Math Discourse and Reflection by Kelli Lundregan https://padlet.com/kalundregan/wirrovejxmrh en-us 2018-11-02 16:25:29 UTC 2018-12-14 20:18:17 UTC hello@padlet.com Courtney https://padlet.com/kalundregan/wirrovejxmrh/wish/314794851 Mistakes are welcome and valued. It's ok to struggle and we should allow students time to work through it without immediately providing answers instead offer strategies or a partner.]]> 2018-12-14 19:19:06 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314794851 https://padlet.com/kalundregan/wirrovejxmrh/wish/314795826 Students should be encouraged to use a variety of representations to building there understanding and justify their thoughts and ideas. Teachers build in routines and structure to offer math talks.]]> 2018-12-14 19:21:03 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314795826 "Mistakes are valued and seen as opportunities for students to discuss, listen, clarify, and justify thinking" - Try not to always rescue the student! https://padlet.com/kalundregan/wirrovejxmrh/wish/314795977 2018-12-14 19:21:23 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314795977 I am encouraging students to be respectful and brave. I am also using questions to encourage talk and move conversation forward. All answers, right or wrong, are valuable. https://padlet.com/kalundregan/wirrovejxmrh/wish/314795989 2018-12-14 19:21:24 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314795989 Mistakes are viewed as learning opportunities and a time for clarification of misconceptions. wplandry https://padlet.com/kalundregan/wirrovejxmrh/wish/314796043 2018-12-14 19:21:30 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314796043 My reflection piece has been more with small group as opposed to whole group. They are more comfortable expressing their struggles and asking others for help. https://padlet.com/kalundregan/wirrovejxmrh/wish/314796090 2018-12-14 19:21:36 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314796090 https://padlet.com/kalundregan/wirrovejxmrh/wish/314796273 Encouraging mistakes/growth mindset moments so students can grow through a productive struggle...using these moments to encourage self-reflection and growth.]]> 2018-12-14 19:21:52 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314796273 A variety of representations and strategies are encouraged through discourse. wplandry https://padlet.com/kalundregan/wirrovejxmrh/wish/314796448 2018-12-14 19:22:07 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314796448 Encouraging students to try problems even when they're not sure. https://padlet.com/kalundregan/wirrovejxmrh/wish/314796475 2018-12-14 19:22:11 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314796475 I am asking students to share their thinking with one another. https://padlet.com/kalundregan/wirrovejxmrh/wish/314796481 2018-12-14 19:22:11 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314796481 https://padlet.com/kalundregan/wirrovejxmrh/wish/314796570 Productive struggle brings perseverance ]]> 2018-12-14 19:22:22 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314796570 Productive struggle helps our students grow! https://padlet.com/kalundregan/wirrovejxmrh/wish/314797071 2018-12-14 19:23:32 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314797071 mistakes... https://padlet.com/kalundregan/wirrovejxmrh/wish/314797409 mistakes are a learning opportunity for everyone... it's always used as a "reteach" moment. ]]> 2018-12-14 19:24:13 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314797409 Encourage students to explain their thinking and elaborate their thoughts. https://padlet.com/kalundregan/wirrovejxmrh/wish/314798373 2018-12-14 19:26:25 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314798373 Courtney https://padlet.com/kalundregan/wirrovejxmrh/wish/314798515 Purposeful questioning can accomplish many goals such as check for student understanding, reflect student thinking, and make the learning more accessible. Good questioning can move the students thinking forward and build their background knowledge on mathematical concepts.]]