Scan Science and Technology
Contact Leading Edge Experts & Companies
Algebraic Problem
The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Jennifer Wiley – One of the best experts on this subject based on the ideXlab platform.
-
Bilingualism and symbolic abstraction: Implications for algebra learning
Learning and Instruction, 2017Co-Authors: Marta K. Mielicki, Natalie A. Kacinik, Jennifer WileyAbstract:Abstract Much of the research on bilingualism and math learning focuses on the potential challenges that bilinguals and language learners may face. The current line of research took an alternative approach and explored whether a bilingual advantage may emerge for a novel Algebraic Problem solving task that requires symbolic thought, the Symbol Math task. No differences were seen between bilingual and monolingual samples on basic math or executive control tasks; however, a bilingual advantage was seen in performance on the Symbol Math task across two experiments. The results suggest that bilingualism may improve the ability to engage in more abstract or symbolic thought processes, which may have important implications for algebra learning.
-
Alternative Representations in Algebraic Problem Solving: When are Graphs Better Than Equations?
The Journal of Problem Solving, 2016Co-Authors: Marta K. Mielicki, Jennifer WileyAbstract:Successful Algebraic Problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation format might affect solution success, and whether the efficiency of solution varies depending on the nature of the Problem solving task. This study addressed the question of whether symbolic or graphical representation format provides different affordances with respect to two different types of Problems: computation and interpretation. Graphical representation was found to facilitate Problem solving among college students, and Problems that required the comparison of slopes were more difficult when presented in a symbolic format than in graphical format. Correspondence: Correspondence concerning this article should be addressed to Marta K. Mielicki, via email to mmieli2@uic.edu.
John R. Anderson – One of the best experts on this subject based on the ideXlab platform.
-
Endogenous Control and Task Representation: An fMRI Study in Algebraic Problem-solving
Journal of Cognitive Neuroscience, 2008Co-Authors: Andrea Stocco, John R. AndersonAbstract:The roles of prefrontal and anterior cingulate cortices have been widely studied, yet little is known on how they interact to enable complex cognitive abilities. We investigated this issue in a complex yet well-defined symbolic paradigm: Algebraic Problem solving. In our experimental Problems, the demands for retrieving arithmetic facts and maintaining intermediate Problem representations were manipulated separately. An analysis of functional brain images acquired while participants were solving the Problems confirmed that prefrontal regions were affected by the retrieval of arithmetic facts, but only scarcely by the need to manipulate intermediate forms of the equations, hinting at a specific role in memory retrieval. Hemodynamic activity in the dorsal cingulate, on the contrary, increased monotonically as more information processing steps had to be taken, independent of their nature. This pattern was essentially mimicked in the caudate nucleus, suggesting a related functional role in the control of cognitive actions. We also implemented a computational model within the Adaptive Control of Thought—Rational (ACT-R) cognitive architecture, which was able to reproduce both the behavioral data and the time course of the hemodynamic activity in a number of relevant regions of interest. Therefore, imaging results and computer simulation provide evidence that symbolic cognition can be explained by the functional interaction of medial structures supporting control and serial execution, and prefrontal cortices engaged in the on-line retrieval of specific relevant information.
C.a. Weatherford – One of the best experts on this subject based on the ideXlab platform.
-
Electron-H{sub 2}{sup +} scattering using the finite-element method with iterative-variational solution of the Algebraic Problem
Bulletin of the American Physical Society, 1993Co-Authors: C.a. WeatherfordAbstract:Coulomb Sturmians are used to calculate the ground state of H{sub 2}{sup +}. The required multicenter integrals are calculated to very high accuracy in momentum space. Differential cross sections describing electron scattering from the ground state of H{sub 2}{sup +} are then calculated using the finite element method. The solution of the resulting linear Algebraic Problem is accomplished using the iterative-variational method.
Marta K. Mielicki – One of the best experts on this subject based on the ideXlab platform.
