2.2+Orchestrating+Discussion

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The article talks about five steps that teachers must do to orchestrate discussion. The first step is anticipating the different ways the math problem can be solved (3-6). Students will interpret the problem and could solve it many different ways. Some of these ways might not work but you have to get them to relate their ideas to the math and if they do get it wrong, have them see if they can figure out a correct answer. In order for a teacher to successfully anticipate what the students would do, they need to try figuring out the problem in as many ways as possible, so if a student does have questions, the teacher can help them work through it (4-2).

The second step is monitoring the students strategies as they work. By monitoring what the students are doing and thinking during group work or solo work, the teacher is able to decide what to talk about in the following lesson or discussion (4-3). The teacher would also have to ask questions to clarify and further student understanding (5-2).

The third step is selecting students to share their work to the class. The teacher picks what students they want to get particular pieces of the problem out for the class to see (5-4). The teacher can choose students who get the problem right and wrong and have the students talk through the findings themselves.

The fourth thing is choosing what order the students go in, as a teacher, that can get your point across in the best way. Depending on what the topic of the lesson is for the day, is what order you should go in for the students (7-1). The fifth and final thing is connecting the students ideas to each other. (7-7) **(Nicole Parry)**

Researchers in education have concluded that mathematical discussions that promote thinking, reasoning, and problem solving promote understanding (1-1). This seems quite sensible to me, but as a future educator, I’m left with wondering how to accomplish this type of discussion. This paper focuses on the implication to educators. Smith has set 5 principles that will orchestrate successful discussions. The first of which is anticipating. In ED 3000, a main focus was student-directed learning, where the teacher is to know the path but students think they are the ones deciding what is being learned because they are in control. This stage deals with predicting what students will come up with on their own (3-1). Math teachers should solve the problems in as many ways possible to consider how students will approach and solve problems (3-1). I agree with the authors’ suggestion that asking other teachers to solve the problem may be beneficial as well (3-2). In our class, we’ve noticed we have different strengths and weaknesses when solving problems, and sometimes it’s difficult to think of different ways to solve problems when use to working one way. The next step is monitoring. This involves “paying close attention to students’ mathematical thinking vand solution strategies as they work” (3-4). Teachers should walk around the room and decide who should present solutions based on meeting pre-established goals ( 4-1) but also to ask questions which further students thinking (4-3). Selecting is the next practice. Here, I predict many challenges: some students do not want to share information, some may never seem to be onto the right path so how does a teacher include them, other students may always have the right answer and get tired of sharing. The authors suggest students to share based on those which meet the goals (5-2), but also wrong solutions for the class to explore why a method did not work (5-5). I could see where this could harm the confidence of some students, and feel that mindfulness plays an important role in selecting students to present as well. The order in which solutions are presented can also affect how students comprehend the information. I like the strategy suggested which uses less-sophisticated approaches first and then brings in more abstract methods (6-2). This would make problems more manageable and also helps students who are not as abstract feel be a part of the discussion. I also found relief in “there is not one right way to select and sequence a set of responses” (6-4) since every teacher has his/her own styles and reasoning behind them. Lastly, “Orchestrating Discussion” claims connecting as the final strategy. When students are able to find similarities and draw connections between different strategies, they are becoming more flexible math students—something our standards asks of us. Of course, we will never know exactly what students will come up with, but there is an amount of predictability within what students will come up with that teachers can work with (7-9). ~Katie

The article, “Orchestrating Discussions”, summarizes the implementation of a five-step model to use whole-class discussions to promote the conceptual understanding of mathematics (1-1). The five practices are anticipation, monitoring, selecting, sequencing and connecting (2-4).

The first practice involves the preparation of the teacher to //__anticipate__// as many student responses as possible, both correct and incorrect (3-1) for a given problem. I have utilized this practice to some extent in making up problems for students that we will be discussing as a whole class. I choose a problem that purposely lends itself to common mathematical errors. I want to highlight the most common mistakes made in class. What also is revealed is that students solve problems in so many different ways. Many times I am surprised by the methods that my students come up with. Many are very creative and are correct, but different from my own. I agree with the author that a teacher may need to work with other teachers (3-2) to brainstorm on the different ways that students may solve a problem.

The second practice of //__monitoring__// involves the teacher paying close attention to the students’ mathematical thinking and solution strategies as they work (3-3). The monitoring process involves more than watching and listening to students. It is a time when the teacher should question the students to clarify their thinking (4-2). As my KVCC class worked in groups on a practice test last week, I watched and listened, but also tried to challenge them to think through problems that they were stuck on. They immediately wanted my assistance. I refrained from feeding them the answer, instead assisting them in their discovery of the answer.

