{"id":35,"date":"2025-02-06T15:56:13","date_gmt":"2025-02-06T15:56:13","guid":{"rendered":"https:\/\/people.mtsu.edu\/rsjones\/?page_id=35"},"modified":"2026-06-19T06:10:22","modified_gmt":"2026-06-19T11:10:22","slug":"materials","status":"publish","type":"page","link":"https:\/\/people.mtsu.edu\/rsjones\/materials\/","title":{"rendered":"Curriculum Materials"},"content":{"rendered":"\n<div class=\"wp-block-mtsu-blocks-expandable-block accordion expandable-group expandable-group-faq\" id=\"newExpandable\">\n<div class=\"wp-block-mtsu-blocks-expandable-item accordion-item expandable-heading expandable-heading-faq\"><h2 class=\"accordion-header\" id=\"headingwisconsin-fast-plants-wfp\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#collapsenewExpandablewisconsin-fast-plants-wfp\" aria-expanded=\"false\" aria-controls=\"collapsenewExpandablewisconsin-fast-plants-wfp\">Wisconsin Fast Plants (WFP)<\/button><\/h2><div id=\"collapsenewExpandablewisconsin-fast-plants-wfp\" class=\"accordion-collapse collapse expandable-content expandable-content-faq\" aria-labelledby=\"headingwisconsin-fast-plants-wfp\" data-bs-parent=\"#newExpandable\"><div class=\"accordion-body\">\n<p><em>Variation,<\/em>&nbsp;differences based on both genetics and environmental factors,<em>&nbsp;<\/em>is a fundamental attribute of life. Individual organisms vary from one another, and organisms vary over time. This investigation allows students to observe, describe, and measure variation using a model organism, Wisconsin Fast Plants (WFPs). Focusing on the guiding question, \u201c<strong>how do plants change as they grow?<\/strong>\u201d, students will plant, observe, and measure WFPs. This activity provides opportunities for students to make observations about individual differences in WFPs and how they change as they grow. They then make decisions about how to measure those observations to generate quantitative data and create data displays to make claims about how plants grow. As they make claims, students will have opportunities to explain how different sources contribute to the variation in the data. These explanations help students consider the different inferences you might make about the variation. For example, if we think all the variation is from measurement error then we might interpret it as mistakes or noise. If we think the variation is from errors in a production process, then we might interpret it as things to improve in the process. In this investigation, though, much of the variation comes from differences in environmental and genetic factors, which provides opportunities to use the variation to explore the factors that impact plant growth.&nbsp;&nbsp;<\/p>\n\n\n\n<p>This investigation equips students to understand that quantitative data emerge from decisions they make as they measure, organize, and analyze their data, and how, ultimately, their choices provide evidence to support their claims about plant growth. This activity also provides opportunities to contrast ways of thinking about variation that students may have been exposed to in their mathematics classes.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-mtsublue-background-color has-background wp-element-button\" href=\"https:\/\/people.mtsu.edu\/rsjones\/wp-content\/uploads\/sites\/13\/2025\/02\/WFPv2.pdf\">Download PDF<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-mtsu-blocks-expandable-item accordion-item expandable-heading expandable-heading-faq\"><h2 class=\"accordion-header\" id=\"headinginventing-data-displays\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#collapsenewExpandableinventing-data-displays\" aria-expanded=\"false\" aria-controls=\"collapsenewExpandableinventing-data-displays\">Inventing Data Displays<\/button><\/h2><div id=\"collapsenewExpandableinventing-data-displays\" class=\"accordion-collapse collapse expandable-content expandable-content-faq\" aria-labelledby=\"headinginventing-data-displays\" data-bs-parent=\"#newExpandable\"><div class=\"accordion-body\">\n<p>Unit 1 focuses on the development of representational and meta-<br>representational competencies, meaning that students progress from case-<br>based interpretations of data representations to those involving characteristics of the aggregate. Students learn that the shape of the data arises from the choices that designers make to show and hide aspects of the data.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-mtsublue-background-color has-background wp-element-button\" href=\"https:\/\/people.mtsu.edu\/rsjones\/wp-content\/uploads\/sites\/13\/2025\/02\/DM1.pdf\">Download PDF<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-mtsu-blocks-expandable-item accordion-item expandable-heading expandable-heading-faq\"><h2 class=\"accordion-header\" id=\"headinginventing-center\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#collapsenewExpandableinventing-center\" aria-expanded=\"false\" aria-controls=\"collapsenewExpandableinventing-center\">Inventing Center<\/button><\/h2><div id=\"collapsenewExpandableinventing-center\" class=\"accordion-collapse collapse expandable-content expandable-content-faq\" aria-labelledby=\"headinginventing-center\" data-bs-parent=\"#newExpandable\"><div class=\"accordion-body\">\n<p>In Unit 2, a simple question is posed: What is the \u201cbest guess\u201d of the real<br>length of (name-of-person)\u2019s arm span? The activities in this unit involve<br>students in the design of a measure of center. Students participate in the<br>important mathematical practice of inventing an algorithm.