The Experts below are selected from a list of 31965 Experts worldwide ranked by ideXlab platform

Andrew Elby - One of the best experts on this subject based on the ideXlab platform.

  • how students blend conceptual and formal Mathematical Reasoning in solving physics problems
    Science Education, 2013
    Co-Authors: Eric Kuo, Michael M Hull, Ayush Gupta, Andrew Elby
    Abstract:

    Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual Reasoning in two ways: for selecting relevant equations (before manipulating them) and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case that problem-solving expertise should include opportunistically blending of conceptual and formal Mathematical Reasoning even while manipulating equations. We present analysis of interviews with two students, Alex and Pat. Interviewed students were asked to explain a particular equation and solve a problem using that equation. Alex used and described the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem. His shortcut blended Mathematical operations with conceptual Reasoning about physical processes, reflecting a view—expressed earlier in his explanation of the equation—that equations can express an overarching conceptual meaning. Using case studies of Alex and Pat, we argue that this opportunistic blending of conceptual and formal Mathematical Reasoning (i) is a part of problem-solving expertise, (ii) can be described in terms of cognitive elements called symbolic forms (Sherin, 2001), and (iii) is a feasible instructional target.

  • how students blend conceptual and formal Mathematical Reasoning in solving physics problems
    arXiv: Physics Education, 2011
    Co-Authors: Eric Kuo, Michael M Hull, Ayush Gupta, Andrew Elby
    Abstract:

    Current conceptions of expert problem solving depict physical/conceptual Reasoning and formal Mathematical Reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual Reasoning in two ways: for selecting relevant equations (before manipulating them), and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case that problem-solving expertise should include opportunistically blending conceptual and formal Mathematical Reasoning even while manipulating equations. We present analysis of interviews with two students, Alex and Pat. Interviewed students were asked to explain a particular equation and solve a problem using that equation. Alex used and described the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem. His shortcut blended Mathematical operations with conceptual Reasoning about physical processes, reflecting a view - expressed earlier in his explanation of the equation - that equations can express an overarching conceptual meaning. Using case studies of Alex and Pat, we argue that this opportunistic blending of conceptual and formal Mathematical Reasoning (i) is a part of problem-solving expertise, (ii) can be described in terms of cognitive elements called symbolic forms (Sherin, 2001), and (iii) is a feasible instructional target.

Yingshan Zhang - One of the best experts on this subject based on the ideXlab platform.

  • acupuncture treating dystrophy based on ph Mathematical Reasoning of treatment principle based on yin yang wu xing theory in traditional chinese medicine iii
    Chinese Medicine, 2019
    Co-Authors: Yingshan Zhang, Bibo Zhang
    Abstract:

    Theory of both Zangxiang (藏象) and Jingluo (经络) is useful in understanding disease. By using Mathematical Reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Medicine (TCM), this paper demonstrates the treatment principle: “Searching for a root cause of disease in cure, treatment of both the root-cause and symptoms at the same time” (治病求本, 标本兼治). It means that for a human body, there is the Mathematical structure of both Zangxiang and Jingluo as her/his second physiological system. It can be used to determine both the root-cause and symptoms of the sick organ by using both Zangxiang and Jingluo. In general, for the human blood pH value, the normal range of theory is [7.34539, 7.45461] nearly to [7.35, 7.45], and the center is 7.4. The first or second transfer law of a human body’s energies changes according to the different blood pH values whether in the normal range or not. Human disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship. As an application, acupuncture is used to treat limb-girdle muscular dystrophy.

  • Mathematical Reasoning of treatment principle based on the stable logic analysis model of complex systems
    Intelligent Control and Automation, 2012
    Co-Authors: Yingshan Zhang
    Abstract:

    The article reviews the stable logic analysis model of complex systems or steady multilateral systems with two non-compatibility relations. Energy concept in Physics is introduced to the multilateral systems and used to deal with the multilateral system diseases. By using Mathematical Reasoning, it is demonstrated that the treatment principle: “Virtual disease is to fill his mother but real disease is to rush down his son” and “Strong inhibition of the same time, support the weak” which due to the “Yin Yang Wu Xing” Theory in Traditional Chinese Medicine (TCM).

