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Associative Property

The Experts below are selected from a list of 81 Experts worldwide ranked by ideXlab platform

Meixia Ding – 1st expert on this subject based on the ideXlab platform

  • teaching of the Associative Property a natural classroom investigation
    Investigations in Mathematics Learning, 2019
    Co-Authors: Eli Barnett, Meixia Ding


    ABSTRACTIn this study we investigate the teaching of the Associative Property in a natural classroom setting through observation of classroom video of several elementary math classes in a large urb…

  • transferring specialized content knowledge to elementary classrooms preservice teachers learning to teach the Associative Property
    International Journal of Mathematical Education in Science and Technology, 2018
    Co-Authors: Meixia Ding, Kayla Heffernan


    This study explores how preservice teachers (PSTs) transfer the
    intended specialized content knowledge (SCK) to elementary classrooms.
    Focusing on the case of the Associative Property of multiplication,
    we compared three PSTs’SCK during enacted lessons in fourth
    grade classrooms with their own learning in professional development
    (PD) settings. Findings revealed the PSTs’ successes and challenges
    in unpacking an example task, especially in areas of making
    connections between concrete and abstract representations and asking
    deep questions that target quantitative interactions. Factors that
    may have supported or hindered PSTs’ SCK transfer include the complex
    nature of teacher knowledge, the PD effort and the outside factors
    such as the support from textbooks and cooperating teachers.
    Implications for teacher education and directions for future research
    are discussed.

  • developing preservice elementary teachers specialized content knowledge the case of Associative Property
    International Journal of STEM Education, 2016
    Co-Authors: Meixia Ding


    Specialized content knowledge (SCK) is a type of mathematical content knowledge specifically needed for teaching. This type of knowledge, although serving as a critical component for preservice teacher education, is often challenging to develop with preservice elementary teachers (PTs). The purpose of this study is to investigate PTs’ development of SCK for teaching fundamental mathematical ideas in a university methods course. Focusing on the case of the Associative Property (AP) of multiplication, the author as the course instructor identified three instructional opportunities (a formal introduction and two delayed revisits) to stress two SCK components, representations, and explanations. PTs’ learning progresses were assessed through three diagnostic tests (a pretest, a mid-term exam, and a final exam) and two prompts, which informed the upcoming lesson design. Meanwhile, the course instructor conducted ongoing reflections on PTs’ learning, which also informed the corresponding lessons. It was found that PTs initially generated abstract number sentences without reasoning about the contexts of word problems. This representational sequence indicates a symbol precedence view. When prompted for explanations, PTs focused on individual numbers rather than quantitative relationships, and they could not consistently apply the basic meaning of multiplication for reasoning. The methods course, when designed to address these issues, promoted PTs’ SCK development. At the end of the course, the majority of PTs were able to generate number sentences based on the word problem structures and provided reasonable explanations; however, the methods course also faced dilemmas due to PTs’ robust symbol precedence view and the tension between PTs’ learning and children’s learning. Very few studies have explored ways to support PTs’ knowledge growth in SCK, especially for teaching fundamental mathematical ideas. This study, by carefully documenting the successes and challenges in developing PTs’ SCK, contributes to the existing literature. Based on our findings, this study highlights the importance of stressing basic meanings so as to develop PTs’ explanation skills. Meanwhile, to develop PTs’ representation skills, university instructors should be aware of the tension between PTs’ and children’s learning as manifested by PTs’ symbol precedence view. Finally, to support PTs’ SCK growth, it is also important to emphasize the role of elementary textbooks.

Yan Zhang – 2nd expert on this subject based on the ideXlab platform

  • preparation of hydrophobic association polyacrylamide in a new micellar copolymerization system and its hydrophobically Associative Property
    Macromolecules, 2008
    Co-Authors: Jian Wang, Yan Zhang


    This paper describes for the first time the combination of a polymerizable surfactant, sodium 2-acrylamido-dodecane sulfonate (NaAMC12S), and a hydrophobic monomer to prepare water-soluble associating polymer via a new micellar process. In this method, the hydrophobic monomer, N-dodecylacrylamide (C12AM) or N,N-didodecylacrylamide (DiC12AM), was first solubilized within NaAMC12S micelles, whereas the hydrophilic monomer acrylamide (AM) was dissolved in the aqueous continuous medium. The micellar copolymerization, therefore, resulted in a ternary hydrophobic association polyacrylamide (HAPAM), namely, C12AM/NaAMC12S/AM or DiC12AM/ NaAMC12S/AM. The chemical structures of these ternary copolymers were characterized with Fourier transform infrared (FTIR) spectroscopy, and their hydrophobic Associative behavior as well as the relationship between microstructure and hydrophobic Associative Property was studied by a combination of the fluorescence probe technique and viscosimetry. The experimental result shows, …

Mary Margaret Capraro – 3rd expert on this subject based on the ideXlab platform

  • supporting meaningful initial learning of the Associative Property cross cultural differences in textbook presentations
    Jornal Internacional de Estudos em Educação Matemática, 2015
    Co-Authors: Meixia Ding, Mary Margaret Capraro, Xiaobao Li, Robert M Capraro


    The purpose of this paper is to examine how Chinese and U.S. textbooks present the Associative Property of multiplication (AP) to support student’s initial learning. For all of the identified worked examples, we analyzed the nature of context and the purpose of using word problems and illustrations. There were important cross-cultural differences in textbook presentations. The U.S. reform textbook did not explicitly introduce AP; the U.S. traditional textbooks introduced AP and applied it to computation while the accompanying word problems and illustrations did not help students understand AP. In contrast, the Chinese textbook introduced AP through a word problem context while seamlessly incorporating sense making of AP. Our findings of cross-cultural differences suggest alternative approaches for grounding fundamental mathematical ideas in word problems and illustrations to support students’ meaningful initial learning.

  • preservice elementary teachers knowledge for teaching the Associative Property of multiplication a preliminary analysis
    The Journal of Mathematical Behavior, 2013
    Co-Authors: Meixia Ding, Xiaobao Li, Mary Margaret Capraro


    Abstract This study examines preservice elementary teachers’ (PTs) knowledge for teaching the Associative Property (AP) of multiplication. Results reveal that PTs hold a common misconception between the AP and commutative Property (CP). Most PTs in our sample were unable to use concrete contexts (e.g., pictorial representations and word problems) to illustrate AP of multiplication conceptually, particularly due to a fragile understanding of the meaning of multiplication. The study also revealed that the textbooks used by PTs at both the university and elementary levels do not provide conceptual support for teaching AP of multiplication. Implications of findings are discussed.