{"id":1158,"date":"2022-10-13T03:01:47","date_gmt":"2022-10-12T22:01:47","guid":{"rendered":"https:\/\/rileymath.com\/?p=1158"},"modified":"2022-10-13T03:23:41","modified_gmt":"2022-10-12T22:23:41","slug":"learning-teaching-math-teaching-magazine-nctm-for-september-2022-reviews","status":"publish","type":"post","link":"https:\/\/rileymath.com\/index.php\/2022\/10\/13\/learning-teaching-math-teaching-magazine-nctm-for-september-2022-reviews\/","title":{"rendered":"Learning Teaching (Math Teaching) Magazine (NCTM) for September 2022 Reviews"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"1158\" class=\"elementor elementor-1158\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<section data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-section elementor-top-section elementor-element elementor-element-856c67f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"856c67f\" 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-f343c08\" data-id=\"f343c08\" 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-f0d7723 elementor-widget elementor-widget-image\" data-id=\"f0d7723\" 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<img fetchpriority=\"high\" decoding=\"async\" width=\"768\" height=\"996\" src=\"https:\/\/rileymath.com\/wp-content\/uploads\/2022\/09\/307765842_10160312576334188_820303886137266030_n-768x996.jpg\" class=\"attachment-medium_large size-medium_large wp-image-1033\" alt=\"\" srcset=\"https:\/\/rileymath.com\/wp-content\/uploads\/2022\/09\/307765842_10160312576334188_820303886137266030_n-768x996.jpg 768w, https:\/\/rileymath.com\/wp-content\/uploads\/2022\/09\/307765842_10160312576334188_820303886137266030_n-231x300.jpg 231w, https:\/\/rileymath.com\/wp-content\/uploads\/2022\/09\/307765842_10160312576334188_820303886137266030_n-790x1024.jpg 790w, https:\/\/rileymath.com\/wp-content\/uploads\/2022\/09\/307765842_10160312576334188_820303886137266030_n.jpg 1080w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\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<section data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-section elementor-top-section elementor-element elementor-element-9f8f49c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9f8f49c\" 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-2eaca93\" data-id=\"2eaca93\" 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-570a00b elementor-widget elementor-widget-heading\" data-id=\"570a00b\" 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\">Here is a table of contents for this month's magazine:<br><\/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 data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-section elementor-top-section elementor-element elementor-element-9851f94 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9851f94\" 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-22a7436\" data-id=\"22a7436\" 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-315c1fd elementor-widget elementor-widget-text-editor\" data-id=\"315c1fd\" 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<div style=\"margin-bottom: 8px; font-family: system-ui, -apple-system, BlinkMacSystemFont, '.SFNSText-Regular', sans-serif; caret-color: #050505; color: #050505; font-size: 15px;\">\u00a0<\/div><h2 style=\"margin-bottom: 8px; font-family: inherit;\"><span style=\"word-break: break-word; max-width: 100%; font-family: inherit; word-wrap: break-word; font-size: 0.9375rem; min-width: 0px; -webkit-font-smoothing: antialiased; line-height: 1.3333; color: var(--primary-text);\"><span style=\"color: #0000ff;\"><strong>Tackling Tangential Student Contributions<\/strong><\/span> &#8211; Minimizing and dealing with tangential comments in class.<strong> (Reviewed)<\/strong><\/span><\/h2><div style=\"margin-bottom: 8px; font-family: inherit;\"><p class=\"MsoNormal\" style=\"font-size: medium; caret-color: #000000; color: #000000;\"><span class=\"creator-type-label\"><span style=\"font-family: Lato, sans-serif; color: #101010;\">Author:<\/span><\/span><span class=\"apple-converted-space\"><span style=\"font-family: Lato, sans-serif; color: #101010; background-color: #d3dade;\"><span style=\"caret-color: #101010;\">\u00a0<\/span><\/span><\/span><span style=\"font-family: Lato, sans-serif; color: #101010;\"><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/search?f_0=author&amp;q_0=Blake+E.