The third practice of //__selecting__// incorporates the sharing of student work so that all can see and learn. It is important to choose students who have solved a problem in different ways (5-4). It also benefits the class to see an incorrect solution (5-5). Today I gave a warm-up question to my class (order of operations) and asked for the final answer. When I received different ones, I had each student who gave a different answer come to the board to present. I knew we had one correct answer, so it was interesting for all of us to look at the work by the other students. We were able to uncover one of the most common mistakes in simplifying an expression.

The fourth practice of //__sequencing__// involves a purposeful choice about the order in which student work will be shared (6-1). The teacher must be prepared in researching the most common strategies and mistakes made by students in the past and plan the sequencing accordingly (6-3). Many times I like to see multiple solutions put on the boards at the same time so that students can compare them simultaneously.

The fifth and final practice of //__connecting__// draws together different solutions to the problem and the key mathematical ideas in the lesson (6-6). The goal is to have student presentations build on each other to develop powerful mathematical ideas (6-6). **//(Susan Copeland)//**

__ Orchestrating Discussions __

This article discusses the importance of classroom discussion, and the role that the teacher plays. According to the authors, there are five important practices to “…help teachers use students’ responses to advance the mathematical understanding of the class as a whole” (550-6). These practices plan out the class discussion so that the teacher knows the likely ways their students will react, and be able to shape the conversation the way they want.

The first practice is anticipating, which is where the teacher plans out the most likely ways their students will solve the problem presented to them. In order to do this, the teacher should solve the problem first and figure out all possible ways to come up with a solution. They might even want to get additional opinions and solutions from other teachers (551-2).

The next practice is called monitoring, which includes “…paying close attention to students’ mathematical thinking and solution strategies as they work” (551-3). This means a teacher should walk around the classroom to observe how the students figure the problem out. It also means that teachers need to ask specific questions to help the students clarify their thinking and make the thought process visible. Using the first practice of anticipating can help plan out which questions to ask when students discover certain ways of solving the problem.

After monitoring the class, the next practice would be selecting students to present their findings to the class. There should be certain solutions that the teacher wants the students to know and understand, so by choosing particular kids with the solutions that are vital can be beneficial to the whole class.

As the teacher chooses particular students to present their findings to the class, we come across the fourth practice which is sequencing. The teacher should select certain students in an order such that it makes sense and the ideas build on each other. Once again, anticipating plays a role in this practice also because by guessing which solutions will be most common will help the teacher pick which students should present their ideas first.

Lastly, the teacher helps students draw conclusions by connecting main ideas with their findings and also other student’s findings. The class discussions can help with this so that the students can work together to build their ideas in order to make the necessary connections.

Overall, by anticipating the way students will solve problems and planning out a class from that can be very beneficial, as you know for the most part what to expect before it happens. **-Shanna Thorn**

When coming up with problems, you need to keep the mathematical ideas at the center of the lesson, while building on student thinking (2-1). This just means that they should be still learning mathematics while they are doing the problem. They need to learn the math while also learning critical thinking so that they can use these skills in relation to math as well as other subjects. A struggle when giving students problems like the bag of marbles task in the article, is how to give them the support they need, without helping too much or too little. Too much or too little help can lead to less of a challenge for the students when dealing with the tasks, and we want to challenge them as much as possible (2-2). The five practices model is a way to help increase the chances that we will challenge the students to build on their knowledge, while still teaching them math. The five practices is useful, because it allows teachers to plan out how to do the problem as long as they understand their students and how they react to different tasks. The advantage to this is it gives teachers control over discussion (2-5). When dealing with a problem that can be solved in multiple ways, as any good problem should be, the teacher has to understand multiple ways to do the problem. This requires the teacher to work out the problem in several ways, and if need be, going to other colleagues and seeing what suggestions they have (3-2). Understanding several ways to do the problem allows the teacher to guide students through discussions, along with knowing what questions to ask in order for them to see how to do the other methods. Teachers have to monitor student responses, so looking at the rationale and solution each student has, so the teacher can understand what each student is doing and how well they are understanding the different concepts involved in each problem. Observation or polling of students is a good way to monitor this without grading them on it. Also, observation and polling are less high-stakes assessment, and that puts less pressure on students. Teachers can also make a tracking sheet, so once the teacher understands multiple solutions, the teacher can track what students did what solution, and possibly have that student explain their method to the class, so others can grasp the concepts used (4-1). Also, while observing and tracking their solutions, asking individuals or a group to explain their rationale to you while walking around can give them the opportunity to change methods before talking with the class (4-3). It is important for the teacher to make sure students are using fractions and rations properly, along with doing the different methods properly, because if they are not, it can cause issues for future concepts. Lastly, there has to be a connection from the different solutions back to the main idea of the lesson, and this can be gained from good classroom discussion. This also allows students to build off each other, and the more students use each other as resources, the more each student gains (7-6). This article is showing teachers how to take a discussion based problem that involves independent and possibly group work, and make it manageable by planning ahead and understanding the possible outcomes. This allows teachers to keep control of the classroom, while still having student interaction. **-Josh Kaylor**

The article //Orchestrating Discussion// highlights the importance of maintaining discussion in the classroom that is on-topic, focused, and organized while also cognitively challenging the students with problem-based questions.

