{"id":4512,"date":"2022-04-13T14:05:04","date_gmt":"2022-04-13T14:05:04","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&#038;p=4512"},"modified":"2022-05-17T18:33:00","modified_gmt":"2022-05-17T18:33:00","slug":"instructor-guide-6c-forming-connections","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/instructor-guide-6c-forming-connections\/","title":{"raw":"Instructor Guide 6C: Forming Connections","rendered":"Instructor Guide 6C: Forming Connections"},"content":{"raw":"<h2>Overview<\/h2>\r\n<ul>\r\n \t<li>In this in-class activity, students will use [latex]R^{2}[\/latex] to evaluate how well different explanatory\u00a0variables predict a response variable of interest (using linear models). Then, they will be\r\nasked to broaden their understanding with respect to correlation and causation.<\/li>\r\n \t<li>Students will use a mock dataset representing different predictors of student test scores in a large school district. The dataset is simulated due to privacy concerns with real student data but its results are representative of results that real school districts have found when studying these variables. The policies discussed in the activity and their results are likewise representative of policies that real school districts have implemented.<\/li>\r\n \t<li>This activity connects back to evaluating the strength of linear relationships, and prepares students for evaluating whether a linear model is appropriate for a set of\u00a0bivariate data.<\/li>\r\n \t<li><span style=\"background-color: #ffff99;\">[a list of tags like S2, O1, B1, V3] \u2190 Link to EBTP descriptions\u00a0<\/span><\/li>\r\n<\/ul>\r\n<h3>Prerequisite assumptions<\/h3>\r\nStudents should be able to do each of the following after completing the <em>What to Know<\/em> assignment.\r\n<ul>\r\n \t<li>Develop intuition about how [latex]R^{2}[\/latex] is related to the shape of a scatterplot.<\/li>\r\n \t<li>Identify variable types (explanatory and response) and plot data in a scatterplot.<\/li>\r\n \t<li>Use technology to calculate [latex]R^{2}[\/latex].<\/li>\r\n \t<li>Interpret the meaning of [latex]R^{2}[\/latex] in context.<\/li>\r\n \t<li>Identify possible values of [latex]R^{2}[\/latex].<\/li>\r\n<\/ul>\r\n<h3>Intended goals for this activity<\/h3>\r\nAfter completing this activity, students should understand that\u00a0[latex]R^{2}[\/latex] is a measure of prediction strength in a linear relationship, and that a high\u00a0[latex]R^{2}[\/latex] value does\u00a0<em>not<\/em> indicated a causal relationship. They should understand that\u00a0[latex]R^{2}[\/latex] can be interpreted as the percentage of variation in the response variable explained by the linear relationship with an explanatory variable. They should be able to interpret\u00a0[latex]R^{2}[\/latex] values and determine their utility in different tasks (gauging prediction strength vs. determining a causal relationship).\r\n<h2>Synchronous Delivery and Activity Flow<\/h2>\r\nThe sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.\r\n<h3>Frame the activity (3 minutes)<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Question 1 -- Think-Pair-Share\u00a0\u00a0S2, C4, V1, V4, O3\r\n<ul>\r\n \t<li aria-level=\"1\">Have students read Question 1 independently then discuss their answers in pairs before sharing with the class.<\/li>\r\n \t<li aria-level=\"1\">Transition to the activity by briefly discussing the Objectives for the activity.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h3>Activity Flow (20 minutes)<\/h3>\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Question 2 - 4 -- Working in pairs or small groups\u00a0V1, V4, O3, S2, C6\r\n<ul>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Pull the class together to discuss Question 2 before moving on the Questions 3 (since Question 3 may give away the responses for Question 2).<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li aria-level=\"1\">Questions 5 and 6 -- Whole Class Discussion\u00a0\u00a0S4, C3, V1, O1, B2, B4\r\n<ul>\r\n \t<li aria-level=\"1\">Question 5\r\n<ul>\r\n \t<li aria-level=\"1\">Give students time to independently think and write their\u00a0responses. Then:\r\n<ul>\r\n \t<li aria-level=\"1\">First: Ask for a student who thinks the attendance policy is\u00a0best to share their thoughts.<\/li>\r\n \t<li aria-level=\"1\">Second: Ask students if they think there is any reason to\u00a0believe an attendance policy wouldn\u2019t work. Allow for think\u00a0time before asking students to answer this follow-up\u00a0question.<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li aria-level=\"1\">Question 6\r\n<ul>\r\n \t<li aria-level=\"1\">Have students answer this question in their pairs\/groups, and then\u00a0ask several groups to share their answers with the whole class.\u00a0Ensure students include specific reasoning as to why attendance\u00a0may not be causally related to exam scores. Complete reasoning\u00a0would include examples of alternative causal mechanisms that\u00a0result in a correlation between attendance and test scores.<\/li>\r\n \t<li aria-level=\"1\">To add emphasis to explanations of confounding, show and ask a student to explain the following causal graph: [<span style=\"background-color: #ffff99;\">link to the graph found in DC instructor guide<\/span>]<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<\/li>\r\n<\/ul>\r\n<h3>Wrap-up\/transition (2 minutes)<\/h3>\r\n<ul>\r\n \t<li>Consider drawing various bivariate relationships on the board\u00a0(positive and negative associations) and asking students which will\u00a0have the lowest\/highest [latex]R^{2}[\/latex] values.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Have students refer back to the Objectives for the activity and\u00a0check the ones they recognize.<\/li>\r\n \t<li style=\"font-weight: 400;\" aria-level=\"1\">Assign the homework or\u00a0<em>Practice<\/em>\u00a0and any <em>What to Know<\/em> pages for the <em>Forming Connections<\/em> activities you plan to complete in the next class meeting. <span style=\"background-color: #ffff99;\">C2<\/span><\/li>\r\n<\/ul>","rendered":"<h2>Overview<\/h2>\n<ul>\n<li>In this in-class activity, students will use [latex]R^{2}[\/latex] to evaluate how well different explanatory\u00a0variables predict a response variable of interest (using linear models). Then, they will be<br \/>\nasked to broaden their understanding with respect to correlation and causation.