Papers by Azita Manouchehri
Learning Leading With Technology, 1997
International Group for the Psychology of Mathematics Education, 2019
We analyzed 5th grade students' interactions with one computer-based modeling simulation to exami... more We analyzed 5th grade students' interactions with one computer-based modeling simulation to examine how they defined and prioritized variables in a dynamically simulated environment. Results revealed that exposure to the simulation environment helped students visualize continuous motions, interpret the different quantities present in the model, and connect how variables related to each other. Additionally, students became more precise and systematic in adjusting the variables to explore the problem, test hypotheses, and achieve desired outcomes.
Educating Prospective Secondary Mathematics Teachers, 2018
In this paper we will report results of our efforts towards providing mathematical modeling exper... more In this paper we will report results of our efforts towards providing mathematical modeling experiences for a cohort of prospective secondary teachers. Using a Teacher Development Experiment design, we traced the impact of these experiences on teachers’ reported efficacy towards and knowledge about utilizing modeling in their teaching. Analysis of results indicate that although teachers maintained modeling to be an important skill to be developed in instruction, absence of extensive experiences with mathematical modeling in the course of their own mathematical preparation served as a barrier to their ability to access specific pedagogical actions they believed could be used in their instruction.
Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
This research was conducted by a fourth-grade teacher and doctoral student in mathematics educati... more This research was conducted by a fourth-grade teacher and doctoral student in mathematics education in conjunction with their advisor, a professor of mathematics education. A growing body of research in mathematics education has highlighted the importance of recognizing mathematics learning as a socially mediated activity. Indeed, mathematics education researchers have increasingly focused on how classroom dialogue can facilitate students’ creation of shared understandings. Aligned with this theoretical heritage, we recognize that human life and learning are inherently social and rooted in communication. We also recognize that student discourse is connected to student cognition and thus learning. Accordingly, this study relied on socio-cultural discourse analysis (Hennesy, et al., 2016, Mercer, 2010) both as a theoretical and a methodological tool to examine the nature of dialogue in one classroom in the context of students’ collaborative work on one visual task. We ask, given the c...
Mathematics Teaching in the Middle School, 1998
The study of geometry in grades 5-8 should incorporate opportunities for students to engage in ex... more The study of geometry in grades 5-8 should incorporate opportunities for students to engage in exploring and analyzing geometric shapes to conjecture about geometric relationships through data collection and model construction, according to the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). In this fashion, students will develop an intuitive understanding of geometric concepts and learn to reason formally and informally. Moreover, it is hoped that through such processes, students will formulate relevant definitions and theorems. The Standards document also encourages the use of computer technologies in middle school mathematics instruction. This suggestion was based on the assumption that interactive environments provided by appropriate geometry software have the potential to foster students' movement from concrete expetiences with mathematics to more formal levels of abstractions, nurture students' conjectuting spirit, and improve their mathematical...
Mathematics Education Research Journal, 2020
In this work we studied the cognitively recursive process of generalizing relying on data collect... more In this work we studied the cognitively recursive process of generalizing relying on data collected from a two-week constructivist teaching experiment where a group of middleschool students were working together to explore and generalize properties of geometric transformations in a dynamic geometry environment. In doing so, we focused on the role of reflection and outcomes of reflective work of learners on their progress towards construction of mathematical generalizations. Relying on the construct of folding back in the Pirie-Kieren theory, we present categories and subcategories that describe sources, forms, and outcomes of students' reflections in the course of construction and refinement of mathematical generalizations. We then discuss the roles of teacher intervention and technology in motivating and supporting students' folding back actions. The results of the study not only elaborate on the construct of folding back in the Pirie-Kieren theory but also provide a useful analytical tool to examine learners' reflective practices.
