[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-588487-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-588487-en":130},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","volume-5-issue-3-investigating-students-difficulties-to-create-a-blackboard-sketch","Volume 5 - Issue 3 - Investigating Students’ Difficulties to Create a Blackboard Sketch","","The paper investigates students’ difficulties in creating a blackboard sketch for teaching the table of multiplication by two. It discusses two instructional stages—discovering relationships within the multiplication table and memorizing results—and critiques approaches that rely mainly on rote learning. Based on prior observation, the study designs a pedagogical micro-experiment to test whether trainee teachers can work with textbook content and transform it into an effective board sketch, targeting comprehension and subsequent memorization.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/research-report/","Research & Report",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/volume-5-issue-3-investigating-students-difficulties-to-create-a-blackboard-sketch/588487/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/volume-5-issue-3-investigating-students-difficulties-to-create-a-blackboard-sketch/588487.png","ImageObject",300,407,{"name":42,"@type":43},"Putri","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-01","2026-10-15",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",6,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What are the two stages of teaching multiplication discussed in the paper?","Question",{"text":63,"@type":64},"The paper distinguishes a first stage focused on discovering results and their connections in the multiplication table, and a second stage centered on memorizing the results.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Why do the authors criticize teachers’ tendency to use rote memorization?",{"text":68,"@type":64},"They argue rote learning can overshadow a more logical approach that helps students understand how results are obtained, and it may neglect the subsequent logical memorization path.",{"name":70,"@type":61,"acceptedAnswer":71},"What is the purpose of the pedagogical micro-experiment?",{"text":72,"@type":64},"It investigates whether students training to become teachers can use textbook content and create a blackboard sketch for the table of multiplication by 2.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},588487,1792934278,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,105,110,114,119,122,126],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":93,"show_sort_weight":94,"slug":95},"Exam",70,"exam",{"id":97,"doc_module":4,"doc_module_name":25,"category_name":98,"show_sort_weight":99,"slug":100},5,"Comic",60,"comic",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},8,30,"research-report",{"id":115,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},9,"Religion & Spirituality",20,"religion-spirituality",{"id":117,"doc_module":4,"doc_module_name":25,"category_name":120,"show_sort_weight":117,"slug":121},"World Cup","world-cup",{"id":123,"doc_module":4,"doc_module_name":25,"category_name":124,"show_sort_weight":123,"slug":125},10,"Lifestyle","lifestyle",{"id":127,"doc_module":4,"doc_module_name":25,"category_name":128,"show_sort_weight":97,"slug":129},19,"General","general",{"code":4,"msg":82,"data":131},{"doc_id":79,"user_id":132,"nickname":42,"user_avatar":133,"doc_module":4,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":123,"language":139,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":12,"update_tm":143,"read_time":144,"preview_page_count":4},962085571259,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Volume 5, Number 3, 2012  \nAN INVESTIGATION OF STUDENTS’ DIFFICULTIES TO CREATE A BLACKBOARD SKETCH FOR THE LESSON: TABLE OF MULTIPLICATION BY TWO  \nIoana Magdaş  \nAbstract: Specialists in the field of mathematical education consider that the learning of multiplication has an extremely important role not only in the area of mathematics, but also in day to day life. We can distinguish two different stages in the process of teaching-learning multiplication: a first step implies the discovery of the results within the multiplication table and the connections that exist between these results, while a second phase deals with memorizing the results. Our experience has shown that teachers tend to make students learn the table of multiplication by heart and this, on the one hand, overshadows a more logical approach that would aim at the students understanding the way in with the results are obtained and, on the other hand, neglects the subsequent logical way of memorizing the results. The way in with the information is presented is key to both the understanding and the remembering of numbers in the table. Starting from the observation presented previously we have created a pedagogical micro-experiment in which wanted to investigate whether students in their training to become teachers had the ability to work with the content offered in school textbooks and to create a blackboard sketch for The table of multiplication by 2.  \nKey words: mathematics, blackboard sketch, multiplication by two, multiplication table  \n1. Introduction  \nSpecialists in the field of mathematical education consider that the learning of multiplication has an extremely important role not only in the area of mathematics, but also in day to day life.  \nOfsted is the United Kingdom Office for Standards in Education, Children’s Services and Skills.“How young learners master maths”, an Ofsted report on best practice in early arithmetic, was published in November 2011. “Primary schools which fail to teach times tables by heart are condemning children to a lifetime struggling with numbers”, inspectors have warned. Nick Gibb, the schools minister, said: \"It is vital that all children can grasp and master arithmetic while they are still at primary school. It is important that pupils are fluent in calculation and have learnt the multiplication tables by heart before they leave primary school”.  \n“We all know that learning multiplication is an essential part of our child's elementary education. Students who have mastered multiplication gain a solid foundation in mathematics that will help them throughout middle school, high school and beyond.”(Susan Jarema, 2007) .  \nLearning multiplication tables can be difficult for some students. These difficulties are owed not only to the students themselves, but also to the teachers who, most often, do not find the appropriate ways to make students understand and memorize multiplication charts.  \nWe can distinguish two different stages in the process of teaching-leaning multiplication: a first step implies the discovery of the results within the multiplication table and the connections that exist between these results, while a second phase deals with memorizing the results. What is more important understanding or memorization?„It's not one or the other, it's both”( Susan Jarema, 2007) . Our experience has shown that teachers tend to make students learn the table of multiplication by heart and this, on the one hand, overshadows a more logical approach that would aim at the students understanding the way in with the results are obtained and, on the other hand, neglects the subsequent  \nlogical way of memorizing the results. The way in with the information is presented is key to both the understanding and the remembering of numbers in the table.  \nThis is precisely why we sought to create a micro-experiment that wanted to investigate whether students in their training to become teachers had the ability to work with the content offered in ","cbCaintrMbw8n79z","https://ap.wps.com/l/cbCaintrMbw8n79z","pdf",671547,"English","# Introduction\n# Methodological considerations regarding the teaching-learning of multiplication","[{\"question\":\"What are the two stages of teaching multiplication discussed in the paper?\",\"answer\":\"The paper distinguishes a first stage focused on discovering results and their connections in the multiplication table, and a second stage centered on memorizing the results.\"},{\"question\":\"Why do the authors criticize teachers’ tendency to use rote memorization?\",\"answer\":\"They argue rote learning can overshadow a more logical approach that helps students understand how results are obtained, and it may neglect the subsequent logical memorization path.\"},{\"question\":\"What is the purpose of the pedagogical micro-experiment?\",\"answer\":\"It investigates whether students training to become teachers can use textbook content and create a blackboard sketch for the table of multiplication by 2.\"}]","Volume 5 - Issue 3 - Investigating Students’ Difficulties to Create a Blackboard Sketch | PDF",1792065347,25]