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Residuals and the Residual-Based Statistic for Testing Goodness of Fit of Structural Equation Models
Peer reviewed
Direct linkFoldnes, Njal; Foss, Tron; Olsson, Ulf Henning – Journal of Educational and Behavioral Statistics, 2012
The residuals obtained from fitting a structural equation model are crucial ingredients in obtaining chi-square goodness-of-fit statistics for the model. The authors present a didactic discussion of the residuals, obtaining a geometrical interpretation by recognizing the residuals as the result of oblique projections. This sheds light on the…
Descriptors: Structural Equation Models, Goodness of Fit, Geometric Concepts, Algebra
Toews, Carl – PRIMUS, 2012
Mathematical modeling occupies an unusual space in the undergraduate mathematics curriculum: typically an "advanced" course, it nonetheless has little to do with formal proof, the usual hallmark of advanced mathematics. Mathematics departments are thus forced to decide what role they want the modeling course to play, both as a component of the…
Descriptors: Majors (Students), Mathematics Curriculum, Undergraduate Students, Communication Skills
Download full textNaidu, Jaideep T.; Sanford, John F. – American Journal of Business Education, 2011
In a recent paper by Wilamowsky et al. [6], an intuitive proof of the area of the circle dating back to the twelfth century was presented. They discuss challenges made to this proof and offer simple rebuttals to these challenges. The alternative solution presented by them is simple and elegant and can be explained rather easily to non-mathematics…
Descriptors: Mathematical Models, Mathematical Logic, Mathematical Formulas, Intellectual History
Contreras, José N.; Martínez-Cruz, Armando M. – North American Chapter of the International Group for the Psychology of Mathematics Education, 2011
This study investigates the extent to which pre-service elementary teachers (PETs) use their realworld knowledge to solve problems for which the result of the arithmetic operation is problematic, if one takes into consideration the reality of the context. A paper-and-pencil test was administered to 566 PETs enrolled in mathematics content courses.…
Descriptors: Preservice Teachers, Elementary School Teachers, Word Problems (Mathematics), Problem Solving
Bartocci, Ezio; Singh, Rupinder; von Stein, Frederick B.; Amedome, Avessie; Caceres, Alan Joseph J.; Castillo, Juan; Closser, Evan; Deards, Gabriel; Goltsev, Andriy; Ines, Roumwelle Sta.; Isbilir, Cem; Marc, Joan K.; Moore, Diquan; Pardi, Dana; Sadhu, Sandeep; Sanchez, Samuel; Sharma, Pooja; Singh, Anoopa; Rogers, Joshua; Wolinetz, Aron; Grosso-Applewhite, Terri; Zhao, Kai; Filipski, Andrew B.; Gilmour, Robert F., Jr.; Grosu, Radu; Glimm, James; Smolka, Scott A.; Cherry, Elizabeth M.; Clarke, Edmund M.; Griffeth, Nancy; Fenton, Flavio H. – Advances in Physiology Education, 2011
As part of a 3-wk intersession workshop funded by a National Science Foundation Expeditions in Computing award, 15 undergraduate students from the City University of New York collaborated on a study aimed at characterizing the voltage dynamics and arrhythmogenic behavior of cardiac cells for a broad range of physiologically relevant conditions…
Descriptors: Undergraduate Students, Mathematical Models, Student Interests, Laboratories
Beke, Tamas – European Journal of Physics, 2011
Thermoacoustic instability can appear in any thermal device when the unsteady heat transfer is favourably coupled with the fluctuations of acoustic pressure. In this paper, we present a project type of physical measuring and modelling task; the aim of our project is to help our students increase their knowledge of thermoacoustics. Our paper…
Descriptors: Thermodynamics, Acoustics, Mathematical Models, College Science
Iiskala, Tuike; Vauras, Marja; Lehtinen, Erno; Salonen, Pekka – Learning and Instruction, 2011
This study investigated how metacognition appears as a socially shared phenomenon within collaborative mathematical word-problem solving processes of dyads of high-achieving pupils. Four dyads solved problems of different difficulty levels. The pupils were 10 years old. The problem-solving activities were videotaped and transcribed in terms of…
Descriptors: Problem Solving, Metacognition, Students, Cooperation
