{"id":830,"date":"2024-07-25T12:51:50","date_gmt":"2024-07-25T12:51:50","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=830"},"modified":"2024-09-30T15:07:45","modified_gmt":"2024-09-30T15:07:45","slug":"teaching-algebra-chapter-6-functions","status":"publish","type":"page","link":"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-algebra\/teaching-algebra-chapter-6-functions\/","title":{"rendered":"Teaching Algebra Chapter 6-Functions"},"content":{"rendered":"\n<p class=\"has-text-color has-link-color wp-elements-d4048526092fa8e41c9ded574ea937cc wp-block-paragraph\" style=\"color:#d14905\"><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/teaching-algebra\/\" data-type=\"page\" data-id=\"71\">Teaching Algebra<\/a> &gt; Chapter 6<\/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-e486ed95ce9490a7b4e4621ba4f4a4b8 has-global-padding is-layout-constrained wp-container-core-group-is-layout-e7ee615e 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-7bc61772 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-bc18b00a 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-17e9b11e 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=\"padding-top:0;padding-bottom:0;padding-left:var(--wp--preset--spacing--10);padding-right:var(--wp--preset--spacing--10);height:150px\" class=\"alignleft wp-block-post-featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"250\" height=\"252\" src=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/alg_page_logo_250x252.png\" class=\"attachment-post-thumbnail size-post-thumbnail wp-post-image\" alt=\"\" style=\"height:150px;object-fit:contain;\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/alg_page_logo_250x252.png 250w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/alg_page_logo_250x252-150x150.png 150w\" sizes=\"auto, (max-width: 250px) 100vw, 250px\" \/><\/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 6-Functions<\/h2><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\">Research around the teaching and learning of function has shown that students have difficulty defining and identifying functions. Students (and teachers) tend to focus on function as either just formulas or \u201cgraphs\u201d that \u201cpass the vertical line test,\u201d rather than the relationships represented. In this chapter, teachers examine definitions of function as well as representations of function using both dynamic algebra and dynamic geometry environments.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-text-color has-base-2-color has-alpha-channel-opacity has-base-2-background-color has-background is-style-wide\" \/>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"padding-right:0;padding-left:0;font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><img loading=\"lazy\" decoding=\"async\" width=\"56\" height=\"56\" src=\"https:\/\/lh7-us.googleusercontent.com\/docsz\/AD_4nXcjAd2LaOquLZl6f1QVpgTFIR0s-x34bYMeOj5KF22AC9imcETtmdweOx7T0KKEbvi6hPoKHHeOmirNbUmwGSZFMsa1rYA1i76c46HlNoe-0_QhuB83R-Btv18oQLTRuFQVQvdyy67SaTOI24g1orW2j8E_?key=_-Ah_2wP0wYww8pv4LkjOg\" alt=\"ESP Logo\"> This chapter could be used alongside a Module within the Examining Students&#8217; Practices (ESP) in Algebra and Function:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><strong><a href=\"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/esp-module-5-function-concept-functions-and-non-functions\/\" data-type=\"page\" data-id=\"774\">Module 5:<\/a>\u00a0<\/strong>The Function Concept- Functions and Non-Functions<\/p>\n<\/div>\n\n\n\n<div style=\"height:10px\" 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-180f4183 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-62b6bb24aa6e906b8074fd271a58ee42 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1Rk-DHUXr0zdpiOvw4gT89GsddhyvItuG\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Chapter Document<\/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\/015-camera-1.png\" alt=\"\" class=\"wp-image-636 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/015-camera-1.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/015-camera-1-150x150.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-46fa8186a15e66dc132f7cf9940e7576 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1RC6SmQwUDxB3AGLFH8Z4DbagJFGd08x7\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Video Transcripts<\/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\/014-download-2.png\" alt=\"\" class=\"wp-image-638 size-full\" srcset=\"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/014-download-2.png 256w, https:\/\/research.ced.ncsu.edu\/ptmt\/wp-content\/uploads\/sites\/21\/2024\/07\/014-download-2-150x150.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-936bbde7d06fba84498f6921fa97adbb wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1cHQ2tRk0zGj3wq3EztWRzcU7K4o0YIpg\/view?usp=drive_link\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Download Tech Files<\/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:10px\" 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-180f4183 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-441db1e7c4f642502d1eb8e36e106045 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1r_WkmPuvJX8RFHjguj7rr9DbuClHgIP3\/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-36429f0d6d9446910e5eddef1d0b0c82 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1GTDMfIdyiqq213nOEikd5njkBIeMf5CK\/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-737077c8aeb507aaef17856ea028a8b9 wp-block-paragraph\" style=\"font-size:clamp(0.984rem, 0.984rem + ((1vw - 0.2rem) * 0.86), 1.5rem);\"><a href=\"https:\/\/drive.google.com\/file\/d\/1RncLx35AKFmzQHlM0FSkK9zEDjccZRb9\/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","protected":false},"excerpt":{"rendered":"<p>Teaching Algebra &gt; Chapter 6 Research around the teaching and learning of function has shown that students have difficulty defining and identifying functions. Students (and teachers) tend to focus on function as either just formulas or \u201cgraphs\u201d that \u201cpass the vertical line test,\u201d rather than the relationships represented. In this chapter, teachers examine definitions of [&hellip;]<\/p>\n","protected":false},"author":66,"featured_media":651,"parent":71,"menu_order":6,"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-830","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/830","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=830"}],"version-history":[{"count":10,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/830\/revisions"}],"predecessor-version":[{"id":1878,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/830\/revisions\/1878"}],"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\/651"}],"wp:attachment":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media?parent=830"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}