> 2018-12-14 19:26:40 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314798515 Ask questions that prompt students to express their thinking. Guide students to expand their answers by questioning them to go further. https://padlet.com/kalundregan/wirrovejxmrh/wish/314799253 2018-12-14 19:28:14 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314799253 Students grow their brains further by explaining their reasoning. It also allows them an opportunity to grow confidence in their math abilities! https://padlet.com/kalundregan/wirrovejxmrh/wish/314799352 2018-12-14 19:28:26 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314799352 Encourage students to elaborate and clarify thinking. wplandry https://padlet.com/kalundregan/wirrovejxmrh/wish/314799377 2018-12-14 19:28:30 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314799377 With the fraction example they used, 2/3 + 1/2, the students all got the answer wrong. This opened up the door to discussing WHY that was not the right answer (something that you might see as answer a on a test), and how to estimate & get the correct answer https://padlet.com/kalundregan/wirrovejxmrh/wish/314799439 2018-12-14 19:28:40 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314799439 Purposeful questions go away from the thinking of whether something is right or wrong, and is more about HOW or WHY the outcome is what it is. wplandry https://padlet.com/kalundregan/wirrovejxmrh/wish/314799692 2018-12-14 19:29:16 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314799692 Students should be able to explain their thinking whether it is right or wrong and it is a valuable tool to do so! https://padlet.com/kalundregan/wirrovejxmrh/wish/314799703 2018-12-14 19:29:17 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314799703 https://padlet.com/kalundregan/wirrovejxmrh/wish/314800077 It was important that the teacher ASKED a how and why question to help them explain and process their thinking.]]> 2018-12-14 19:30:06 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314800077 Using reflection questions can help students be able to identify where they went wrong as opposed to being told where they went wrong. Using visuals for understanding and hearing other students' thought process also helps students identify where they can improve. https://padlet.com/kalundregan/wirrovejxmrh/wish/314800157 2018-12-14 19:30:15 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314800157 https://padlet.com/kalundregan/wirrovejxmrh/wish/314800553 Students being able to justify their answers shows a deep understanding of the concept...most students can get the "answer" but not many can explain or show how they did it.]]> 2018-12-14 19:31:09 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314800553 Do not just rely on rubrics to check student understanding, but rather asking specific questions to guide student knowledge of concept, in order for the student to figure it out on their own. https://padlet.com/kalundregan/wirrovejxmrh/wish/314800795 2018-12-14 19:31:40 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314800795 Discourse can help students identify their own mistakes and grow more significantly than they would if we simply told them their answer was incorrect. https://padlet.com/kalundregan/wirrovejxmrh/wish/314800910 2018-12-14 19:31:55 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314800910 https://padlet.com/kalundregan/wirrovejxmrh/wish/314801028 It's okay for students to wrestle to get to the root of a problem.]]> 2018-12-14 19:32:10 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314801028 "This is designed to advance student learning, not simply assess it" https://padlet.com/kalundregan/wirrovejxmrh/wish/314801599 2018-12-14 19:33:34 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314801599 The funneling technique may be an appropriate strategy to use when introducing a topic or seeing what background knowledge the student already has on the topic, but it should not be the only "questioning technique" used because responses are limited. https://padlet.com/kalundregan/wirrovejxmrh/wish/314801711 2018-12-14 19:33:48 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314801711 "Great teachers don't tell you what to see, they show you where to look" --don't tell the kids the answer, guide them by activating their knowledge to find the answer themselves. https://padlet.com/kalundregan/wirrovejxmrh/wish/314802139 2018-12-14 19:34:55 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314802139 Courtney https://padlet.com/kalundregan/wirrovejxmrh/wish/314802207 Funneling questions the teacher is doing the work/thinking and in the focusing questions the student is doing the work/thinking. We want the student learning so we need to create and embed focusing questions to encourage more student driven learning.]]> 2018-12-14 19:35:05 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314802207 Pose invitational questions, not interrogative. wplandry https://padlet.com/kalundregan/wirrovejxmrh/wish/314802396 2018-12-14 19:35:30 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314802396 https://padlet.com/kalundregan/wirrovejxmrh/wish/314802646 Helps students think for themselves as opposed to memorizing or following patterns]]> 2018-12-14 19:36:03 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314802646 wplandry https://padlet.com/kalundregan/wirrovejxmrh/wish/314802977 Funneling questions may look like deep understanding, but really just show the ability to respond to the teacher's questions.
