{"id":774,"date":"2024-08-15T01:49:01","date_gmt":"2024-08-15T01:49:01","guid":{"rendered":"https:\/\/research.ced.ncsu.edu\/ptmt\/?page_id=774"},"modified":"2024-09-30T11:39:18","modified_gmt":"2024-09-30T11:39:18","slug":"esp-module-5-function-concept-functions-and-non-functions","status":"publish","type":"page","link":"https:\/\/research.ced.ncsu.edu\/ptmt\/examining-students-practices-in-algebra-and-function\/esp-module-5-function-concept-functions-and-non-functions\/","title":{"rendered":"ESP_AF Module 5-Function Concept – Functions and Non-Functions"},"content":{"rendered":"\n

Examining Students’ Practices in Algebra and Function<\/a> > Module 5<\/p>\n\n\n\n

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ESP_AF Module 5-Function Concept – Functions and Non-Functions<\/h2><\/div>\n<\/div>\n<\/div>\n\n\n\n
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This module uses a Vending Machine GeoGebra applet designed to support students\u2019 understanding of the concept of function. Video clips of students\u2019 work with the applet and their resulting proposed definitions of function provide the context in which teachers will notice and predict student thinking, as well as select, sequence, and connect student work. Finally, teachers will consider how to use this work along with the technology to facilitate the development of the definition of function.<\/p>\n\n\n\n

There are two versions of some of the activities in this module that use different versions of the Vending Machine applet: a version designed for students revisiting<\/em> the concept of function and a version designed to introduce <\/em>the concept of function.<\/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 6:<\/strong><\/a>\u00a0Functions<\/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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5.1 Vending Machine Task (Revisiting the Concept of Function Version)<\/strong>

Teachers engage individually with the Vending Machine applet. As they work through the applet, they complete a written worksheet that has them classify each machine as either function or non-function and describe how they know.
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Class Materials<\/a><\/strong>

Instructor Materials<\/a>
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5.2 Noticing Student Thinking: Machine G of the Vending Machine Task<\/strong>

Teachers examine video clips of multiple pairs of students engaging with a specific machine, G, and are tasked with focusing on how the students\u2019 interactions with the Vending Machine applet lead them to their determination of function\/non-function.<\/td>
Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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5.3 Noticing and Predicting: The Vending Machine Task<\/strong>

Teachers attend and interpret students\u2019 understanding of function and engagement with the Vending Machine applet. Teachers are then asked to predict how the students will respond to the following vending machines based on their analysis.

*There are two versions of this activity. One for introducing the concept of function and another for revisiting the concept of function. See the Facilitation Notes for more information.
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Class Materials – Introducing Functions<\/strong><\/a>

Class Materials – Revisiting Functions<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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5.4 Selecting and Sequencing: Defining Function with the Vending Machine Task<\/strong>

Teachers are given 20 student created definitions, asked to select 4-5, sequence them and discuss connections they would make during a whole class discussion.

*There are two versions of this activity. One for introducing the concept of function and another for revisiting the concept of function. See the Facilitation Notes for more information.<\/td>
Class Materials – Introducing Functions<\/strong><\/a>

Class Materials – Revisiting Functions<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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5.5 Anticipating Student Thinking: Concept Images of Function and the Vending Machine Task<\/strong>

Teachers will consider how students\u2019 concept images of function led to their classification of Vending machines as functions or non-functions. Teachers are asked to consider how anticipating students\u2019 concept images can help inform their practice.<\/td>
Class Materials<\/strong><\/a>

Instructor Materials<\/strong><\/a><\/td><\/tr>
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5.6 Orchestrating Whole Class Discussions: Defining Function with the Vending Machine Task<\/strong>

Teachers are presented with the first few lines of a whole class discussion that would follow students engaging with the Vending Machine applet and creating their own definitions of function. They are asked to script out the next 8 – 10 lines of the discussion and explain how their choices met the stated discussion goal.

*There are two versions of this activity. One for introducing the concept of function and another for revisiting the concept of function. See the Facilitation Notes for more information.<\/td>
Class Materials – Introduction Functions<\/strong><\/a>

Class Materials – Revisiting Functions<\/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 5 This module uses a Vending Machine GeoGebra applet designed to support students\u2019 understanding of the concept of function. Video clips of students\u2019 work with the applet and their resulting proposed definitions of function provide the context in which teachers will notice and predict student thinking, […]<\/p>\n","protected":false},"author":66,"featured_media":230,"parent":313,"menu_order":5,"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-774","page","type-page","status-publish","has-post-thumbnail","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/774","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=774"}],"version-history":[{"count":16,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/774\/revisions"}],"predecessor-version":[{"id":1860,"href":"https:\/\/research.ced.ncsu.edu\/ptmt\/wp-json\/wp\/v2\/pages\/774\/revisions\/1860"}],"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=774"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}