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ERIC- https://tinyurl.com/y8kl9qjs
Library- https://tinyurl.com/y9np5wen

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- students in class
- temperature of room
- behaviors
- time of day
- readiness

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- what is important in guided discussions?
- how much discussion vs. computing
- group work vs. independent work
- how do I make sure students are discussing what I want them to discuss?
- How do I teach them to discuss?
- time factor, how to be more efficient?
- what should I spend time discussing, vs. give less time
- Do I give them the answer?
- What if they can't find the answer, how do they get it??
- how do I use error-test?
- how do I make sure misconceptions are fixed?
- progress monitor?

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TBD

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1. guided discussions in math problem solving
2. guided discussions on reading comprehension

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Quantitative- quizes, end of unit assessment, story problem quizzes

Qualitative- Observation of what?, observation of student to student discussion (cognitive, metacognitive, collaborative?) Maybe listen to student conversations with eachother and myself, and document key words. Look to when/how these are spoken.

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- How do I get this?
- How long will it take to get school consent?
- If a parent says no, do I not include the student in the lesson? Or just not his/her data?
- Will I change things as I go?

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- not sharing with other educators
- keep student data private
- pick a random sampling
- how could students be harmed in this?

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1. Keys To Productive Discussions in the Math Classroom
- sentence starters
- tips to facilitate
- sharing strategies for the class

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Heather Clayton, the author of Making the Standards Come Alive!, is the principal of Mendon Center Elementary School in Pittsford Central School District, New York. She is also a co-author of Creating a Culture for Learning published by Just ASK.

Keys to Productive Discussions
in the Math Classroom

To listen well is as powerful a means of influence as to talk well
and is as essential to all true conversation.

- Chinese Proverb

A challenge faced by math educators of all levels is how to engage students in their mathematical content through rich discussion or discourse. In classrooms where there is high-quality mathematical discourse, teachers and students ask challenging and thought-provoking questions, and there is skillful facilitation of meaningful discussions focused on the mathematics. The discussions emphasize reasoning, proof, evaluation, and justification. Students learn from one another and value the thinking of their peers. The focus of the conversation is not simply the answer to the problem, but also the students' strategies, discoveries, conjectures, and reasoning.

The third Standard for Mathematical Practice places a strong emphasis on meaningful discourse. In this standard, students are expected to construct viable arguments and critique the reasoning of others. Meaningful discussions in the mathematics classroom rely on purposeful instructional moves from the teacher, as well as a clear understanding of the demands that are placed on students. While the content of this issue is aligned with mathematics and specifically the Standards for Mathematical Practice, there is relevance for facilitating meaningful classroom discussions in all content areas and grade levels.

The K-12 Standards for Mathematical Practice

Make sense of problems and persevere in solving them

Reason abstractly and quantitatively

Construct viable arguments and critique the reasoning of others

Model with mathematics

Use appropriate tools strategically

Attend to precision

Look for and make use of structure

Look for and express regularity in repeated reasoning

The Common Core places a strong emphasis on mathematical reasoning and deep content understanding. Creating the right conditions for these discussions and facilitating conversations that emphasize a deep study of the mathematics is a challenging task. The following keys can help teachers ensure that the discourse in their mathematics classrooms is rich and extends the learning of students. The single most important thing teachers should do to ensure the success of discussions is to ask meaningful questions and facilitate the dialogue among students. The goal in any mathematical discussion is to support the students' in constructing viable arguments and critiquing the reasoning of others.

Keys for Preparing for the Discussion

Anticipate the strategies students might use, how they will represent their thinking, and predict students' misconceptions.
In addition to drawing on their knowledge of mathematical content, teachers must also bring to classroom discussions an understanding of their students' prior knowledge and experiences. Once the task has been designed, the teacher must be ready to handle the different strategies that the students will propose. One way to prepare is to draft all possible student strategies, prioritize how those will be shared with the class, and anticipate places where there may be flaws in students' thinking or misconceptions. By making these predictions in advance of the class discussion, teachers will have a clear sense of the critical "look-fors" as the students are working and an idea of how they wish to shape the classroom discussion. Undoubtedly, students will come up with strategies that the teacher has not predicted; however, teachers will be far more prepared to make sense of these approaches to problem solving when they have thought ahead about what students might bring to the experience.

For instance, consider the following problem:

Anna is collecting pennies for a school-wide penny drive. She has 357 pennies saved in the first week and 225 pennies saved in the second week. Her goal is to donate 1,000 pennies. How many more pennies will Anna need to reach her goal?

