Teacher education by Juhaina. A. Shahbari
Mathematical Thinking & Learning
Whole-class discussions in mathematics are envisioned as spaces for the sharing of ideas and maki... more Whole-class discussions in mathematics are envisioned as spaces for the sharing of ideas and making connections among them. We pursue how Palestinian/Arab Israeli teachers consider making use of multiple solutions to a task: which three they indicate that they would prioritize for a whole-class discussion and in what sequence. Under the hypothetical assumption that these solutions have been authored by boys and girls (with grades above and below the class' average), how do teachers consider distributing opportunities to present the designated solutions? Participants most commonly selected a direct model, an error, or an inductive approach supported by a geometric representation, typically in that sequence (or error, direct model, inductive). With respect to the direct model, participants tended to indicate that they would invite a lower-achieving girl to present it; higher-achieving students to present the error; and a higher-achieving boy to present the inductive/geometric solution. Our analysis extends to participants' explanations of their choices and illuminates their intentions: making use of existing status arrangements, leveraging existing hierarchies to benefit others in the class, or modifying the indicated student's status by making space for them to participate on the public floor. Our analysis highlights implications of these patterns, especially in terms of classroom opportunities to learn.
Papers by Juhaina. A. Shahbari
The Mathematical Gazette, Feb 24, 2022
HAL (Le Centre pour la Communication Scientifique Directe), Feb 6, 2019
Canadian Journal of Science, Mathematics and Technology Education, Sep 23, 2015
This study analyzes the development of percentages knowledge by seventh graders given a sequence ... more This study analyzes the development of percentages knowledge by seventh graders given a sequence of activities starting with a realistic modeling task, in which students were expected to create a model that would facilitate the reinvention of percentages. In the first two activities, students constructed their own pricing model using fractions and then extended the model while experiencing reinvention and extension of their knowledge of percentages. In the last two activities, they coped with a realistic changing reference situation. A control group used a traditional instructional unit. A pretest and two posttests showed between-group differences.RésuméCette étude analyse l’acquisition de la connaissance des pourcentages par des élèves de 7e année qui doivent effectuer une suite d’activités débutant par une tache de modélisation réaliste dans laquelle ils doivent créer un modèle qui faciliterait la réinvention des pourcentages. Au cours des deux premières activités, les élèves ont construit leur propre modèle de tarification à l’aide de fractions, puis ils l’ont étendu au fur et à mesure qu’ils faisaient l’expérience de la réinvention et de la progression de leurs connaissances en matière de pourcentages. Dans les deux dernières activités, ils ont dû gérer un changement de situation de référence réaliste. Un groupe de contrôle a utilisé, pour sa part, une unité d’instructions traditionnelles. Un test préliminaire et deux tests postérieurs ont mis en évidence les différences entre les deux groupes.
Scientia in Educatione, Jun 5, 2020
The current study investigated the relationship between students' mathematical thinking style and... more The current study investigated the relationship between students' mathematical thinking style and their modeling processes and routes. Thirty-five eighth-grade students were examined. In the first stage, the students solved questions and, based on their solutions, they were assigned to one of three groups according to their thinking styles, namely visual, analytic and integrative. The focus in the current study was the analytic and visual thinking style; we chose five students from the analytic group and five from the visual group (totaling 10 participants). The analytic group therefore comprised five analytic students, while the visual group comprised the visual students. The two groups engaged in three modeling activities. Findings indicated some differences in the groups' modeling processes while performing the three activities. The primary differences in the modeling processes were manifested in simplifying, mathematizing, and eliciting a mathematical model. Besides, the analytic thinking group skipped the real-model phase in the three activities, while the visual group built a real model for each activity.
International Journal of Research in Education and Science, Jan 4, 2019
Mistakes made by students with logical connectives when solving equations and inequalities, and h... more Mistakes made by students with logical connectives when solving equations and inequalities, and how teachers assess these mistakes.
