{"id":3602,"date":"2018-08-02T13:59:31","date_gmt":"2018-08-02T13:59:31","guid":{"rendered":"https:\/\/lessonresearch.net\/?page_id=3602"},"modified":"2026-01-28T05:49:17","modified_gmt":"2026-01-28T05:49:17","slug":"discussion","status":"publish","type":"page","link":"https:\/\/lessonresearch.net\/teaching-problem-solving\/discussion\/","title":{"rendered":"Discussion"},"content":{"rendered":"<p>[et_pb_section fb_built=&#8221;1&#8243; make_equal=&#8221;on&#8221; specialty=&#8221;on&#8221; padding_top_1=&#8221;0px&#8221; padding_top_2=&#8221;0px&#8221; padding_right_2=&#8221;0px&#8221; padding_bottom_2=&#8221;0px&#8221; padding_left_2=&#8221;0px&#8221; padding_top_bottom_link_1=&#8221;false&#8221; padding_top_bottom_link_2=&#8221;false&#8221; padding_left_right_link_1=&#8221;false&#8221; padding_left_right_link_2=&#8221;false&#8221; padding_1_tablet=&#8221;0px||||false|false&#8221; padding_1_phone=&#8221;&#8221; padding_1_last_edited=&#8221;on|phone&#8221; admin_label=&#8221;Header&#8221; module_id=&#8221;inner-banner&#8221; _builder_version=&#8221;4.16&#8243; background_color=&#8221;#FFFFFF&#8221; module_alignment=&#8221;center&#8221; min_height=&#8221;300px&#8221; custom_padding=&#8221;0px||0px||false|false&#8221; bottom_divider_color=&#8221;#f6f7f7&#8243; bottom_divider_flip=&#8221;horizontal&#8221; custom_css_main_element=&#8221;border-bottom-left-radius: 50%;||border-bottom-right-radius: 50%;&#8221; box_shadow_style=&#8221;preset1&#8243; box_shadow_vertical=&#8221;5px&#8221; box_shadow_blur=&#8221;12px&#8221; box_shadow_color=&#8221;rgba(0,0,0,0.14)&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;1_2&#8243; specialty_columns=&#8221;2&#8243; _builder_version=&#8221;4.16&#8243; custom_padding=&#8221;|||&#8221; global_colors_info=&#8221;{}&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_row_inner use_custom_gutter=&#8221;on&#8221; gutter_width=&#8221;1&#8243; module_id=&#8221;innner-row-1&#8243; module_class=&#8221;innner-row-1&#8243; _builder_version=&#8221;4.16&#8243; max_width=&#8221;1280px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;||||false|false&#8221; custom_margin_last_edited=&#8221;off|tablet&#8221; custom_padding=&#8221;||0px||false|false&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column_inner saved_specialty_column_type=&#8221;1_2&#8243; module_id=&#8221;inner-vol&#8221; admin_label=&#8221;Column&#8221; _builder_version=&#8221;4.16&#8243; custom_padding=&#8221;|||70px|false|false&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text _builder_version=&#8221;4.16&#8243; text_font=&#8221;Georgia||||||||&#8221; text_font_size=&#8221;20px&#8221; text_line_height=&#8221;1.8em&#8221; header_font=&#8221;GalanoGrotesqueAltBold|700|||||||&#8221; header_text_color=&#8221;gcid-260c2782-8cd7-4212-a449-cc62fe15ef25&#8243; header_font_size=&#8221;52px&#8221; header_line_height=&#8221;52px&#8221; width=&#8221;100%&#8221; custom_padding=&#8221;|0px||||&#8221; header_font_size_tablet=&#8221;40px&#8221; header_font_size_phone=&#8221;30px&#8221; header_font_size_last_edited=&#8221;on|phone&#8221; global_colors_info=&#8221;{%22gcid-260c2782-8cd7-4212-a449-cc62fe15ef25%22:%91%22header_text_color%22%93}&#8221;]<\/p>\n<h1 style=\"text-align: left;\">Teaching Through Problem-solving<br \/>\n<\/h1>\n<p>In Teaching Through Problem-solving (TTP), students develop each new mathematical concept by solving a problem that illuminates it.[\/et_pb_text][\/et_pb_column_inner][\/et_pb_row_inner][et_pb_row_inner module_id=&#8221;innner-row-2&#8243; module_class=&#8221;innner-row-2&#8243; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column_inner saved_specialty_column_type=&#8221;1_2&#8243; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Scroll Button&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; link_option_url=&#8221;#what-is-lesson-study&#8221; global_colors_info=&#8221;{}&#8221;]<a class=\"arrow-top resource\" href=\"#what-is-lesson-study\">arrow<\/a>[\/et_pb_text][\/et_pb_column_inner][\/et_pb_row_inner][\/et_pb_column][et_pb_column type=&#8221;1_2&#8243; _builder_version=&#8221;4.16&#8243; custom_padding=&#8221;|||&#8221; global_colors_info=&#8221;{}&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_image src=&#8221;https:\/\/lessonresearch.net\/wp-content\/uploads\/2018\/06\/MG_0338_optimized.jpg&#8221; alt=&#8221;An elementary-age male student points while his female teacher stands beside him and observes&#8221; title_text=&#8221;MG_0338_optimized&#8221; admin_label=&#8221;Image&#8221; module_id=&#8221;innner-row-img&#8221; module_class=&#8221;innner-row-img&#8221; _builder_version=&#8221;4.16&#8243; background_enable_image=&#8221;off&#8221; width=&#8221;90%&#8221; module_alignment=&#8221;right&#8221; max_height_last_edited=&#8221;off|tablet&#8221; custom_margin=&#8221;0px||0px|-21px|true|false&#8221; custom_padding=&#8221;0px||0px|1px|true|false&#8221; border_radii=&#8221;off||||&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][\/et_pb_column][\/et_pb_section][et_pb_section fb_built=&#8221;1&#8243; module_id=&#8221;what-is-lesson-study&#8221; module_class=&#8221;nopadding-bottom understand-study-section&#8221; _builder_version=&#8221;4.16&#8243; background_color=&#8221;#f6f7f7&#8243; custom_padding=&#8221;0px||||false|false&#8221; top_divider_flip=&#8221;vertical&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row _builder_version=&#8221;4.27.5&#8243; _module_preset=&#8221;default&#8221; max_width=&#8221;1136px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;0px||||false|false&#8221; custom_padding=&#8221;0px||20px||false|false&#8221; hover_enabled=&#8221;0&#8243; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221; sticky_enabled=&#8221;0&#8243;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_code _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; text_orientation=&#8221;center&#8221; custom_margin=&#8221;0px|-135px|||false|false&#8221; global_colors_info=&#8221;{}&#8221;]<div class=\"toolbox-header-menu-container12 learning-menu\"><ul id=\"menu-ttp-menu\" class=\"menu\"><li id=\"menu-item-3586\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3586\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/overview\/\" data-pageid=\"3585\">Overview<\/a><\/li>\n<li id=\"menu-item-3600\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3600\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/journals\/\" data-pageid=\"3598\">Journals<\/a><\/li>\n<li id=\"menu-item-3601\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3601\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/boardwork\/\" data-pageid=\"3599\">Boardwork<\/a><\/li>\n<li id=\"menu-item-3607\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3607\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/discussion\/\" data-pageid=\"3602\">Discussion<\/a><\/li>\n<li id=\"menu-item-16896\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16896\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/get-started\/\" data-pageid=\"16894\">Get started<\/a><\/li>\n<li id=\"menu-item-3606\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3606\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/ttp-in-action\/\" data-pageid=\"3603\">TTP in Action<\/a><\/li>\n<li id=\"menu-item-3605\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3605\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/ttp-resources\/\" data-pageid=\"3604\">Resources<\/a><\/li>\n<\/ul><\/div><!-- [et_pb_line_break_holder] --><div class=\"inner-mobile-menu\"><form><select><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/overview\/\">Overview<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/journals\/\">Journals<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/boardwork\/\">Boardwork<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/discussion\/\">Discussion<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/get-started\/\">Get started<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/ttp-in-action\/\">TTP in Action<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/ttp-resources\/\">Resources<\/option><\/select><\/form><\/div><!-- [et_pb_line_break_holder] -->[\/et_pb_code][et_pb_code _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; custom_margin=&#8221;90px|||||&#8221; custom_padding=&#8221;0px||||false|false&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_code][\/et_pb_column][\/et_pb_row][et_pb_row make_equal=&#8221;on&#8221; _builder_version=&#8221;4.16&#8243; max_width=&#8221;1110px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;10px|auto||auto||&#8221; custom_padding=&#8221;||1px|||&#8221; width_unit=&#8221;off&#8221; custom_width_percent=&#8221;100%&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.16&#8243; custom_padding=&#8221;|||&#8221; global_colors_info=&#8221;{}&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_text admin_label=&#8221;Description&#8221; module_class=&#8221;page-description custom-width-65&#8243; _builder_version=&#8221;4.16&#8243; text_font=&#8221;GalanoGrotesqueAltMedium|500|||||||&#8221; text_text_color=&#8221;#343085&#8243; text_font_size=&#8221;18px&#8221; text_line_height=&#8221;31px&#8221; width=&#8221;65%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;10px||10px||false|false&#8221; custom_padding=&#8221;||0px||false|false&#8221; z_index_tablet=&#8221;500&#8243; text_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; text_text_shadow_vertical_length_tablet=&#8221;0px&#8221; text_text_shadow_blur_strength_tablet=&#8221;1px&#8221; link_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; link_text_shadow_vertical_length_tablet=&#8221;0px&#8221; link_text_shadow_blur_strength_tablet=&#8221;1px&#8221; ul_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; ul_text_shadow_vertical_length_tablet=&#8221;0px&#8221; ul_text_shadow_blur_strength_tablet=&#8221;1px&#8221; ol_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; ol_text_shadow_vertical_length_tablet=&#8221;0px&#8221; ol_text_shadow_blur_strength_tablet=&#8221;1px&#8221; quote_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; quote_text_shadow_vertical_length_tablet=&#8221;0px&#8221; quote_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_2_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_2_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_2_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_3_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_3_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_3_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_4_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_4_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_4_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_5_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_5_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_5_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_6_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_6_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_6_text_shadow_blur_strength_tablet=&#8221;1px&#8221; box_shadow_horizontal_tablet=&#8221;0px&#8221; box_shadow_vertical_tablet=&#8221;0px&#8221; box_shadow_blur_tablet=&#8221;40px&#8221; box_shadow_spread_tablet=&#8221;0px&#8221; saved_tabs=&#8221;all&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<blockquote><p>The teacher should never say anything that a student could say.