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-mtsublue-background-color has-background wp-element-button\" href=\"https:\/\/people.mtsu.edu\/rsjones\/wp-content\/uploads\/sites\/13\/2025\/02\/DM2.pdf\">Download PDF<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-mtsu-blocks-expandable-item accordion-item expandable-heading expandable-heading-faq\"><h2 class=\"accordion-header\" id=\"headinginventing-precision\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#collapsenewExpandableinventing-precision\" aria-expanded=\"false\" aria-controls=\"collapsenewExpandableinventing-precision\">Inventing Precision<\/button><\/h2><div id=\"collapsenewExpandableinventing-precision\" class=\"accordion-collapse collapse expandable-content expandable-content-faq\" aria-labelledby=\"headinginventing-precision\" data-bs-parent=\"#newExpandable\"><div class=\"accordion-body\">\n<p>In Unit 3, students invent a measure of precision\u2014the tendency of the<br>measurements to agree. Focusing on precision, and not only spread,<br>invites students to consider how to develop a quantity that measures<br>\u201cclumpiness\u201d or proximity of the measurements. Focusing on clumps,<br>especially the center clump, often spurs simultaneous consideration of<br>center and spread as students focus on distances (deviations) from the<br>center or consider the neighborhood of values around the center.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-mtsublue-background-color has-background wp-element-button\" href=\"https:\/\/people.mtsu.edu\/rsjones\/wp-content\/uploads\/sites\/13\/2025\/02\/DM3.pdf\">Download PDF<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-mtsu-blocks-expandable-item accordion-item expandable-heading expandable-heading-faq\"><h2 class=\"accordion-header\" id=\"headingexploring-generalization\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#collapsenewExpandableexploring-generalization\" aria-expanded=\"false\" aria-controls=\"collapsenewExpandableexploring-generalization\">Exploring Generalization<\/button><\/h2><div id=\"collapsenewExpandableexploring-generalization\" class=\"accordion-collapse collapse expandable-content expandable-content-faq\" aria-labelledby=\"headingexploring-generalization\" data-bs-parent=\"#newExpandable\"><div class=\"accordion-body\">\n<p>This unit focuses on the important mathematical idea of generalization. Do<br>statistics invented previously work well to describe new samples? When<br>attributes of the distribution of sample values change, do the statistics also<br>change in sensible ways? At the teacher\u2019s option, the attribute measured in<br>Unit 1 (e.g., a teacher\u2019s arm-span) is measured again with another tool<br>(e.g., a meter stick) that tends to produce less variation in the resulting<br>collection of measurements. Students use statistics of center and variation<br>developed in Units 2,3 to characterize this change, usually in variability<br>(the precision of the measures) but not in center.<\/p>\n\n\n\n<p>Generalization is promoted further by exploring production processes. A<br>production process is one with a target value and with variation about the<br>target value that arises just by chance. In manufacturing, products that are<br>consistently produced to match target specification are valued. Statistics of<br>center estimate the tendency of the production process to meet its target<br>specification. Statistics of variability measure the consistency with which<br>the target value is attained. Production processes featured in this unit are<br>Toothpick Factory and Rate Walk. Teachers choose one or more<br>production process for students to explore. Other production processes can<br>be found in the Teacher\u2019s Corner of the modelingdata.org website.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-mtsublue-background-color has-background wp-element-button\" href=\"https:\/\/people.mtsu.edu\/rsjones\/wp-content\/uploads\/sites\/13\/2025\/02\/DM4.pdf\">Download PDF<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-mtsu-blocks-expandable-item accordion-item expandable-heading expandable-heading-faq\"><h2 class=\"accordion-header\" id=\"headinginvestigating-chance-data-modeling-curriculum\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#collapsenewExpandableinvestigating-chance-data-modeling-curriculum\" aria-expanded=\"false\" aria-controls=\"collapsenewExpandableinvestigating-chance-data-modeling-curriculum\">Investigating Chance (Data Modeling Curriculum)<\/button><\/h2><div id=\"collapsenewExpandableinvestigating-chance-data-modeling-curriculum\" class=\"accordion-collapse collapse expandable-content expandable-content-faq\" aria-labelledby=\"headinginvestigating-chance-data-modeling-curriculum\" data-bs-parent=\"#newExpandable\"><div class=\"accordion-body\">\n<p>Probability relies on intuitions about chance events, but unfortunately, our<br>intuitions are often misleading. This unit addresses everyday intuitions but<br>provides opportunities for students to elaborate and revise their intuitions<br>through investigation of the behavior of simple chance devices. Peering<br>through the lens of the behavior of these devices, the unit develops probability\u2014the measure of uncertainty&#8211;from two perspectives: long- term trends in outcomes of random events, also called empirical probability, and analysis of the structure of the devices producing these<br>long-term trends, also called theoretical probability. In principle, these two<br>forms of estimation should converge on common values.