{"id":781,"date":"2024-08-19T10:04:55","date_gmt":"2024-08-19T10:04:55","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=781"},"modified":"2024-09-30T11:39:52","modified_gmt":"2024-09-30T11:39:52","slug":"esp-module-7-key-features-of-the-sine-function","status":"publish","type":"page","link":"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/esp-module-7-key-features-of-the-sine-function\/","title":{"rendered":"ESP_AF Module 7-Key Features of the Sine Function"},"content":{"rendered":"\n

Examining Students’ Practices in Algebra and Function<\/a> > Module 7<\/p>\n\n\n\n

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ESP_AF Module 7-Key Features of the Sine Function<\/h2><\/div>\n<\/div>\n<\/div>\n\n\n\n
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This module uses a teacher-created Desmos activity which engages students in analyzing the sine graph through investigating the relationship between parameters of the sine function f(x)=asin(bx)+c and key characteristics of the graph of the sine function (i.e., amplitude, midline, and period). Video clips of the task launch with the whole class in a remote setting, and teacher monitoring of student thinking among multiple pairs of students (in both remote and face to face settings) provide a context for teachers to develop their noticing skills with a focus on eliciting and using student thinking.<\/p>\n<\/div>

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This module could be used alongside a chapter from Teaching Algebra materials:<\/p>\n\n\n\n

Chapter 7:<\/strong><\/a>\u00a0Function Families<\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n

Overview Documents<\/strong><\/h3>\n\n\n\n
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Read the Overview Document<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n

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How to Read a Module Overview Document<\/strong><\/a><\/p>\n<\/div><\/div>\n<\/div>\n\n\n\n

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Download All Materials<\/a><\/strong><\/p>\n<\/div><\/div>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n

Module Elements<\/strong><\/h3>\n\n\n\n
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7.1 Introduction to the Graph of the Sine Function<\/strong>

Teachers will engage with a Desmos Activity titled Introduction to the Sine Function in which they use sliders to examine the relationship between the parameters of the sine function and amplitude, midline, and period.<\/td>
\"Desmos\"
Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a>
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7.2 Launching a Technology Enhanced Math Task<\/strong>

Teachers will consider the characteristics of an effective technology task launch when examining a video clip of the launch of the Introduction to Sine activity.
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Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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7.3 Noticing Student-Teacher Interactions<\/strong>

Teachers practice using technology to respond to students with the goal of advancing student thinking.<\/td>
Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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7.4 Monitoring Student Thinking: Introduction to the Sine Function<\/strong>

Teachers practice monitoring student thinking using the Desmos Teacher Dashboard.<\/td>
Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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7.5 Noticing Student Thinking about Amplitude<\/strong>

Teachers engage with noticing one pair of students as they are making sense of which parameters of the sine function are related to the amplitude of the function.
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Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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7.6 Noticing Student Thinking about Period<\/strong>

Teachers engage with noticing one pair of students as they are making sense of the relationship between the value of b (i.e., the coefficient of x) and the period of a sine function.<\/td>
Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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7.7 Designing a Sequence of Tasks<\/strong>

Teachers design a technology enhanced task to follow the Introduction to the Sine Graph task.<\/td>
Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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<\/div>\n","protected":false},"excerpt":{"rendered":"

Examining Students’ Practices in Algebra and Function > Module 7 This module uses a teacher-created Desmos activity which engages students in analyzing the sine graph through investigating the relationship between parameters of the sine function f(x)=asin(bx)+c and key characteristics of the graph of the sine function (i.e., amplitude, midline, and period). Video clips of the […]<\/p>\n","protected":false},"author":66,"featured_media":230,"parent":313,"menu_order":7,"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-781","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/781","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=781"}],"version-history":[{"count":16,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/781\/revisions"}],"predecessor-version":[{"id":1861,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/781\/revisions\/1861"}],"up":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/313"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media\/230"}],"wp:attachment":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/media?parent=781"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}