Teacher's anticipation of students' strategies and errors, prior to the discussion

Plan questions that will guide students in answering both how they solved a problem and why they chose the solution they used.
Preplanning thought-provoking questions will ensure a high level of intellectual engagement during the lesson. Including the context of the problems is essential when forming these questions. By asking students to use the context of the problem when determining their solutions, they are more likely to have solid reasoning for why they solved the problem in the way that they did. For instance, the teacher might ask:

Why did you _____________ when the problem asked for _____________?

What does _________ mean in terms of _________________ as it stated in the problem?

Does this solution make sense given what the problem is asking?

Why are we ______________ in this problem?

Decide which strategies should be prioritized when sharing with the whole class.
It can be overwhelming for students to hear and understand the reasoning behind too many different strategies at once. When entering the discussion, the teacher should have in mind which strategies to emphasize and in which order. For instance, if it is a problem dealing with subtraction, the teacher may choose to emphasize the use of an unmarked number line or adding up before having discussions about adding or subtracting the same number from the minuend and subtrahend in order to create an easier problem and not change the answer.
Keys for Facilitating Discussion
Establish a safe environment where students can take risks and where there are norms for classroom discussions.
In order for students to openly share their thinking and risk-making mistakes in front of their peers, it is imperative that there is a supportive classroom environment. Everyone should understand their role in the classroom through the development of classroom norms. The teacher is expected to pose thought-provoking questions, support students' conversations, listen carefully to monitor students' understanding and misconceptions, encourage student participation in discussions, and promote student reflection about the learning experience.

Nancy Anderson, one of the authors of the National Council of Teacher of Mathematics' book entitled, Classroom Discussions: Using Math Talk to Help Students Learn, suggests that teachers instruct their students on the importance of and expectations for mathematical conversations at the start of the school year. She explains how talking like mathematicians can enable students to be stronger mathematical thinkers. As Anderson tells her students:

Talking and thinking together can help all students understand math better

It is necessary for more than one person to help solve challenging problems

There is a great deal to be learned from listening to how other's think

Talking about your thinking helps you to clarify your own thoughts

When talking about the mathematics, you practice using important math vocabulary

You can learn a great deal about what it takes to understand the ideas of others.

Along with establishing a rationale for mathematical discussions, it is also critical to establish expectations for respectful listening. Students need to be seated where they can see and hear the speaker, and they are expected to listen actively and be prepared to respond to the ideas of others. Students are taught how to respectfully disagree and question one another. Above all, there is acceptance of all ideas and all contributions to the discussion are honored. Once the school year is under way, it is important to revisit the established norms in order to maintain the quality of conversations.

Teach students the expectations for classroom discussions.
Despite efforts to establish a rationale for discussions and expectations for listening, rich discussions in mathematics do not happen by chance. The explicit teaching of how students are expected to respond and interact during a classroom discussion in mathematics is necessary. students sharing their thinking should know that their explanations require more than just a description of the strategy they used to solve a problem. Rather, students need to include some sort of visual representation, along with an explanation of how they solved the problem and why they chose to solve the problem in that way.

Students who are listening should be attentive to the thinking of others, reflect on the ideas they have heard to evaluate their efficiency, determine if they agree or disagree, if they understand the thinking of their peers, and what similarities and differences they see between their own thinking and the thinking of others. Students need to be taught how to agree and disagree and how to ask questions for clarification. Provide students with prompts to use during discussions. For instance, students might say:

The way ______ solved the problem makes sense to me because...

______'s strategy was similar to mine because...

______'s strategy was different than mine because...

What I don't understand about ______'s explanation is why _______.

I will need to hear _______ explain how _________ again.

Why did you _____ when you were solving this problem?

I understand how you ______, but why did you ______?

Present meaningful problems.
Teachers should focus on assigning mathematical tasks that are appropriately challenging and enhance students' learning. Mathematical tasks should investigate important mathematical ideas and have authentic contexts and relevance for students. The problems posed should have multiple solution strategies, encourage investigation, promote reasoning, and require students to provide justifications for their thinking. Ultimately, mathematical tasks should be worthy of student discussion and emphasize important mathematical concepts.

Build in opportunities for independent work and partner or small group work.
In order to help students summarize and understand their thinking as well as the thinking of others, it is essential to provide opportunities for students to "turn and talk" about their ideas. For instance, after presenting a problem, students may be asked to represent or state in their own words what the problem is asking, then share that with a partner. After finding an entry point and solving a problem independently, students should share their strategies with a partner or in a group, prior to sharing with the whole class. This gives students practice constructing arguments, providing justifications, and critiquing the thinking of others. Students learn how to listen in a way that prepares them to restate their partner's thinking in their own words, as well as listening to understand and pose questions of their partner. Partnerships ensure a higher level of accountability and student engagement than is possible with only whole class discussions.