Heit, Evan; Hayes, Brett K. – Journal of Experimental Psychology: General, 2011
In an effort to assess the relations between reasoning and memory, in 8 experiments, the authors examined how well responses on an inductive reasoning task are predicted from responses on a recognition memory task for the same picture stimuli. Across several experimental manipulations, such as varying study time, presentation frequency, and the…
Descriptors: Visual Stimuli, Mathematical Models, Recognition (Psychology), Memory
Reiss, Michael; Hoyles, Celia; Mujtaba, Tamjid; Riazi-Farzad, Bijan; Rodd, Melissa; Simon, Shirley; Stylianidou, Fani – International Journal of Science and Mathematics Education, 2011
We report on a project currently in progress that aims to identify through research the range of factors (individual, school and out-of-school, including home) and their interactions that influence post-16 (i.e. post-compulsory) participation in mathematics and physics in the UK and to assess their relative importance among different student…
Descriptors: Student Participation, Ethnography, Physics, Discourse Analysis
Murdiyani, Nila Mareta; Zulkardi; Putri, Ratu Ilma Indra; van Eerde, Dolly; van Galen, Frans – Indonesian Mathematical Society Journal on Mathematics Education, 2013
Subtraction has two meanings and each meaning leads to the different strategies. The meaning of "taking away something" suggests a direct subtraction, while the meaning of "determining the difference between two numbers" is more likely to be modeled as indirect addition. Many prior researches found that the second meaning and…
Descriptors: Subtraction, Mathematical Models, Mathematical Formulas, Problem Solving
Ciltas, Alper; Isik, Ahmet – Educational Sciences: Theory and Practice, 2013
The aim of this study was to examine the modelling skills of prospective elementary mathematics teachers who were studying the mathematical modelling method. The research study group was composed of 35 prospective teachers. The exploratory case analysis method was used in the study. The data were obtained via semi-structured interviews and a…
Descriptors: Mathematical Models, Teaching Skills, Elementary School Mathematics, Mathematics Teachers
Lai, Mun Yee – Mathematics Teacher Education and Development, 2013
Current debates about successful mathematics pedagogy suggest that mathematical learning and problem solving can be enhanced by using metaphors as they provide students with a tool for thinking. But assisting pre-service teachers to understand the importance of careful and accurate explanations for mathematical concepts remains an issue. This…
Descriptors: Foreign Countries, Figurative Language, Logical Thinking, Mathematical Models
Ray, Darrell L. – American Biology Teacher, 2013
Students often enter biology programs deficient in the math and computational skills that would enhance their attainment of a deeper understanding of the discipline. To address some of these concerns, I developed a series of spreadsheet simulation exercises that focus on some of the mathematical foundations of scientific inquiry and the benefits…
Descriptors: Science Instruction, Mathematics Skills, Educational Technology, Spreadsheets
Schell-Straub, Sigrid – International Journal of Development Education and Global Learning, 2013
This article describes a scientific and practical journey through the worlds of mathematics education and development education/global education. It explores one link in detail: critical mathematics education and the competency 'mathematical modelling' in theory and practice. It describes a case study of a secondary school in Baden-Württemberg,…
Descriptors: Mathematics Education, Competency Based Teacher Education, Global Education, Secondary School Curriculum
Kapur, Manu – Instructional Science: An International Journal of the Learning Sciences, 2012
In a study with ninth-grade mathematics students on learning the concept of variance, students experienced either direct instruction (DI) or productive failure (PF), wherein they were first asked to generate a quantitative index for variance without any guidance before receiving DI on the concept. Whereas DI students relied only on the canonical…
Descriptors: Direct Instruction, Mathematics Instruction, Multivariate Analysis, Mathematical Models
