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Students reflect, share, and explain their learning to the group.

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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.

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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.

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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

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Have students share so they can add to each others' tool kits.

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Have students share so they can add to each others' tool kits.

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Students are in charge of reporting what strategies their partner used

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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.

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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.

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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.

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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.

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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 ___?").

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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.

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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.

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-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

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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.

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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.

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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

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collaboration allows students to build on each others answers. Students can validate their answers and dive deeper into their thinking. 

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collaboration allows students to build on each others answers. Students can validate their answers and dive deeper into their thinking. 

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Utilize evidence to justify math answers

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Utilize evidence to justify math answers

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Follow students line of thinking instead of overtaking the conversation

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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)

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Asking students about the language used in story problems, facts you know, and facts you don't know.

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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.

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"Everything has to be evidence...otherwise how can you justify that what you said makes sense?"

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"Everything has to be evidence...otherwise how can you justify that what you said makes sense?"

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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.

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Using questioning words that help students extend their thinking helps them have deeper learning,.

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Using questioning words that help students extend their thinking helps them have deeper learning,.

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One teacher said that they were mathematical lawyers and students needed to prove their thinking with evidence of what they know.

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One teacher said that they were mathematical lawyers and students needed to prove their thinking with evidence of what they know.

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-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.

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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.

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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.

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She went with the students' thinking to guide the learning, rather than inputting teacher thoughts.

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She went with the students' thinking to guide the learning, rather than inputting teacher thoughts.

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Students should state and SHOW their thinking.

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Students should state and SHOW their thinking.

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-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.

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Prompting can help students see problems in different ways or shift their thinking. Guide towards strategies students may not have considered. 

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Prompting can help students see problems in different ways or shift their thinking. Guide towards strategies students may not have considered. 

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Prompts can help students to try another strategy or check their answer instead of directly telling them if they are right/wrong.

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Prompts are just as important as the questions asked to lead the lesson.

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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.

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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.

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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.

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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.

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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.

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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.

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Funneling and focusing questions have more lasting impact than go beyond just the correct answer.

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Funneling and focusing questions have more lasting impact than go beyond just the correct answer.

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The prompts that we use are just important as the actual concepts

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The prompts that we use are just important as the actual concepts

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Include both prompts and cues within math reflections. Have students apply their background knowledge reflecting on new concepts.

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Include both prompts and cues within math reflections. Have students apply their background knowledge reflecting on new concepts.

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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.

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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.

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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.

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Helps students think for themselves as opposed to memorizing or following patterns

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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.

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Pose invitational questions, not interrogative.

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Pose invitational questions, not interrogative.

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"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. 

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"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. 

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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.

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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.

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"This is designed to advance student learning, not simply assess it"

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"This is designed to advance student learning, not simply assess it"

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It's okay for students to wrestle to get to the root of a problem.

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Discourse can help students identify their own mistakes and grow more significantly than they would if we simply told them their answer was incorrect.

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Discourse can help students identify their own mistakes and grow more significantly than they would if we simply told them their answer was incorrect.

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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.

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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.

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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.

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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.

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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.

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It was important that the teacher ASKED a how and why question to help them explain and process their thinking.

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Students should be able to explain their thinking whether it is right or wrong and it is a valuable tool to do so!

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Students should be able to explain their thinking whether it is right or wrong and it is a valuable tool to do so!

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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.

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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.

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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

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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

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Encourage students to elaborate and clarify thinking.

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Encourage students to elaborate and clarify thinking.

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Ask questions that prompt students to express their thinking. Guide students to expand their answers by questioning them to go further. 

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Ask questions that prompt students to express their thinking. Guide students to expand their answers by questioning them to go further. 

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Students grow their brains further by explaining their reasoning. It also allows them an opportunity to grow confidence in their math abilities!

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Students grow their brains further by explaining their reasoning. It also allows them an opportunity to grow confidence in their math abilities!

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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.

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Encourage students to explain their thinking and elaborate their thoughts.

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Encourage students to explain their thinking and elaborate their thoughts.

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Productive struggle helps our students grow!

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Productive struggle helps our students grow!

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mistakes are a learning opportunity for everyone... it's always used as a "reteach" moment.

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Encouraging students to try problems even when they're not sure.

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Encouraging students to try problems even when they're not sure.

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I am asking students to share their thinking with one another.

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I am asking students to share their thinking with one another.

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Productive struggle brings perseverance

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Encouraging mistakes/growth mindset moments so students can grow through a productive struggle...using these moments to encourage self-reflection and growth.

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A variety of representations and strategies are encouraged through discourse.

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A variety of representations and strategies are encouraged through discourse.

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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.

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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.

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"Mistakes are valued and seen as opportunities for students to discuss, listen, clarify, and justify thinking" - Try not to always rescue the student!

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"Mistakes are valued and seen as opportunities for students to discuss, listen, clarify, and justify thinking" - Try not to always rescue the student!

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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.

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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.

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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.

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Mistakes are viewed as learning opportunities and a time for clarification of misconceptions.

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Mistakes are viewed as learning opportunities and a time for clarification of misconceptions.

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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.

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Focusing questions can help guide students to figure out the why / how and not just the what / answer

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Focusing questions can help guide students to figure out the why / how and not just the what / answer