[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-588409-105":59,"doc-detail-588409-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","is-algebra-really-difficult-for-all-students-issue-4-2009-paper","IS ALGEBRA REALLY DIFFICULT FOR ALL STUDENTS? - Issue 4 - 2009 - Paper","","Research examines why students find the transition from arithmetic to algebra difficult, analyzing high school students’ errors for patterns and underlying causes. The study identifies misconceptions rooted in intuitive assumptions, weak understanding of algebraic syntax, analogies to familiar symbol systems (e.g., the English alphabet), and interference from arithmetic. Psychological factors such as carelessness, anxiety, overconfidence, and low motivation are also considered. Three major error types are discussed using a cognitive-psychological approach, and student solution methods are compared to argue for using creative algebraic approaches to support learning.",{"@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/is-algebra-really-difficult-for-all-students-issue-4-2009-paper/588409/",{"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/is-algebra-really-difficult-for-all-students-issue-4-2009-paper/588409.png","ImageObject",300,407,{"name":92,"@type":93},"Putri","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-04","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the study identify as the main sources of errors in learning algebra?","Question",{"text":112,"@type":113},"It attributes errors to intuitive assumptions, failure to understand algebra’s syntax, analogies with familiar symbol systems, and interference from arithmetic, alongside psychological factors such as anxiety and low motivation.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How are psychological and cultural-historical approaches used in the paper?",{"text":117,"@type":113},"The psychological approach explains cognition through individual cognitive development, while the cultural-historical approach treats learning as constructing understanding through activities embedded in social and physical contexts.",{"name":119,"@type":110,"acceptedAnswer":120},"What solution strategies does the paper discuss to improve algebra learning?",{"text":121,"@type":113},"It compares solution methods from another group of students, noting their eagerness to use algebraic methods, and argues that creative algebraic approaches should be used to reinforce learning for other students.","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},588409,1792210054,{"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":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":29,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},962085571259,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Volume 2, Number 4, 2009  \nIS ALGEBRA REALLY DIFFICULT FOR ALL STUDENTS?  \nGunawardena Egodawatte  \nAbstract. Research studies have shown that students encounter difficulties in transitioning from arithmetic to algebra. Errors made by high school students were analyzed for patterns and their causes. The origins of errors were: intuitive assumptions, failure to understand the syntax of algebra, analogies with other familiar symbol systems such as the English alphabet and interference from arithmetic. There were other psychological factors such as carelessness, anxiety, overconfidence, and lack of motivation. Three major error types are discussed with their causes using a cognitive psychological approach. Solution methods of another group of students show that they were eager to use algebraic methods over arithmetic procedures even though arithmetic procedures are more straightforward. The paper argues that creative methods used by some students should be used to reinforce the learning of other students.  \nKeywords: Algebra, error analysis, misconceptions in algebra  \nIntroduction  \nIn recent years, many research projects on mathematics education have focused on learning difficulties of students related to algebra. Research suggest that solutions to the problem of student inability to be successful in algebra are many and frequently interconnected (Norton & Irvin, 2007) . After studying several research findings, Norton & Irvin (2007) suggested some solutions which include: making explicit algebraic thinking inherent in arithmetic in children’s earlier learning (Lins & Kaput, 2004; Warren & Cooper, 2006), explicit teaching of nuances and processes of algebra in an algebraic and symbolic setting (Kirshner & Awtry, 2004; Sleeman, 1986; Stacey & MacGregor, 1997, 1999; Stacey & Chick, 2004), especially in transformational activities (Kieran & Yerushalmy, 2004; Stacey & Chick, 2004), using multiple representations including the use of technology (Kieran & Yerushalmy, 2004; Van de Walle, 2006), and recognizing the importance of embedding algebra into contextual themes (National Council of Teachers of Mathematics, 1998; Stacey & Chick, 2004) . Other research have shown that student errors in algebra can be ascribed to fundamental differences between arithmetic and algebra. For instance, if students want to adopt an algebraic way of reasoning, they have to break away from certain arithmetical conventions and need to learn to deal with algebraic symbolism.  \nThe psychological approach to study cognition  \nPsychology plays an important role in mathematics education especially in cognitive analysis of children’s mathematical thinking. The disciplines of psychology and cognitive science have a seminal influence on how mathematics is learned and taught. The contemporary psychology starts with the concept of an abstract mind. This paradigm implicitly makes the claim that the mind is universal. According to this view, local conditions like settings and cultures are external to the mind and detached from it. Contemporary psychology also believes that mind can be studied explicitly with the use of appropriate psychometric methods without any priori value judgments in seeking for what’s going on in the mind. One of the pioneers of this view was Jean Piaget. He regarded learning as being subordinate to cognitive development and viewed the development of knowledge as a spontaneous process (Piaget, 1970) . Piaget’s explanation of the idea that children learn from reflecting on their actions is widely accepted even today. The constructivist perspective, derived in part from the work of Piaget asserts that conceptual knowledge cannot be transferred from one person to another. Rather, it must be constructed by each child based on his/her own experiences. The concept accounts for the  \nReceived 25 November 2009, accepted 18 December 2009, published 31 December 2009  \nindividual idiosyncratic construction of meaning for systematic errors, misconceptions,","cbCaimSUUvOLekJh","https://ap.wps.com/l/cbCaimSUUvOLekJh","pdf",65780,"English","# Introduction\n## The psychological approach to study cognition\n## The cultural historical approach to study cognition\n## Contemporary perspectives on cognitive analysis","[{\"question\":\"What does the study identify as the main sources of errors in learning algebra?\",\"answer\":\"It attributes errors to intuitive assumptions, failure to understand algebra’s syntax, analogies with familiar symbol systems, and interference from arithmetic, alongside psychological factors such as anxiety and low motivation.\"},{\"question\":\"How are psychological and cultural-historical approaches used in the paper?\",\"answer\":\"The psychological approach explains cognition through individual cognitive development, while the cultural-historical approach treats learning as constructing understanding through activities embedded in social and physical contexts.\"},{\"question\":\"What solution strategies does the paper discuss to improve algebra learning?\",\"answer\":\"It compares solution methods from another group of students, noting their eagerness to use algebraic methods, and argues that creative algebraic approaches should be used to reinforce learning for other students.\"}]","IS ALGEBRA REALLY DIFFICULT FOR ALL STUDENTS? - Issue 4 - 2009 - Paper | PDF",1792065183,15]