{"id":795,"date":"2024-07-25T12:43:43","date_gmt":"2024-07-25T12:43:43","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=795"},"modified":"2024-09-29T22:10:25","modified_gmt":"2024-09-29T22:10:25","slug":"teaching-algebra-chapter-1-introduction-to-algebraic-technological-representations","status":"publish","type":"page","link":"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-algebra\/teaching-algebra-chapter-1-introduction-to-algebraic-technological-representations\/","title":{"rendered":"Teaching Algebra Chapter 1-Introduction to Algebraic Technological Representations"},"content":{"rendered":"\n<p class=\"has-text-color has-link-color wp-elements-a464e7b4176d81519b2d3940ab132b49\" style=\"color:#d14905\"><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-algebra\/\" data-type=\"page\" data-id=\"71\">Teaching Algebra<\/a> &gt; Chapter 1<\/p>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-group alignwide has-base-2-color has-text-color has-background has-link-color wp-elements-9141da12a0a5ad96edf4ba5447607523 has-global-padding is-layout-constrained wp-container-core-group-is-layout-9daa8ca1 wp-block-group-is-layout-constrained\" style=\"background-color:#d14905;margin-top:0;margin-bottom:0;padding-top:var(--wp--preset--spacing--10);padding-right:var(--wp--preset--spacing--10);padding-bottom:var(--wp--preset--spacing--10);padding-left:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-group alignwide has-background has-global-padding is-layout-constrained wp-container-core-group-is-layout-1be0671b wp-block-group-is-layout-constrained\" style=\"background-color:#d14905;padding-right:var(--wp--preset--spacing--10);padding-left:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-group alignwide is-vertical is-content-justification-center is-layout-flex wp-container-core-group-is-layout-ce155fab wp-block-group-is-layout-flex\">\n<div class=\"wp-block-columns has-base-2-color has-text-color has-background has-link-color wp-elements-5aade4b5c3938c0cdb5f5ba6bc0dbd7d is-layout-flex wp-container-core-columns-is-layout-28747e1f wp-block-columns-is-layout-flex\" style=\"background-color:#d14905;padding-top:0;padding-right:var(--wp--preset--spacing--10);padding-bottom:0;padding-left:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-column is-vertically-aligned-center is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:15%\"><figure style=\"height:150px; padding-top:0;padding-bottom:0;padding-left:var(--wp--preset--spacing--10);padding-right:var(--wp--preset--spacing--10);\" class=\"alignleft wp-block-post-featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"1305\" height=\"1318\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/05\/alg_page_logo.png\" class=\"attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" style=\"height:150px;object-fit:contain;\" \/><\/figure><\/div>\n\n\n\n<div class=\"wp-block-column is-vertically-aligned-top is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:85%\"><h2 style=\"background-color:#d14905; font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);font-style:normal;font-weight:800;\" class=\"has-link-color wp-elements-fbed58c1dcfb124481494af6efad93d2 wp-block-post-title has-text-color has-base-2-color has-background\">Teaching Algebra Chapter 1-Introduction to Algebraic Technological Representations<\/h2><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\">In this first chapter we have two goals. The first is to consider multiple representations of sequences of numbers and to use those representations to interpret the sequences and ultimately make some generalizations, making an explicit link between number and algebra. The second goal is to consider the ways that technology tools can enhance representations of number and patterns, by linking them in ways that cannot be done on paper; essentially making new, more descriptive representations. Teachers will become familiar with a variety of different features of dynamic environments, spreadsheets, and computer algebra systems and pedagogical issues that arise when students are using linked dynamic representations.<\/p>\n<\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center\" style=\"font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);\"><strong>Class Materials<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-group alignwide has-background has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"background-color:#d14905\">\n<div style=\"height:5px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-28b55a6e wp-block-columns-is-layout-flex\" style=\"padding-top:var(--wp--preset--spacing--10);padding-bottom:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile is-vertically-aligned-center\" style=\"margin-right:var(--wp--preset--spacing--60);margin-left:var(--wp--preset--spacing--60);padding-right:var(--wp--preset--spacing--60);padding-left:var(--wp--preset--spacing--60);grid-template-columns:18% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-2856e0e4ae5a514e19972b7dda9da195\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1bszy-UEZnjuRWsG8_-hBgM8SNpyAyrvV\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Chapter Document<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:20px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<h3 class=\"wp-block-heading has-text-align-center\" style=\"font-size:clamp(1.743rem, 1.743rem + ((1vw - 0.2rem) * 2.095), 3rem);\"><strong>Instructor Materials<\/strong><\/h3>\n\n\n\n<div class=\"wp-block-group alignwide has-background has-global-padding is-layout-constrained wp-block-group-is-layout-constrained\" style=\"background-color:#d14905\">\n<div style=\"height:5px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<div class=\"wp-block-columns alignwide is-layout-flex wp-container-core-columns-is-layout-28b55a6e wp-block-columns-is-layout-flex\" style=\"padding-top:var(--wp--preset--spacing--10);padding-bottom:var(--wp--preset--spacing--10)\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-3594c2f4ca0e4b691ebe70dcaa500dda\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1IZ2qgMwHsBk6kSspaCP4p_2lMAl3sUax\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Teaching Tips<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-b787ff5787c165b2769aea621100181c\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1Mgu5b3yFoKL_Q550s9i4zMAoSWSAfMZj\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Suggested Readings<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<div class=\"wp-block-media-text is-stacked-on-mobile\" style=\"grid-template-columns:22% auto\"><figure class=\"wp-block-media-text__media\"><img loading=\"lazy\" decoding=\"async\" width=\"256\" height=\"256\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png\" alt=\"\" class=\"wp-image-634 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/document_white-150x150.png 150w\" sizes=\"auto, (max-width: 256px) 100vw, 256px\" \/><\/figure><div class=\"wp-block-media-text__content\">\n<p class=\"has-base-2-color has-text-color has-link-color wp-elements-96caa59aeff32b8d364b847804421059\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1tgpJHtQTZZqMtgmj8_WGU_BiareSVC7N\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Sample Solutions<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<div style=\"height:50px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Teaching Algebra &gt; Chapter 1 In this first chapter we have two goals. The first is to consider multiple representations of sequences of numbers and to use those representations to interpret the sequences and ultimately make some generalizations, making an explicit link between number and algebra. The second goal is to consider the ways that [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":229,"parent":71,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"test-blank-page","meta":{"_acf_changed":false,"ncst_custom_author":"","ncst_show_custom_author":false,"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-795","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/795","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/users\/66"}],"replies":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/comments?post=795"}],"version-history":[{"count":18,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/795\/revisions"}],"predecessor-version":[{"id":1792,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/795\/revisions\/1792"}],"up":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/71"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media\/229"}],"wp:attachment":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media?parent=795"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}