International Journal for mathematics teaching and learning, May 14, 2017
The study investigates the mathematical and the pedagogical content knowledge among inservice and... more The study investigates the mathematical and the pedagogical content knowledge among inservice and pre-service first-and second-grade mathematics teachers. The sample of 300 subjects consisted of 150 first-and second-grade in-service teachers and 150 pre-service teachers studying in a college of education, 75 of whom were first-year students and 75 thirdand fourth-year students. The data was collected using two tools-a mathematical content knowledge (MCK) test and a mathematics pedagogical content knowledge (MPCK) test, the items on each of these representing the four sub-domains studied in first-and second-grade: numbers, arithmetic operations, geometry/measurements, and word problems. The principal findings of the study indicate that all three groups possess limited knowledge of both MCK and MPCK in all sub-domains. The in-service teachers achieved the highest mean in the MCK and MPCK and the differences between the in-service teachers and the two groups of preservice teachers were statistically significant in general MCK and MPCK and in all the domains. Moreover, the lowest MCK mean was in the geometry/measurements domain, and the lowest MPCK mean was in the word-problems domain.
International Journal of Science and Mathematics Education, Feb 7, 2014
ABSTRACT
International Journal of Mathematical Education in Science and Technology, Nov 27, 2017
ABSTRACT The current study examines whether the engagement of mathematics teachers in modelling a... more ABSTRACT The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.
International Journal of Science and Mathematics Education, Nov 9, 2015
This article describes sixth-grade students’ engagement in two model-eliciting activities offerin... more This article describes sixth-grade students’ engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students were also able to generalize the fraction model and transfer it to a new situation. Analysis of the students’ work demonstrates that they made use of four fraction constructs—part-whole, operator, quotients, and ratio. The activities also revealed difficulties in the students’ knowledge of fractions, some of which were overcome in the process of organizing and mathematizing the problem.
International Journal of Mathematical Education in Science and Technology, Sep 28, 2021
International Journal of Science and Mathematics Education, Jul 6, 2017
This study explored the training of prospective and practicing mathematics teachers in alternativ... more This study explored the training of prospective and practicing mathematics teachers in alternative assessment and its impact on their attitudes toward alternative assessment methods and their beliefs about the nature of mathematics. Data were collected from 51 prospective teachers and 50 practicing teachers who took a course on alternative assessment in mathematics. Findings indicated a significant change in the correlation between the positivist and constructivist dimensions of their beliefs about the nature of mathematics following the course. No significant differences were found between the prospective and practicing teachers' beliefs either before or after the course nor in their attitudes toward alternative assessment after the course. Before the course, however, the two groups differed significantly in their attitudes toward alternative assessment. Findings also revealed significant changes in attitudes toward alternative assessment and beliefs about the nature of mathematics following participation in the course. These changes in attitudes and beliefs were accompanied by a shift in the nature of the assessment tasks written by the participants. Participants who demonstrated more positive attitudes and constructivist beliefs tended to write more conceptual problems and less procedural exercises. Implications for mathematics teacher training and professional development in alternative assessment are discussed.
Educational Studies in Mathematics, Sep 25, 2020
Mathematical models that are constructed through modeling activities should be appropriate for th... more Mathematical models that are constructed through modeling activities should be appropriate for the situation at hand. In this study, we seek to monitor the modeling routes of different learners as well as their modeling sub-competencies in order to learn how these are related to the semiotic characteristics of the resulting mathematical models. Our data sources include video recordings of six groups of pre-service and practicing teachers engaging with one modeling activity, their working drafts, and their final written reports. The mathematical models constructed by the six groups were written in different semiotic registers (numeric and algebraic) and hence differ in their appropriateness to the situation demands. The analyses of these modeling processes suggest that the mathematical models constructed in the activity are indicative both of the groups' modeling sub-competencies and of their modeling routes. Algebraic models emerged from more complicated and less sequential modeling routes compared with the modeling routes of the groups that produced numeric models. In addition, the groups that produced the less effective numeric models lacked certain sub-competencies in the transition from the situation model to the real model and in the transition from the real model to the mathematical model.
Canadian Journal of Science, Mathematics and Technology Education, Jun 23, 2009
... In Proceedings of the 29th Conference of the International Group for the Psychology of Mathem... more ... In Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education , Edited by: Chick, HL and Vincent, JL Vol. 1, 19–36. Melbourne: PME. ... In Number and measurement: papers from a research workshop , Edited by: Lesh, R. 101–144. ...
Applied Sciences, 2020
Ethnomathematics makes school mathematics more relevant and meaningful for students. The current ... more Ethnomathematics makes school mathematics more relevant and meaningful for students. The current research aims to study the effect of using ethnomathematics in the context of Islamic ornamentation on learning the topic of congruent triangles. To achieve this aim, 30 10th-grade students engaged in ethnomathematics by learning about congruent triangles using Islamic ornamentation. Data was gathered via (a) videotaping and transcribing students’ learning and (b) students answering two parallel questionnaires that included proof questions on the three congruence theorems. The students were required to answer one questionnaire before the learning process and one after it. The main results indicated that the students succeeded in constructing the concepts of congruence and congruent triangles via the ethnomathematics learning process. In addition, the students succeeded in arriving at and formulating the three congruence theorems. Moreover, findings obtained from the questionnaires indica...