The Bag of Marbles example talks about how students had different methods, some leading to the right answer and some to the wrong answer, and how each of the students treated the question differently. Some students simply looked at the total number of marbles and thought that since there was more marbles that there was a better chance of drawing a blue marble. Other students looked to using ratios to see what the odds were to selecting the marble they wished to pull. Orchestrating this task was about giving enough directions and not too much or too little, otherwise the task would not really make you think (2-2).

The “Five Practices Model” describes the steps to which a teacher can take to successfully orchestrate high-level tasks and make these tasks manageable (2-4). The headings of the five practices are given by headings: anticipating, monitoring, selecting, sequencing, and connecting (2-5). These practices integrate student discussion with the structure of the task that is lead by the teacher. The students are really the ones that are in the driver’s seat; the teacher can be said to be the conductor of the symphony, where the class is the symphony. These practices are given as a way for the class as a whole to develop their understanding of mathematics, the teacher is given more time to make decisions and the teacher can nudge the direction in which the discussion of the class heads in (2-6).

Anticipation allows the teacher to think of all of the ways that the students would be able to figure out the task, or how the task can be done. Some factors of this could be, clearness of the question, different ways the task can be interpreted, the different strategies that can be used to come to the “answer”, and the real meaning to why the students would use a certain strategy (3-1). Eight students gave their own answer to the Bag of Marbles example and half of them came to the correct answer while the others may have been misinterpreted or the wrong strategy was executed. Sequencing allows the teacher to order the presentations of the students to his or her desire. The sequence may want to select those students whose strategy was more solid in understanding and practicality while other strategies that follow may be ones that can work but not as useful for a variety of tasks (6-2). The reasons behind choosing the correct sequence is all about how the teacher wants to portray what is important, what the class as a whole thought was a good strategy, or what was the best or easiest way to approach the task at hand. Teachers make the connections between the students’ discussions and the mathematical ideas that are trying to be communicated to the class. Rather than having the discussions be about how different everyone was in interpreting the task, the focus is on how everyone’s ideas are connected to each other and how the strategies really work (6-7).

Managing these five practices may allow a teacher to effectively creating cognitive discussions that emphasize students working together and developing their understanding of mathematics. Establishing these sort of discussions may also create a sense of efficacy that the students feel about the tasks, instruction, and their mathematical understanding (7-2). **(Ryan Sherman)**

The article “//Orchestrating Discussions//” is an in depth look at a particular method of using student questions and responses in classroom discussions to elevate the understanding of mathematical concepts for students. This particular method is called the “Five Practices Model” (2-4) which is broken down into five steps; anticipating, monitoring, selecting, sequencing, and connecting.


 * Anticipating**: The essence of the first practice “anticipating” is for the teacher to anticipate the different ways in which students will try to solve mathematical tasks given to them. This means that a teacher needs to use all the resources available to them to predict the strategies of their students (i.e. working out problems as many ways as they can, reviewing previous students’ works, as well as looking into research on the learning of the task)(3-1). This can help a teacher guide their students in the right direction and make it possible to bring to light information that students might skip or miss.


 * Monitoring**: As the name suggests “monitoring” is the act of paying close attention of what your students are doing. This means that you need to observe your students’ thought processes and approaches to solving the problems. A good way to do this is to make a list of possible solution methods and as you walk around and observer your class mark which students used which methods (4-4). This will help you decide on a strategy for in class discussions as well as the added benefit of making sure all students are fully participating.


 * Selecting**: The third practice “selecting” means that after the teacher has monitored the class and come up with a strategy for their class discussion, the teacher picks particular students that incorporated the individual mathematical ideas or solutions that is need to guide the class as a whole towards the mathematical goals of the teacher.


 * Sequencing**: After the students are selected, for presenting their solutions, comes the next step which is “sequencing”. This means that the teacher decides on the sequence or order that the students will present their solutions (6-4). The order is important because it can allow the teacher a way to dictate what the class is learning and also help with comparing similar methods to finding the solution.


 * Connecting**: The final practice of “connecting” is where the teacher helps the students make connections between their work/solutions and that of their fellow students (7-5). This can also help solidify mathematical ideas by showing how they can be used in more than one method and may help students judge how to best approach such problems in the future.

In conclusion the “Five Practice Model” is way to allow teachers to effectively guide their class to work as a learning community and hopefully predict ways to overcome possible difficulties that could come to pass. - **HUTCH**