{"id":1955,"date":"2021-03-16T11:21:01","date_gmt":"2021-03-16T16:21:01","guid":{"rendered":"https:\/\/denisegoetz.com\/CZMathConsulting\/?page_id=1955"},"modified":"2021-03-19T12:21:30","modified_gmt":"2021-03-19T17:21:30","slug":"launching-lessons","status":"publish","type":"page","link":"https:\/\/denisegoetz.com\/CZMathConsulting\/launching-lessons\/","title":{"rendered":"Launching Lessons"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1955\" class=\"elementor elementor-1955\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-08dd0e9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"08dd0e9\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\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-0e1e761\" data-id=\"0e1e761\" 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-13da442 elementor-widget elementor-widget-heading\" data-id=\"13da442\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h1 class=\"elementor-heading-title elementor-size-default\">Launching Math Lessons<\/h1>\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-d005252 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d005252\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-bfa7832\" data-id=\"bfa7832\" 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-45100c5 elementor-widget elementor-widget-heading\" data-id=\"45100c5\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Proven Practices<\/h2>\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-09082df elementor-section-content-middle elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"09082df\" data-element_type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t\t<div class=\"elementor-background-overlay\"><\/div>\n\t\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d3c61a0\" data-id=\"d3c61a0\" 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-e826546 elementor-view-default elementor-widget elementor-widget-icon\" data-id=\"e826546\" data-element_type=\"widget\" data-widget_type=\"icon.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-icon-wrapper\">\n\t\t\t<div class=\"elementor-icon\">\n\t\t\t<i aria-hidden=\"true\" class=\"fas fa-quote-left\"><\/i>\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2ce6262 elementor-widget elementor-widget-text-editor\" data-id=\"2ce6262\" 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<p>\u201cNo other decision that teachers make has greater impact on students\u2019 opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics. Here, the teacher is the architect, the designer of the curriculum.\u201d<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-0c20679 elementor-widget elementor-widget-heading\" data-id=\"0c20679\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h3 class=\"elementor-heading-title elementor-size-medium\">- Reys &amp; Long 1995<\/h3>\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<section class=\"elementor-section elementor-top-section elementor-element elementor-element-c7a5660 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"c7a5660\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-no\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-74d9e97\" data-id=\"74d9e97\" 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-df4734d elementor-widget__width-auto elementor-widget elementor-widget-heading\" data-id=\"df4734d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h5 class=\"elementor-heading-title elementor-size-default\"><span style=\"font-size: 1.125rem;font-style: normal;font-weight: 400\">Tried &amp; True Practice<\/span> -  by Dr. Carrie Zielinski<\/h5>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-020c4d5 elementor-widget__width-auto elementor-widget-divider--view-line elementor-widget elementor-widget-divider\" data-id=\"020c4d5\" data-element_type=\"widget\" data-widget_type=\"divider.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<div class=\"elementor-divider\">\n\t\t\t<span class=\"elementor-divider-separator\">\n\t\t\t\t\t\t<\/span>\n\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d526321 elementor-widget elementor-widget-heading\" data-id=\"d526321\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Launching a Mathematics Lesson\n<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-a5bac10 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a5bac10\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-custom\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-53715c7\" data-id=\"53715c7\" 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-40a6096 elementor-widget elementor-widget-image\" data-id=\"40a6096\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/opening-question-launching-lessons.jpg\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"launching a lesson open with a question\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjI5NywidXJsIjoiaHR0cHM6XC9cL2RlbmlzZWdvZXR6LmNvbVwvQ1pNYXRoQ29uc3VsdGluZ1wvd3AtY29udGVudFwvdXBsb2Fkc1wvMjAyMVwvMDNcL29wZW5pbmctcXVlc3Rpb24tbGF1bmNoaW5nLWxlc3NvbnMuanBnIn0%3D\">\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/elementor\/thumbs\/opening-question-launching-lessons-p4ekbch8x2swv2v0f89yygjijtu6bs15k3rmflzpsm.jpg\" title=\"launching a lesson open with a question\" alt=\"launching math lessons opening question\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-105f5a0\" data-id=\"105f5a0\" 