{"id":110,"date":"2016-12-09T20:35:46","date_gmt":"2016-12-09T20:35:46","guid":{"rendered":"http:\/\/sites.soe.umich.edu\/at-practice\/?page_id=110"},"modified":"2025-06-18T15:31:40","modified_gmt":"2025-06-18T19:31:40","slug":"design","status":"publish","type":"page","link":"https:\/\/sites.marsal.umich.edu\/at-practice\/design\/","title":{"rendered":"Design: How We Assess It"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"110\" class=\"elementor elementor-110\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-71997089 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"71997089\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-7bfa093b\" data-id=\"7bfa093b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e102ff6 elementor-widget elementor-widget-text-editor\" data-id=\"e102ff6\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<table style=\"height: 30px;\" width=\"100%\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/sites.marsal.umich.edu\/at-practice\/content\/\"><u>&lt;&lt; Previous: Content<\/u><\/a><\/td>\n<td style=\"text-align: right;\"><a href=\"https:\/\/sites.marsal.umich.edu\/at-practice\/interpretation\/\"><u>Next: Interpretation &gt;&gt;<\/u><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Our Simulation Assessments<\/h2>\nWe assess the practices of eliciting and interpreting student thinking through the use of simulation assessments, in which preservice teachers interact with a \u201cstudent\u201d (i.e., someone trained to respond in standardized ways guided by a highly specified student thinking and interaction profile). Each assessment has three stages:\n<table style=\"vertical-align: top;\" width=\"720;\" align=\"top;\">\n<tbody>\n<tr style=\"vertical-align: top;\">\n<td width=\"200;\">\n<h4 align=\"center\"><u>Preparation<\/u><\/h4>\n<a href=\"#preparation\"><img decoding=\"async\" width=\"140\" height=\"140\" class=\"aligncenter size-thumbnail wp-image-188\" style=\"width: 140px;\" src=\"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/preparation-icon-150x150.png\" srcset=\"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/preparation-icon-150x150.png 150w, https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/preparation-icon-300x300.png 300w, https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/preparation-icon-250x250.png 250w, https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/preparation-icon-174x174.png 174w, https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/preparation-icon.png 640w\" sizes=\"(max-width: 140px) 100vw, 140px\" \/><\/a>\n\nA preservice teacher analyzes a student\u2019s written work on a mathematics problem and prepares to interact with the \u201cstudent\u201d about the problem<\/td>\n<td style=\"text-align: center;\" width=\"60;\">\n<h4>\u2501\u2501\u2501\u27a4<\/h4>\n<\/td>\n<td width=\"200;\">\n<h4 align=\"center\"><u>Simulation<\/u><\/h4>\n<a href=\"#simulation\"><img decoding=\"async\" class=\"aligncenter\" style=\"height: 140px;\" src=\"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/simulation-icon.png\" \/><\/a>\n\nA preservice teacher interacts with a \u201cstudent\u201d about the written work<\/td>\n<td style=\"text-align: center;\" width=\"60;\">\n<h4>\u2501\u2501\u2501\u27a4<\/h4>\n<\/td>\n<td width=\"200;\">\n<h4 align=\"center\"><u>Interview<\/u><\/h4>\n<a href=\"#interview\"><img decoding=\"async\" class=\"aligncenter\" style=\"width: 140px;\" src=\"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/interview-icon.png\" \/><\/a>\n\nAn assessment proctor interviews the preservice teacher about his or her interpretations of the student\u2019s thinking<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nThe three stages are elaborated below using one of our simulation assessments as an example.\n<table style=\"background-color: gainsboro;\">\n<tbody>\n<tr>\n<td style=\"padding-left: 25px; padding-right: 25px; padding-top: 25px;\">\n<h4>Example: Long Division<\/h4>\nDeveloping each simulation involves a number of design decisions. These include choices about:\n<ul>\n \t<li>the focal mathematical content<\/li>\n \t<li>the correctness of the student\u2019s answer (correct or incorrect)<\/li>\n \t<li>the type of process being used (standard, invented, alternative)<\/li>\n \t<li>the degree to which the student understands the process<\/li>\n \t<li>the developmental\/grade level of the student<\/li>\n \t<li>the student\u2019s \u201cway of being\u201d in the interaction<\/li>\n<\/ul>\nIn the example below, we selected division using a standard long-division algorithm with a correct answer. We decided that the student would know the procedure for long division, but would think that the remainder can simply be written to the right of a decimal point. In other words, the student is not thinking of the 3 in the quotient as 3 tenths. We identified the student as a fifth-grade student who was not predisposed to elaboration or explaining her thinking. The numerical example chosen, in particular the divisor of 10, is key because the student\u2019s process happens to yield the correct answer. In many situations this would not be the case.