Mathematics Teacher: Learning and Teaching PK–12, Apr 1, 1986
Finding word problems is not the easiest task of mathematics teachers. Basic practical questions ... more Finding word problems is not the easiest task of mathematics teachers. Basic practical questions often degenerate into boring exercises, and whimsical puzzles are sometimes deemed too outlandish to pursue. Sometimes, however, a real situation arises that stimulates discussion beyond the limits of the textbook so that problem-solving techniques are sharpened, and the end of class comes all too soon.
International Electronic Journal of Mathematics Education
This study aims to explore in-service preschool teachers' attitudes towards and beliefs about geo... more This study aims to explore in-service preschool teachers' attitudes towards and beliefs about geometry and its teaching and to investigate their knowledge of shapes and solids. The study uses a mixed descriptive approach employing quantitative and qualitative research methods. Thirty-four Israeli preschool teachers of children aged 3-6 from 34 different preschools and kindergartens participated in the study and responded to a questionnaire comprised of closed and open items. Regarding their attitudes and beliefs, the preschool teachers were asked about: the meaning of geometry; affinity for geometry, importance of geometry; need to use accurate mathematical language, and about their enjoyment of engaging young children in activities connected with learning geometry. As to the knowledge of shapes and solids, the preschool teachers were asked to describe or define shapes and solids, name shapes and solids and distinguish between rectangles and other shapes. The results illustrate that most of the preschool teachers like geometry or expressed a neutral position towards geometry, but some hate geometry. Most of the preschool teachers comprehend the importance of engaging in activities that relate to geometry in preschool and enjoy involving young children in activities connected with learning geometry. As to the use of accurate language, most of the preschool teachers maintain that accurate mathematical language should be applied when preschool children aged 3-6 deal with shapes and solids. Yet, only about half of them believe that it is necessary to use accurate language when the children are at an earlier age. Certain preschool teachers lack the knowledge to name shapes and solids, even those which are part the mathematics curriculum for ages 3-6. They exhibited difficulties in using accurate mathematical language when describing shapes and solids, and were influenced by the shapes' visual appearance rather than by their definitions and properties. It is recommended that preschool teachers attend further development programs so they can appropriately involve young children in activities connected to learning geometry, as required by the curriculum.
Already at a very young age, children come across mathematical situations as part of their everyd... more Already at a very young age, children come across mathematical situations as part of their everyday life in preschool and at home. Engagement in mathematical situations helps children in developing their mathematical thinking. Listening to children while they are coping with such situations, help us learn more about their ways of thinking. This study describes the ways of thinking of four children aged 5.2–6.4 when dealing with nine everyday mathematical situations, involving addition, subtraction and division into equal groups. The children have given correct answers to almost all situations and used a variety of solution strategies. They have used mental calculations in some of the situations, while in others they have used their fingers and/or manipulatives. The children have paid attention to the numbers given in the situations and one child has surprized us by showing number sense, when using the compensation method for solving 7+5 and 8+4.
608 pre-service teachers from Israel and from Turkey, in their first year and in their fourth (an... more 608 pre-service teachers from Israel and from Turkey, in their first year and in their fourth (and last) year of study, were asked to complete a questionnaire in order to explore the reasons that led them to choose teaching as their career and to reveal their beliefs regarding several aspects of the status of the teaching profession. Results show some similarities as well as some differences between pre-service teachers in Israel and Turkey as well as between first year and fourth year preservice teachers in both countries.
In this study we reveal the beliefs about mathematics held by 42 prospective preschool teachers p... more In this study we reveal the beliefs about mathematics held by 42 prospective preschool teachers prior to and after a one semester course devoted to the teaching of mathematics in the early childhood years. Results suggest that many of the prospective teachers explicitly expressed negative beliefs about mathematics as well as implicitly via the ‘animal metaphor’. The course made a small change in teachers’ beliefs, suggesting that much more has to be done for a meaningful change, so that prospective preschool teachers can engage in mathematics with young children positively.
It seems that visual thinking will be the primary way of thinking in the future. In modern life t... more It seems that visual thinking will be the primary way of thinking in the future. In modern life the presentation of phenomena has changed from tables and formulas heavy with numbers and symbols to a dynamic visual presentation using computers. To understand, analyze, and predict, we will have to engage in some form of visual thinking. To communicate visually and to develop advanced visual thinking, we need certain linguistic elements—a language.
Gender differences in mathematics learning outcomes are still evident in many countries participa... more Gender differences in mathematics learning outcomes are still evident in many countries participating in large scale international testing, as well as in national testing in Israel, the context in which the study reported here was conducted. The participants were 281 students from three Israeli elementary schools and were in grades 4 and 6. The students completed a questionnaire with items based on a selection of variables included in explanatory models for gender differences in mathematics. It was found that many students held gendered beliefs related to mathematics learning, particularly when the questions asked related to themselves or to significant others in their lives (parents and teachers); the views of the majority of students were gender neutral. When presented with two photographs-a man, and a woman-and asked who was the one more likely to work with mathematics, it was clear that the students' choices and explanations echoed perceptions of mathematics as a male domain.