Mathematics Teaching in the Middle School, 1999
The NCTM's Professional Standards for Teaching Mathematics (1991) has directed attention to “... more The NCTM's Professional Standards for Teaching Mathematics (1991) has directed attention to “discourse” in the mathematics classroom. This document recommends that mathematics instruction should promote students' discourse by orchestrating situations in which each individual's thinking is challenged and by asking students to clarify and justify ideas. “Discourse,” as described by the Standards document, highlights the way in which knowledge is constructed and exchanged in the classroom (Ball 1992). Teaching mathematics from the perspective of developing mathematical discourse requires building a new vision for mathematics classrooms and poses a major challenge for mathematics teachers at all levels. This challenge was recognized by D'Ambrosio (1995). She identified the need to build environments in which students construct a “personal relationship” with mathematics as one of the most important requirements for promoting and sustaining the type of discourse envisioned...
Encyclopedia of Mathematics Education, 2014
Educational Studies in Mathematics, 2000
A qualitative case study research was conducted to investigate the process of evaluation and impl... more A qualitative case study research was conducted to investigate the process of evaluation and implementation of a Standard-based textbook by two seventh grade middle school mathematics teachers over a period of two years. The data suggested that teachers' mathematical knowledge was the greatest influence on how they evaluated and implemented the textbook. This mathematical knowledge manifested itself in how the
The Journal of Educational Research, 1998
In this chapter we present illustrative examples from school learners’ modelling efforts to highl... more In this chapter we present illustrative examples from school learners’ modelling efforts to highlight how knowledge of extra-mathematical contexts can influence students’ mathematical practices during various phases in the mathematical modelling cycle. We propose that future research may need to focus on how to constructively utilize students’ intuitions drawn from their personal and cultural backgrounds to advance their modelling cognition.
Encyclopedia of Mathematics Education, 2020
Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 2020
Karoline Smucker The Ohio State University [email protected] Azita Manouchehri The Ohio State Un... more Karoline Smucker The Ohio State University [email protected] Azita Manouchehri The Ohio State University [email protected] Context plays a crucial role when students engage in analysis and interpretation of data, and is broadly recognized as one of the main elements that separate the studies of mathematics and statistics (Cobb & Moore, 1997). The ways that students engage with the environment surrounding data within a statistical task are of interest to researchers because of this. In this analysis of a teaching experiment with third grade students, interactions with self-collected wingspan data led to insights about graphs as students attended to individual values, but students varied in their willingness to use the data to describe/infer more broadly.
International Group for the Psychology of Mathematics Education, 2011
In this work we investigated the problem solving behaviors of 3 highschool students as each solve... more In this work we investigated the problem solving behaviors of 3 highschool students as each solved four common non-routine problems with the goal to trace performance constancy across different subject areas and problem types. Additionally, we aimed to identify possible factors that influenced children's choices of heuristics in different problem contexts. The results suggested the individual's confidence and preference for the use of certain strategies. Inconsistency in the same individual's mathematics problem solving behaviors across different subject areas was revealed.
Ten hours of whole group discussions in a US Grade 5 classroom were analysed to identify teacher ... more Ten hours of whole group discussions in a US Grade 5 classroom were analysed to identify teacher interventions aimed to stabilize student work on modelling tasks and the type of mathematical actions those interventions provoked. Analysis of group interactions highlights that teacher interventions impacted students’ reasoning, structuring, and mathematizing processes. These processes corresponded to the stages of the modelling cycle, including interpreting, structuring, working mathematically, and validating ideas.
In this work we investigated the problem solving behaviors of 3 high school students as each solv... more In this work we investigated the problem solving behaviors of 3 high school students as each solved three common non-routine problems with the goal to trace patterns of behaviors and performance consistency across different subject areas and problem types. Additionally, we aimed to identify possible factors that influenced children's choices of heuristics in different problem contexts. The results suggested the individual's confidence and preference for the use of certain strategies greatly impacted their mathematical problem solving practices. Inconsistency in the same individual's mathematics problem solving behaviors across different subject areas was revealed.
International Group for the Psychology of Mathematics Education, 2015
In this paper we report the interview questions used in a study of middle school students’ mathem... more In this paper we report the interview questions used in a study of middle school students’ mathematical problem solving behaviors which were chosen based on Vygotsky’s concept formation theory and Berger’s appropriation theory. We discuss the task design/selection process along with the findings associated with the use of these tasks so to provide new direction for gauging research on mathematical problem solving.
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Papers by Azita Manouchehri