+Peterson\" data-feathr-click-track=\"true\"><span style=\"box-sizing: inherit; caret-color: #101010;\"><span style=\"color: #701471; text-decoration: none;\">Blake E. Peterson<\/span><\/span><\/a><\/span><sup style=\"box-sizing: inherit;\"><span style=\"font-size: 9pt; font-family: Lato, sans-serif; color: #101010;\"><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/view\/journals\/mtlt\/115\/9\/article-p618.xml?tab_body=p618#affiliation0\" data-feathr-click-track=\"true\"><span style=\"color: #701471; text-decoration: none;\">1<\/span><\/a><\/span><\/sup><span style=\"font-family: Lato, sans-serif; color: #101010;\"><span style=\"box-sizing: inherit; caret-color: #101010;\">,<span class=\"apple-converted-space\">\u00a0<\/span><\/span><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/search?f_0=author&amp;q_0=Shari+L.+Stockero\" data-feathr-click-track=\"true\"><span style=\"box-sizing: inherit; caret-color: #101010;\"><span style=\"color: #701471; text-decoration: none;\">Shari L. Stockero<\/span><\/span><\/a><\/span><sup style=\"box-sizing: inherit;\"><span style=\"font-size: 9pt; font-family: Lato, sans-serif; color: #101010;\"><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/view\/journals\/mtlt\/115\/9\/article-p618.xml?tab_body=p618#affiliation1\" data-feathr-click-track=\"true\"><span style=\"color: #701471; text-decoration: none;\">2<\/span><\/a><\/span><\/sup><span style=\"font-family: Lato, sans-serif; color: #101010;\"><span style=\"box-sizing: inherit; caret-color: #101010;\">,<span class=\"apple-converted-space\">\u00a0<\/span><\/span><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/search?f_0=author&amp;q_0=Keith+R.+Leatham\" data-feathr-click-track=\"true\"><span style=\"box-sizing: inherit; caret-color: #101010;\"><span style=\"color: #701471; text-decoration: none;\">Keith R. Leatham<\/span><\/span><\/a><\/span><sup style=\"box-sizing: inherit;\"><span style=\"font-size: 9pt; font-family: Lato, sans-serif; color: #101010;\"><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/view\/journals\/mtlt\/115\/9\/article-p618.xml?tab_body=p618#affiliation0\" data-feathr-click-track=\"true\"><span style=\"color: #701471; text-decoration: none;\">1<\/span><\/a><\/span><\/sup><span style=\"font-family: Lato, sans-serif; color: #101010;\"><span style=\"box-sizing: inherit; caret-color: #101010;\">, and<span class=\"apple-converted-space\">\u00a0<\/span><\/span><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/search?f_0=author&amp;q_0=Laura+R.+Van+Zoest\" data-feathr-click-track=\"true\"><span style=\"box-sizing: inherit; caret-color: #101010;\"><span style=\"color: #701471; text-decoration: none;\">Laura R. Van<\/span><\/span><\/a><\/span>\u00a0ZOEST<\/p><\/div><ul style=\"margin-top: 8px; margin-bottom: 8px; padding: 0px 0px 0px 32px; caret-color: #050505; color: #050505; font-family: system-ui, -apple-system, BlinkMacSystemFont, '.SFNSText-Regular', sans-serif; font-size: 15px;\"><li><div style=\"margin-bottom: 8px; font-family: inherit;\"><span style=\"word-break: break-word; max-width: 100%; font-family: inherit; word-wrap: break-word; font-size: 0.9375rem; min-width: 0px; -webkit-font-smoothing: antialiased; line-height: 1.3333; color: var(--primary-text);\">(PK-2) Mathematics through Children&#8217;s Literature<\/span><\/div><\/li><li><div style=\"margin-bottom: 8px; font-family: inherit;\"><span style=\"word-break: break-word; max-width: 100%; font-family: inherit; word-wrap: break-word; font-size: 0.9375rem; min-width: 0px; -webkit-font-smoothing: antialiased; line-height: 1.3333; color: var(--primary-text);\">(3-5) Centering Families&#8217; Mathematical Practices in a Multilingual Space<\/span><\/div><\/li><li><div style=\"margin-bottom: 8px; font-family: inherit;\"><span style=\"word-break: break-word; max-width: 100%; font-family: inherit; word-wrap: break-word; font-size: 0.9375rem; min-width: 0px; -webkit-font-smoothing: antialiased; line-height: 1.3333; color: var(--primary-text);\">(6-8) Understanding Similarity through Dilations of Nonstandard Shapes<\/span><\/div><\/li><li><div style=\"margin-bottom: 8px; font-family: inherit;\"><span style=\"word-break: break-word; max-width: 100%; font-family: inherit; word-wrap: break-word; font-size: 0.9375rem; min-width: 0px; -webkit-font-smoothing: antialiased; line-height: 1.3333; color: var(--primary-text);\">(9-12) Exploring Geometry with Origami One-Cut-Heart<\/span><\/div><\/li><li><div style=\"margin-bottom: 