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-d0d53d0 elementor-widget elementor-widget-image\" data-id=\"d0d53d0\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/opening-question-launching-lessons-fifth-grade.jpg\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"opening question launching lessons fifth grade\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjMwMSwidXJsIjoiaHR0cHM6XC9cL2RlbmlzZWdvZXR6LmNvbVwvQ1pNYXRoQ29uc3VsdGluZ1wvd3AtY29udGVudFwvdXBsb2Fkc1wvMjAyMVwvMDNcL29wZW5pbmctcXVlc3Rpb24tbGF1bmNoaW5nLWxlc3NvbnMtZmlmdGgtZ3JhZGUuanBnIn0%3D\">\n\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"300\" height=\"328\" src=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/opening-question-launching-lessons-fifth-grade.jpg\" class=\"attachment-medium_large size-medium_large wp-image-2301\" alt=\"launching math lessons opening questions fifth grade\" srcset=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/opening-question-launching-lessons-fifth-grade.jpg 300w, https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/opening-question-launching-lessons-fifth-grade-274x300.jpg 274w\" sizes=\"(max-width: 300px) 100vw, 300px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\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 class=\"elementor-element elementor-element-1d5bbdb elementor-widget elementor-widget-text-editor\" data-id=\"1d5bbdb\" 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<p>Begin with Questions<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-766d6a7 elementor-widget elementor-widget-heading\" data-id=\"766d6a7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Description of the launch for a lesson<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ed51ca7 elementor-widget elementor-widget-text-editor\" data-id=\"ed51ca7\" 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<p>A launch is a brief (5 \u2013 15 minutes) inquiry-based investigation. Grounded in learning theory, the launch invokes and makes visible students\u2019 existing schema relative to the goals of a lesson. An effective launch acknowledges learners as active participants, assists them in connecting prior knowledge to new insights, and provides all students access to the content and concepts of a lesson.<\/p><p>To effectively launch a mathematics lesson, the teacher poses a mathematical representation such as a model, a story problem, a question, or claim. The representation should provoke students\u2019 curiosities, as well as activate their perceptions of significant or informative mathematical details related to the intended goals of the lesson (Learner &amp; Johns, 2012).<\/p><p>Once presented, students need time to observe, analyze, and make sense of the mathematical representation for themselves. (Garner, 2007). Thus, teachers do not tell students what to notice, nor should they anticipate a specific response. Rather, teachers use <em><a href=\"https:\/\/teaching.cornell.edu\/teaching-resources\/engaging-students\/using-effective-questions\" target=\"_blank\" rel=\"noopener\"> open-ended questions <i class=\"fas fa-external-link-square-alt\"><\/i><\/a><\/em> such as: \u201cWhat sense can you make of this?\u201d or, \u201cWhat do you notice?\u201d or, \u201cWhat do you wonder?\u201d Open-ended questions unlock cognitive space and emboldens students\u2019 initial associations, impressions, and references.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-3f6cb3e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3f6cb3e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-custom\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-0ca7718\" data-id=\"0ca7718\" 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-ed25b8f elementor-widget elementor-widget-image\" data-id=\"ed25b8f\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/02\/third-grade-math-notebook-example-2.jpg\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"third graders mathematical thinking\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MTM0MiwidXJsIjoiaHR0cHM6XC9cL2RlbmlzZWdvZXR6LmNvbVwvQ1pNYXRoQ29uc3VsdGluZ1wvd3AtY29udGVudFwvdXBsb2Fkc1wvMjAyMVwvMDJcL3RoaXJkLWdyYWRlLW1hdGgtbm90ZWJvb2stZXhhbXBsZS0yLmpwZyJ9\">\n\t\t\t\t\t\t\t<img decoding=\"async\" width=\"415\" height=\"271\" src=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/02\/third-grade-math-notebook-example-2.jpg\" class=\"attachment-full size-full wp-image-1342\" alt=\"third grader recording their math generalizations\" srcset=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/02\/third-grade-math-notebook-example-2.jpg 415w, https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/02\/third-grade-math-notebook-example-2-300x196.jpg 300w\" sizes=\"(max-width: 415px) 100vw, 415px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-56fbf4e\" data-id=\"56fbf4e\" 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-9bb6c7e elementor-widget elementor-widget-image\" data-id=\"9bb6c7e\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/mathematicians-notebook-observation-from-lesson.jpg\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"mathematicians notebook observation from lesson\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjM1NiwidXJsIjoiaHR0cHM6XC9cL2RlbmlzZWdvZXR6LmNvbVwvQ1pNYXRoQ29uc3VsdGluZ1wvd3AtY29udGVudFwvdXBsb2Fkc1wvMjAyMVwvMDNcL21hdGhlbWF0aWNpYW5zLW5vdGVib29rLW9ic2VydmF0aW9uLWZyb20tbGVzc29uLmpwZyJ9\">\n\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/elementor\/thumbs\/mathematicians-notebook-observation-from-lesson-p4eoycgz5fevl0a99ezrybfq0aptvv0ciod7xedoba.jpg\" title=\"mathematicians