Focusing questions provide the student with opportunities to push their own thinking and think deeper about the math concept.]]> 2018-12-14 19:36:42 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314802977 Focus questions require the students to think beyond "finding the right answer". They help students link what they already know to what they are getting ready to learn. https://padlet.com/kalundregan/wirrovejxmrh/wish/314803576 2018-12-14 19:38:03 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314803576 Include both prompts and cues within math reflections. Have students apply their background knowledge reflecting on new concepts. https://padlet.com/kalundregan/wirrovejxmrh/wish/314803906 2018-12-14 19:38:46 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314803906 The prompts that we use are just important as the actual concepts https://padlet.com/kalundregan/wirrovejxmrh/wish/314804704 2018-12-14 19:40:29 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314804704 Funneling and focusing questions have more lasting impact than go beyond just the correct answer. https://padlet.com/kalundregan/wirrovejxmrh/wish/314805299 2018-12-14 19:41:51 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314805299 Prompting with visuals can able incredibly helpful for students to understand certain concepts such as fractions, for example. Environmental scaffolds can also assist students who think of math in a more hands on way. https://padlet.com/kalundregan/wirrovejxmrh/wish/314805314 2018-12-14 19:41:54 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314805314 Cues should be used to draw the students' attention in on the relevant information and not to make a student feel singled out. Cues should be done quietly with a student. https://padlet.com/kalundregan/wirrovejxmrh/wish/314805640 2018-12-14 19:42:41 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314805640 Focusing questions can help guide students to figure out the why / how and not just the what / answer https://padlet.com/kalundregan/wirrovejxmrh/wish/314805862 2018-12-14 19:43:16 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314805862 Prompts allow students to focus very specifically on certain aspects of their work, whether it is an error they made or a strategy they tried. wplandry https://padlet.com/kalundregan/wirrovejxmrh/wish/314805988 2018-12-14 19:43:37 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314805988 https://padlet.com/kalundregan/wirrovejxmrh/wish/314806035 Prompts can help students to try another strategy or check their answer instead of directly telling them if they are right/wrong.]]> 2018-12-14 19:43:45 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314806035 https://padlet.com/kalundregan/wirrovejxmrh/wish/314806162 Prompts are just as important as the questions asked to lead the lesson. ]]> 2018-12-14 19:44:07 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314806162 Prompting can help students see problems in different ways or shift their thinking. Guide towards strategies students may not have considered. https://padlet.com/kalundregan/wirrovejxmrh/wish/314806251 2018-12-14 19:44:19 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314806251 Courtney https://padlet.com/kalundregan/wirrovejxmrh/wish/314806479 2018-12-14 19:44:55 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314806479 Summary wplandry https://padlet.com/kalundregan/wirrovejxmrh/wish/314809751 -Allow students to add ideas to the conversation
-Use discourse to guide your teaching
-Who agrees or disagrees? And, why?
-Tell me more.
-What do you know? What don't you know? What do we need to gather to answer what you don't know?
-Students build off of one another's comments.
-Have students repeat what another student has already shared.
-Listen to student discourse to gauge their understanding.]]> 2018-12-14 19:54:19 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314809751 Students should state and SHOW their thinking. https://padlet.com/kalundregan/wirrovejxmrh/wish/314810597 2018-12-14 19:56:56 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314810597 Summary Video 1 https://padlet.com/kalundregan/wirrovejxmrh/wish/314810649 -Female teacher didn't say, "Where should I put the 4 & the 2?", but instead says, "I saw some of you do this, let's talk about this & why it doesn't make sense" (open ended)
-Male math teacher clarified vocabulary & focused a lot on the students using evidence
-Male teacher focuses on what the student does know rather than what they don't get, that way they have a starting point.]]> 2018-12-14 19:57:05 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314810649 She went with the students' thinking to guide the learning, rather than inputting teacher thoughts. https://padlet.com/kalundregan/wirrovejxmrh/wish/314810768 2018-12-14 19:57:28 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314810768 Having the students figure out what they know helps them understand what they don't know and what they need to find. It is also important to follow the thinking of the student as opposed to telling them what thought process they should have. https://padlet.com/kalundregan/wirrovejxmrh/wish/314810782 2018-12-14 19:57:30 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314810782 One teacher said that they were mathematical lawyers and students needed to prove their thinking with evidence of what they know. https://padlet.com/kalundregan/wirrovejxmrh/wish/314811233 2018-12-14 19:58:52 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314811233 Using questioning words that help students extend their thinking helps them have deeper learning,. https://padlet.com/kalundregan/wirrovejxmrh/wish/314811751 2018-12-14 20:00:12 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314811751 https://padlet.com/kalundregan/wirrovejxmrh/wish/314811754 Ask students WHY and HOW they know parts of the problems. Use visuals (highlighting, variety of colored markers) to help with there thinking. Honor what students already know. Ask questions to investigate their own thinking.]]> 2018-12-14 20:00:13 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314811754 "Everything has to be evidence...otherwise how can you justify that what you said makes sense?" https://padlet.com/kalundregan/wirrovejxmrh/wish/314811825 They need to be able to see it from every angle as well. Funnel it down from broad concepts to specific concepts in order to recognize misconceptions and guide them to understanding. ]]> 2018-12-14 20:00:24 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314811825 https://padlet.com/kalundregan/wirrovejxmrh/wish/314811894 Asking students about the language used in story problems, facts you know, and facts you don't know. ]]> 2018-12-14 20:00:35 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314811894 Courtney https://padlet.com/kalundregan/wirrovejxmrh/wish/314811986 Investigate their own thinking!!!  Allowing students to extend their thinking by posing questions or sentence starters such as..Tell me more about that.. or Show me your thinking or How can you justify or make sense of that?  Follow the student thinking instead of teacher's (Focusing questions not funneling questions).
