{"id":132550,"date":"2024-08-29T13:37:12","date_gmt":"2024-08-29T10:37:12","guid":{"rendered":"https:\/\/azbuki.bg\/?p=132550"},"modified":"2024-09-03T11:09:26","modified_gmt":"2024-09-03T08:09:26","slug":"geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions","status":"publish","type":"post","link":"https:\/\/science.azbuki.bg\/en\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/","title":{"rendered":"GeoGebra Impact in Avoiding Common Mistakes Students Make in Handling Exponential Functions"},"content":{"rendered":"<p><strong>Shpresa Tuda, Shpetim Rexhepi<\/strong><br \/>\n<em>Mother Teresa University \u2013 Skopje (North Macedonia)<\/em><\/p>\n<p><a href=\"https:\/\/doi.org\/10.53656\/math2024-4-7-geo\" target=\"_blank\" rel=\"noopener\">https:\/\/doi.org\/10.53656\/math2024-4-7-geo<\/a><\/p>\n<p><strong>Abstract.<\/strong> Exponential functions, symbolized by f(x) = ax, represent fundamental mathematical concepts with extensive applications in real-world scenarios, ranging from population growth to compound interest and radioactive decay (Tuda &amp; Rexhepi 2023). This abstract highlights the significance of GeoGebra, an intuitive mathematical software, in interactive visualization and analysis, particularly in addressing common mistakes students make when engaging with exponential functions. Through its user-friendly interface, GeoGebra facilitates a hands-on approach to learning, offering students a practical and engaging environment to rectify misconceptions and deepen their understanding of the mathematical principles governing exponential functions.<br \/>\nThis study incorporates a comparative analysis of traditional and technological teaching methods, focused on 2nd-year students at high school \u201c8-Shtatori\u201d in Skopje. By evaluating the efficacy of both approaches in fostering a deeper comprehension of exponential functions, the outcomes contribute valuable insights into pedagogical strategies, shedding light on optimizing the learning experience for students grappling with exponential functions. Additionally, surveys and direct comparisons of solutions with students in the classroom setting provided firsthand observations on how learners interact with the material and identified common mistakes made during problem-solving. The insights gained from these surveys and discussions further informed the development and refinement of the approach, ensuring a comprehensive understanding of both the benefits and challenges associated with learning exponential functions through GeoGebra.<br \/>\nKeywords: exponential functions, analysis, students, GeoGebra<\/p>\n<a href=\"https:\/\/science.azbuki.bg\/en\/member-login\/\">Log in to read the full text<\/a>","protected":false},"excerpt":{"rendered":"<p>Shpresa Tuda, Shpetim Rexhepi Mother Teresa University \u2013 Skopje (North Macedonia) https:\/\/doi.org\/10.53656\/math2024-4-7-geo Abstract. Exponential functions, symbolized by f(x) = ax, represent fundamental mathematical concepts with extensive applications in real-world scenarios, ranging from population growth to compound interest and radioactive decay (Tuda &amp; Rexhepi 2023). This abstract highlights the significance of GeoGebra, an intuitive mathematical software, [&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":{"source_name":"","source_url":"","via_name":"","via_url":"","override_template":"0","override":[{"template":"1","single_blog_custom":"","parallax":"1","fullscreen":"1","layout":"right-sidebar","sidebar":"default-sidebar","second_sidebar":"default-sidebar","sticky_sidebar":"1","share_position":"bottom","share_float_style":"share-monocrhome","show_share_counter":"1","show_view_counter":"1","show_featured":"0","show_post_meta":"1","show_post_author":"1","show_post_author_image":"1","show_post_date":"1","post_date_format":"custom","post_date_format_custom":"d-m-Y","show_post_category":"1","show_post_reading_time":"0","post_reading_time_wpm":"300","show_zoom_button":"1","zoom_button_out_step":"2","zoom_button_in_step":"3","show_post_tag":"1","show_prev_next_post":"1","show_popup_post":"1","number_popup_post":"3","show_author_box":"0","show_post_related":"0","show_inline_post_related":"0"}],"override_image_size":"0","image_override":[{"single_post_thumbnail_size":"crop-500","single_post_gallery_size":"crop-500"}],"trending_post":"0","trending_post_position":"meta","trending_post_label":"Trending","sponsored_post":"0","sponsored_post_label":"Sponsored