<br \/>\n<span class=\"quote-name\">\u2014Akihiko Takahashi<\/span><\/p>\n<p>Associate Professor of Elementary Mathematics, DePaul University, Chicago, IL\n<\/p><\/blockquote>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Section Title: Understand Lesson Study&#8221; module_class=&#8221;page-sub-title&#8221; _builder_version=&#8221;4.16&#8243; header_text_align=&#8221;center&#8221; header_2_font=&#8221;GalanoGrotesqueAltSemiBold|700|||||||&#8221; header_2_text_align=&#8221;left&#8221; header_2_letter_spacing=&#8221;0.5px&#8221; header_2_line_height=&#8221;38px&#8221; max_width=&#8221;732px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;|0px|5px|0px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Speaking and Listening Routines<\/h2>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Description&#8221; module_class=&#8221;page-description custom-width-65&#8243; _builder_version=&#8221;4.16&#8243; text_font=&#8221;Georgia||||||||&#8221; text_font_size=&#8221;16px&#8221; text_line_height=&#8221;26px&#8221; width=&#8221;65%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;10px||10px||false|false&#8221; custom_padding=&#8221;||0px||false|false&#8221; z_index_tablet=&#8221;500&#8243; text_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; text_text_shadow_vertical_length_tablet=&#8221;0px&#8221; text_text_shadow_blur_strength_tablet=&#8221;1px&#8221; link_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; link_text_shadow_vertical_length_tablet=&#8221;0px&#8221; link_text_shadow_blur_strength_tablet=&#8221;1px&#8221; ul_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; 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header_4_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_4_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_4_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_5_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_5_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_5_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_6_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_6_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_6_text_shadow_blur_strength_tablet=&#8221;1px&#8221; box_shadow_horizontal_tablet=&#8221;0px&#8221; box_shadow_vertical_tablet=&#8221;0px&#8221; box_shadow_blur_tablet=&#8221;40px&#8221; box_shadow_spread_tablet=&#8221;0px&#8221; saved_tabs=&#8221;all&#8221; global_colors_info=&#8221;{}&#8221;]Visitors to Teaching Through Problem-solving lessons often remark on the quality of student-led discussions. As one educator who visited a public research lesson commented, \u201cThe students ask \u2018teacher questions.&#8217;\u201d Typically, students expect to field questions from classmates after they present their work at the board; you can see examples of this routine in the video below. [\/et_pb_text][et_pb_video_slider show_image_overlay=&#8221;on&#8221; show_thumbnails=&#8221;off&#8221; use_icon_font_size=&#8221;on&#8221; icon_font_size=&#8221;50px&#8221; controls_color=&#8221;dark&#8221; _builder_version=&#8221;4.23.4&#8243; max_width=&#8221;550px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;18px||42px||false|false&#8221; border_radii=&#8221;on|14px|14px|14px|14px&#8221; box_shadow_style=&#8221;preset1&#8243; box_shadow_vertical=&#8221;8px&#8221; box_shadow_blur=&#8221;20px&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_video_slider_item admin_title=&#8221;TTP excerpt&#8221; src=&#8221;https:\/\/player.vimeo.com\/video\/282161922?h=3c07a8bd64&#038;dnt=1&#038;app_id=122963&#038;wmode=transparent&#8221; _builder_version=&#8221;4.11.1&#8243; global_colors_info=&#8221;{}&#8221; show_image_overlay=&#8221;on&#8221;][\/et_pb_video_slider_item][\/et_pb_video_slider][et_pb_text admin_label=&#8221;Description&#8221; module_class=&#8221;page-description custom-width-65&#8243; _builder_version=&#8221;4.16&#8243; text_font=&#8221;Georgia||||||||&#8221; text_font_size=&#8221;16px&#8221; text_line_height=&#8221;26px&#8221; width=&#8221;65%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;10px||10px||false|false&#8221; custom_padding=&#8221;||0px||false|false&#8221; z_index_tablet=&#8221;500&#8243; text_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; text_text_shadow_vertical_length_tablet=&#8221;0px&#8221; text_text_shadow_blur_strength_tablet=&#8221;1px&#8221; link_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; link_text_shadow_vertical_length_tablet=&#8221;0px&#8221; link_text_shadow_blur_strength_tablet=&#8221;1px&#8221; ul_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; ul_text_shadow_vertical_length_tablet=&#8221;0px&#8221; ul_text_shadow_blur_strength_tablet=&#8221;1px&#8221; ol_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; ol_text_shadow_vertical_length_tablet=&#8221;0px&#8221; ol_text_shadow_blur_strength_tablet=&#8221;1px&#8221; quote_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; quote_text_shadow_vertical_length_tablet=&#8221;0px&#8221; quote_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_2_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_2_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_2_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_3_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_3_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_3_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_4_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_4_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_4_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_5_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_5_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_5_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_6_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_6_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_6_text_shadow_blur_strength_tablet=&#8221;1px&#8221; box_shadow_horizontal_tablet=&#8221;0px&#8221; box_shadow_vertical_tablet=&#8221;0px&#8221; box_shadow_blur_tablet=&#8221;40px&#8221; box_shadow_spread_tablet=&#8221;0px&#8221; saved_tabs=&#8221;all&#8221; global_colors_info=&#8221;{}&#8221;]Routines for presenting and discussing work are built beginning in Kindergarten, when teachers help students speak in a loud voice, use hand signals to show their responses, and formulate questions for the presenter.  