8px; font-family: inherit;\"><span style=\"word-break: break-word; max-width: 100%; font-family: inherit; word-wrap: break-word; font-size: 0.9375rem; min-width: 0px; -webkit-font-smoothing: antialiased; line-height: 1.3333; color: var(--primary-text);\">Five reasons to include statistics in Algebra<\/span><\/div><\/li><li><div style=\"margin-bottom: 8px; font-family: inherit;\"><span style=\"word-break: break-word; max-width: 100%; font-family: inherit; word-wrap: break-word; font-size: 0.9375rem; min-width: 0px; -webkit-font-smoothing: antialiased; line-height: 1.3333; color: var(--primary-text);\">Growing Problem Solvers &#8211; Mathematical Modeling Tasks<\/span><\/div><\/li><li><div style=\"margin-bottom: 8px; font-family: inherit;\"><span style=\"word-break: break-word; max-width: 100%; font-family: inherit; word-wrap: break-word; font-size: 0.9375rem; min-width: 0px; -webkit-font-smoothing: antialiased; line-height: 1.3333; color: var(--primary-text);\">Ear to the Ground &#8211; Becoming Students of our students<\/span><\/div><\/li><li><div style=\"margin-bottom: 8px; font-family: inherit;\"><span style=\"word-break: break-word; max-width: 100%; font-family: inherit; word-wrap: break-word; font-size: 0.9375rem; min-width: 0px; -webkit-font-smoothing: antialiased; line-height: 1.3333; color: var(--primary-text);\">Teaching is a Journey &#8211; General Studies in Education<\/span><\/div><\/li><\/ul>\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<section data-particle_enable=\"false\" data-particle-mobile-disabled=\"false\" class=\"elementor-section elementor-top-section elementor-element elementor-element-48263b7 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"48263b7\" 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-ab47630\" data-id=\"ab47630\" 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-ab6796e elementor-widget elementor-widget-text-editor\" data-id=\"ab6796e\" 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 class=\"MsoNormal\" style=\"font-size: medium; caret-color: #000000; color: #000000;\"><span class=\"creator-type-label\"><span style=\"font-family: Lato, sans-serif; color: #101010;\">Author:<\/span><\/span><span class=\"apple-converted-space\"><span style=\"font-family: Lato, sans-serif; color: #101010; background-color: #d3dade;\"><span style=\"caret-color: #101010;\">\u00a0<\/span><\/span><\/span><span style=\"font-family: Lato, sans-serif; color: #101010;\"><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/search?f_0=author&amp;q_0=Blake+E.+Peterson\" data-feathr-click-track=\"true\"><span style=\"box-sizing: inherit; caret-color: #101010;\"><span style=\"color: #701471; text-decoration: none;\">Blake E. Peterson<\/span><\/span><\/a><\/span><sup style=\"box-sizing: inherit;\"><span style=\"font-size: 9pt; font-family: Lato, sans-serif; color: #101010;\"><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/view\/journals\/mtlt\/115\/9\/article-p618.xml?tab_body=p618#affiliation0\" data-feathr-click-track=\"true\"><span style=\"color: #701471; text-decoration: none;\">1<\/span><\/a><\/span><\/sup><span style=\"font-family: Lato, sans-serif; color: #101010;\"><span style=\"box-sizing: inherit; caret-color: #101010;\">,<span class=\"apple-converted-space\">\u00a0<\/span><\/span><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/search?f_0=author&amp;q_0=Shari+L.+Stockero\" data-feathr-click-track=\"true\"><span style=\"box-sizing: inherit; caret-color: #101010;\"><span style=\"color: #701471; text-decoration: none;\">Shari L. Stockero<\/span><\/span><\/a><\/span><sup style=\"box-sizing: inherit;\"><span style=\"font-size: 9pt; font-family: Lato, sans-serif; color: #101010;\"><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/view\/journals\/mtlt\/115\/9\/article-p618.xml?tab_body=p618#affiliation1\" data-feathr-click-track=\"true\"><span style=\"color: #701471; text-decoration: none;\">2<\/span><\/a><\/span><\/sup><span style=\"font-family: Lato, sans-serif; color: #101010;\"><span style=\"box-sizing: inherit; caret-color: #101010;\">,<span class=\"apple-converted-space\">\u00a0<\/span><\/span><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/search?f_0=author&amp;q_0=Keith+R.