Facilitate the sharing of strategies with the whole class.
While students are engaged in discussion, it is the teacher's role to promote students' reasoning, ensure that multiple solutions and answers are considered, hold students accountable for sharing both how they solved a problem and why they solved it using a specific strategy, and to make sure that students are actively listening and responding to each other. Teachers can do this is through the use of meaningful questions that will support and extend students' understanding of the reasoning of others, along with the important mathematical ideas.

The teacher should begin by collecting all students' answers and encouraging students to think about whether or not more than one answer could be correct given the context of the problem. Then, as chosen students defend their solutions and share arguments for their strategies, the teacher ensures active listening and reflection through the use of guiding questions. For instance, the teacher might ask the student who is sharing:

Why did you ______?

Where did ______ come from?

Where are the original numbers in the problem?

How did you represent your thinking?

Questions to ask the rest of the class might be:

Could somebody repeat what _____ has shared in their own words?

Is _______'s reasoning reasonable? Why or why not?

Is _______'s strategy an efficient way to solve this problem? Why or why not?

Do you agree with ______? Why or why not?

What do you wonder after hearing ______'s thinking?

Can you think of a counter example? In other words, can you think of an example that would disprove an idea that has been presented?

Promote student reflection on the different strategies.
A powerful instructional move after students have heard the thinking of others is to send them back to work in partners or in small groups to reflect on the arguments of others. Carefully crafted questions such as the following can help guide these discussions:

Which strategy have you heard is the most efficient for solving this problem? Why?

What are some similarities you have seen between the strategies being used? What are some differences?

What new ideas did you hear today?

What confused you?

What strategies do you think you could try when solving future problems?

In summary, how successfully a teacher facilitates a discussion drives how mathematically rigorous the work is for students. In order for students to be successful with constructing viable arguments and critiquing the reasonableness of answers, students need ample practice solving problems in a variety of ways and defending their thinking with others. Equally important is that students know how to listen to the thinking of others, and pose questions and counter examples as a way of deepening their mathematical understanding. The success of these small and large group discussions rests on the ability of the teacher to plan thoughtfully and facilitate purposefully.

Resources and References

"Annotated Tasks." New York, NY: Achieve the Core. www.achievethecore.org/dashboard/300/search/6/2/0/1/2/3/4/5/6/7/8/9/10/11/12/page/786/annotated-tasks
This link contains annotated tasks and assessments that are aligned with the Common Core, grades K-2, 3-5, 6-8, and high school.

Cai, Jinfa and Frank Lester. "Why Is Teaching With Problem Solving Important to Student Learning?" Reston, VA: National Council of Teachers of Mathematics, 2010. Accessed at: www.nctm.org/news/content.aspx?id=25713.
This link from the National Council of Teachers of Mathematics explains why teaching with problem solving is important to student learning and gives criteria for the kinds of problem solving activities in which students should be engaged.

Chapin, Suzanne, Catherine O'Connor, and Nancy Canavan Anderson. Classroom Discussions: Using Math Talk to Help Students Learn. Sausalito, CA: Math Solutions, 2009.

Cengiz, Nancy. "Facilitating Productive Discussions." Teaching Children Mathematics. Sausalito, CA: Math Solutions, March 2013.

"Common Core Standards for Mathematical Practice." Los Altos, CA: Inside Mathematics. Accessed at: www.insidemathematics.org/index.php/commmon-core-math-intro.

Hintz, Allison. "Strengthening Discussions." Teaching Children Mathematics. Sausalito, CA: Math Solutions, December 2013.

"Implementing Standards for Mathematical Practices." Ed. Melisa Hancock. Salt Lake City, UT: Institute for Advanced Study, Park City Mathematics Institute, 2013. Accessed at: www.louisianabelieves.com/docs/common-core-state-standards-resources/guide-teacher-planning-for-math-practice-implementation.pdf?sfvrsn=2.
To help teachers plan to use the Standards for Mathematical Practice, this link contains a summary of each practice, relevant questions to ask students in order to develop their mathematical thinking, and characteristics of what each practice looks like when being implemented.

"Introduction to the Common Core State Standards." Washington, D.C.: National Governors Association Center for Best Practices, Council of Chief State School Officers, 2010. Accessed at: www.corestandards.org/assets/ccssi-introduction.pdf.