Video from Prieto Mathematics and Science Academy (a Chicago public school) captures presentation and discussion routines at different grade levels, along with teachers\u2019 reflections on how they built these routines.[\/et_pb_text][et_pb_video_slider show_image_overlay=&#8221;on&#8221; show_thumbnails=&#8221;off&#8221; use_icon_font_size=&#8221;on&#8221; icon_font_size=&#8221;50px&#8221; controls_color=&#8221;dark&#8221; module_id=&#8221;video-slider&#8221; module_class=&#8221;video-slider&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; background_enable_color=&#8221;off&#8221; max_width=&#8221;55%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;30px||60px||false|false&#8221; custom_padding=&#8221;0px||0px||true|false&#8221; border_radii=&#8221;on|20px|20px|20px|20px&#8221; border_style_all=&#8221;none&#8221; box_shadow_style=&#8221;preset2&#8243; global_colors_info=&#8221;{}&#8221;][et_pb_video_slider_item src=&#8221;https:\/\/player.vimeo.com\/video\/282249744?h=4d7a30eaa6&#038;dnt=1&#038;app_id=122963&#038;wmode=transparent&#8221; _builder_version=&#8221;4.11.1&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221; show_image_overlay=&#8221;on&#8221;][\/et_pb_video_slider_item][et_pb_video_slider_item src=&#8221;https:\/\/player.vimeo.com\/video\/282249955?h=426030d9f8&#038;dnt=1&#038;app_id=122963&#038;wmode=transparent&#8221; _builder_version=&#8221;4.11.1&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221; show_image_overlay=&#8221;on&#8221;][\/et_pb_video_slider_item][\/et_pb_video_slider][\/et_pb_column][\/et_pb_row][et_pb_row column_structure=&#8221;2_3,1_3&#8243; use_custom_gutter=&#8221;on&#8221; gutter_width=&#8221;2&#8243; make_equal=&#8221;on&#8221; _builder_version=&#8221;4.16&#8243; width=&#8221;65%&#8221; max_width=&#8221;1110px&#8221; module_alignment=&#8221;center&#8221; custom_padding=&#8221;30px||30px||true|false&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;2_3&#8243; _builder_version=&#8221;4.16&#8243; 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ul_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; ul_text_shadow_vertical_length_tablet=&#8221;0px&#8221; ul_text_shadow_blur_strength_tablet=&#8221;1px&#8221; ol_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; ol_text_shadow_vertical_length_tablet=&#8221;0px&#8221; ol_text_shadow_blur_strength_tablet=&#8221;1px&#8221; quote_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; quote_text_shadow_vertical_length_tablet=&#8221;0px&#8221; quote_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_2_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_2_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_2_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_3_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_3_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_3_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_4_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_4_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_4_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_5_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_5_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_5_text_shadow_blur_strength_tablet=&#8221;1px&#8221; header_6_text_shadow_horizontal_length_tablet=&#8221;0px&#8221; header_6_text_shadow_vertical_length_tablet=&#8221;0px&#8221; header_6_text_shadow_blur_strength_tablet=&#8221;1px&#8221; box_shadow_horizontal_tablet=&#8221;0px&#8221; box_shadow_vertical_tablet=&#8221;0px&#8221; box_shadow_blur_tablet=&#8221;40px&#8221; box_shadow_spread_tablet=&#8221;0px&#8221; saved_tabs=&#8221;all&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Teacher Questioning<\/h2>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;1_3&#8243; _builder_version=&#8221;4.16&#8243; custom_padding=&#8221;|||&#8221; global_colors_info=&#8221;{}&#8221; custom_padding__hover=&#8221;|||&#8221;][et_pb_button button_url=&#8221;\/wp-content\/uploads\/2018\/08\/TTP-Teacher-Questioning-Table.pdf&#8221; url_new_window=&#8221;on&#8221; button_text=&#8221;Download&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; custom_button=&#8221;on&#8221; button_text_size=&#8221;14px&#8221; button_text_color=&#8221;#FFFFFF&#8221; button_bg_color=&#8221;#00c5c9&#8243; button_border_width=&#8221;0px&#8221; button_border_radius=&#8221;50px&#8221; button_letter_spacing=&#8221;0.5px&#8221; button_font=&#8221;GalanoGrotesqueAltMedium||||||||&#8221; button_icon=&#8221;&#xe092;||divi||400&#8243; button_icon_placement=&#8221;left&#8221; button_on_hover=&#8221;off&#8221; custom_padding=&#8221;15px|25px|15px|45px|true|false&#8221; box_shadow_style=&#8221;preset1&#8243; box_shadow_vertical=&#8221;5px&#8221; box_shadow_blur=&#8221;12px&#8221; box_shadow_color=&#8221;rgba(0,0,0,0.1)&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_button][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; custom_margin=&#8221;28px|auto|28px|auto|true|false&#8221; custom_padding=&#8221;0px||0px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Section Title: Understand Lesson Study&#8221; module_class=&#8221;page-sub-title&#8221; _builder_version=&#8221;4.16&#8243; text_font=&#8221;Georgia||||||||&#8221; header_text_align=&#8221;center&#8221; header_2_font=&#8221;GalanoGrotesqueAltSemiBold|700|||||||&#8221; header_2_text_align=&#8221;left&#8221; header_2_letter_spacing=&#8221;0.5px&#8221; header_2_line_height=&#8221;38px&#8221; max_width=&#8221;700px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;|0px|5px|0px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<p>A second powerful influence on student-led discussion is the questions that teachers ask, which provide a model for the questions that we hope students will internalize and will learn to ask on their own. Click on the arrows below to see examples of teacher questions during each phase of a TTP lesson and the purpose of questioning during each phase.