+Leatham\" data-feathr-click-track=\"true\"><span style=\"box-sizing: inherit; caret-color: #101010;\"><span style=\"color: #701471; text-decoration: none;\">Keith R. Leatham<\/span><\/span><\/a><\/span><sup style=\"box-sizing: inherit;\"><span style=\"font-size: 9pt; font-family: Lato, sans-serif; color: #101010;\"><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/view\/journals\/mtlt\/115\/9\/article-p618.xml?tab_body=p618#affiliation0\" data-feathr-click-track=\"true\"><span style=\"color: #701471; text-decoration: none;\">1<\/span><\/a><\/span><\/sup><span style=\"font-family: Lato, sans-serif; color: #101010;\"><span style=\"box-sizing: inherit; caret-color: #101010;\">, and<span class=\"apple-converted-space\">\u00a0<\/span><\/span><a style=\"color: #954f72; text-decoration: underline; box-sizing: inherit; min-width: auto; min-height: auto; text-transform: unset;\" href=\"https:\/\/pubs.nctm.org\/search?f_0=author&amp;q_0=Laura+R.+Van+Zoest\" data-feathr-click-track=\"true\"><span style=\"box-sizing: inherit; caret-color: #101010;\"><span style=\"color: #701471; text-decoration: none;\">Laura R. Van<\/span><\/span><\/a><\/span>\u00a0ZOEST<\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-family: Lato, sans-serif; color: #101010;\">THIS ARTICLE GIVES SOME ADVICE AND STRATEGIES FOR MANAGING MATHEMATICAL DISCOURSE IN THE CLASSROOM. This article gives some advice and strategies for manageing mathematical discourse in ther classroom. The fourth effective math teachiung practice from Principles to Actions (NCTM 2014) i:\u00a0<\/span><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">Facilitate meaningful mathematical discourse.<\/span><span style=\"font-family: 'Times New Roman', serif;\">\u00a0\u00a0We all have mathematical discourse in our classrooms, but we all also need to have strategies to keep it focused and on track other than shouting \u201cStop Talking \u201c\u00a0\u00a0or \u201cPut her down right now!)\u00a0<\/span><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">As we take on the challenge of facilitating a mathematical discussion, there are many strategies and methods to keep the conversation productive and on track.\u00a0\u00a0This can be challenging for young children.\u00a0\u00a0There are also many many ways the conversations could deviate, become unfocused and go off on a tangent.\u00a0\u00a0This articles gives advice in stuations where a student makes a valuable contribution that is only loosely related to the topic at hand.\u00a0\u00a0I recently was having a mathematical discussion with a 6<sup>th<\/sup>\u00a0grade class.\u00a0\u00a0The conversation began on the topic of percents and ended up as a discussion of black holes, the nature of reality and how we see colors.\u00a0\u00a0It was a lot of fun for me, but the original topic was quickly lost.\u00a0\u00a0BTW they walked out thinking about the question \u201cWhat if everyone had the same favorite color, but our eyes and brains perceive it differently?\u201d\u00a0\u00a0No one slept that night.<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">One example is when a student has offered a solution to a problem and the class is discussing the solution and then another student offers a different method.\u00a0\u00a0Do you begin discussing the new solution or stay with the current idea?\u00a0\u00a0If you divert, you could fragment the class and the discussion and also dishonor the original student\u2019s contribution.<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">They introduce a couple different terms we can use to understand\u00a0<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p style=\"margin-right: 0in; margin-left: 0in; font-size: medium; font-family: 'Times New Roman', serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">Focal Instance \u2013 a\u00a0<\/span><span style=\"font-size: 9pt; font-family: SourceSerifPro, serif;\">\u00a0<\/span><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">student contribution that the teacher has chosen to pursue for some particular purpose.\u00a0\u00a0It is that moment that a student offeres a contribution to the claa and you decide to focus the class on this contribution for a short discussion.\u00a0\u00a0Choosing these focal instances is the foundation of mathematical classroom discourse.<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">Mathematical Opportunity in Student Thinking (MOST) \u2013 When a student offers their thinking and you recognize\u00a0\u00a0a teachable moment in their contribution you have a MOST.<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">Facilitating mathematicsl discourse is often an exercise recognizing Mosts and turning them into focal instances.