"Math Solutions Professional Development." Sausalito, CA: Math Solutions, 2011. Accessed at: www.mathsolutions.com/documents/qanda_usingmathtalk.pdf.
This link includes strategies for administrators wishing to engage their faculties in conversations about student talk in the classroom as a way to enhance learning. This document also includes strategies for creating a classroom culture that is conducive to mathematical discussions.

Miller, Kirsten. "Unlocking Engagement Through Mathematical Discourse." ASCD Express. Alexandria, VA: ASCD, January 2013. Acccessed at: www.ascd.org/ascd-express/vol8/807-miller.aspx.

Rigelman, Nicole. "Bring-Do-Leave: Nurturing Reasoning and Sense Making." Teaching Children Mathematics. Sausalito, CA: Math Solutions, October 2011.

Permission is granted for reprinting and distribution of this newsletter for non-commercial use only.

Please include the following citation on all copies:

Clayton, Heather. "Keys to Productive Discussions in the Math Classroom." Making the Common Core Come Alive! Volume III, Issue IV, 2014. Available at www.justaskpublications.com. Reproduced with permission of Just ASK Publications & Professional Development (Just ASK). ©2014 by Just ASK. All rights reserved.

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Keys to Productive Discussions in the Math Classroom

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Heather Clayton, the author of Making the Standards Come Alive! , is the principal of Mendon Center Elementary School in Pittsford Central School District, New York. She is also a co-author of Creating a Culture for Learning published by Just ASK.

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https://libguides.uwf.edu/c.php?g=215199&p=1420828

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Citation Producer - APA Citation, APA Citation Generator and APA Citation Maker

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This APA citation tool generates the works cited page entries by using the proper APA format. The tool follows the latest style and rules.

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Backer, David I. (2014). The Distortion of Discussion (Doctoral dissertation). Retrieved from Colombia Universities Library. https://doi.org/10.7916/D8GX48QX

Backer, in his article “The Distortion of Discussion” (2018), looks at what the word “discussion” means in relation to how it is being used in classrooms.  Backer states that a discussion should be “a kind of international pattern in educational contexts and connotes participation, dialogue, openness, equality and freedom, as well as other values associated with democracy”.  His articles talks about how instead, the educator speaks at length and questions foster a more controlled, unequal recitation of information occurs.Backer gives suggestions for facilitation practices and calls for greater emphasis on the form of interaction, not the content.

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Seeley, C. (2017). Turning Teaching Upside Down. Educational Leadership, 75(2), 32-36. Retrieved , from https://www.tandfonline.com/action/showCitFormats?doi=10.1080%2F1475939X.2016.1173089 doi:ASCD

Seeley (2017) states that the traditional method of teaching math- showing students how to do a procedure, then having them do that procedure, leads to adults who do not know how to solve math problems that do not look like those in their math books.  In the article, Seeley describes an upside down math method where students are given a problem that they do not know how to solve, and they work and discuss together a problem-solving approach to a solution.  Seeley says that students will learn to improve their problem-solving skills.

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Murphy, C. (2016). Changing the way to Teach Maths: Preservice Primary Teachers’ Reflections on using Exploratory Talk in Teaching Mathematics. Mathematics Teacher Education and Development , 18(2), 29-47. Retrieved , from https://files.eric.ed.gov/fulltext/EJ1113962.pdf

In this article, Murphy looks at the reflections of 21 primary preservice teachers following a microteaching experience that focuses on the use of talk and collaborative group work as part of a special education program (Murphy, 2016). The teachers’ reflections mentioned tensions between collaborative talk and mathematics content (Murphy, 2016).  Murphy says the tensions suggests the resistance to change the practice of novice teachers may not be due to a conceptualisation of teaching mathematics, but also to awareness of student mathematic thinking as “knowing-to”.

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Troci, A., Taylor, C., Starling, T., Sztajn, P., & Heck, D. (2015). Launching A Discourse-Rich Mathematics Lesson. Teaching Children Mathematics, 21(5). Retrieved , from file:///C:/Users/WillisMa/Downloads/tcm2014-12-276a.pdf

Heck, Starling, Sztajn, Taylor and Trocki (2015) in their article “Launching A Discourse-Rich Mathematics Lesson” discusses the importances of fostering opportunities for students to make connections, analyze situations, and create and argue solutions with one another.  Their article talks about how purposeful discourse promotes these behaviors, and it can be done in mathematics.  The article looks at the launch phase of a lesson and explains three different think-aloud strategies.