<\/li>\n<li>Students will use a mock dataset representing different predictors of student test scores in a large school district. The dataset is simulated due to privacy concerns with real student data but its results are representative of results that real school districts have found when studying these variables. The policies discussed in the activity and their results are likewise representative of policies that real school districts have implemented.<\/li>\n<li>This activity connects back to evaluating the strength of linear relationships, and prepares students for evaluating whether a linear model is appropriate for a set of\u00a0bivariate data.<\/li>\n<li><span style=\"background-color: #ffff99;\">[a list of tags like S2, O1, B1, V3] \u2190 Link to EBTP descriptions\u00a0<\/span><\/li>\n<\/ul>\n<h3>Prerequisite assumptions<\/h3>\n<p>Students should be able to do each of the following after completing the <em>What to Know<\/em> assignment.<\/p>\n<ul>\n<li>Develop intuition about how [latex]R^{2}[\/latex] is related to the shape of a scatterplot.<\/li>\n<li>Identify variable types (explanatory and response) and plot data in a scatterplot.<\/li>\n<li>Use technology to calculate [latex]R^{2}[\/latex].<\/li>\n<li>Interpret the meaning of [latex]R^{2}[\/latex] in context.<\/li>\n<li>Identify possible values of [latex]R^{2}[\/latex].<\/li>\n<\/ul>\n<h3>Intended goals for this activity<\/h3>\n<p>After completing this activity, students should understand that\u00a0[latex]R^{2}[\/latex] is a measure of prediction strength in a linear relationship, and that a high\u00a0[latex]R^{2}[\/latex] value does\u00a0<em>not<\/em> indicated a causal relationship. They should understand that\u00a0[latex]R^{2}[\/latex] can be interpreted as the percentage of variation in the response variable explained by the linear relationship with an explanatory variable. They should be able to interpret\u00a0[latex]R^{2}[\/latex] values and determine their utility in different tasks (gauging prediction strength vs. determining a causal relationship).<\/p>\n<h2>Synchronous Delivery and Activity Flow<\/h2>\n<p>The sample activity delivery below assumes a face-to-face class meeting but can be adapted to a fully online or hybrid delivery by using break-out rooms for pairs and small groups.<\/p>\n<h3>Frame the activity (3 minutes)<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Question 1 &#8212; Think-Pair-Share\u00a0\u00a0S2, C4, V1, V4, O3\n<ul>\n<li aria-level=\"1\">Have students read Question 1 independently then discuss their answers in pairs before sharing with the class.<\/li>\n<li aria-level=\"1\">Transition to the activity by briefly discussing the Objectives for the activity.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>Activity Flow (20 minutes)<\/h3>\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Question 2 &#8211; 4 &#8212; Working in pairs or small groups\u00a0V1, V4, O3, S2, C6\n<ul>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Pull the class together to discuss Question 2 before moving on the Questions 3 (since Question 3 may give away the responses for Question 2).<\/li>\n<\/ul>\n<\/li>\n<li aria-level=\"1\">Questions 5 and 6 &#8212; Whole Class Discussion\u00a0\u00a0S4, C3, V1, O1, B2, B4\n<ul>\n<li aria-level=\"1\">Question 5\n<ul>\n<li aria-level=\"1\">Give students time to independently think and write their\u00a0responses. Then:\n<ul>\n<li aria-level=\"1\">First: Ask for a student who thinks the attendance policy is\u00a0best to share their thoughts.<\/li>\n<li aria-level=\"1\">Second: Ask students if they think there is any reason to\u00a0believe an attendance policy wouldn\u2019t work. Allow for think\u00a0time before asking students to answer this follow-up\u00a0question.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<li aria-level=\"1\">Question 6\n<ul>\n<li aria-level=\"1\">Have students answer this question in their pairs\/groups, and then\u00a0ask several groups to share their answers with the whole class.\u00a0Ensure students include specific reasoning as to why attendance\u00a0may not be causally related to exam scores. Complete reasoning\u00a0would include examples of alternative causal mechanisms that\u00a0result in a correlation between attendance and test scores.<\/li>\n<li aria-level=\"1\">To add emphasis to explanations of confounding, show and ask a student to explain the following causal graph: [<span style=\"background-color: #ffff99;\">link to the graph found in DC instructor guide<\/span>]<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h3>Wrap-up\/transition (2 minutes)<\/h3>\n<ul>\n<li>Consider drawing various bivariate relationships on the board\u00a0(positive and negative associations) and asking students which will\u00a0have the lowest\/highest [latex]R^{2}[\/latex] values.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Have students refer back to the Objectives for the activity and\u00a0check the ones they recognize.<\/li>\n<li style=\"font-weight: 400;\" aria-level=\"1\">Assign the homework or\u00a0<em>Practice<\/em>\u00a0and any <em>What to Know<\/em> pages for the <em>Forming Connections<\/em> activities you plan to complete in the next class meeting. <span style=\"background-color: #ffff99;\">C2<\/span><\/li>\n<\/ul>\n","protected":false},"author":25777,"menu_order":6,"template":"","meta":{"_candela_citation":"[]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-4512","chapter","type-chapter","status-publish","hentry"],"part":4483,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4512","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/users\/25777"}],"version-history":[{"count":5,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4512\/revisions"}],"predecessor-version":[{"id":4771,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4512\/revisions\/4771"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/parts\/4483"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4512\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4512"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4512"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4512"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4512"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}