<\/p>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row module_id=&#8221;grasp-row&#8221; module_class=&#8221;grasp-row&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; max_width=&#8221;1110px&#8221; custom_padding=&#8221;35px|10px|5px|10px|false|false&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; border_width_all=&#8221;2px&#8221; border_color_all=&#8221;gcid-260c2782-8cd7-4212-a449-cc62fe15ef25&#8243; locked=&#8221;off&#8221; global_colors_info=&#8221;{%22gcid-260c2782-8cd7-4212-a449-cc62fe15ef25%22:%91%22border_color_all%22%93}&#8221;][et_pb_column type=&#8221;4_4&#8243; module_id=&#8221;grasp-row1&#8243; module_class=&#8221;grasp-row1&#8243; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_tabs active_tab_text_color=&#8221;#FFFFFF&#8221; module_id=&#8221;tab-box&#8221; module_class=&#8221;tab-box&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; tab_text_color=&#8221;#FFFFFF&#8221; body_font=&#8221;Georgia||||||||&#8221; body_font_size=&#8221;16px&#8221; tab_font=&#8221;GalanoGrotesqueAltSemiBold|500|||||||&#8221; custom_padding=&#8221;||0px||false|false&#8221; border_width_all=&#8221;0px&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_tab title=&#8221;1. Grasp the Problem&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; tab_font=&#8221;GalanoGrotesqueAltBold|700|||||||&#8221; tab_font_size=&#8221;15px&#8221; tab_letter_spacing=&#8221;0.3px&#8221; tab_line_height=&#8221;1.25em&#8221; custom_padding=&#8221;||||false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div class=\"et_pb_row  tab-row\">\n<div class=\"et_pb_column et_pb_column_1_3\">\n<div class=\"et_pb_text_inner\">\n<h4 class=\"sh2-subhead-bold\" style=\"text-align: left;\">PURPOSE OF TEACHER QUESTIONING<\/h4>\n<p>Encourages students to:<\/p>\n<ul class=\"sosymbol-paragraph\">\n<li>want to solve the problem<\/li>\n<li>notice what is similar or different from prior problems they have solved<\/li>\n<li>notice what is similar or different from prior problems they have solved<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"et_pb_column et_pb_column_1_3\">\n<div class=\"et_pb_text_inner\">\n<h4 class=\"sh2-subhead-bold\" style=\"text-align: left;\">EXAMPLES OF TEACHER QUESTIONS<\/h4>\n<ul class=\"sosymbol-paragraph\">\n<li class=\"sosymbol-paragraph\">What is the problem asking?<\/li>\n<li class=\"sosymbol-paragraph\">What do we know that might help us solve this problem?<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"et_pb_column et_pb_column_1_3 last-column\">\n<div class=\"et_pb_text_inner\">\n<\/div>\n<\/div>\n<\/div>\n<p>[\/et_pb_tab][et_pb_tab title=&#8221;2. Try to Solve&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div class=\"et_pb_row  tab-row\">\n<div class=\"et_pb_column et_pb_column_1_3\">\n<div class=\"et_pb_text_inner\">\n<h4 class=\"sh2-subhead-bold\" style=\"text-align: left;\">PURPOSE OF TEACHER QUESTIONING<\/h4>\n<p>Encourages students to:<\/p>\n<ul class=\"sosymbol-paragraph\">\n<li>try to use what they know<\/li>\n<li>try to solve the problem using important reasoning tools (mathematical expressions, models, etc.)<\/li>\n<li>try to solve the problem using important reasoning tools (mathematical expressions, models, etc.)<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"et_pb_column et_pb_column_1_3\">\n<div class=\"et_pb_text_inner\">\n<h4 class=\"sh2-subhead-bold\" style=\"text-align: left;\">EXAMPLES OF TEACHER QUESTIONS<\/h4>\n<ul class=\"sosymbol-paragraph\">\n<li class=\"sosymbol-paragraph\">What do you know?<\/li>\n<li class=\"sosymbol-paragraph\">What do the numbers in the problem mean?<\/li>\n<li class=\"sosymbol-paragraph\">How do the numbers in the problem show up in your picture?<\/li>\n<li class=\"sosymbol-paragraph\">How can you convince others?<\/li>\n<li class=\"sosymbol-paragraph\">Can you write a mathematical expression for your method?<\/li>\n<li class=\"sosymbol-paragraph\">Can you write a mathematical expression for your method?<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"et_pb_column et_pb_column_1_3 last-column\">\n<div class=\"et_pb_text_inner\"><\/div>\n<\/div>\n<\/div>\n<p>[\/et_pb_tab][et_pb_tab title=&#8221;3. Present &#038; Discuss&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div class=\"et_pb_row  tab-row\">\n<div class=\"et_pb_column et_pb_column_1_3\">\n<div class=\"et_pb_text_inner\">\n<h4 class=\"sh2-subhead-bold\" style=\"text-align: left;\">PURPOSE OF TEACHER QUESTIONING<\/h4>\n<p>Encourages students to:<\/p>\n<ul class=\"sosymbol-paragraph\">\n<li>understand classmates\u2019 ideas and compare and connect them<\/li>\n<li>consider the accuracy, efficiency, and generalizability of presented ideas<\/li>\n<li>connect their own ideas with presented ideas<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"et_pb_column et_pb_column_1_3\">\n<div class=\"et_pb_text_inner\">\n<h4 class=\"sh2-subhead-bold\" style=\"text-align: left;\">EXAMPLES OF TEACHER QUESTIONS<\/h4>\n<ul class=\"sosymbol-paragraph\">\n<li class=\"sosymbol-paragraph\">How many solved it this way?