  • Mathematical Reasoning of treatment principle based on yin yang wu xing theory in traditional chinese medicine
    Chinese Medicine, 2011
    Co-Authors: Yingshan Zhang
    Abstract:

    By using Mathematical Reasoning, this paper demonstrates the treatment principle: “Virtual disease is to fill his mother but real disease is to rush down his son” and “Strong inhibition of the same time, support the weak” based on “Yin Yang Wu Xing” Theory in Traditional Chinese Medicine (TCM). We defined two kinds of opposite relations and one kind of equivalence relation, introduced the concept of steady multilateral systems with two non-compatibility relations, and discussed its energy properties. Later based on the treatment of TCM and treated the healthy body as a steady multilateral system, it has been proved that the treatment principle is true. The kernel of this paper is the existence and Reasoning of the non-compatibility relations in steady multilateral systems, and it accords with the oriental thinking model.

Johan Lithner - One of the best experts on this subject based on the ideXlab platform.

  • Mathematical Reasoning in teachers presentations
    The Journal of Mathematical Behavior, 2012
    Co-Authors: Tomas Bergqvist, Johan Lithner
    Abstract:

    This paper presents a study of the opportunities presented to students that allow them to learn different types of Mathematical Reasoning during teachers’ ordinary task solving presentations. The c ...

  • Mathematical Reasoning requirements in swedish upper secondary level assessments
    Mathematical Thinking and Learning, 2011
    Co-Authors: Torulf Palm, Jesper Boesen, Johan Lithner
    Abstract:

    We investigate the Mathematical Reasoning required to solve the tasks in the Swedish national tests and a random selection of Swedish teacher-made tests. The results show that only a small proportion of the tasks in the teacher-made tests require the students to produce new Reasoning and to consider the intrinsic Mathematical properties involved in the tasks. In contrast, the national tests include a large proportion of tasks for which memorization of facts and procedures are not sufficient. The conditions and constraints under which the test development takes place indicate some of the reasons for this discrepancy and difference in alignment with the reform documents.

  • the relation between types of assessment tasks and the Mathematical Reasoning students use
    Educational Studies in Mathematics, 2010
    Co-Authors: Johan Lithner, Jesper Boesen, Torulf Palm
    Abstract:

    The relation between types of tasks and the Mathematical Reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did not require conceptual understanding. In contrast, test tasks that do not share important properties with the textbook mostly elicited creative Mathematically founded Reasoning. In addition, most successful solutions to such tasks were based on this type of Reasoning.

  • Mathematical Reasoning in calculus textbook exercises
    The Journal of Mathematical Behavior, 2004
    Co-Authors: Johan Lithner
    Abstract:

    The aim of this paper is to study some of the strategies that are possible to use in order to solve the exercises in undergraduate calculus textbooks. It is described in detail how most exercises ...

  • students Mathematical Reasoning in university textbook exercises
    Educational Studies in Mathematics, 2003
    Co-Authors: Johan Lithner
    Abstract:

    Video recordings of three undergraduate students' textbook-based homework are analysed. A focus is on the ways their exercise Reasoning is Mathematically well-founded or superficial. Most strategy choices and implementations are carried out without considering the intrinsic Mathematical properties of the components involved in their work. It is essential in their strategies to find procedures to mimick and few constructive Reasoning attempts are made.

Eric Kuo - One of the best experts on this subject based on the ideXlab platform.

  • how students blend conceptual and formal Mathematical Reasoning in solving physics problems
    Science Education, 2013
    Co-Authors: Eric Kuo, Michael M Hull, Ayush Gupta, Andrew Elby
    Abstract:

    Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual Reasoning in two ways: for selecting relevant equations (before manipulating them) and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case that problem-solving expertise should include opportunistically blending of conceptual and formal Mathematical Reasoning even while manipulating equations. We present analysis of interviews with two students, Alex and Pat. Interviewed students were asked to explain a particular equation and solve a problem using that equation. Alex used and described the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem. His shortcut blended Mathematical operations with conceptual Reasoning about physical processes, reflecting a view—expressed earlier in his explanation of the equation—that equations can express an overarching conceptual meaning. Using case studies of Alex and Pat, we argue that this opportunistic blending of conceptual and formal Mathematical Reasoning (i) is a part of problem-solving expertise, (ii) can be described in terms of cognitive elements called symbolic forms (Sherin, 2001), and (iii) is a feasible instructional target.