<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">CONERSATIONAL BUBBLE \u2013 When the teacher temporarily pauses the broader mathematically activity to explicitely take up the focal instance.<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">This article focuses on teacher moves that keep the whole-class discussion centered on a contribution that the teacher has decided is a focal instance.\u00a0<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">How to reduce the frequency of tangential student contributions<\/span><\/p><p class=\"MsoNormal\" style=\"margin: 0in; font-size: medium; font-family: Calibri, sans-serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p class=\"MsoListParagraphCxSpFirst\" style=\"text-indent: -.25in; mso-list: l0 level1 lfo1;\"><!-- [if !supportLists]--><span style=\"font-size: 12.5pt; font-family: 'Arial',sans-serif; mso-fareast-font-family: Arial;\"><span style=\"mso-list: Ignore;\">1.<span style=\"font: 7.0pt 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span><!--[endif]--><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0Ask targeted questions \u2013 The questions should be explicitely about the the focal instance and not general questions like : \u201cWhat do you think?\u201d or questions aboiut the broader activity like: \u201cDid anyone else use this solution?\u201d<\/span><\/p><p class=\"MsoListParagraphCxSpLast\" style=\"text-indent: -.25in; mso-list: l0 level1 lfo1;\"><!-- [if !supportLists]--><span style=\"font-size: 12.5pt; font-family: 'Arial',sans-serif; mso-fareast-font-family: Arial;\"><span style=\"mso-list: Ignore;\">2.<span style=\"font: 7.0pt 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span><!--[endif]--><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">Help keep students in the conversational bubble.\u00a0\u00a0Calling on one of the random hands that go up is the \u201cBox of Chocolates arpproach.\u00a0\u00a0It leaves open the risk of a student sharing their own solution and taking the conversation away from the focal instance.\u00a0\u00a0Instead the teacher can ask the spontaneous volunteer a targeted question like :\u00a0\u00a0\u201cDO you have something to share about Julie\u2019s solution (the Focal instance).\u201d\u00a0\u00a0This can also be discussed in classroom norms.<\/span><\/p><p style=\"margin-right: 0in; margin-left: 0in; font-size: medium; font-family: 'Times New Roman', serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0Responding to tangential Student contributions:\u00a0\u00a0In this instanmce you can find yourself torn between remaining within the conversational bubble and honoring the new student\u2019s contribution.\u00a0\u00a0a teacher might say, \u201cYou\u2019ve just shared another way you could think about this task, but remem- ber that right now we\u2019re making sense of Sonia\u2019s claim\u201d\u2014a statement that positions Edward as a legitimate mathematical thinker but keeps the discussion centered on the focal instance. You can use a combination of putting aside and recentering\u00a0\u00a0moves like this to keep the discussion centered on the focal instance. The key is that it should be both putting aside and reentering.\u00a0\u00a0If not, another tangential contribution will frequently surface.\u00a0\u00a0Some teachers might go to another \u201cbox of Chocolates move\u201d by calling for spontaneous contributions or returning to the general actifity by asking \u201cWhat did others think?\u201d which values more participation but not their thinking.<\/span><\/p><p style=\"margin-right: 0in; margin-left: 0in; font-size: medium; font-family: 'Times New Roman', serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p style=\"margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo1;\"><!-- [if !supportLists]--><span style=\"font-size: 12.5pt; font-family: 'Arial',sans-serif; mso-fareast-font-family: Arial;\"><span style=\"mso-list: Ignore;\">3.<span style=\"font: 7.0pt 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span><!--[endif]--><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0You could stay with a tangential contribution:\u00a0\u00a0The teacher may not want to immediately put aside a tangential contribution but rather allow a few conversational turns before deciding whether to put aside and recenter on thw focal instance.