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This paper reviews exploratory and confirmatory factor analysis from dependable sources and provides a step-by-step workflow for conducting EFA, including guidance on question types, purposes, analysis stages, and report writing. Procedures are demonstrated using SPSS and Montecarlo software, supporting teachers and researchers applying heuristic analysis.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/exploratory-factor-analysis-for-tpack-among-mathematics-teachers-why-what-and-how/591678/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/exploratory-factor-analysis-for-tpack-among-mathematics-teachers-why-what-and-how/591678.png","ImageObject",300,407,{"name":92,"@type":93},"Dipper","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-27","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the main goal of factor analysis described in the paper?","Question",{"text":112,"@type":113},"Factor analysis aims to summarize relationships between observed variables to help conceptualize the phenomenon under study and evaluate whether measures capture the intended theoretical constructs.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) differ?",{"text":117,"@type":113},"EFA is used to construct or uncover latent structure and theory, while CFA is used to test an existing theory and the latent factors implied by it.",{"name":119,"@type":110,"acceptedAnswer":120},"Why does the paper emphasize exploratory factor analysis and its common misunderstandings?",{"text":121,"@type":113},"Although EFA is important, the paper states that many researchers still hold false views and do not understand or apply exploratory factor analysis correctly, motivating a practical guide.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},591678,1792144756,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":24,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":144,"read_time":145,"preview_page_count":4},1374404997633,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","Exploratory Factor Analysis for TPACK among Mathematics Teachers: Why, What and How  \nFereshteh Zeynivandnezhad  \nOrganization for Educational Research and Planning, [fzeynivand@gmail.com](fzeynivand@gmail.com)  \nFatemeh Rashed  \nAzad University (Neyshabor Branch), Neyshabor, Iran, [rashed_um@yahoo.com](rashed_um@yahoo.com)  \nArman Kanooni  \nThe Johns Hopkins University (Advanced Academic Programs), [kanooni@sprynet.com](kanooni@sprynet.com)  \nFactor analysis is a statistical technique that is widely used in psychology and social sciences. Using computers and statistical packages, implementation of multivariate factor analysis and other multivariate methods becomes possible for researchers. Exploratory factor analysis and confirmatory factor analysis are applied in different studies; however, exploratory factor analysis as one of the most important data analysis methods is not well understood. Despite the rising number of researchers who understand it many researchers in various fields still have a false view. This paper reviews methods based on reliable sources and provides a practical guide to conduct an exploratory factor analysis. This paper presents step-by-step of different stages of exploratory factor analysis using SPSS and Montecarlo software. This study could pave the way for students, researchers and teachers who want to use heuristic analysis in their studies of different types of questions, purpose, method of analysis and report writing.  \nKeywords: factor analysis, exploratory factor analysis, confirmatory factor analysis, principal component analysis  \nINTRODUCTION  \nFactor analysis (FA) is a broad term that includes a range of statistical techniques that make it possible to estimate about the total population. This estimate is achieved by a variety of observed variables and relationships between them (Akyuz, 2018; Gorsuch, 1983; Kline, 2011; Matsunaga, 2010) . In other words, the goal of factor analysis is to summarize the relationships between variables which enable to conceptualize the phenomena under study (Hair et al., 2010; Gorsuch, 1983) . In the strict sense of the word, factor analysis responds to research questions of validity as stated that the heart of the management of psychological constructs is factor analysis (Nunnally, 1978) . Psychological constructs are variables such as love, motivation, happiness and satisfaction that are not directly measurable (Pallant, 2011; Kline, 2011) . In other words, factor analysis is a diagnostic tool for the evaluation of data collected in line with the theoretical model, or the expected target constructs under study. In this case, were the measures used in fact able to measure what they claim? Factor analysis is of great importance in the social sciences and interdisciplinary studies (Yip and Tse, 2019); however, one of the most important methods of statistical analysis is not understood and is not used correctly (Matsunaga, 2010) .  \nAlthough the number of researchers that understood the issue is on the rise, the evidence suggests that the overwhelming of researches in various fields still have the wrong perspective (Fabrigar, Wegener,  \nMacCallum, & Strahan, 1999; Henson & Roberts, 2006; Matsunaga, 2010; Park, Dailey & Lemus, 2002; Preacher & MacCallum, 2002). Hoping to make a change in factor analysis, the present article is a practical guide as the best method for performing factor analysis that allow widespread use of different software. There are two ways to do factor analysis, i.e., exploratory factor analysis and confirmatory factor analysis (Hair et al., 2010; Thomason, 2004) . Even though both methods are used to test the hidden or latent factors in the data, they play different roles according to the purpose of a research; exploratory factor analysis is to construct the theory and confirmatory factor analysis is to test the theory (Kline, 2011) .  \nThis article is depicting a hybrid approach to exploratory factor analysis. Exploratory factor analysis c","cbCailAgrt0GMtXu","https://ap.wps.com/l/cbCailAgrt0GMtXu","pdf",1111757,18,"English","# Introduction\n## Factor analysis and its purpose\n## Exploratory vs confirmatory factor analysis\n## Hybrid approach to exploratory factor analysis\n## EFA, PCA, and CFA: conceptual differences","[{\"question\":\"What is the main goal of factor analysis described in the paper?\",\"answer\":\"Factor analysis aims to summarize relationships between observed variables to help conceptualize the phenomenon under study and evaluate whether measures capture the intended theoretical constructs.\"},{\"question\":\"How do exploratory factor analysis (EFA) and confirmatory factor analysis (CFA) differ?\",\"answer\":\"EFA is used to construct or uncover latent structure and theory, while CFA is used to test an existing theory and the latent factors implied by it.\"},{\"question\":\"Why does the paper emphasize exploratory factor analysis and its common misunderstandings?\",\"answer\":\"Although EFA is important, the paper states that many researchers still hold false views and do not understand or apply exploratory factor analysis correctly, motivating a practical guide.\"}]","Exploratory Factor Analysis for TPACK among Mathematics Teachers - Why, What and How | PDF",1792072973,45]