  • how students blend conceptual and formal Mathematical Reasoning in solving physics problems
    arXiv: Physics Education, 2011
    Co-Authors: Eric Kuo, Michael M Hull, Ayush Gupta, Andrew Elby
    Abstract:

    Current conceptions of expert problem solving depict physical/conceptual Reasoning and formal Mathematical Reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual Reasoning in two ways: for selecting relevant equations (before manipulating them), and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case that problem-solving expertise should include opportunistically blending conceptual and formal Mathematical Reasoning even while manipulating equations. We present analysis of interviews with two students, Alex and Pat. Interviewed students were asked to explain a particular equation and solve a problem using that equation. Alex used and described the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem. His shortcut blended Mathematical operations with conceptual Reasoning about physical processes, reflecting a view - expressed earlier in his explanation of the equation - that equations can express an overarching conceptual meaning. Using case studies of Alex and Pat, we argue that this opportunistic blending of conceptual and formal Mathematical Reasoning (i) is a part of problem-solving expertise, (ii) can be described in terms of cognitive elements called symbolic forms (Sherin, 2001), and (iii) is a feasible instructional target.

Michael M Hull - One of the best experts on this subject based on the ideXlab platform.

  • how students blend conceptual and formal Mathematical Reasoning in solving physics problems
    Science Education, 2013
    Co-Authors: Eric Kuo, Michael M Hull, Ayush Gupta, Andrew Elby
    Abstract:

    Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual Reasoning in two ways: for selecting relevant equations (before manipulating them) and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case that problem-solving expertise should include opportunistically blending of conceptual and formal Mathematical Reasoning even while manipulating equations. We present analysis of interviews with two students, Alex and Pat. Interviewed students were asked to explain a particular equation and solve a problem using that equation. Alex used and described the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem. His shortcut blended Mathematical operations with conceptual Reasoning about physical processes, reflecting a view—expressed earlier in his explanation of the equation—that equations can express an overarching conceptual meaning. Using case studies of Alex and Pat, we argue that this opportunistic blending of conceptual and formal Mathematical Reasoning (i) is a part of problem-solving expertise, (ii) can be described in terms of cognitive elements called symbolic forms (Sherin, 2001), and (iii) is a feasible instructional target.

  • how students blend conceptual and formal Mathematical Reasoning in solving physics problems
    arXiv: Physics Education, 2011
    Co-Authors: Eric Kuo, Michael M Hull, Ayush Gupta, Andrew Elby
    Abstract:

    Current conceptions of expert problem solving depict physical/conceptual Reasoning and formal Mathematical Reasoning as separate steps: a good problem solver first translates a physical Current conceptions of quantitative problem-solving expertise in physics incorporate conceptual Reasoning in two ways: for selecting relevant equations (before manipulating them), and for checking whether a given quantitative solution is reasonable (after manipulating the equations). We make the case that problem-solving expertise should include opportunistically blending conceptual and formal Mathematical Reasoning even while manipulating equations. We present analysis of interviews with two students, Alex and Pat. Interviewed students were asked to explain a particular equation and solve a problem using that equation. Alex used and described the equation as a computational tool. By contrast, Pat found a shortcut to solve the problem. His shortcut blended Mathematical operations with conceptual Reasoning about physical processes, reflecting a view - expressed earlier in his explanation of the equation - that equations can express an overarching conceptual meaning. Using case studies of Alex and Pat, we argue that this opportunistic blending of conceptual and formal Mathematical Reasoning (i) is a part of problem-solving expertise, (ii) can be described in terms of cognitive elements called symbolic forms (Sherin, 2001), and (iii) is a feasible instructional target.