[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-592704-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-592704-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","teaching-college-probability-for-higher-achievement-study-results-on-instructional-methods-and-student-performance","Teaching College Probability for Higher Achievement - Study Results on Instructional Methods and Student Performance","","Teaching College Probability for Higher Achievement presents a mixed-methods study examining how specific tasks delivered through two instructional methods affect college students’ achievement in probability. The design uses a pre-test and post-test in treatment and control groups within an introductory statistics course. Pre-test scores show comparable initial probability knowledge across groups. Post-test analysis using Wilcoxon Signed-Ranks and Mann-Whitney tests indicates the control group declines on multiple-choice performance, while the treatment group shows significantly higher normalized gains and better results on open-ended items. Overall, post-test achievement is higher for the treatment group.",{"@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/teaching-college-probability-for-higher-achievement-study-results-on-instructional-methods-and-student-performance/592704/",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/teaching-college-probability-for-higher-achievement-study-results-on-instructional-methods-and-student-performance/592704.png","ImageObject",300,407,{"name":42,"@type":43},"Mimi","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-11-03","2026-10-15",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",9,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What was the main goal of the study?","Question",{"text":63,"@type":64},"To examine the role of particular tasks implemented through two instructional methods and their effects on college students’ achievement in probability.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"How were the instructional methods A and B different?",{"text":68,"@type":64},"Method A relied on lectures and small-group cooperative sessions where students solve textbook probability problems. Method B used lectures and cooperative sessions involving probability experiments that generate real data to connect experimental and theoretical probability.",{"name":70,"@type":61,"acceptedAnswer":71},"What did the statistical tests show about students’ results?",{"text":72,"@type":64},"Wilcoxon results showed the control group’s multiple-choice scores were significantly lower on the post-test than the pre-test. Mann-Whitney results showed the treatment group had significantly different normalized gains from the control group and higher scores on open-ended post-test items.","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},592704,1792165390,{"code":4,"msg":82,"data":83},"success",[84,88,92,96,101,106,111,115,119,122,126],{"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":102,"doc_module":4,"doc_module_name":25,"category_name":103,"show_sort_weight":104,"slug":105},6,"Technology",50,"technology",{"id":107,"doc_module":4,"doc_module_name":25,"category_name":108,"show_sort_weight":109,"slug":110},7,"Healthcare",40,"healthcare",{"id":112,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":113,"slug":114},8,30,"research-report",{"id":55,"doc_module":4,"doc_module_name":25,"category_name":116,"show_sort_weight":117,"slug":118},"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":112,"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":139,"language":140,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":12,"update_tm":144,"read_time":113,"preview_page_count":4},2336477974920,"https://ap-avatar.wpscdn.com/davatar_155a257f0dc6eb9ab79c44ca47cae57d","Teaching College Probability for Higher Achievement  \nBy Irini Papaieronymou􀀍  \nThis paper presents the results of a study which examined the role of particular tasks implemented through two instructional methods on college students’ achievement in probability. A mixed methods design that utilized a pre-test (with multiple-choice items) and post-test (with multiple-choice and open-ended items) in treatment and control groups in an introductory statistics course was used. An analysis of pre-test scores indicated that students in the control and treatment groups had comparable initial probability knowledge. The results of the Wilcoxon Signed-Ranks test indicated that the multiple-choice scores of students in the control group were significantly lower on the post-test compared to the pre-test. In the case of the treatment group, student scores on the multiple-choice items did not increase significantly from the pretest to the post-test. In addition, the results of the Mann-Whitney test showed that the normalized gain scores of the treatment group were significantly different from those of the control group. Relative to the open-ended post-test items, the Mann-Whitney test indicated that the scores of the treatment group on these items were significantly higher than the scores of the control group. Overall, the total post-test achievement of students in the treatment group was significantly higher than that of students in the control group.  \nKeywords: achievement, college, instructional methods, probability.  \nIntroduction  \nOver the past couple of decades there have been various reform initiatives concerning the content and means of instruction in mathematics classrooms atthe college level. In particular, the Mathematical Association of America (MAA, 1998) has supported an increase in the importance placed on probability at the post-secondary level and the use of more active learning methods. To this end, it is recommended that statistics instruction relies less on lecturing and more on active learning that uses group problem-solving, activities and discussions (Cobb, 2000) . Given that curriculum reform has brought data handling to the forefront, less emphasis should be placed on\"formal\" probability and\"an empirical frequency-based approach to probability that is also an important foundation for later work in theoretical probability\"should be used (Watson, 2006, p.127) .  \nWith regards to Cyprus – where this study took place - the results of TIMSS 2007 revealed that at the 8th grade level only 3% of class time was devoted to data and chance (Mullis, Martin, & Foy, 2008) . Topics relative to this domain are considered to be for the more able students and as such, only  \n􀀍 Lecturer, Michigan State Univeristy/University of Nicosia, USA/Cuprus.  \n[https://doi.org/10.30958/aje.4-3-1](https://doi.org/10.30958/aje.4-3-1) doi=10.30958/aje.4-3-1  \n3% of Cypriot 8th graders receive formal instruction in this domain; that is, this 3% of Cypriot students receive the 3% of instructional time devoted to data and chance. Given the importance of probability in everyday life and its recommended increased focus in school curricula, it is encouraging that the Ministry of Education and Culture in Cyprus (MoEC) has recently initiated educational reform efforts which include revisions to the national curriculum in grades K- 12 (MoEC, 2008) . In 2010, reports published by the MoEC of Cyprus regarding the intended curriculum in mathematics, introduced probability at the elementary school level with increased emphasis as students move through the grades.  \nIn the last couple of decades a considerable number of studies have been carried out on the teaching and learning of probability (Jones, Langrall, & Mooney, 2007) . However, most of this research relates to students’ thinking of probability with a minimal amount having been carried out relative to instructional methods (Hirsch & O’Donnell, 2001) . In addition, Shaughnessy (1992) indicated a lack of r","cbCaibdxgz6qlu3y","https://ap.wps.com/l/cbCaibdxgz6qlu3y","pdf",557481,12,"English","# Introduction\n## Purpose and Research Questions\n## Literature Review\n### Cooperative Learning and Student Achievement","[{\"question\":\"What was the main goal of the study?\",\"answer\":\"To examine the role of particular tasks implemented through two instructional methods and their effects on college students’ achievement in probability.\"},{\"question\":\"How were the instructional methods A and B different?\",\"answer\":\"Method A relied on lectures and small-group cooperative sessions where students solve textbook probability problems. Method B used lectures and cooperative sessions involving probability experiments that generate real data to connect experimental and theoretical probability.\"},{\"question\":\"What did the statistical tests show about students’ results?\",\"answer\":\"Wilcoxon results showed the control group’s multiple-choice scores were significantly lower on the post-test than the pre-test. Mann-Whitney results showed the treatment group had significantly different normalized gains from the control group and higher scores on open-ended post-test items.\"}]","Teaching College Probability for Higher Achievement - Study Results on Instructional Methods and Student Performance | PDF",1792075149]