{"id":165973,"date":"2025-09-25T15:59:19","date_gmt":"2025-09-25T12:59:19","guid":{"rendered":"https:\/\/azbuki.bg\/?p=165973"},"modified":"2025-10-06T09:51:55","modified_gmt":"2025-10-06T06:51:55","slug":"bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets","status":"publish","type":"post","link":"https:\/\/bel.azbuki.bg\/en\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/","title":{"rendered":"Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets"},"content":{"rendered":"<p><strong>D\u00e1vid Paksi<sup>1)<\/sup>, M\u00e1rk Cs\u00f3ka<sup>1)<\/sup>, Szil\u00e1rd Svitek<sup>2)<br \/>\n<\/sup><\/strong><em><sup>1)<\/sup><\/em><em>Department of Informatics, J. Selye University \u2013 Kom\u00e1rno (Slovakia)<br \/>\n<sup>2)<\/sup>Department of Mathematics, J. Selye University \u2013 Kom\u00e1rno (Slovakia)<\/em><\/p>\n<p><a href=\"https:\/\/doi.org\/10.53656\/math2025-4-6-bgp\" target=\"_blank\" rel=\"noopener\">https:\/\/doi.org\/10.53656\/math2025-4-6-bgp<\/a><\/p>\n<p><strong>Abstract<\/strong>. The widespread use of information and communication technologies (ICT) offers new opportunities in many topics of mathematics education. As science and technology are constantly evolving, information technology is becoming increasingly intertwined with education. Modeling, simulation and visualization are already proven methods in teaching subjects such as physics, chemistry or engineering. These methods can help students see connections more clearly and develop their creative thinking. This paper aims to further explore this direction in the field of mathematics education, with focus on differential equations. We chose spreadsheets as our tool to calculate and visualize the processes described by differential equations. We demonstrate a wide range of applications of differential equations through real-life examples, such as in modeling physical, biological, and economic processes. This method provides students with a better understanding of the practical usefulness and applicability of these equations. The study thus shows how integrating ICT into mathematics education can help students gain a deeper understanding of the underlying mathematical concepts and improve their mathematical thinking and problem-solving skills. ICT tools enable teachers to use interactive and engaging teaching methods, resulting in an exciting and practical education for students. This paper outlines the potential of ICT in mathematics education, with a focus on the use of spreadsheets for modeling and visualization. It highlights the benefits of integrating technology into the classroom to enhance student learning and engagement.<\/p>\n<p><em>Keywords: <\/em>mathematics education, spreadsheets, differential equations, interdisciplinary education, advanced uses of ICT, real-world problems<\/p>\n<a href=\"https:\/\/bel.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>","protected":false},"excerpt":{"rendered":"<p>D\u00e1vid Paksi1), M\u00e1rk Cs\u00f3ka1), Szil\u00e1rd Svitek2) 1)Department of Informatics, J. Selye University \u2013 Kom\u00e1rno (Slovakia) 2)Department of Mathematics, J. Selye University \u2013 Kom\u00e1rno (Slovakia) https:\/\/doi.org\/10.53656\/math2025-4-6-bgp Abstract. The widespread use of information and communication technologies (ICT) offers new opportunities in many topics of mathematics education. As science and technology are constantly evolving, information technology is becoming [&hellip;]<\/p>","protected":false},"author":124332423427287,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jnews-multi-image_gallery":[],"jnews_single_post":[],"jnews_primary_category":[]},"categories":[1],"tags":[13483,13481,13482,10633,13484,13480],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets - \u0410\u0437-\u0431\u0443\u043a\u0438<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"D\u00e1vid Paksi1), M\u00e1rk Cs\u00f3ka1), Szil\u00e1rd Svitek2) 1)Department of Informatics, J. Selye University \u2013 Kom\u00e1rno (Slovakia) 2)Department of Mathematics, J. Selye University \u2013 Kom\u00e1rno (Slovakia) https:\/\/doi.org\/10.53656\/math2025-4-6-bgp Abstract. The widespread use of information and communication technologies (ICT) offers new opportunities in many topics of mathematics education. As science and technology are constantly evolving, information technology is becoming [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/\" \/>\n<meta property=\"og:site_name\" content=\"\u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/Azbuki55\/\" \/>\n<meta property=\"article:published_time\" content=\"2025-09-25T12:59:19+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2025-10-06T06:51:55+00:00\" \/>\n<meta name=\"author\" content=\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/\"},\"author\":{\"name\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd\"},\"headline\":\"Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets\",\"datePublished\":\"2025-09-25T12:59:19+00:00\",\"dateModified\":\"2025-10-06T06:51:55+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/\"},\"wordCount\":315,\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"keywords\":[\"advanced uses of ICT\",\"differential equations\",\"interdisciplinary education\",\"mathematics education\",\"real-world problems\",\"spreadsheets\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/\",\"url\":\"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/\",\"name\":\"Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets - \u0410\u0437-\u0431\u0443\u043a\u0438\",\"isPartOf\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#website\"},\"datePublished\":\"2025-09-25T12:59:19+00:00\",\"dateModified\":\"2025-10-06T06:51:55+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/strategies.azbuki.bg\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#website\",\"url\":\"https:\/\/vocedu.azbuki.bg\/en\/\",\"name\":\"\u0410\u0437-\u0431\u0443\u043a\u0438\",\"description\":\"\u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0438\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e \u0437\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u043d\u0430\u0443\u043a\u0430\",\"publisher\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/vocedu.azbuki.bg\/en\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#organization\",\"name\":\"\u0410\u0437-\u0431\u0443\u043a\u0438\",\"url\":\"https:\/\/vocedu.azbuki.bg\/en\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png\",\"contentUrl\":\"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png\",\"width\":250,\"height\":70,\"caption\":\"\u0410\u0437-\u0431\u0443\u043a\u0438\"},\"image\":{\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.facebook.com\/Azbuki55\/\",\"https:\/\/www.instagram.com\/nion_azbuki\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd\",\"name\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g\",\"caption\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\"},\"sameAs\":[\"https:\/\/azbuki.bg\/\"],\"url\":\"https:\/\/bel.azbuki.bg\/en\/author\/azbuki_ekip\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets - \u0410\u0437-\u0431\u0443\u043a\u0438","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/","og_locale":"en_US","og_type":"article","og_title":"Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets - \u0410\u0437-\u0431\u0443\u043a\u0438","og_description":"D\u00e1vid Paksi1), M\u00e1rk Cs\u00f3ka1), Szil\u00e1rd Svitek2) 1)Department of Informatics, J. Selye University \u2013 Kom\u00e1rno (Slovakia) 2)Department of Mathematics, J. Selye University \u2013 Kom\u00e1rno (Slovakia) https:\/\/doi.org\/10.53656\/math2025-4-6-bgp Abstract. The widespread use of information and communication technologies (ICT) offers new opportunities in many topics of mathematics education. As science and technology are constantly evolving, information technology is becoming [&hellip;]","og_url":"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/","og_site_name":"\u0410\u0437-\u0431\u0443\u043a\u0438","article_publisher":"https:\/\/www.facebook.com\/Azbuki55\/","article_published_time":"2025-09-25T12:59:19+00:00","article_modified_time":"2025-10-06T06:51:55+00:00","author":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","twitter_card":"summary_large_image","twitter_misc":{"Written by":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/#article","isPartOf":{"@id":"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/"},"author":{"name":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd"},"headline":"Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets","datePublished":"2025-09-25T12:59:19+00:00","dateModified":"2025-10-06T06:51:55+00:00","mainEntityOfPage":{"@id":"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/"},"wordCount":315,"publisher":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#organization"},"keywords":["advanced uses of ICT","differential equations","interdisciplinary education","mathematics education","real-world problems","spreadsheets"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/","url":"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/","name":"Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets - \u0410\u0437-\u0431\u0443\u043a\u0438","isPartOf":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#website"},"datePublished":"2025-09-25T12:59:19+00:00","dateModified":"2025-10-06T06:51:55+00:00","breadcrumb":{"@id":"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/science.azbuki.bg\/uncategorized\/bridging-the-gap-a-pedagogical-tool-for-teaching-mathematical-modeling-with-spreadsheets\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/strategies.azbuki.bg\/"},{"@type":"ListItem","position":2,"name":"Bridging the Gap: A Pedagogical Tool for Teaching Mathematical Modeling with Spreadsheets"}]},{"@type":"WebSite","@id":"https:\/\/vocedu.azbuki.bg\/en\/#website","url":"https:\/\/vocedu.azbuki.bg\/en\/","name":"\u0410\u0437-\u0431\u0443\u043a\u0438","description":"\u041d\u0430\u0446\u0438\u043e\u043d\u0430\u043b\u043d\u043e \u0438\u0437\u0434\u0430\u0442\u0435\u043b\u0441\u0442\u0432\u043e \u0437\u0430 \u043e\u0431\u0440\u0430\u0437\u043e\u0432\u0430\u043d\u0438\u0435 \u0438 \u043d\u0430\u0443\u043a\u0430","publisher":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/vocedu.azbuki.bg\/en\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/vocedu.azbuki.bg\/en\/#organization","name":"\u0410\u0437-\u0431\u0443\u043a\u0438","url":"https:\/\/vocedu.azbuki.bg\/en\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/","url":"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png","contentUrl":"https:\/\/azbuki.bg\/wp-content\/uploads\/2019\/04\/logo-azbuki-e1580374651845.png","width":250,"height":70,"caption":"\u0410\u0437-\u0431\u0443\u043a\u0438"},"image":{"@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/Azbuki55\/","https:\/\/www.instagram.com\/nion_azbuki\/"]},{"@type":"Person","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd","name":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/vocedu.azbuki.bg\/en\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/d08ccbd951212deb604aa2d403575d4e?s=96&d=mm&r=g","caption":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c"},"sameAs":["https:\/\/azbuki.bg\/"],"url":"https:\/\/bel.azbuki.bg\/en\/author\/azbuki_ekip\/"}]}},"_links":{"self":[{"href":"https:\/\/bel.azbuki.bg\/en\/wp-json\/wp\/v2\/posts\/165973"}],"collection":[{"href":"https:\/\/bel.azbuki.bg\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/bel.azbuki.bg\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/bel.azbuki.bg\/en\/wp-json\/wp\/v2\/users\/124332423427287"}],"replies":[{"embeddable":true,"href":"https:\/\/bel.azbuki.bg\/en\/wp-json\/wp\/v2\/comments?post=165973"}],"version-history":[{"count":4,"href":"https:\/\/bel.azbuki.bg\/en\/wp-json\/wp\/v2\/posts\/165973\/revisions"}],"predecessor-version":[{"id":167231,"href":"https:\/\/bel.azbuki.bg\/en\/wp-json\/wp\/v2\/posts\/165973\/revisions\/167231"}],"wp:attachment":[{"href":"https:\/\/bel.azbuki.bg\/en\/wp-json\/wp\/v2\/media?parent=165973"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/bel.azbuki.bg\/en\/wp-json\/wp\/v2\/categories?post=165973"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/bel.azbuki.bg\/en\/wp-json\/wp\/v2\/tags?post=165973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}