Ensure students know exactly what is asked (things you know vs. things you don't know)]]> 2018-12-14 20:00:49 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314811986 Utilize evidence to justify math answers https://padlet.com/kalundregan/wirrovejxmrh/wish/314812172 2018-12-14 20:01:05 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314812172 https://padlet.com/kalundregan/wirrovejxmrh/wish/314812204 Follow students line of thinking instead of overtaking the conversation


]]> 2018-12-14 20:01:11 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314812204 collaboration allows students to build on each others answers. Students can validate their answers and dive deeper into their thinking. https://padlet.com/kalundregan/wirrovejxmrh/wish/314812570 2018-12-14 20:02:18 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314812570 https://padlet.com/kalundregan/wirrovejxmrh/wish/314813481 It means more to the students to figure out the answer for themselves by discussing with other students than it does for a teacher to simply "give" the answer]]> 2018-12-14 20:04:53 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314813481 Summary wplandry https://padlet.com/kalundregan/wirrovejxmrh/wish/314815493 Students write and later share reflections with peers.
Share strategies from anything they have done that class.
Encouraged to share what worked and what might not have worked.
Share someone else's strategy aloud with the class.
Was not about completion, but understanding.]]> 2018-12-14 20:12:00 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314815493 https://padlet.com/kalundregan/wirrovejxmrh/wish/314815813 Teacher linked students responses to one another when discussing math center activities on patterns. She asked guiding questions after each student response. Gave all students an opportunity to share their work.]]> 2018-12-14 20:13:12 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314815813 Math Share https://padlet.com/kalundregan/wirrovejxmrh/wish/314815827 -gives the opportunity for students to be exposed to reflection on all the concepts/stations in one sitting
-many examples
-negative could be that students don't like the spotlight (turn & talk would be more appropriate & comfortable for the shy students)
-easier to monitor understanding than turn and talk would be]]> 2018-12-14 20:13:15 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314815827 students share out their learning from their center. Teacher asks follow up questions. Teacher had some specific examples in mind and made sure those students shared, these were students who had misunderstandings. https://padlet.com/kalundregan/wirrovejxmrh/wish/314815957 2018-12-14 20:13:35 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314815957 Teacher gave students sentence stems to help them have positive discourse and have something to talk about with their partner. She avoided students saying "I don't know what to say" by giving them something to specifically say. https://padlet.com/kalundregan/wirrovejxmrh/wish/314816723 2018-12-14 20:15:50 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314816723 Students were able to openly share what they did whether the work was finished or not. In addition students were encouraged to share and questioned about what they did. https://padlet.com/kalundregan/wirrovejxmrh/wish/314816741 2018-12-14 20:15:53 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314816741 https://padlet.com/kalundregan/wirrovejxmrh/wish/314816786 Students share by showing their work or answering questions, and then the teacher asks more questions to guide (i.e. "Does anyone else have a pattern similar to ___?").]]> 2018-12-14 20:15:59 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314816786 Have students share so they can add to each others' tool kits. https://padlet.com/kalundregan/wirrovejxmrh/wish/314816787 2018-12-14 20:15:59 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314816787 https://padlet.com/kalundregan/wirrovejxmrh/wish/314816896 Students are in charge of reporting what strategies their partner used]]> 2018-12-14 20:16:15 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314816896 https://padlet.com/kalundregan/wirrovejxmrh/wish/314817084 Sharing does not necessarily have to be what worked or what gave them the right answer...sharing can be whatever strategies they tried and discussing why it worked for them or why it did not]]> 2018-12-14 20:16:48 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314817084 Students felt confident sharing with the class. Each student had something to share after their math lesson/activity. When a student incorrectly labeled their pattern, the teacher did not say they were wrong, but instead asked if someone else could figure out the pattern. https://padlet.com/kalundregan/wirrovejxmrh/wish/314817177 2018-12-14 20:17:05 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314817177 Courtney https://padlet.com/kalundregan/wirrovejxmrh/wish/314817503 Students reflect, share, and explain their learning to the group. ]]> 2018-12-14 20:17:54 UTC https://padlet.com/kalundregan/wirrovejxmrh/wish/314817503