The aim of this study was to explore the beliefs of elementary school students about mathematics ... more The aim of this study was to explore the beliefs of elementary school students about mathematics and about themselves as mathematics learners. The participants, Israeli grade 4 and grade 6 students, completed questionnaires. Using an Banimal metaphor^to tap beliefs, some students perceived mathematics as difficult and complicated, while for others, mathematics was connected to wisdom. The data from other questionnaire items indicated that students at both grade levels generally did not enjoy learning mathematics, but believed it was very important to study this subject. They also believed that they were good at mathematics, but the grade 6 students' self-perceptions of achievement were lower than those of the grade 4 students. Compared to the boys, the girls in both grades 4 and 6 expressed lower perceptions of their mathematics achievement levels.
The purpose of this study was to investigate the beliefs held by preschool prospective teachers t... more The purpose of this study was to investigate the beliefs held by preschool prospective teachers toward mathematics and its teaching and the changes in their beliefs (if any) following their participation in a one semester course. 166 prospective teachers were asked to fill in an open-ended questionnaire at the beginning and at the end of the course. Data analysis shows that many prospective teachers hold negative beliefs toward mathematics, but less negative beliefs toward its teaching in preschool. Comparison of the two questionnaires shows an improvement in the way prospective teachers refer to mathematics and its teaching.
Journal for Research in Mathematics Education, 1994
Few students exhibit number sense when solving arithmetic problems in school. This study examined... more Few students exhibit number sense when solving arithmetic problems in school. This study examined the effects of an intervention in the instruction of seventh-grade students for the purpose of developing number sense. Students were taught by the classroom teacher from experimental units on number magnitude, mental computation, and computational estimation. Instruction was designed to provide rich opportunities for exploring numbers, number relationships, and number operations and to discover rules and invent algorithms. Written measures and interviews before instruction, immediately after instruction, and several months later revealed that after instruction students were more likely to elect to use strategies that reflected number sense and that this was a long-term change. It appeared to the investigators that the students reorganized and used existing knowledge rather than acquiring new knowledge structures.
Constructing and using meaning for mathematical symbols: The case of decimal fractions. Number co... more Constructing and using meaning for mathematical symbols: The case of decimal fractions. Number concepts and operations in the middle grades (pp.220-235). Hillsdale, NJ: Erlbaum & Reston, VA: National Council of Teachers of Mathematics.
... EJ447759 - Conquer Mathematics Concepts by Developing Visual Thinking. ... Click on any of th... more ... EJ447759 - Conquer Mathematics Concepts by Developing Visual Thinking. ... Click on any of the links below to perform a new search. ERIC #: EJ447759. Title: Conquer Mathematics Concepts by Developing Visual Thinking. Authors: Hershkowitz, Rina; Markovits, Zvia. ...
Http Dx Doi Org 10 1080 02188790902859012, Jun 1, 2009
This study focuses on the knowledge exhibited by 30 elementary school in-service and pre-service ... more This study focuses on the knowledge exhibited by 30 elementary school in-service and pre-service teachers in solving non-routine mathematical problems and on their beliefs regarding these kinds of problems. Interviews were used to reveal teachers' knowledge and beliefs. The findings indicated that these teachers had difficulty in solving non-routine problems and that their ability to solve these problems was influenced
... EJ447759 - Conquer Mathematics Concepts by Developing Visual Thinking. ... Click on any of th... more ... EJ447759 - Conquer Mathematics Concepts by Developing Visual Thinking. ... Click on any of the links below to perform a new search. ERIC #: EJ447759. Title: Conquer Mathematics Concepts by Developing Visual Thinking. Authors: Hershkowitz, Rina; Markovits, Zvia. ...
Http Dx Doi Org 10 1080 0020739950260407, Jul 9, 2006
ABSTRACT Teachers’ ability to help students learn mathematics requires an understanding of studen... more ABSTRACT Teachers’ ability to help students learn mathematics requires an understanding of student thinking. No less important is what teachers do with this knowledge; i.e. the nature of their decisions and actions which are based on this knowledge. Two interviews were conducted: one with two junior‐high school teachers, and the other with two eleventh grade students. The interviews consisted of two parts: (1) responding to students’ questions and ideas, and (2) reacting to teachers’ responses. The paper concentrates on teachers’ and students’ points of view on the issues of helping students to (a) reason about problem situations, and (b) construct their own knowledge.