notebook observation from lesson\" alt=\"recording observations from lesson in mathematicians notebook\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\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 class=\"elementor-element elementor-element-960d4ce elementor-widget elementor-widget-text-editor\" data-id=\"960d4ce\" 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<p>Recorded Observations in Mathematician&#8217;s Notebooks<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7677ed2 elementor-widget elementor-widget-text-editor\" data-id=\"7677ed2\" 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<p>Once students observe and make sense of the representation, they are encouraged to record their observations, ideas, and impressions within their mathematician\u2019s notebooks.\u00a0<\/p><p>As students record their descriptions, wonderings, and own models, the teacher circulates around the room and invites specific learners to publicly share their thinking. Students are invited to place their own representations, strategies, or models under a document camera and vocally share and physically model their ideas for others.<\/p><p>Alternatively, students may share their interpretations or observations whereby the teacher records, verbatim, students\u2019 words onto large chart paper, white board, or SMART Board. Even students\u2019 non-mathematical observations and misconceptions are shared because they provide rich opportunities for learning and discussion. Such actions allow all to hear, see, make sense of, access, critique and review classmates\u2019 perceptions, strategies, and models. In all cases, however, artful scaffolding of students\u2019 work supports struggling learners, as well as advanced learners contributing to the entire learning community.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-cb59e1c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cb59e1c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-custom\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-bf89305\" data-id=\"bf89305\" 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-f63b3b0 elementor-widget elementor-widget-image\" data-id=\"f63b3b0\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/mathematicians-notebook-sharing-observations-with-class.jpg\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"mathematicians notebook sharing observations with class\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjM2NCwidXJsIjoiaHR0cHM6XC9cL2RlbmlzZWdvZXR6LmNvbVwvQ1pNYXRoQ29uc3VsdGluZ1wvd3AtY29udGVudFwvdXBsb2Fkc1wvMjAyMVwvMDNcL21hdGhlbWF0aWNpYW5zLW5vdGVib29rLXNoYXJpbmctb2JzZXJ2YXRpb25zLXdpdGgtY2xhc3MuanBnIn0%3D\">\n\t\t\t\t\t\t\t<img decoding=\"async\" width=\"300\" height=\"261\" src=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/mathematicians-notebook-sharing-observations-with-class.jpg\" class=\"attachment-full size-full wp-image-2364\" alt=\"mathematicians notebook observations shared with class\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\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<div class=\"elementor-column elementor-col-50 elementor-inner-column elementor-element elementor-element-7eb06c6\" data-id=\"7eb06c6\" 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-6a62c1c elementor-widget elementor-widget-image\" data-id=\"6a62c1c\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/mathematicians-notebook-sharing-observations-with-class-2.jpg\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"mathematicians notebook sharing observations with class 2\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjM2NSwidXJsIjoiaHR0cHM6XC9cL2RlbmlzZWdvZXR6LmNvbVwvQ1pNYXRoQ29uc3VsdGluZ1wvd3AtY29udGVudFwvdXBsb2Fkc1wvMjAyMVwvMDNcL21hdGhlbWF0aWNpYW5zLW5vdGVib29rLXNoYXJpbmctb2JzZXJ2YXRpb25zLXdpdGgtY2xhc3MtMi5qcGcifQ%3D%3D\">\n\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"261\" src=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/mathematicians-notebook-sharing-observations-with-class-2.jpg\" class=\"attachment-full size-full wp-image-2365\" alt=\"mathematicians notebook sharing observations with class example 2\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\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 class=\"elementor-element elementor-element-7578b85 elementor-widget elementor-widget-text-editor\" data-id=\"7578b85\" 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<p>Sharing Their Observations with the Class<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-fbf32f3 elementor-widget elementor-widget-text-editor\" data-id=\"fbf32f3\" 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<p>The resulting anchor chart of students\u2019 \u201cnoticings\u201d offers invaluable information for teacher and students alike. Students\u2019 shared ideas scaffold fellow classmates\u2019 opportunities for enhanced group learning. Student descriptions reflect their current understandings whereby teachers make decisions regarding next steps for instruction. Finally, students\u2019 posted information offers the entire group a reference point or \u201ccollective memory\u201d (e.g., pre-assessment data) to reference during the remaining segments of the lesson.