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The study addresses low mathematics pass rates and wide variation in students’ backgrounds by building a test grounded in the pervasive mathematical idea of proportional reasoning, then pairing it with a clinical interview. The combination supports individualization, enabling teachers to adapt instruction to learners’ starting points and life-relevant conditions, improving access to mathematics.",{"@graph":69,"@context":114},[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/designing-a-research-based-detection-test-for-eliciting-students-prior-understanding-on-proportional-reasoning/588799/",{"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/designing-a-research-based-detection-test-for-eliciting-students-prior-understanding-on-proportional-reasoning/588799.png","ImageObject",300,407,{"name":92,"@type":93},"Chumphorn","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-03","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":29},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108],{"name":109,"@type":110,"acceptedAnswer":111},"How is proportional reasoning used in the test design?","Question",{"text":112,"@type":113},"Research findings on proportional reasoning are used to construct a test tailored to students with widely varying prior knowledge, followed by a clinical interview for additional insight.","Answer","https://schema.org",{"og:url":83,"og:type":116,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":118,"canonical":83},"index,follow",{"doc_id":120,"site_id":62},588799,1792171376,{"code":4,"msg":5,"data":123},{"doc_id":120,"user_id":124,"nickname":92,"user_avatar":125,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":126,"file_id":127,"file_url":128,"file_type":129,"file_size":130,"view_count":29,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":131,"language":132,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":133,"faqs":134,"seo_title":135,"seo_description":67,"update_tm":136,"read_time":137,"preview_page_count":4},2336475401981,"https://ap-avatar.wpscdn.com/avatar/22000c94efd8d5204d?x-image-process=image/resize,m_fixed,w_180,h_180&k=1786935347598174694","Designing a research-based detection test for eliciting students’ prior understanding on proportional reasoning  \nLinda Marie Ahl  \nKriminalvården and Stockholm University  \nStockholm, Sweden  \n\u003C[linda.ahl2@kriminalvarden.se](linda.ahl2@kriminalvarden.se)>  \nAbstract  \nIn the Swedish Prison Education Program only two out often reach a passing grade in their mathematics courses. Large variation in prior knowledge makes it difficult to meet the students at their level. This paper reports on a project aiming to enhance students’ possibilities to access mathematics through individualization. Research findings on the development of the pervasive mathematical idea of proportional reasoning are used to construct a test on proportional reasoning, designed to work specifically with students with large variation in prior knowledge. The test presented here, combined with a follow-up clinical interview, can be used in adult education in general as a basis for individualizing instruction.  \nKey words: proportional reasoning; adult education; prison; individualized instruction  \nIntroduction  \nAlready in 1968, Freudenthal drew attention to the inequity of an unbalanced mathematics education system that provides mathematics education to only a small group of citizens who “fit” within the system. He proposed that instead of worrying that the highest level may be too low for the gifted students, we should strive for educational justice for all people in society. Educational injustice is particularly prominent in mathematics (Stinson, 2004). The illusion that mathematics is only for people with special gifts has lived on for at least 2300 years, as illustrated by Plato’s claim that “We shall persuade those who are to perform high functions in the city to undertake calculation, but not as amateurs.”(Plato, trans. 1996, p. 219) . In our modern society, mathematics acts as a key for passing through the gates to economic access, full citizenship, and higher education (Stinson, 2004) . This gatekeeping function makes equitable access to mathematics education a question of democracy. To enhance democracy, mathematics needs to be an inclusive instrument for empowerment rather than an exclusive instrument for stratification. Instead, in most school systems, some students become disqualified from mathematics while others qualify (Jurdak et al., 2016; Popkewitz, 2002) . When these disqualified students return to mathematics as adults we cannot expect success by repeating educational practices that did not work in their past. Therefore, an equitable access to mathematics education for such a disadvantaged group needs to acknowledge not only prior knowledge, but also life conditions alongside personal study narratives.  \nThe Swedish prison education program is an educational environment where students with without an upper secondary diploma cluster. Close to 50 % of the prisoners lacks an upper secondary diploma (Riksrevsionen, 2015). In the prison education program a second chance to obtain this diploma is provided. Nevertheless, only two out often students pass their mathematics courses. This is disturbing in itself, but particularly in light of the resources available. The teachers are university trained upper secondary school mathematics teachers and the students sign up voluntarily. These conditions should  \nensure a high potential for effectiveness. However, the student group shows significant variation in age, ethnicity, socioeconomic and school backgrounds and life experience in general. These factors may account for such low pass rates, and justifies, a plausible reason to focus on such individualized differences.  \nIt is an unchallenged claim that teaching accounts for an individual's prior knowledge, his [1] life conditions and his rationale for studying mathematics have better prospects to succeed than a “one size fits all” teaching practice. When teaching adults returning to mathematics, such considerations are of particular importance. Given ","cbCaioHag6sJt8SS","https://ap.wps.com/l/cbCaioHag6sJt8SS","pdf",351105,17,"English","# Abstract\n# Introduction\n## Educational justice and inclusive access to mathematics\n## Adult return to mathematics and the need for individualization\n## Swedish prison education context and pass-rate challenges\n## Rationale for focusing on prior mathematical knowledge\n# Research-based detection test design (proportional reasoning)\n## Test requirements for vertical and horizontal information","[{\"question\":\"How is proportional reasoning used in the test design?\",\"answer\":\"Research findings on proportional reasoning are used to construct a test tailored to students with widely varying prior knowledge, followed by a clinical interview for additional insight.\"}]","Designing a research-based detection test for eliciting students’ prior understanding on proportional reasoning | PDF",1792065957,43]