This research examines the discursive positionings and emotions related to them of a group of thr... more This research examines the discursive positionings and emotions related to them of a group of three seventh class students. We videoed the group of students' discussions regarding the definition of terms associated with the circle topic and interviewed them regarding their emotions during the process of defining the geometric terms. We used the discursive analysis of Evans, Morgan and Tsatsaroni to analyze the participants' positionings and emotions. The research results indicate that the learning atmosphere in the group was positive due to type of leadership that prevailed, as well as to the collaborative working with a technological tool. This atmosphere resulted in the students having positive emotions about their learning.
Mathematics, 2021
This study was conducted among 28 seventh-grade students. They worked in groups in an activity wi... more This study was conducted among 28 seventh-grade students. They worked in groups in an activity with modeling features; the activity consisted of three tasks dealing with an intuitive error, namely, same A–same B. The data source was nine video recordings of three groups across the three activities. The results obtained from analyses of students’ discussions and interactions indicate that they moved through three central stages: the intuitive error stage, the revealing of the intuitive error connected with cognitive conflict and the stage of overcoming the intuitive errors. In each of the three stages in the three tasks, we identified similar emotion features among the three groups across the three tasks. In the intuitive error stage, the participants were characterized by confidence, comfort and enjoyment. In revealing the intuitive errors, we identified several indicators and signs of non-comfortable situations by revealing the errors in the three tasks, such as a high sound or sad...
The study investigates the relationship between mathematical knowledge and cognitive and metacogn... more The study investigates the relationship between mathematical knowledge and cognitive and metacognitive processes exhibited by 83 students from Grades 6, 7, and 8 who engaged in a set of model-eliciting activities in groups of 4-5 students each. The data sources include audiotapes of their group work, worksheets, and notes. The findings indicate that the groups in each grade use different mathematical concepts. While they employed cognitive and metacognitive processes, these differed in number and distribution. The highest percent of cognitive processes and lowest percent of metacognitive processes occurred amongst the Grade 6 students. The lowest percent of cognitive processes and highest percent of metacognitive processes occurred amongst the Grade 8 students. The Grade 6 students’ metacognitive processes indicate that they exhibited greater awareness than regulation and evaluation skills. Conversely, the Grade 7 and 8 students employed more regulation and evaluation processes.
European Journal of Science and Mathematics Education, 2016
This study came to characterize the features of mathematical models built by mathematics pre-serv... more This study came to characterize the features of mathematical models built by mathematics pre-service teachers for a model eliciting activity. Fourteen groups participated in building the models. We used a combination of deductive and inductive content analysis to characterize the pre-service teachers' elicited models, taking into account features mentioned in the literature: content factors, representation form, operations, generalization, reality, accuracy, precision, robustness and fruitfulness. Moreover, two features were introduced by us, namely the interactivity and the finalization features. The findings of the research indicate that models utilized mainly the list and text representations. Moreover, most of the participantsʹ models had substantial accuracy and substantial preciseness. At the same time, most of the models had partial or no generalization, partial or no reality, partial or no interactivity and partial or no finalization. Furthermore, most of the models were without robustness and without fruitfulness.
Lines of Inquiry in Mathematical Modelling Research in Education, 2019
Teachers play an important role in determining how students work on modelling activities. In the ... more Teachers play an important role in determining how students work on modelling activities. In the current study, practising and prospective teachers engaged with modelling activities to develop their ability to identify students' modelling process. The study sought to answer the research question as to how the teachers' participation in modelling affects their interpretation of students' modelling activity. Data included two sets of participants' reports on their observations of a video-recorded modelling activity carried out by a group of five sixth-grade students, pre and post participation in four modelling activities. The findings indicate that prior to engaging with modelling activities, most participants described the students' modelling as linear, noting only the final mathematical model and mathematical results. After participating in the activities, most of the practising teachers' reports and a third of the prospective teachers's reports identified cyclical processes in the modelling.
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Teacher education by Juhaina. A. Shahbari
Papers by Juhaina. A. Shahbari