{"id":4522,"date":"2022-04-13T14:06:46","date_gmt":"2022-04-13T14:06:46","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/?post_type=chapter&p=4522"},"modified":"2022-05-10T19:55:48","modified_gmt":"2022-05-10T19:55:48","slug":"instructor-guide-6c-corequisite-support","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/chapter\/instructor-guide-6c-corequisite-support\/","title":{"raw":"Instructor Guide 6C: Corequisite Support","rendered":"Instructor Guide 6C: Corequisite Support"},"content":{"raw":"While this support activity is designed for a face-to-face, synchronous delivery, it should be noted that supporting text and interactive examples have been embedded in the digital assignment page to assist asynchronous or hybrid course delivery and to be made more accessible to students performing make-up work.<\/em>\r\n

Notes for synchronous active-learning delivery<\/h2>\r\nUse this corequisite support activity to prepare students for finding and interpreting the\u00a0coefficient of determination, [latex]R^{2}[\/latex]. This support activity\u2019s main aim is to develop students\u2019\u00a0intuitive understanding of [latex]R^{2}[\/latex] and support number sense around its value.\r\n\r\nA large component of this support activity is exploration using the DCMP Data Analysis\u00a0Tools<\/em>. The tools perform fairly well on smartphones, so small group work may be\u00a0possible if at least one person in each group has a phone they are willing to use. If not,\u00a0then you may work through the exploratory questions as a whole class.\r\n\r\nQuestions 12 and 13 exemplify the exploratory approach. To wrap up the class period,\u00a0you could pose these questions as a challenge to the whole class and indicate that you\u00a0will discuss all the groups\u2019 plots at the end of the period. If all groups or students have\u00a0access to their own computers, then they could take screenshots of their scatterplots\u00a0along with the [latex]R^{2}[\/latex] values and insert them into shared, editable Google documents for the\u00a0whole class. If not every group has their own computer or phone, you will again have to\u00a0rely on the classroom\u2019s computer and projector to conduct these parts of the support\u00a0activity. Here are some ideas for executing the exploratory components as a large\u00a0group:\r\n
    \r\n \t
  • Groups can sketch their ideas on paper and submit the sketches to the instructor,\u00a0who can then reproduce the sketches on the Explore Linear Regression tool.<\/li>\r\n \t
  • If the projector is projecting the image on the screen onto a whiteboard or\u00a0smartboard, have students indicate with a pen on the board where the instructor\u00a0should place data points.<\/li>\r\n \t
  • Have each group (or a subset of the groups) come up to the computer to make\u00a0their plots themselves.<\/li>\r\n<\/ul>\r\nAfter all groups have presented their scatterplots, discuss as a class the similarities and\u00a0differences among the different scatterplots. What ultimately led to [latex]R^{2}[\/latex] being so small in\u00a0all these cases?\r\n\r\nHighlight the last question, and if you have time, ask what other information we might\u00a0need besides [latex]r[\/latex] and [latex]R^{2}[\/latex] to make decisions about the appropriateness of fitting a line.\r\n\r\nIn this support activity, there are two skills that support number sense surrounding [latex]R^{2}[\/latex]:\u00a0conversion of decimals to and from percentages and squaring. Consider relating these\u00a0operations explicitly to the numbers students saw in the exploratory phase.\r\n\r\nPossible student confusions or pitfalls:\r\n
      \r\n \t
    • In Question 3, students may answer that the coefficient of determination is\u00a0always less than the correlation coefficient based on their exploration. Once you\u00a0have finished the squaring section of the lesson, explicitly revisit this question\u00a0and highlight the fact that the coefficient of determination may be equal to the\u00a0correlation coefficient in the case of 0 or 1.<\/li>\r\n \t
    • Be prepared to address that due to rounding in the tool, a correlation coefficient\u00a0of (approximately) 1 could lead to a coefficient of determination that is less than 1\u00a0(see sample answer to Question 2, Part A, for example). This could be a time to\u00a0highlight the fact that [latex]R^{2}[\/latex] is more sensitive than [latex]r[\/latex].<\/li>\r\n<\/ul>","rendered":"