Mathematics Teacher: Learning and Teaching PK–12, Apr 1, 1986
Finding word problems is not the easiest task of mathematics teachers. Basic practical questions ... more Finding word problems is not the easiest task of mathematics teachers. Basic practical questions often degenerate into boring exercises, and whimsical puzzles are sometimes deemed too outlandish to pursue. Sometimes, however, a real situation arises that stimulates discussion beyond the limits of the textbook so that problem-solving techniques are sharpened, and the end of class comes all too soon.
International Electronic Journal of Mathematics Education
This study aims to explore in-service preschool teachers' attitudes towards and beliefs about geo... more This study aims to explore in-service preschool teachers' attitudes towards and beliefs about geometry and its teaching and to investigate their knowledge of shapes and solids. The study uses a mixed descriptive approach employing quantitative and qualitative research methods. Thirty-four Israeli preschool teachers of children aged 3-6 from 34 different preschools and kindergartens participated in the study and responded to a questionnaire comprised of closed and open items. Regarding their attitudes and beliefs, the preschool teachers were asked about: the meaning of geometry; affinity for geometry, importance of geometry; need to use accurate mathematical language, and about their enjoyment of engaging young children in activities connected with learning geometry. As to the knowledge of shapes and solids, the preschool teachers were asked to describe or define shapes and solids, name shapes and solids and distinguish between rectangles and other shapes. The results illustrate that most of the preschool teachers like geometry or expressed a neutral position towards geometry, but some hate geometry. Most of the preschool teachers comprehend the importance of engaging in activities that relate to geometry in preschool and enjoy involving young children in activities connected with learning geometry. As to the use of accurate language, most of the preschool teachers maintain that accurate mathematical language should be applied when preschool children aged 3-6 deal with shapes and solids. Yet, only about half of them believe that it is necessary to use accurate language when the children are at an earlier age. Certain preschool teachers lack the knowledge to name shapes and solids, even those which are part the mathematics curriculum for ages 3-6. They exhibited difficulties in using accurate mathematical language when describing shapes and solids, and were influenced by the shapes' visual appearance rather than by their definitions and properties. It is recommended that preschool teachers attend further development programs so they can appropriately involve young children in activities connected to learning geometry, as required by the curriculum.
Already at a very young age, children come across mathematical situations as part of their everyd... more Already at a very young age, children come across mathematical situations as part of their everyday life in preschool and at home. Engagement in mathematical situations helps children in developing their mathematical thinking. Listening to children while they are coping with such situations, help us learn more about their ways of thinking. This study describes the ways of thinking of four children aged 5.2–6.4 when dealing with nine everyday mathematical situations, involving addition, subtraction and division into equal groups. The children have given correct answers to almost all situations and used a variety of solution strategies. They have used mental calculations in some of the situations, while in others they have used their fingers and/or manipulatives. The children have paid attention to the numbers given in the situations and one child has surprized us by showing number sense, when using the compensation method for solving 7+5 and 8+4.
608 pre-service teachers from Israel and from Turkey, in their first year and in their fourth (an... more 608 pre-service teachers from Israel and from Turkey, in their first year and in their fourth (and last) year of study, were asked to complete a questionnaire in order to explore the reasons that led them to choose teaching as their career and to reveal their beliefs regarding several aspects of the status of the teaching profession. Results show some similarities as well as some differences between pre-service teachers in Israel and Turkey as well as between first year and fourth year preservice teachers in both countries.
In this study we reveal the beliefs about mathematics held by 42 prospective preschool teachers p... more In this study we reveal the beliefs about mathematics held by 42 prospective preschool teachers prior to and after a one semester course devoted to the teaching of mathematics in the early childhood years. Results suggest that many of the prospective teachers explicitly expressed negative beliefs about mathematics as well as implicitly via the ‘animal metaphor’. The course made a small change in teachers’ beliefs, suggesting that much more has to be done for a meaningful change, so that prospective preschool teachers can engage in mathematics with young children positively.
It seems that visual thinking will be the primary way of thinking in the future. In modern life t... more It seems that visual thinking will be the primary way of thinking in the future. In modern life the presentation of phenomena has changed from tables and formulas heavy with numbers and symbols to a dynamic visual presentation using computers. To understand, analyze, and predict, we will have to engage in some form of visual thinking. To communicate visually and to develop advanced visual thinking, we need certain linguistic elements—a language.
Gender differences in mathematics learning outcomes are still evident in many countries participa... more Gender differences in mathematics learning outcomes are still evident in many countries participating in large scale international testing, as well as in national testing in Israel, the context in which the study reported here was conducted. The participants were 281 students from three Israeli elementary schools and were in grades 4 and 6. The students completed a questionnaire with items based on a selection of variables included in explanatory models for gender differences in mathematics. It was found that many students held gendered beliefs related to mathematics learning, particularly when the questions asked related to themselves or to significant others in their lives (parents and teachers); the views of the majority of students were gender neutral. When presented with two photographs-a man, and a woman-and asked who was the one more likely to work with mathematics, it was clear that the students' choices and explanations echoed perceptions of mathematics as a male domain.