\u00a0\u00a0Maybe the teacher askes for clarification in order to search for a better connection to the focal instance. Say .g., \u201cThank you for sharing\u201d or \u201cI understand what you\u2019re saying\u201d), and then recenter the focal instance (e.g., \u201cSo, where are we in making sense of [the focal instance]?\u201d) It is helpful to try to connect the new contribution to the focal instance.\u00a0\u00a0\u201cHow does this help us make sense of the focal instance?\u201d<\/span><\/p><p style=\"margin-right: 0in; margin-left: 0.5in; font-size: medium; font-family: 'Times New Roman', serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p style=\"margin-left: .5in; text-indent: -.25in; mso-list: l0 level1 lfo1;\"><!-- [if !supportLists]--><span style=\"font-size: 12.5pt; font-family: 'Arial',sans-serif; mso-fareast-font-family: Arial;\"><span style=\"mso-list: Ignore;\">4.<span style=\"font: 7.0pt 'Times New Roman';\">\u00a0\u00a0\u00a0\u00a0<\/span><\/span><\/span><!--[endif]--><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">In some cases, the teacher may need to stay with the tangential student contribution in order to address pre-requisite mathematics such as:\u00a0\u00a0you cannot compare x and x+x or any variable equations unless you agree that the x values must be the same.\u00a0\u00a0SO setting x to different values is not a valid solution.\u00a0\u00a0Ask yourself\u00a0\u00a0\u201cMust the students make sense of this idea before they can make sense of the focal instance?\u201d\u00a0<\/span><\/p><p style=\"margin-right: 0in; margin-left: 0.5in; font-size: medium; font-family: 'Times New Roman', serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><b><span style=\"font-size: 14pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/b><\/p><p style=\"margin-right: 0in; margin-left: 0.5in; font-size: medium; font-family: 'Times New Roman', serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><b><span style=\"font-size: 14pt; font-family: Arial, sans-serif;\">Conclusion:\u00a0\u00a0One way to facilitate math discourse is to pause the broader activity and create a conversational bubble around a focal instance contributed by student thinking. It may take time and some classroom norming to become more effective at creating, facilitating and maintaining conversationbal bubbles to their effective conclusion.<\/span><\/b><\/p><p style=\"margin-right: 0in; margin-left: 0.5in; font-size: medium; font-family: 'Times New Roman', serif; caret-color: #000000; color: #000000; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; orphans: auto; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; widows: auto; word-spacing: 0px; -webkit-text-size-adjust: auto; -webkit-text-stroke-width: 0px; text-decoration: none;\"><span style=\"font-size: 12.5pt; font-family: Arial, sans-serif;\">\u00a0<\/span><\/p><p><style class=\"WebKit-mso-list-quirks-style\">\n<!-- \/* Style Definitions *\/ p.MsoNormal, li.MsoNormal, div.MsoNormal {mso-style-unhide:no; mso-style-qformat:yes; mso-style-parent:\"\"; margin:0in; mso-pagination:widow-orphan; font-size:12.0pt; font-family:\"Calibri\",sans-serif; 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(Reviewed) Author:\u00a0Blake E. Peterson1,\u00a0Shari L. Stockero2,\u00a0Keith R. Leatham1, and\u00a0Laura R. Van\u00a0ZOEST (PK-2) Mathematics through Children&#8217;s Literature (3-5) Centering Families&#8217; Mathematical Practices in a Multilingual Space (6-8) Understanding Similarity through Dilations of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_uag_custom_page_level_css":"","footnotes":""},"categories":[1],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v22.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Learning Teaching (Math Teaching) Magazine (NCTM) for September 2022 Reviews - Riley Math Education<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/rileymath.com\/index.php\/2022\/10\/13\/learning-teaching-math-teaching-magazine-nctm-for-september-2022-reviews\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Learning Teaching (Math Teaching) Magazine (NCTM) for September 2022 Reviews - Riley Math Education\" \/>\n<meta property=\"og:description\" content=\"Here is a table of contents for this month&#8217;s magazine: \u00a0 Tackling Tangential Student Contributions &#8211; Minimizing and dealing with tangential comments in class. 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