<\/li>\n<li class=\"sosymbol-paragraph\">Can you explain what Shavon did?<\/li>\n<li class=\"sosymbol-paragraph\">Do you agree with this method?<\/li>\n<li class=\"sosymbol-paragraph\">What is the same and different about Sam\u2019s and Marika\u2019s methods?<\/li>\n<li class=\"sosymbol-paragraph\">What are the good points and difficulties of each solution method?<\/li>\n<li class=\"sosymbol-paragraph\">Are there any more ways to solve this?<\/li>\n<li class=\"sosymbol-paragraph\">Will this always be true?<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"et_pb_column et_pb_column_1_3 last-column\">\n<div class=\"et_pb_text_inner\"><\/div>\n<\/div>\n<\/div>\n<p>[\/et_pb_tab][et_pb_tab title=&#8221;4. Summarize &#038; Reflect&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div class=\"et_pb_row  tab-row\">\n<div class=\"et_pb_column et_pb_column_1_3\">\n<div class=\"et_pb_text_inner\">\n<h4 class=\"sh2-subhead-bold\" style=\"text-align: left;\">PURPOSE OF TEACHER QUESTIONING<\/h4>\n<p>Encourages students to:<\/p>\n<ul class=\"sosymbol-paragraph\">\n<li>summarize what they learned<\/li>\n<li>individually write about their own learning after hearing classmates\u2019 summaries<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"et_pb_column et_pb_column_1_3\">\n<div class=\"et_pb_text_inner\">\n<h4 class=\"sh2-subhead-bold\" style=\"text-align: left;\">EXAMPLES OF TEACHER QUESTIONS<\/h4>\n<ul class=\"sosymbol-paragraph\">\n<li class=\"sosymbol-paragraph\">What did we learn today?<\/li>\n<li class=\"sosymbol-paragraph\">How did my ideas change?<\/li>\n<li class=\"sosymbol-paragraph\">What method used by a classmate do I want to try?<\/li>\n<li class=\"sosymbol-paragraph\">What do I wonder about?<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"et_pb_column et_pb_column_1_3 last-column\">\n<div class=\"et_pb_text_inner\"><\/div>\n<\/div>\n<\/div>\n<p>[\/et_pb_tab][et_pb_tab title=&#8221;New Learning&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<div class=\"et_pb_row tab-row\">\n<div class=\"sub-tab-text\">The <strong>New Learning<\/strong> is what students actually take away from the lesson, as reflected in their journal writing, their work and ideas during class, and the exit task, if any. Identifying what students took away, and noticing any ideas that are fragile or partial, allows teachers to develop questions for the next lesson.<\/div>\n<\/div>\n<p>[\/et_pb_tab][\/et_pb_tabs][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; custom_margin=&#8221;0px||0px||true|false&#8221; custom_padding=&#8221;7px||7px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Section Title: Understand Lesson Study&#8221; module_class=&#8221;page-sub-title&#8221; _builder_version=&#8221;4.16&#8243; text_font=&#8221;Georgia||||||||&#8221; header_text_align=&#8221;center&#8221; header_2_font=&#8221;GalanoGrotesqueAltSemiBold|700|||||||&#8221; header_2_text_align=&#8221;left&#8221; header_2_letter_spacing=&#8221;0.5px&#8221; header_2_line_height=&#8221;38px&#8221; max_width=&#8221;800px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;15px|0px|5px|0px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<p>Students will internalize questioning only if they find it useful. The next section explores how to plan a discussion in which students\u2019 presentations and questioning build the new mathematics of the lesson. When students experience insights and build new mathematical concepts through discussion of classmates\u2019 work, they will be hooked on the power of questioning.<\/p>\n<p>[\/et_pb_text][et_pb_text admin_label=&#8221;Section Title: Understand Lesson Study&#8221; module_class=&#8221;page-sub-title&#8221; _builder_version=&#8221;4.16&#8243; text_font=&#8221;Georgia||||||||&#8221; header_text_align=&#8221;center&#8221; header_2_font=&#8221;GalanoGrotesqueAltSemiBold|700|||||||&#8221; header_2_text_align=&#8221;left&#8221; header_2_letter_spacing=&#8221;0.5px&#8221; header_2_line_height=&#8221;38px&#8221; max_width=&#8221;800px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;20px|0px|39px|0px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Neriage Discussion<\/h2>\n<p>Perhaps the most difficult aspect of a problem-solving lesson is neriage (pronounced nary-ah-gay) \u2013 a Japanese term for \u201ckneading\u201d or \u201cpolishing\u201d students\u2019 ideas through discussion. As shown in the figure below, neriage occurs after students come up with solutions to the problem. The point of a problem-solving lesson is not simply to solve the problem; it is to develop important new mathematical ideas through neriage that helps students build a bridge from their current solution methods to these mathematical ideas.