\u00a0<\/p><p>Additional options for launching a lesson include sharing students\u2019 previous work or intentionally selecting student work samples that are mathematically correct or incorrect. Once again, the teacher asks students to closely examine and make sense of classmates\u2019 strategies, representation(s), misconceptions, or generalizations. Asking students to notice important mathematical details, while making connections to what they already know, further support students\u2019 investigations, engagement, and refinement of concepts central to learning mathematics.<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e015cd6 elementor-widget elementor-widget-heading\" data-id=\"e015cd6\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">In a \u201cNutshell\u201d, the Launch:<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ce54b99 elementor-icon-list--layout-traditional elementor-list-item-link-full_width elementor-widget elementor-widget-icon-list\" data-id=\"ce54b99\" data-element_type=\"widget\" data-widget_type=\"icon-list.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items\">\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-circle\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Is inquiry-based.<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-circle\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Invites students to make sense of a mathematical representation.<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-circle\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Provides all students access to the content of a lesson.<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-circle\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Actively engages students with the concepts of a lesson.<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-circle\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Supports students accessing prior knowledge by placing it into short-term and working memories.<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-circle\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Offers opportunities for students to build upon each other\u2019s ideas, to validate one another\u2019s thinking, and\/or correct misconceptions.<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-check-circle\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Provides formative assessment data for teacher and for students.<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c68ab6d elementor-widget elementor-widget-heading\" data-id=\"c68ab6d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Ideas to Consider When Selecting the Mathematical Representation:<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-642cda7 elementor-icon-list--layout-traditional elementor-list-item-link-full_width elementor-widget elementor-widget-icon-list\" data-id=\"642cda7\" data-element_type=\"widget\" data-widget_type=\"icon-list.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items\">\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-lightbulb\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">What mathematical ideas (conceptual and procedural) do you want your students to understand, know, and do by the end of the lesson?<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-lightbulb\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">How might students interpret the representation(s) you have selected?<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-lightbulb\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">In what ways will the selected representation build upon students\u2019 existing schema?<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-lightbulb\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">How will you introduce students to the task or representation, provide access to all, and NOT undermine student thinking?<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-lightbulb\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">What questions will you ask to assist students accessing their prior knowledge?<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"far fa-lightbulb\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">What possible mathematical misconceptions might arise?<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6bff157 elementor-widget elementor-widget-heading\" data-id=\"6bff157\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Questions to pose during the enactment of the Launch**:<\/h4>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-b9fc710 elementor-icon-list--layout-traditional elementor-list-item-link-full_width elementor-widget elementor-widget-icon-list\" data-id=\"b9fc710\" data-element_type=\"widget\" data-widget_type=\"icon-list.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul class=\"elementor-icon-list-items\">\n\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"fas fa-question\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">What do you notice? What sense can you make of this?<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"fas fa-question\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">What might this statement or question ask you to think about? How do you know?