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-mtsublue-background-color has-background wp-element-button\" href=\"https:\/\/people.mtsu.edu\/rsjones\/wp-content\/uploads\/sites\/13\/2025\/02\/DM5.pdf\">Download PDF<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-mtsu-blocks-expandable-item accordion-item expandable-heading expandable-heading-faq\"><h2 class=\"accordion-header\" id=\"headingmodeling-measurements\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#collapsenewExpandablemodeling-measurements\" aria-expanded=\"false\" aria-controls=\"collapsenewExpandablemodeling-measurements\">Modeling Measurements<\/button><\/h2><div id=\"collapsenewExpandablemodeling-measurements\" class=\"accordion-collapse collapse expandable-content expandable-content-faq\" aria-labelledby=\"headingmodeling-measurements\" data-bs-parent=\"#newExpandable\"><div class=\"accordion-body\">\n<p>Unit 6 introduces students to building and testing models of the process<br>that produced the measurements of the arm-span (or other attribute)<br>generated by the class. The measurement process has two components.<br>The first is the true measure of the arm-span, estimated by a statistic such<br>as the mean or median. Real measurements tend to clump because there is<br>a true measure. The second component is random errors of measurement.<br>The unit assumes that Tinkerplots is available for use.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-mtsublue-background-color has-background wp-element-button\" href=\"https:\/\/people.mtsu.edu\/rsjones\/wp-content\/uploads\/sites\/13\/2025\/02\/DM6.pdf\">Download PDF<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-mtsu-blocks-expandable-item accordion-item expandable-heading expandable-heading-faq\"><h2 class=\"accordion-header\" id=\"headingmaking-inferences-in-light-of-uncertainty\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#collapsenewExpandablemaking-inferences-in-light-of-uncertainty\" aria-expanded=\"false\" aria-controls=\"collapsenewExpandablemaking-inferences-in-light-of-uncertainty\">Making Inferences in Light of Uncertainty<\/button><\/h2><div id=\"collapsenewExpandablemaking-inferences-in-light-of-uncertainty\" class=\"accordion-collapse collapse expandable-content expandable-content-faq\" aria-labelledby=\"headingmaking-inferences-in-light-of-uncertainty\" data-bs-parent=\"#newExpandable\"><div class=\"accordion-body\">\n<p>Building on concepts of sampling distribution and modeling introduced in<br>the previous unit, students develop models, create model-based sampling<br>distributions, and then make inferences by comparing the values of sample<br>statistics to model-based sampling distributions. Investigations include<br>inferences about claims made about (a) changes in person or<br>improvements in methods for repeated measure of a person\u2019s arm-span,<br>and (b) the reality of the power of illusion in a psychophysics experiment<br>that students conduct. Extensions and formative assessments provide<br>further opportunities for exploring model-based inference.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-mtsublue-background-color has-background wp-element-button\" href=\"https:\/\/people.mtsu.edu\/rsjones\/wp-content\/uploads\/sites\/13\/2025\/02\/DM7.pdf\">Download PDF<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-mtsu-blocks-expandable-item accordion-item expandable-heading expandable-heading-faq\"><h2 class=\"accordion-header\" id=\"headinginvestigating-chance-our-curriculum\"><button class=\"accordion-button collapsed\" type=\"button\" data-bs-toggle=\"collapse\" data-bs-target=\"#collapsenewExpandableinvestigating-chance-our-curriculum\" aria-expanded=\"false\" aria-controls=\"collapsenewExpandableinvestigating-chance-our-curriculum\">Investigating Chance (Our Curriculum)<\/button><\/h2><div id=\"collapsenewExpandableinvestigating-chance-our-curriculum\" class=\"accordion-collapse collapse expandable-content expandable-content-faq\" aria-labelledby=\"headinginvestigating-chance-our-curriculum\" data-bs-parent=\"#newExpandable\"><div class=\"accordion-body\">\n<p>This unit addresses probability, by examining students\u2019 everyday intuitions then providing opportunities for students to investigate, challenge, and refine their intuitions using both simple and chance devices and Tinkerplots.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-mtsublue-background-color has-background wp-element-button\" href=\"https:\/\/people.mtsu.edu\/rsjones\/wp-content\/uploads\/sites\/13\/2025\/02\/InvestigatingChance.pdf\">Download PDF<\/a><\/div>\n<\/div>\n<\/div><\/div><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":21,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-35","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/people.mtsu.edu\/rsjones\/wp-json\/wp\/v2\/pages\/35","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.mtsu.edu\/rsjones\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.mtsu.edu\/rsjones\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.mtsu.edu\/rsjones\/wp-json\/wp\/v2\/users\/21"}],"replies":[{"embeddable":true,"href":"https:\/\/people.mtsu.edu\/rsjones\/wp-json\/wp\/v2\/comments?post=35"}],"version-history":[{"count":1,"href":"https:\/\/people.mtsu.edu\/rsjones\/wp-json\/wp\/v2\/pages\/35\/revisions"}],"predecessor-version":[{"id":134,"href":"https:\/\/people.mtsu.edu\/rsjones\/wp-json\/wp\/v2\/pages\/35\/revisions\/134"}],"wp:attachment":[{"href":"https:\/\/people.mtsu.edu\/rsjones\/wp-json\/wp\/v2\/media?parent=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}