      While this support activity is designed for a face-to-face, synchronous delivery, it should be noted that supporting text and interactive examples have been embedded in the digital assignment page to assist asynchronous or hybrid course delivery and to be made more accessible to students performing make-up work.<\/em><\/p>\n

      Notes for synchronous active-learning delivery<\/h2>\n

      Use this corequisite support activity to prepare students for finding and interpreting the\u00a0coefficient of determination, [latex]R^{2}[\/latex]. This support activity\u2019s main aim is to develop students\u2019\u00a0intuitive understanding of [latex]R^{2}[\/latex] and support number sense around its value.<\/p>\n

      A large component of this support activity is exploration using the DCMP Data Analysis\u00a0Tools<\/em>. The tools perform fairly well on smartphones, so small group work may be\u00a0possible if at least one person in each group has a phone they are willing to use. If not,\u00a0then you may work through the exploratory questions as a whole class.<\/p>\n

      Questions 12 and 13 exemplify the exploratory approach. To wrap up the class period,\u00a0you could pose these questions as a challenge to the whole class and indicate that you\u00a0will discuss all the groups\u2019 plots at the end of the period. If all groups or students have\u00a0access to their own computers, then they could take screenshots of their scatterplots\u00a0along with the [latex]R^{2}[\/latex] values and insert them into shared, editable Google documents for the\u00a0whole class. If not every group has their own computer or phone, you will again have to\u00a0rely on the classroom\u2019s computer and projector to conduct these parts of the support\u00a0activity. Here are some ideas for executing the exploratory components as a large\u00a0group:<\/p>\n

        \n
      • Groups can sketch their ideas on paper and submit the sketches to the instructor,\u00a0who can then reproduce the sketches on the Explore Linear Regression tool.<\/li>\n
      • If the projector is projecting the image on the screen onto a whiteboard or\u00a0smartboard, have students indicate with a pen on the board where the instructor\u00a0should place data points.<\/li>\n
      • Have each group (or a subset of the groups) come up to the computer to make\u00a0their plots themselves.<\/li>\n<\/ul>\n

        After all groups have presented their scatterplots, discuss as a class the similarities and\u00a0differences among the different scatterplots. What ultimately led to [latex]R^{2}[\/latex] being so small in\u00a0all these cases?<\/p>\n

        Highlight the last question, and if you have time, ask what other information we might\u00a0need besides [latex]r[\/latex] and [latex]R^{2}[\/latex] to make decisions about the appropriateness of fitting a line.<\/p>\n

        In this support activity, there are two skills that support number sense surrounding [latex]R^{2}[\/latex]:\u00a0conversion of decimals to and from percentages and squaring. Consider relating these\u00a0operations explicitly to the numbers students saw in the exploratory phase.<\/p>\n

        Possible student confusions or pitfalls:<\/p>\n

          \n
        • In Question 3, students may answer that the coefficient of determination is\u00a0always less than the correlation coefficient based on their exploration. Once you\u00a0have finished the squaring section of the lesson, explicitly revisit this question\u00a0and highlight the fact that the coefficient of determination may be equal to the\u00a0correlation coefficient in the case of 0 or 1.<\/li>\n
        • Be prepared to address that due to rounding in the tool, a correlation coefficient\u00a0of (approximately) 1 could lead to a coefficient of determination that is less than 1\u00a0(see sample answer to Question 2, Part A, for example). This could be a time to\u00a0highlight the fact that [latex]R^{2}[\/latex] is more sensitive than [latex]r[\/latex].<\/li>\n<\/ul>\n","protected":false},"author":25777,"menu_order":5,"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-4522","chapter","type-chapter","status-publish","hentry"],"part":4483,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4522","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":4,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4522\/revisions"}],"predecessor-version":[{"id":4686,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapters\/4522\/revisions\/4686"}],"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\/4522\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/media?parent=4522"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/pressbooks\/v2\/chapter-type?post=4522"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/contributor?post=4522"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/lumen-danacenter-statsmockup\/wp-json\/wp\/v2\/license?post=4522"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}