<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<a href=\"#\">\n\n\t\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"fas fa-question\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">What mathematical ideas comes to mind?<\/span>\n\t\t\t\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"fas fa-question\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">How might this representation connect to concepts we\u2019ve already studied?<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"fas fa-question\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">What patterns or structure do you see within this mathematical representation?<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t\t\t<li class=\"elementor-icon-list-item\">\n\t\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-icon\">\n\t\t\t\t\t\t\t<i aria-hidden=\"true\" class=\"fas fa-question\"><\/i>\t\t\t\t\t\t<\/span>\n\t\t\t\t\t\t\t\t\t\t<span class=\"elementor-icon-list-text\">Where might you have seen this before?<\/span>\n\t\t\t\t\t\t\t\t\t<\/li>\n\t\t\t\t\t\t<\/ul>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-0fc2bae elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0fc2bae\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-custom\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-inner-column elementor-element elementor-element-7948ecb\" data-id=\"7948ecb\" 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-a3783e7 elementor-widget elementor-widget-heading\" data-id=\"a3783e7\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Visual Model for Math Workshop<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-3dc86fb elementor-widget elementor-widget-image\" data-id=\"3dc86fb\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/carrie-zielinski-visual-model-math-workshop.jpg\" data-elementor-open-lightbox=\"yes\" data-elementor-lightbox-title=\"carrie zielinski visual model math workshop\" data-e-action-hash=\"#elementor-action%3Aaction%3Dlightbox%26settings%3DeyJpZCI6MjQxNiwidXJsIjoiaHR0cHM6XC9cL2RlbmlzZWdvZXR6LmNvbVwvQ1pNYXRoQ29uc3VsdGluZ1wvd3AtY29udGVudFwvdXBsb2Fkc1wvMjAyMVwvMDNcL2NhcnJpZS16aWVsaW5za2ktdmlzdWFsLW1vZGVsLW1hdGgtd29ya3Nob3AuanBnIn0%3D\">\n\t\t\t\t\t\t\t<img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"289\" src=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/carrie-zielinski-visual-model-math-workshop.jpg\" class=\"attachment-medium_large size-medium_large wp-image-2416\" alt=\"carrie zielinskis visual model for math workshops\" srcset=\"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/carrie-zielinski-visual-model-math-workshop.jpg 500w, https:\/\/denisegoetz.com\/CZMathConsulting\/wp-content\/uploads\/2021\/03\/carrie-zielinski-visual-model-math-workshop-300x173.jpg 300w\" sizes=\"(max-width: 500px) 100vw, 500px\" \/>\t\t\t\t\t\t\t\t<\/a>\n\t\t\t\t\t\t\t\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 class=\"elementor-element elementor-element-d45c06d elementor-widget elementor-widget-heading\" data-id=\"d45c06d\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">References<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2a3452f elementor-widget elementor-widget-text-editor\" data-id=\"2a3452f\" 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<p>**Garner, B. K. (2007). Getting to got it: Helping struggling students learn how to learn. Alexandria, VA: Association for Supervision and Curriculum Development.<\/p><p>Learner, J. W., &amp; Johns, B. H. (2012). Learning Disabilities and Related Mild Disabilities: Teaching Strategies and New Directions. Belmont, CA: Wadsworth Cengage Learning.<\/p><p>Monroe Public Schools: Math Workshop Model. Monroe, MI.<\/p><p>Reys, B.J., &amp; Long, V. (1995). Teacher as architect of mathematical tasks. Teaching Children Mathematics, 1(5), 296-299.<\/p><p>**Smith, M., Bill, V., &amp; Hughes, E. (2008). Thinking through a Lesson: Successfully Implementing High-Level Tasks. Mathematics Teaching in the Middle School 14(3), 132-138.<\/p><p>Zielinski, C. D. (2018). A re-envisioned instruction model: Minimizing students\u2019 learning difficulties in mathematics. [Doctoral dissertation, University of Michigan \u2013 Dearborn.]<\/p>\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>Launching Math Lessons Proven Practices \u201cNo other decision that teachers make has greater impact on students\u2019 opportunities to learn and on their perceptions about what mathematics is than the selection or creation of the tasks with which the teacher engages the students in studying mathematics. Here, the teacher is the architect, the designer of the &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/denisegoetz.com\/CZMathConsulting\/launching-lessons\/\"> <span class=\"screen-reader-text\">Launching Lessons<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1955","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-json\/wp\/v2\/pages\/1955","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-json\/wp\/v2\/comments?post=1955"}],"version-history":[{"count":5,"href":"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-json\/wp\/v2\/pages\/1955\/revisions"}],"predecessor-version":[{"id":2555,"href":"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-json\/wp\/v2\/pages\/1955\/revisions\/2555"}],"wp:attachment":[{"href":"https:\/\/denisegoetz.com\/CZMathConsulting\/wp-json\/wp\/v2\/media?parent=1955"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}