<\/p>\n<p>[\/et_pb_text][et_pb_image src=&#8221;https:\/\/lessonresearch.net\/wp-content\/uploads\/2018\/08\/Screen-Shot-2018-08-03-at-11.51.55-AM.png&#8221; title_text=&#8221;Screen Shot 2018-08-03 at 11.51.55 AM&#8221; show_in_lightbox=&#8221;on&#8221; show_bottom_space=&#8221;off&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; width=&#8221;60%&#8221; module_alignment=&#8221;center&#8221; border_radii=&#8221;on|10px|10px|10px|10px&#8221; box_shadow_style=&#8221;preset1&#8243; global_colors_info=&#8221;{}&#8221;][\/et_pb_image][et_pb_text admin_label=&#8221;Section Title: Understand Lesson Study&#8221; module_class=&#8221;page-sub-title&#8221; _builder_version=&#8221;4.16&#8243; text_font=&#8221;Georgia||||||||&#8221; header_text_align=&#8221;center&#8221; header_2_font=&#8221;GalanoGrotesqueAltSemiBold|700|||||||&#8221; header_2_text_align=&#8221;left&#8221; header_2_letter_spacing=&#8221;0.5px&#8221; header_2_line_height=&#8221;38px&#8221; max_width=&#8221;800px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;37px|0px|7px|0px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<em>Neriage<\/em>\u00a0provides the bridge from students\u2019 current understanding to the new concept or procedure you want them to understand by the end of the lesson. (This understanding may be fragile at first, to be strengthened through future use.) Questions to help you plan the\u00a0<em>neriage<\/em>\u00a0are:[\/et_pb_text][et_pb_text module_id=&#8221;list-btn1&#8243; module_class=&#8221;list-btn1&#8243; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; text_font=&#8221;Georgia||||||||&#8221; text_text_color=&#8221;#343085&#8243; max_width=&#8221;730px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;|||-28px||&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<ul class=\"list-n\">\n<li>What knowledge will students bring to the problem?<\/li>\n<li>What new understanding will they build during the lesson?  (What actions or words will show their new understanding?)<\/li>\n<li>What experiences and insights will help students progress from their initial knowledge to the new understanding?  For example, what do you expect students to learn from the task itself and from comparing different solution approaches?<\/li>\n<li>What specific features of different solution approaches will be important for students to notice? What questions will help students notice them?\n<\/li>\n<\/ul>\n<p>[\/et_pb_text][\/et_pb_column][\/et_pb_row][et_pb_row _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; custom_margin=&#8221;0px||0px||true|false&#8221; custom_padding=&#8221;0px||0px||true|false&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;4_4&#8243; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text admin_label=&#8221;Section Title: Understand Lesson Study&#8221; module_class=&#8221;page-sub-title&#8221; _builder_version=&#8221;4.16&#8243; text_font=&#8221;Georgia||||||||&#8221; header_text_align=&#8221;center&#8221; header_2_font=&#8221;GalanoGrotesqueAltSemiBold|700|||||||&#8221; header_2_text_align=&#8221;left&#8221; header_2_letter_spacing=&#8221;0.5px&#8221; header_2_line_height=&#8221;38px&#8221; max_width=&#8221;800px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;20px|0px|9px|0px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Summary and Reflection<\/h2>\n<p>Following the\u00a0<em>neriage<\/em>\u00a0discussion, be sure to save time (at least 5 minutes) for the class to generate a lesson Summary, followed by time for students to write individually in their math journals about what they learned. The Summary can be initiated with a question like \u201cWhat did we learn as a class today?\u201d followed by sharing ideas. As you plan the\u00a0<em>neriage<\/em>, you should have developed a clear statement of the summary you hope will emerge from the lesson, but it is powerful to use students\u2019 own language to create the Summary on the board. If students do not summarize their learning in the way you hoped, this is powerful (if disappointing!) feedback for you.[\/et_pb_text][et_pb_text admin_label=&#8221;Section Title: Understand Lesson Study&#8221; module_class=&#8221;page-sub-title&#8221; _builder_version=&#8221;4.16&#8243; text_font=&#8221;Georgia||||||||&#8221; header_text_align=&#8221;center&#8221; header_2_font=&#8221;GalanoGrotesqueAltSemiBold|700|||||||&#8221; header_2_text_align=&#8221;left&#8221; header_2_letter_spacing=&#8221;0.5px&#8221; header_2_line_height=&#8221;38px&#8221; max_width=&#8221;800px&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;12px|0px|39px|0px|false|false&#8221; global_colors_info=&#8221;{}&#8221;]By copying the Summary from the board into their math journals, students may be able to solidify their thinking; they also create a record of their learning from each lesson that can provide a valuable future reference. \u00a0After students have written the Summary in their notes, they can immediately go on to write their Reflections, which highlight their own personal learning from the lesson. The Journals tab provides further information on nurturing student Reflections and using them to introduce each TTP lesson.[\/et_pb_text][et_pb_video_slider show_image_overlay=&#8221;on&#8221; show_thumbnails=&#8221;off&#8221; use_icon_font_size=&#8221;on&#8221; icon_font_size=&#8221;50px&#8221; controls_color=&#8221;dark&#8221; module_id=&#8221;video-slider&#8221; module_class=&#8221;video-slider&#8221; _builder_version=&#8221;4.17.0&#8243; _module_preset=&#8221;default&#8221; background_enable_color=&#8221;off&#8221; max_width=&#8221;55%&#8221; module_alignment=&#8221;center&#8221; custom_margin=&#8221;61px||61px||false|false&#8221; custom_padding=&#8221;0px||0px||true|false&#8221; border_radii=&#8221;on|20px|20px|20px|20px&#8221; border_style_all=&#8221;none&#8221; box_shadow_style=&#8221;preset2&#8243; global_colors_info=&#8221;{}&#8221;][et_pb_video_slider_item src=&#8221;https:\/\/player.vimeo.com\/video\/279955239?h=9c34b925cb&#038;dnt=1&#038;app_id=122963&#038;wmode=transparent&#8221; src_webm=&#8221;https:\/\/lessonresearch.net\/wp-content\/uploads\/2021\/10\/713308691_295.jpg&#8221; _builder_version=&#8221;4.17.0&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221; show_image_overlay=&#8221;on&#8221;][\/et_pb_video_slider_item][et_pb_video_slider_item src=&#8221;https:\/\/player.vimeo.com\/video\/281319595?h=0ccb233912&#038;dnt=1&#038;app_id=122963&#038;wmode=transparent&#8221; image_src=&#8221;https:\/\/lessonresearch.net\/wp-content\/uploads\/2022\/04\/11.png&#8221; _builder_version=&#8221;4.17.0&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221; show_image_overlay=&#8221;on&#8221;][\/et_pb_video_slider_item][et_pb_video_slider_item