by","sponsored_post_name":"","sponsored_post_url":"","sponsored_post_logo_enable":"0","sponsored_post_logo":"","sponsored_post_desc":"","disable_ad":"0"},"jnews_primary_category":{"id":"","hide":""}},"categories":[1],"tags":[7601,7600,7598,4992],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>GeoGebra Impact in Avoiding Common Mistakes Students Make in Handling Exponential Functions - \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\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"GeoGebra Impact in Avoiding Common Mistakes Students Make in Handling Exponential Functions - \u0410\u0437-\u0431\u0443\u043a\u0438\" \/>\n<meta property=\"og:description\" content=\"Shpresa Tuda, Shpetim Rexhepi Mother Teresa University \u2013 Skopje (North Macedonia) https:\/\/doi.org\/10.53656\/math2024-4-7-geo Abstract. Exponential functions, symbolized by f(x) = ax, represent fundamental mathematical concepts with extensive applications in real-world scenarios, ranging from population growth to compound interest and radioactive decay (Tuda &amp; Rexhepi 2023). This abstract highlights the significance of GeoGebra, an intuitive mathematical software, [&hellip;]\" \/>\n<meta property=\"og:url\" content=\"https:\/\/science.azbuki.bg\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/\" \/>\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=\"2024-08-29T10:37:12+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-03T08:09:26+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\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/science.azbuki.bg\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/\"},\"author\":{\"name\":\"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c\",\"@id\":\"https:\/\/mathinfo.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd\"},\"headline\":\"GeoGebra Impact in Avoiding Common Mistakes Students Make in Handling Exponential Functions\",\"datePublished\":\"2024-08-29T10:37:12+00:00\",\"dateModified\":\"2024-09-03T08:09:26+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/science.azbuki.bg\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/\"},\"wordCount\":275,\"publisher\":{\"@id\":\"https:\/\/mathinfo.azbuki.bg\/en\/#organization\"},\"keywords\":[\"analysis\",\"exponential functions\",\"GeoGebra\",\"students\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/science.azbuki.bg\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/\",\"url\":\"https:\/\/science.azbuki.bg\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/\",\"name\":\"GeoGebra Impact in Avoiding Common Mistakes Students Make in Handling Exponential Functions - 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Exponential functions, symbolized by f(x) = ax, represent fundamental mathematical concepts with extensive applications in real-world scenarios, ranging from population growth to compound interest and radioactive decay (Tuda &amp; Rexhepi 2023). This abstract highlights the significance of GeoGebra, an intuitive mathematical software, [&hellip;]","og_url":"https:\/\/science.azbuki.bg\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/","og_site_name":"\u0410\u0437-\u0431\u0443\u043a\u0438","article_publisher":"https:\/\/www.facebook.com\/Azbuki55\/","article_published_time":"2024-08-29T10:37:12+00:00","article_modified_time":"2024-09-03T08:09:26+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\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/#article","isPartOf":{"@id":"https:\/\/science.azbuki.bg\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/"},"author":{"name":"\u201e\u0410\u0437-\u0431\u0443\u043a\u0438\u201c","@id":"https:\/\/mathinfo.azbuki.bg\/en\/#\/schema\/person\/de220d282eaa494f914ce0fd838645dd"},"headline":"GeoGebra Impact in Avoiding Common Mistakes Students Make in Handling Exponential Functions","datePublished":"2024-08-29T10:37:12+00:00","dateModified":"2024-09-03T08:09:26+00:00","mainEntityOfPage":{"@id":"https:\/\/science.azbuki.bg\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/"},"wordCount":275,"publisher":{"@id":"https:\/\/mathinfo.azbuki.bg\/en\/#organization"},"keywords":["analysis","exponential functions","GeoGebra","students"],"inLanguage":"en-US"},{"@type":"WebPage","@id":"https:\/\/science.azbuki.bg\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/","url":"https:\/\/science.azbuki.bg\/uncategorized\/geogebra-impact-in-avoiding-common-mistakes-students-make-in-handling-exponential-functions\/","name":"GeoGebra Impact in Avoiding Common Mistakes Students Make in Handling Exponential Functions - 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