative research on classroom-based mathematics learning in inquiry-oriented classrooms is scarce. This paper presents a methodology aimed at developing a rich understanding of the interplay of mathematical progress in the different settings in which learning in such classrooms occurs - individuals, small groups, and the whole class. For this purpose, we enhance a theoretical-methodological approach of coordinating Documenting Collective Activity and the RBC-model of Abstraction in Context that has been developed in earlier studies. We do this using an intact lesson on the area and perimeter of the Sierpiński triangle in a mathematics education master’s level course on Chaos and Fractals. The enhancement of the methodology allowed integrating the Collective and Individual Mathematical Progress (CIMP) by Layering the Explanations (LE) provided by the two approaches and thus exhibiting the complexity of learning processes in inquiry-oriented classrooms.
This paper describes kindergarten children’s engagement with two patterning activities. The first... more This paper describes kindergarten children’s engagement with two patterning activities. The first activity includes two tasks in which children are asked to choose possible ways for extending two different repeating patterns and the second activity calls for comparing different pairs of repeating patterns. Children’s recognition of the unit of repeat and their recognition of the structure of the repeating patterns are investigated. Findings suggest differences between children’s responses to patterns that end with a complete unit of repeat and those that end with a partial unit. In addition, the issue of presenting repeating patterns using different media is discussed.
International Journal of Science and Mathematics Education, Apr 5, 2019
We focus on teachers’ ways of leading whole class discussions (WCDs) in mathematics, with the goa... more We focus on teachers’ ways of leading whole class discussions (WCDs) in mathematics, with the goal of uncovering their traces (if any) in their students’ responses (a) while participating in the WCDs and (b) in the written responses in a final test. For this purpose, two 8th-grade probability classes learning a 10-lesson unit with different teachers were observed. Our data sources include (1) video-recordings of the WCDs and (2) the responses of students to final test items. We analyzed the teachers’ talk-moves, students’ accountable participation, and students’ reasoning in the final test items. Interweaving the findings from all analyses we found differences between the classes in students’ ways of participation in WCDs and in their corresponding final test responses. The teachers’ ways of leading the WCDs contribute to the explanation of these differences.
Patterning activities, specifically those related to repeating patterns, may encourage young chil... more Patterning activities, specifically those related to repeating patterns, may encourage young children’s appreciation for underlying structures. This paper investigates preschool teachers’ knowledge and self-efficacy for defining, drawing, and continuing repeating patterns. Results indicated that teachers were able to draw and continue various repeating patterns but had difficulties defining repeating patterns. In general, teachers had a high self-efficacy for all tasks. However, teachers’ had a significantly lower self-efficacy for defining repeating patterns than for drawing and continuing repeating patterns.
The aim of this study is to investigate the geometrical knowledge as well as the geometrical self... more The aim of this study is to investigate the geometrical knowledge as well as the geometrical self-efficacy of kindergarten children, including abused and neglected kindergarten children. Individual interviews were conducted with 141 kindergarten children, ages 5–6 years old, of which 69 children were labeled as abused and neglected by the social welfare department of their municipality. Results indicated that both groups of kindergarten children had high self-efficacy beliefs related to identifying geometrical figures which were not significantly related to knowledge. In addition, significant differences in knowledge were found between the two groups.
Patterning activities, specifically those related to repeating patterns, may encourage young chil... more Patterning activities, specifically those related to repeating patterns, may encourage young children’s appreciation for underlying structures. This paper investigates preschool teachers’ knowledge and self-efficacy for defining, drawing, and continuing repeating patterns. Results indicated that teachers were able to draw and continue various repeating patterns but had difficulties defining repeating patterns. In general, teachers had a high self-efficacy for all tasks. However, teachers’ had a significantly lower self-efficacy for defining repeating patterns than for drawing and continuing repeating patterns.
Qualitative research on classroom-based mathematics learning in inquiry-oriented classrooms is sc... more Qualitative research on classroom-based mathematics learning in inquiry-oriented classrooms is scarce. This paper presents a methodology aimed at developing a rich understanding of the interplay of mathematical progress in the different settings in which learning in such classrooms occurs - individuals, small groups, and the whole class. For this purpose, we enhance a theoretical-methodological approach of coordinating Documenting Collective Activity and the RBC-model of Abstraction in Context that has been developed in earlier studies. We do this using an intact lesson on the area and perimeter of the Sierpiński triangle in a mathematics education master’s level course on Chaos and Fractals. The enhancement of the methodology allowed integrating the Collective and Individual Mathematical Progress (CIMP) by Layering the Explanations (LE) provided by the two approaches and thus exhibiting the complexity of learning processes in inquiry-oriented classrooms.
This paper describes kindergarten children’s engagement with two patterning activities. The first... more This paper describes kindergarten children’s engagement with two patterning activities. The first activity includes two tasks in which children are asked to choose possible ways for extending two different repeating patterns and the second activity calls for comparing different pairs of repeating patterns. Children’s recognition of the unit of repeat and their recognition of the structure of the repeating patterns are investigated. Findings suggest differences between children’s responses to patterns that end with a complete unit of repeat and those that end with a partial unit. In addition, the issue of presenting repeating patterns using different media is discussed.
International Journal of Science and Mathematics Education, Apr 5, 2019
We focus on teachers’ ways of leading whole class discussions (WCDs) in mathematics, with the goa... more We focus on teachers’ ways of leading whole class discussions (WCDs) in mathematics, with the goal of uncovering their traces (if any) in their students’ responses (a) while participating in the WCDs and (b) in the written responses in a final test. For this purpose, two 8th-grade probability classes learning a 10-lesson unit with different teachers were observed. Our data sources include (1) video-recordings of the WCDs and (2) the responses of students to final test items. We analyzed the teachers’ talk-moves, students’ accountable participation, and students’ reasoning in the final test items. Interweaving the findings from all analyses we found differences between the classes in students’ ways of participation in WCDs and in their corresponding final test responses. The teachers’ ways of leading the WCDs contribute to the explanation of these differences.
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Papers by Michal Tabach