\n\n<a name=\"preparation\"><\/a><img decoding=\"async\" class=\"aligncenter size-full wp-image-121\" src=\"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/long-division-example.png\" width=\"118\" height=\"200\" \/><a name=\"preparation\"><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>Stage 1: Preparation<\/h3>\nIn the first stage of the assessment, preservice teachers are given a copy of the standardized student\u2019s work on a problem and have 10 minutes to prepare for their upcoming interaction. In this division example, even though the student produces a correct answer, preservice teachers still need to determine how the student reasoned and what the student understands and does not understand. There is not much residue of the student\u2019s understanding in the mathematical work. Students can produce correct answers using procedural knowledge without understanding the concepts behind the procedure. An important task of teaching is to probe and make sense of students\u2019 mathematical processes and understanding, both when students have correct answers and when they do not. Preservice teachers are told that they should elicit and probe the standardized student\u2019s thinking to understand the steps she took, why she performed particular steps, and her understanding of the key mathematical ideas involved.\n<table style=\"background-color: gainsboro;\">\n<tbody>\n<tr>\n<td style=\"padding-left: 25px; padding-right: 25px; padding-top: 25px;\"><a href=\"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/example-division-preparation-materials.pdf\" target=\"_blank\" rel=\"noopener noreferrer\"><u>Example of the preparation materials given to preservice teachers<\/u><\/a>\n\n<a href=\"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-content\/uploads\/sites\/13\/2016\/12\/example-division-anticipation.pdf\" target=\"_blank\" rel=\"noopener noreferrer\"><u>Example of a preservice teacher&#8217;s preparation<\/u><\/a>\n\n<a name=\"simulation\"><\/a>\n\nIn these preparation notes, the preservice teacher observed that the student\u2019s answer is correct and that the student appears to know the steps for the procedure. The preservice teacher questioned whether the student understands those steps and concluded that it was not clear from the written work how the student \u201cused the 3 to get the .3 part\u201d or whether the student understands remainders. The potential questions generated include general questions about the problem and the steps used, as well as more specific questions and additional examples to probe the student\u2019s understanding of the remainder.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>Stage 2: Simulation<\/h3>\nPreservice teachers have five minutes to interact with the \u201cstudent\u201d in the role of the teacher. The \u201cstudent\u201d acts in accordance with a highly specified \u201cstudent profile.\u201d The profile details how the problem was completed and the thinking behind it. The profile articulates rules for reasoning and responding to the preservice teacher\u2019s questions, and includes specific replies to commonly asked questions.\n<h4>Student Profile<\/h4>\n<a href=\"https:\/\/sites.marsal.umich.edu\/at-practice\/student-profile\/\"><img decoding=\"async\" style=\"width: 300px; height: 177px;\" src=\"\/wp-content\/uploads\/sites\/13\/2016\/12\/students-process.png\" \/><\/a>\n<br>\n<a href=\"https:\/\/sites.marsal.umich.edu\/at-practice\/student-profile\/\"><u>View excerpts from a student profile<\/u><\/a>\n<br><br>\n<p>A teacher educator (the \u201cassessor\u201d) observes and scores the assessment. The assessment is video recorded.<\/p>\n<table style=\"background-color: gainsboro;\">\n<tbody>\n<tr>\n<td style=\"padding-left: 25px; padding-right: 25px; padding-top: 25px;\">Below are two performances on the example task. For each performance, two videos are provided: (1) a record of the performance without commentary and (2) that same performance annotated with observations a teacher educator might make. These observations are tied to how we interpret the assessment in connection with the decomposition of the practice.\n<table align=\"center;\">\n<thead>\n<tr>\n<th style=\"text-align: center;\" colspan=\"2\">\n<h3>Simulation \u2013 Sample Preservice Teacher Performance A<\/h3>\n<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\" valign=\"middle;\"><iframe id=\"kaltura_player\" style=\"width: 640px; height: 360px; border: 0;\" title=\"Example video A\" src=\"https:\/\/cdnapisec.kaltura.com\/p\/1038472\/embedPlaykitJs\/uiconf_id\/54883762?iframeembed=true&amp;entry_id=1_uqxsp1sm&amp;config%5Bprovider%5D=%7B%22widgetId%22%3A%221_wmse5xac%22%7D&amp;config%5Bplayback%5D=%7B%22startTime%22%3A0%7D\" sandbox=\"allow-forms allow-same-origin allow-scripts allow-top-navigation allow-pointer-lock allow-popups allow-modals allow-orientation-lock allow-popups-to-escape-sandbox allow-presentation allow-top-navigation-by-user-activation\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<h4>Without annotations<\/h4>\n<\/td>\n<td style=\"text-align: center;\" valign=\"middle;\"><iframe id=\"kaltura_player\" style=\"width: 640px; height: 360px; border: 0;\" title=\"Example video A (with text)\" src=\"https:\/\/cdnapisec.kaltura.com\/p\/1038472\/embedPlaykitJs\/uiconf_id\/54883762?iframeembed=true&amp;entry_id=1_g2g6zwsc&amp;config%5Bprovider%5D=%7B%22widgetId%22%3A%221_ywdcdfft%22%7D&amp;config%5Bplayback%5D=%7B%22startTime%22%3A0%7D\" sandbox=\"allow-forms