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Akman, O., & Alagoz, B. (2018). Relation between Metacognitive Awareness and Participation to Class Discussion of University Students. Universal Journal of Educational Research, 6(1), 11-24. Retrieved , from eric.ed.gov doi:www.hrpub.org

Akman and Alagoz (2018) in their article “Relation between Metacognitive Awareness and Participation to Class Discussion of University Students state that inquiry should be “based on cognitive approach, student-centered, question and inquiry-based, free of memorization and focused on high-level cognitive skills”.  In their article, they say that learning should not be teacher-centered.  Also, they state that they found a positive correlation between books read and participation in class, and a moderate correlation between participation in class discussion and metacognition awareness.

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Andrew Joyce-Gibbons (2016) Observe, interact and act: teachers’ initiation of mini-plenaries to scaffold small-group collaboration, Technology, Pedagogy and Education, 26:1, 51-68, DOI: 10.1080/1475939X.2016.1173089

Joyce-Gibbons (2015) looks at the behaviors or two teachers prior to deciding to initiate a mini-plenary. In his article, Joyce-Gibbons looks at the role technology and and classroom conditions play into this decision.  He also looks at the impact of mini-plenary on student learning and discusses what the initiation of mini-plenary can signify “current theoretical framing of classroom orchestration and teacher–student interaction” (Joyce-Gibbons, 2015).

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Arias de Sanchez, G., Gabriel 1, M., Anderson, A., & Turnbull, M. (2018). Code-Switching Explorations in Teaching Early Number Sense. Education Sciences, 8(38). Retrieved , from https://files.eric.ed.gov/fulltext/EJ1174980.pdf

The study in this article focuses on code switching- the mixing of words from from two languages- by teachers as they switch from the language of instruction, to the language of mathematics (Sanchez, Gabriel, Anderson, and Turnbull, 2018).  They did a case study on three early years’ teachers math talk.  The study found that that the teachers code switch to the mathematics register when they talked about numbers, number words and counting, to revoice students’ ideas, to explain students’ and teachers’ actions, to provide new math information, and when they choose between two terms that belonged to the math register (Sanchez, Gabriel, Anderson, and Turnbull, 2018). The article also discusses that educators avoid the using the mathematics’ register and relied instead on what the educators called “familiar language” (Sanchez, Gabriel, Anderson, and Turnbull, 2018).

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Julie M. Smith & Rebecca Mancy (2018) Exploring the relationship between metacognitive and collaborative talk during group mathematical problem-solving – what do we mean by collaborative metacognition?,Research in Mathematics Education, 20:1, 14-36, DOI: 10.1080/14794802.2017.1410215

Mancy and Smith (2018) in their article want to better understand the relationship between collaborative talk and metacognitive talk during group mathematical problem solving.  They videotaped primary students, ages 9 to 10, in a naturalistic classroom setting during group mathematical problem-solving. Student talk was coded for metacognitive, cognitive, social, and collaborative content.  They found that metacognitive talk was more was more likely to meet the criteria for collaborative than cognitive talk was.  In the article, they state that their results suggest that collaborative metacognition arises from combined individual and group processes.

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Su, H.F., Ricci, F.A., & Mnatsakanian, M. (2016). Mathematical teaching strategies: Pathways to critical thinking and metacognition. Journal of Research in Education and Science (IJRES), 2 (1), 190-200.

This article, Su, Ricci and Mnatsakanian (2016) indicate the necessity of applying critical thinking and gives an example of how critical thinking, creativity, and flexibility in finding ways to help students better understand the concepts of number sense.  The article states that a teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as “an effective way of practicing critical thinking” (Su, Ricci and Mnatsakanian, 2016).

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LaRusso, M., Jones, S., Yeon Kim, H., Kim, J., Donovan, S., & Snow, C. (2016). Impacts of a Discussion-based Academic Language Program on Classroom Interactions in 4th through 7th Grades. Society for Research on Educational Effectiveness.

LaRusso, Jones, Kim, Donovan and Snow (2016) researched the potential of high quality classroom interactions for promoting children’s academic success.  The article presents an exploratory analysis of treatment-control differences in the quality of classroom interactions in 4th through 7th grade urban classrooms (LaRusso, Jones, Kim, Donovan and Snow, 2016).

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1. Watch time
2. figure out how much time to spend on each question
3. Make higher order thinking questions
4. some way for thinking to be written down
5. ticket to exit?
6. google doc of questions to ask?
7. spend time teaching how to discuss
8. Do more with students asking for clarification, what to do if you and your partner don't have the same answer,
9 keep in mind brain breaks