src=&#8221;https:\/\/player.vimeo.com\/video\/281118155?h=22c120237b&#038;dnt=1&#038;app_id=122963&#038;wmode=transparent&#8221; image_src=&#8221;https:\/\/lessonresearch.net\/wp-content\/uploads\/2022\/04\/122.png&#8221; _builder_version=&#8221;4.17.0&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221; show_image_overlay=&#8221;on&#8221;][\/et_pb_video_slider_item][\/et_pb_video_slider][\/et_pb_column][\/et_pb_row][\/et_pb_section][et_pb_section fb_built=&#8221;1&#8243; admin_label=&#8221;Get in touch&#8221; module_class=&#8221;get-in-touch-section&#8221; _builder_version=&#8221;4.16&#8243; background_color=&#8221;#343085&#8243; custom_padding=&#8221;90px||0px||false|false&#8221; top_divider_style=&#8221;curve&#8221; top_divider_color=&#8221;#f6f7f7&#8243; top_divider_height=&#8221;70px&#8221; locked=&#8221;off&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_row column_structure=&#8221;3_4,1_4&#8243; use_custom_gutter=&#8221;on&#8221; gutter_width=&#8221;1&#8243; make_equal=&#8221;on&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; max_width=&#8221;1100px&#8221; module_alignment=&#8221;center&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_column type=&#8221;3_4&#8243; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_text _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; header_2_font=&#8221;GalanoGrotesqueAltBold|700|||||||&#8221; header_2_text_align=&#8221;center&#8221; header_2_text_color=&#8221;#FFFFFF&#8221; header_2_letter_spacing=&#8221;0.5px&#8221; header_2_line_height=&#8221;26px&#8221; global_colors_info=&#8221;{}&#8221;]<\/p>\n<h2>Can&#8217;t find a resource you need? Get in touch.<\/h2>\n<p>[\/et_pb_text][\/et_pb_column][et_pb_column type=&#8221;1_4&#8243; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; global_colors_info=&#8221;{}&#8221;][et_pb_button button_url=&#8221;\/contact\/&#8221; url_new_window=&#8221;on&#8221; button_text=&#8221;Contact Us&#8221; _builder_version=&#8221;4.16&#8243; _module_preset=&#8221;default&#8221; custom_button=&#8221;on&#8221; button_text_size=&#8221;14px&#8221; button_text_color=&#8221;#FFFFFF&#8221; button_bg_color=&#8221;#00c5c9&#8243; button_border_width=&#8221;0px&#8221; button_border_radius=&#8221;50px&#8221; button_letter_spacing=&#8221;0.5px&#8221; button_font=&#8221;GalanoGrotesqueAltMedium||||||||&#8221; button_use_icon=&#8221;off&#8221; custom_margin=&#8221;|||0px|false|false&#8221; custom_padding=&#8221;15px|45px|15px|45px|true|false&#8221; box_shadow_style=&#8221;preset1&#8243; box_shadow_vertical=&#8221;5px&#8221; box_shadow_blur=&#8221;12px&#8221; box_shadow_color=&#8221;rgba(0,0,0,0.1)&#8221; global_colors_info=&#8221;{}&#8221;][\/et_pb_button][\/et_pb_column][\/et_pb_row][\/et_pb_section]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Teaching Through Problem-solving In Teaching Through Problem-solving (TTP), students develop each new mathematical concept by solving a problem that illuminates it.arrow<div class=\"toolbox-header-menu-container12 learning-menu\"><ul id=\"menu-ttp-menu-2\" class=\"menu\"><li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3586\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/overview\/\" data-pageid=\"3585\">Overview<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3600\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/journals\/\" data-pageid=\"3598\">Journals<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3601\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/boardwork\/\" data-pageid=\"3599\">Boardwork<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3607\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/discussion\/\" data-pageid=\"3602\">Discussion<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16896\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/get-started\/\" data-pageid=\"16894\">Get started<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3606\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/ttp-in-action\/\" data-pageid=\"3603\">TTP in Action<\/a><\/li>\n<li class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-3605\"><a href=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/ttp-resources\/\" data-pageid=\"3604\">Resources<\/a><\/li>\n<\/ul><\/div><div class=\"inner-mobile-menu\"><form><select><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/overview\/\">Overview<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/journals\/\">Journals<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/boardwork\/\">Boardwork<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/discussion\/\">Discussion<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/get-started\/\">Get started<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/ttp-in-action\/\">TTP in Action<\/option><option  value=\"https:\/\/lessonresearch.net\/teaching-problem-solving\/ttp-resources\/\">Resources<\/option><\/select><\/form><\/div>The teacher should never say anything that a student could say. \u2014Akihiko Takahashi Associate Professor of Elementary Mathematics, DePaul University, Chicago, IL Speaking and Listening RoutinesVisitors to Teaching Through Problem-solving [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":3584,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"_et_pb_use_builder":"on","_et_pb_old_content":"","_et_gb_content_width":"","footnotes":""},"class_list":["post-3602","page","type-page","status-publish","hentry"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.8 - 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