-
Bilingualism and symbolic abstraction: Implications for algebra learning
Learning and Instruction, 2017Co-Authors: Marta K. Mielicki, Natalie A. Kacinik, Jennifer WileyAbstract:Abstract Much of the research on bilingualism and math learning focuses on the potential challenges that bilinguals and language learners may face. The current line of research took an alternative approach and explored whether a bilingual advantage may emerge for a novel Algebraic Problem solving task that requires symbolic thought, the Symbol Math task. No differences were seen between bilingual and monolingual samples on basic math or executive control tasks; however, a bilingual advantage was seen in performance on the Symbol Math task across two experiments. The results suggest that bilingualism may improve the ability to engage in more abstract or symbolic thought processes, which may have important implications for algebra learning.
-
Alternative Representations in Algebraic Problem Solving: When are Graphs Better Than Equations?
The Journal of Problem Solving, 2016Co-Authors: Marta K. Mielicki, Jennifer WileyAbstract:Successful Algebraic Problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation format might affect solution success, and whether the efficiency of solution varies depending on the nature of the Problem solving task. This study addressed the question of whether symbolic or graphical representation format provides different affordances with respect to two different types of Problems: computation and interpretation. Graphical representation was found to facilitate Problem solving among college students, and Problems that required the comparison of slopes were more difficult when presented in a symbolic format than in graphical format. Correspondence: Correspondence concerning this article should be addressed to Marta K. Mielicki, via email to mmieli2@uic.edu.
-
Affordances of Graphical and Symbolic Representations in Algebraic Problem Solving
, 2015Co-Authors: Marta K. MielickiAbstract:Successful Algebraic Problem solving entails adaptability of solution methods using different representations. Research suggests that students are more likely to choose symbolic solution methods over graphical ones even when graphical methods are more efficient. However, existing research has not addressed whether the efficiency of solution method varies depending on the nature of the Problem solving task. This masters project addressed the question of whether symbolic and graphical solution methods provide different affordances with respect to computation and interpretation Problems by presenting students with either symbolic or a graphical representation. Graphical representation was found to facilitate Problem solving, particularly for interpretation Problems. Participants experienced the most difficulty with interpretation Problems that required the comparison of slopes when these Problems were presented in symbolic format. Results suggest that this difficulty may be caused by symbolic representation biasing participants towards incorrect strategies. Participants rated graphical Problems to be less difficult than symbolic Problems, and the majority of participants reported a preference for graphical representation. These results set the stage for follow-up studies that will explore whether the nature of the Problem solving task affects students’ choice of solution method.
Andrea Stocco – One of the best experts on this subject based on the ideXlab platform.
-
Endogenous Control and Task Representation: An fMRI Study in Algebraic Problem-solving
Journal of Cognitive Neuroscience, 2008Co-Authors: Andrea Stocco, John R. AndersonAbstract:The roles of prefrontal and anterior cingulate cortices have been widely studied, yet little is known on how they interact to enable complex cognitive abilities. We investigated this issue in a complex yet well-defined symbolic paradigm: Algebraic Problem solving. In our experimental Problems, the demands for retrieving arithmetic facts and maintaining intermediate Problem representations were manipulated separately. An analysis of functional brain images acquired while participants were solving the Problems confirmed that prefrontal regions were affected by the retrieval of arithmetic facts, but only scarcely by the need to manipulate intermediate forms of the equations, hinting at a specific role in memory retrieval. Hemodynamic activity in the dorsal cingulate, on the contrary, increased monotonically as more information processing steps had to be taken, independent of their nature. This pattern was essentially mimicked in the caudate nucleus, suggesting a related functional role in the control of cognitive actions. We also implemented a computational model within the Adaptive Control of Thought—Rational (ACT-R) cognitive architecture, which was able to reproduce both the behavioral data and the time course of the hemodynamic activity in a number of relevant regions of interest. Therefore, imaging results and computer simulation provide evidence that symbolic cognition can be explained by the functional interaction of medial structures supporting control and serial execution, and prefrontal cortices engaged in the on-line retrieval of specific relevant information.