This is Analytic 3 (of 3) of "Tracing Romina's Growth In Reasoning And Sense-Making about Math Problems and Development of Beliefs about Math Teaching/Learning". This analytic explores Romina's later adult views about learning mathematics in college and post-graduate studies and the development of her beliefs regarding the knowledge, conditions, and processes of mathematical learning. Through clinical and semi-structured interviews from 1999 to 2009 while she was in college, graduate [more ...]
This is Analytic 2 (of 3) of "Tracing Romina's Growth In Reasoning And Sense-Making about Math Problems and Development of Beliefs about Math Teaching/Learning". This analytic examines the development of Romina's problem-solving heuristics and examples of her behaviors in collaborative settings in tenth and twelfth grades. We watch Romina argue, make meaning, and generalize as she revisits the Tower Problem through an extension known as "Ankur's Challenge." Two years later, we [more ...]
This is Analytic 1 (of 3) of "Tracing Romina's Growth In Reasoning And
Sense-Making about Math Problems and Development of Beliefs about Math
Teaching/Learning". This analytic traces the development of Romina's
problem-solving heuristics and examines examples of her behaviors in
collaborative settings from fourth and sixth grades. Specifically, we
examine video data from February 6, 1992 when Romina was in 4 th grade
and working with a partner during her first exposure to the Towers
[more ...]
This is Analytic 4 (of 4) of "Last steps to the 'Aha!' - Recognizing the Isomorphism: A Series of Four Analytics". This Analytic represents the culmination of the students' exploration into combinatorial reasoning, where they uncover and articulate the structural similarities between and among the various counting problems whose solutions were structurally equivalent. This Analytic centers on the students' synthesis of their understanding of Pascal's Triangle with their experiences in [more ...]
This is Analytic 3 (of 4) of "Last steps to the 'Aha!' - Recognizing the Isomorphism: A Series of Four Analytics". This Analytic examines the students' continued mathematical journey as they unravel the connections between the combinatorial problems they have been solving and the addition property inherent in Pascal's Triangle. Specifically, the students apply their understanding of pizza topping combinations to grasp the addition principle that allows Pascal's Triangle to grow - each [more ... ]
This is Analytic 2 (of 4) of "Last steps to the 'Aha!' - Recognizing the Isomorphism: A Series of Four Analytics". In this second of four Analytics, Shelly, Stephanie, Amy-Lynn, and Robert delve deeper into the combinatorial reasoning that has emerged through their mathematical explorations. The 4-Topping Pizza Problem serves as a gateway to discovering the inherent patterns of Pascal's Triangle within their combinatorial framework. This Analytic documents the critical transition from [more ...]
This is Analytic 1 (of 4) of "Last steps to the 'Aha!' - Recognizing the Isomorphism: A Series of Four Analytics". This first Analytic marks a significant step in the mathematical explorations of Shelly, Stephanie, Amy-Lynn, and Robert. The students draw upon their rich history of combinatorial reasoning as they continue to delve into the 4-Topping Pizza Problem. At this juncture, they continue to lay groundwork for uncovering the isomorphic relationships connecting solutions to Pizza and [more ...]
This analytic explores how the four twelfth grade students (Michael, Romina, Brian, and Jeff) used mathematics discourse throughout their problem-solving process of the Taxicab problem. Mathematical discourse refers to the way in which students talk, write, and reason about mathematics, including the use of language, symbols, representations, and practices. While acknowledging that discourse does not only refer to language, the mathematics register can be used to characterize mathematical [more ...]
The purpose of this analytic is to examine the development of probabilistic reasoning and representations shown by Justina, a sixth-grade student, when working with Adanna, a sixth-grade student, on both dice games (see problem statements below). The video narrative is a compilation of events that documents Justina's reasoning on what makes the dice games fair as well as the representations that she used to support her argument. The first event showcases the structure and format of dice game [more ...]
This analytic examines researcher Ralph Pantozzi's questioning style when posing open-ended tasks to students. This analysis focuses on three female students: Romina, Magda, and Angela, who were former AP Calculus students of Researcher Pantozzi's and at the time of the observed sessions were juniors in college, over the course of two sessions. The first session took place on June 25, 2003 and the second session occurred on July 24, 2003. Both sessions showcased evolving thoughts and [more ...]
This analytic is the third of three analytics that showcase the formulation of two students' ideas of mathematical fairness. The analytics follow the argumentation of two students, Chris and Jerel, throughout two after-school sessions and one interview session as they investigate what makes a game involving rolling one or two dice fair. The first after-school session occurred on April 29, 2004. The second after-school session occurred on May 5, 2004, with the interview happening directly [more ...]
This analytic is the second of three analytics that showcase the formulation of two students' ideas of mathematical fairness. The analytics follow the argumentation of two students, Chris and Jerel, throughout two after-school sessions and one interview session as they investigate what makes a game involving rolling one or two dice fair. The first after-school session occurred on April 29, 2004. The second after-school session occurred on May 5, 2004, with the interview happening [more ...]
This analytic is the first of three analytics that showcase the formulation of two students' ideas of mathematical fairness. The analytics follow the argumentation of two students, Chris and Jerel, throughout two after-school sessions and one interview session as they investigate what makes a game involving rolling one or two dice fair. The first after-school session occurred on April 29, 2004. The second after-school session occurred on May 5, 2004, with the interview happening directly [more ...]
