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The activity, presented as a pictorial/geometric linear pattern of counting dots, is analyzed from a student-oriented perspective to understand how learners perceive their own generalizing actions. Findings identify two broad categories of variable use: whether students view the variable as a generalized number or not. Results also show variables may be treated as linked to a referred object, as superfluous, or as constant, and equivalence proved difficult to grasp.",{"@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/the-use-of-variables-in-a-patterning-activity-counting-dots/599014/",{"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/the-use-of-variables-in-a-patterning-activity-counting-dots/599014.png","ImageObject",300,407,{"name":92,"@type":93},"jay","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-01","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":14},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What kind of patterning activity does the paper study?","Question",{"text":112,"@type":113},"It studies a pictorial/geometric linear pattern activity where students count dots to engage in pattern generalisation.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do students use variables according to the paper’s analysis?",{"text":117,"@type":113},"Students’ variable use falls into two broad categories: treating the variable as a generalized number or not.",{"name":119,"@type":110,"acceptedAnswer":120},"What difficulties did students have with variables?",{"text":121,"@type":113},"Equivalence, an important step toward understanding variables, proved difficult for students to grasp.","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},599014,1792316722,{"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":14,"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":36},3985747858866,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","doi: 10.26529/cepsj.309  \nThe Use of Variables in a Patterning Activity: Counting Dots  \nBożena Maj-Tatsis*1 and Konstantinos Tatsis2  \n• The present paper examines a patterning activity that was organised within a teaching experiment in order to analyse the different uses of variables by secondary school students. The activity presented in the paper can be categorised as a pictorial/geometric linear pattern. We adopted a student-oriented perspective for our analysis, in order to grasp how students perceive their own generalising actions. The analysis of our data led us to two broad categories for variable use, according to whether the variable is viewed as a generalised number or not. Our results also show that students sometimes treat the variable as closely linked to a referred object, as a superfluous entity or as a constant. Finally, the notion of equivalence, which is an important step towards understanding variables, proved difficult for our students to grasp.  \nKeywords: generalisation, patterning activity, variable  \n1 *Corresponding Author. University of Rzeszow, Department of Mathematics and Natural Sciences, Poland; [bmaj@ur.edu.pl](bmaj@ur.edu.pl).  \n2 University of Ioannina, Department of Primary Education, Greece.  \nUporaba spremenljivk pri zaporedjih: štetje pik  \nBożena Maj-Tatsis in Konstantinos Tatsis  \n• Prispevek prikazuje, kako dijaki interpretirajo različna zaporedja pik. Zanimalo nas je, kako znajo uporabljati spremenljivke pri zapisovanjusplošnega pravila zaporedja. Aktivnost, v katero so bili vključeni dijaki, je imela s pikami predstavljena zaporedja geometrijskih oblik. Vraziskavi smo se osredinili na posameznega dijaka z namenom, da bi bolje razumeli, kako dijaki oblikujejo posplošitve. Analiza podatkov nas je pripeljala do dveh kategorij uporabe spremenljivk pri dijakih, in sicerali so jo uporabljali kot zapis za poljubno/splošno število ali ne. Naši podatki tudi kažejo, da dijaki spremenljivko obravnavajo v tesni povezavi znarisanim členom v zaporedju, ali kot konstanto, ali pa ji pripišejo nepomemben pomen. Pokazalo se je še, da je ideja enakosti, ki je pomembnav procesu razumevanja spremenljivk, dijakom težko razumljiva.  \nKljučne besede: posploševanje, aktivnosti z zaporedji, spremenljivka  \nIntroduction  \nThe use of variables is a process closely linked to algebraic knowledge, a link that is manifested in many different ways in mathematics teaching and learning. Students encounter variables as early as in their first years of schooling, sometimes in the form of empty boxes signifying the unknowns of an equation. Later, still in the primary school years, students experience the use of letters to signify the elements ofa geometrical figure, usually in the formulas that are used to designate the figure’s perimeter or area. However, the use of variables becomes really significant in secondary education, when students are expected to be able to create, understand and manipulate symbolic expressions, while at the sametime having an ability to “generalize patterns using explicitly defined and recursively defined functions” (NCTM 2000, p. 296). Thus, a “patterning approach”, especially in a figural form, has been proposed as a fruitful way to introduce even young students to the notion of the variable: “Figural growing patterns and reallife contexts for developing knowledge of variables seem most suitable to support younger students’ conceptual learning and their ability to reason algebraically and express generalizations symbolically.”(Wilkie, 2016, pp. 353–354)  \nWhat, then, are the actions to be performed in a patterning activity? A patterning activity usually begins with a (free or guided) exploration by the students, followed by discussion and comparisons that are expected to lead them to a general rule (or a set of rules) to describe their pattern. The “linearity” of actions implied in the previous description should not be taken literally; Rivera (2010) eloquently describes the following indep","cbCaigjnKcfFnWYC","https://ap.wps.com/l/cbCaigjnKcfFnWYC","pdf",458137,16,"English","# Introduction\n## Theoretical Framework: Patterning Activities and the Use of Variables","[{\"question\":\"What kind of patterning activity does the paper study?\",\"answer\":\"It studies a pictorial/geometric linear pattern activity where students count dots to engage in pattern generalisation.\"},{\"question\":\"How do students use variables according to the paper’s analysis?\",\"answer\":\"Students’ variable use falls into two broad categories: treating the variable as a generalized number or not.\"},{\"question\":\"What difficulties did students have with variables?\",\"answer\":\"Equivalence, an important step toward understanding variables, proved difficult for students to grasp.\"}]","The Use of Variables in a Patterning Activity - Counting Dots | PDF",1792088011]