allow-same-origin allow-scripts allow-top-navigation allow-pointer-lock allow-popups allow-modals allow-orientation-lock allow-popups-to-escape-sandbox allow-presentation allow-top-navigation-by-user-activation\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<h4>With annotations<\/h4>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<table align=\"center;\">\n<thead>\n<tr>\n<th style=\"text-align: center;\" colspan=\"2\">\n<h3>Simulation \u2013 Sample Preservice Teacher Performance B<\/h3>\n<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\" valign=\"middle;\"><a name=\"interview\"><\/a>\n<iframe id=\"kaltura_player\" style=\"width: 640px; height: 360px; border: 0;\" title=\"Example video B\" src=\"https:\/\/cdnapisec.kaltura.com\/p\/1038472\/embedPlaykitJs\/uiconf_id\/54883762?iframeembed=true&amp;entry_id=1_9w00sc2d&amp;config%5Bprovider%5D=%7B%22widgetId%22%3A%221_v3gsjhx5%22%7D&amp;config%5Bplayback%5D=%7B%22startTime%22%3A0%7D\" sandbox=\"allow-forms allow-same-origin allow-scripts allow-top-navigation allow-pointer-lock allow-popups allow-modals allow-orientation-lock allow-popups-to-escape-sandbox allow-presentation allow-top-navigation-by-user-activation\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<h4>Without annotations<\/h4>\n<\/td>\n<td style=\"text-align: center;\" valign=\"middle;\"><iframe id=\"kaltura_player\" style=\"width: 640px; height: 360px; border: 0;\" title=\"Example video B (with text)\" src=\"https:\/\/cdnapisec.kaltura.com\/p\/1038472\/embedPlaykitJs\/uiconf_id\/54883762?iframeembed=true&amp;entry_id=1_d5q1cpb2&amp;config%5Bprovider%5D=%7B%22widgetId%22%3A%221_p8clenac%22%7D&amp;config%5Bplayback%5D=%7B%22startTime%22%3A0%7D\" sandbox=\"allow-forms allow-same-origin allow-scripts allow-top-navigation allow-pointer-lock allow-popups allow-modals allow-orientation-lock allow-popups-to-escape-sandbox allow-presentation allow-top-navigation-by-user-activation\" allowfullscreen=\"allowfullscreen\"><\/iframe>\n<h4>With annotations<\/h4>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3>Stage 3: Interview<\/h3>\nFollowing the interaction with the \u201cstudent\u201d, the assessor asks the preservice teacher a series of questions. These questions focus on the preservice teacher\u2019s interpretation of the student\u2019s process and understanding, as well as the preservice teacher\u2019s mathematical knowledge for teaching relevant to the situation. Specifically, preservice teachers are asked to:\n<ul>\n \t<li>Describe the student\u2019s process<\/li>\n \t<li>Characterize the student\u2019s understanding of the process, including underlying mathematical ideas<\/li>\n \t<li>Generate a follow-up problem which could be used to confirm the student\u2019s process<\/li>\n \t<li>Anticipate how the student would solve a similar problem, if the student used the same process<\/li>\n \t<li>Anticipate the student\u2019s understanding of specific parts of the process, using evidence from the simulation interaction to support the anticipation<\/li>\n \t<li>Characterize the generalizability of the student\u2019s process<\/li>\n<\/ul>\n<table style=\"height: 30px;\" width=\"100%\">\n<tbody>\n<tr>\n<td><a href=\"https:\/\/sites.marsal.umich.edu\/at-practice\/content\/\"><u>&lt;&lt; Previous: Content<\/u><\/a><\/td>\n<td style=\"text-align: right;\"><a href=\"https:\/\/sites.marsal.umich.edu\/at-practice\/interpretation\/\"><u>Next: Interpretation &gt;&gt;<\/u><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>&lt;&lt; Previous: Content Next: Interpretation &gt;&gt; Our Simulation Assessments We assess the practices of eliciting and interpreting student thinking through the use of simulation assessments, in which preservice teachers interact with a \u201cstudent\u201d (i.e., someone trained to respond in standardized ways guided by a highly specified student thinking and interaction profile). Each assessment has three&hellip;&nbsp;<a href=\"https:\/\/sites.marsal.umich.edu\/at-practice\/design\/\" rel=\"bookmark\">Read More &raquo;<span class=\"screen-reader-text\">Design: How We Assess It<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"neve_meta_sidebar":"","neve_meta_container":"","neve_meta_enable_content_width":"off","neve_meta_content_width":0,"neve_meta_title_alignment":"","neve_meta_author_avatar":"","neve_post_elements_order":"","neve_meta_disable_header":"","neve_meta_disable_footer":"","neve_meta_disable_title":"","_kadence_starter_templates_imported_post":false,"footnotes":""},"class_list":["post-110","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-json\/wp\/v2\/pages\/110","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-json\/wp\/v2\/comments?post=110"}],"version-history":[{"count":49,"href":"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-json\/wp\/v2\/pages\/110\/revisions"}],"predecessor-version":[{"id":642,"href":"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-json\/wp\/v2\/pages\/110\/revisions\/642"}],"wp:attachment":[{"href":"https:\/\/sites.marsal.umich.edu\/at-practice\/wp-json\/wp\/v2\/media?parent=110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}