The aim of this study was to explore the beliefs of elementary school students about mathematics ... more The aim of this study was to explore the beliefs of elementary school students about mathematics and about themselves as mathematics learners. The participants, Israeli grade 4 and grade 6 students, completed questionnaires. Using an Banimal metaphor^to tap beliefs, some students perceived mathematics as difficult and complicated, while for others, mathematics was connected to wisdom. The data from other questionnaire items indicated that students at both grade levels generally did not enjoy learning mathematics, but believed it was very important to study this subject. They also believed that they were good at mathematics, but the grade 6 students' self-perceptions of achievement were lower than those of the grade 4 students. Compared to the boys, the girls in both grades 4 and 6 expressed lower perceptions of their mathematics achievement levels.
The purpose of this study was to investigate the beliefs held by preschool prospective teachers t... more The purpose of this study was to investigate the beliefs held by preschool prospective teachers toward mathematics and its teaching and the changes in their beliefs (if any) following their participation in a one semester course. 166 prospective teachers were asked to fill in an open-ended questionnaire at the beginning and at the end of the course. Data analysis shows that many prospective teachers hold negative beliefs toward mathematics, but less negative beliefs toward its teaching in preschool. Comparison of the two questionnaires shows an improvement in the way prospective teachers refer to mathematics and its teaching.
Journal for Research in Mathematics Education, 1994
Few students exhibit number sense when solving arithmetic problems in school. This study examined... more Few students exhibit number sense when solving arithmetic problems in school. This study examined the effects of an intervention in the instruction of seventh-grade students for the purpose of developing number sense. Students were taught by the classroom teacher from experimental units on number magnitude, mental computation, and computational estimation. Instruction was designed to provide rich opportunities for exploring numbers, number relationships, and number operations and to discover rules and invent algorithms. Written measures and interviews before instruction, immediately after instruction, and several months later revealed that after instruction students were more likely to elect to use strategies that reflected number sense and that this was a long-term change. It appeared to the investigators that the students reorganized and used existing knowledge rather than acquiring new knowledge structures.
Constructing and using meaning for mathematical symbols: The case of decimal fractions. Number co... more Constructing and using meaning for mathematical symbols: The case of decimal fractions. Number concepts and operations in the middle grades (pp.220-235). Hillsdale, NJ: Erlbaum & Reston, VA: National Council of Teachers of Mathematics.
... EJ447759 - Conquer Mathematics Concepts by Developing Visual Thinking. ... Click on any of th... more ... EJ447759 - Conquer Mathematics Concepts by Developing Visual Thinking. ... Click on any of the links below to perform a new search. ERIC #: EJ447759. Title: Conquer Mathematics Concepts by Developing Visual Thinking. Authors: Hershkowitz, Rina; Markovits, Zvia. ...
Http Dx Doi Org 10 1080 02188790902859012, Jun 1, 2009
This study focuses on the knowledge exhibited by 30 elementary school in-service and pre-service ... more This study focuses on the knowledge exhibited by 30 elementary school in-service and pre-service teachers in solving non-routine mathematical problems and on their beliefs regarding these kinds of problems. Interviews were used to reveal teachers' knowledge and beliefs. The findings indicated that these teachers had difficulty in solving non-routine problems and that their ability to solve these problems was influenced
... EJ447759 - Conquer Mathematics Concepts by Developing Visual Thinking. ... Click on any of th... more ... EJ447759 - Conquer Mathematics Concepts by Developing Visual Thinking. ... Click on any of the links below to perform a new search. ERIC #: EJ447759. Title: Conquer Mathematics Concepts by Developing Visual Thinking. Authors: Hershkowitz, Rina; Markovits, Zvia. ...
Http Dx Doi Org 10 1080 0020739950260407, Jul 9, 2006
ABSTRACT Teachers’ ability to help students learn mathematics requires an understanding of studen... more ABSTRACT Teachers’ ability to help students learn mathematics requires an understanding of student thinking. No less important is what teachers do with this knowledge; i.e. the nature of their decisions and actions which are based on this knowledge. Two interviews were conducted: one with two junior‐high school teachers, and the other with two eleventh grade students. The interviews consisted of two parts: (1) responding to students’ questions and ideas, and (2) reacting to teachers’ responses. The paper concentrates on teachers’ and students’ points of view on the issues of helping students to (a) reason about problem situations, and (b) construct their own knowledge.
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