2.3+Reflection+4+Never+Say+Anything

The readings reflections have two main purposes: 1) to hold you accountable for careful reading of and reflection on the readings assigned in class; and 2) to provide you with a record of what you've learned and thought about as a result of the readings.
 * Readings Reflections**

The readings reflections will be evaluated using the following criteria:
 * completeness and timeliness of the entries;
 * comprehension of the main ideas of the readings; and
 * depth and quality of integration of the ideas with your own thinking.

Submit your readings reflection **before** reading anyone's on the Wiki page and then paste it into the existing reflection page for that current reading. This is due by Sun 9/25 at 11pm.

This reading will also have a Wiki page discussion. The purpose of this is to engage in a conversation with your peers about the article, based on what you have written for your Readings Reflection. While you are not expected to read all of the reflections for each article, you are expected to read enough of them (**after** you have written yours so you are not unduly influenced) to be able to **compare and contrast** the thoughts of others with your thoughts about the article. Your contribution will be evaluated using the Math 3500 Online Readings Discussions Rubric handed out in class. The reading discussion will "close" for my examination by Sun 9/25 at 11:57pm.
 * Readings Discussions**

The author of “Never Say Anything a Kid Can Say” has made a vow to change his teaching style from teacher-centered, direct instruction to a more student-centered approach by changing 10% of his style each year. “I noticed that the familiar teacher-centered, direct-instruction model often did not fit well with the more in-depth problems and tasks that I was using,” (1-3). In order to implement the changes he identified the fundamental flaw in his previous style of teaching and researched different questioning strategies.

The author realized that few teachers take time to plan specific questioning techniques for each lesson they present (2-2), so he outlined a few tips that educators can try to use in their own classrooms. Thus far, this has been my favorite article and I will highlight some of my favorite tip because there are SO many great ideas to test out when we are all in a classroom. Ask good questions that make students think and, more importantly, reflect on what they are learning (3-2). Use more process questions than product questions (3-3). Do not ask questions that have short answers or yes/no because students don’t provide very much knowledge on the topic of the question. Replace lectures with sets of questions (3-4). The definition the author used for “lecture” struck me because in college lectures I feel it is so true, so how could it not be true for adolescents as well? He says a lecture is “the transfer of information from the notes of the lecturer to the notes of the student without passing through the minds of either,” (3-4).

In previous education courses, professors have stressed the importance of constant praise and feedback. This article highlights and important “flaw”, if you will, with too enthusiastic of praise. He advises teachers to be nonjudgmental about a response or comment in a whole class discussion because too enthusiastic of a response can discourage others to comment next (3-9). Also, try not to repeat students’ answers. “If students are to listen to one another and value on another’s input, I cannot repeat or improve on what they say,” (4-2).

In the author’s new model of teaching participation is not optional (5-1). I really like the think-pair-share strategy (5-2). The progression from individual thinking to small groups to whole classroom discussion sounds like the best way to go about getting full participation in a task. I feel like this is how our MATH 3500 class is often run right now! I know that one of my classroom “rules” is going to be full participation because I’ve seen students engage more in the think-pair-share discussion-style lessons than solely direct instruction mathematics.

“Merely telling them answers, doing things for them, or showing them shortcuts, I relieve students of their responsibilities and cheat them of the opportunity to make sense of the mathematics that they are learning,” (6-7). It is a student’s responsibility to ask questions that might help them understand and simply “I don’t get it” doesn’t fly (5-6), if a student doesn’t understand something everyone needs to work together to help them understand.

Tori Ward

The title of Steven Reinhart’s article, “Never Say Anything a Kid Can Say”, made me think critically about its meaning. As it was explained in the article, the idea is his own and he believes a teacher should never say anything with in the classroom which one of their student’s could say themselves (3-2). Reinhart explained where he was coming from and his goals and this shed light, for me, on the whole idea of what the teacher’s role was as far as their actual talking in discussions. A big idea discussed in this article was that of asking questions of the students. It is important to ask them questions while they are working on problems as well as when they are asking for help. The best kinds of questions are those which are open ended. As many of us know, this forces the student to say more than yes or no. Students should be able to learn from their answering of the questions posed by the teacher (3-3). By being able to answer the questions and explain why this is the answer, students have the ability to understand what they are doing and why it is correct. Along the same lines of the idea of questions being pertinent for the growth of the students came what to say when a student asks, “Is this right?” As someone who always double checks their work and wonders if they have come to the right conclusion, I can see the validity of the students for wanting to ask for confirmation. However, I feel the answer Reinhart gives is something students will be able to grow more from. When a student asks about the correctness of their answer, a teacher should ask them to explain their thinking to them (5-1). This idea sticks out to me because it goes along with what Reinhart stated earlier. It is important to ask students to explain because it allows the teacher to evaluate if the student knows what they are explaining as well as give the teacher insight as to how their students think (6-7). One main idea I noticed throughout the article was the avoidance of the student stopping thinking. When the teacher repeats the solution stated by a student, the other students will get into the hang of just waiting for the teacher to answer their questions rather than listen to what their peers have to offer (6-2). In my opinion, students can learn just as much if not more from their own peers. I have noticed throughout my schooling career that not only do the students explaining what they are doing and why help them better understand, but also being taught by your peers is beneficial. Your peers are your equals and when you see they know what they are doing, you can be more confident that you can too be able to do this. Like many other articles we have read, Reinhart talked about the importance of working together and in groups. The think-pair-share model was especially interesting to me. The model has students work alone at first, which encourages the student to come up with their own thoughts and ideas before even hearing what others have to say (5-3). This is very important in my opinion because I believe students should have their own thoughts of something before going into a discussion, or in this model the share portion, in order to bring something worth while to the discussion. Katey Cook

In his article “Never Say Anything a Kid Can Say!” Steven C. Reinhart writes about his method for moving from a teacher-centered, direct-instruction style classroom to a student-centered, problem-based approach (1-3). His basic philosophy is that if students are to truly understand mathematics, they must do the explaining, and the teacher should do the listening, rather than the other way around (1-4). Similar to the views presented in the article “Orchestrating Discussion”, Reinhart shares that the teacher’s role becomes one of listening and asking good questions (1-5), which cause the students to discuss, make connections, and participate (1-5). They should “never say anything a kid can say” (3-1).

He offers multiple specific strategies on how to carry this strategy out, all of which seemed very practical to me. I appreciated the practical application of his ideas rather than simply a philosophical discussion of them. These realistic suggestions include giving nonjudgmental feedback (3-9), requiring students to ask questions when they don’t understand (5-6), refusing the temptation to carry a pencil (6-2), and being patient (3-5). In Reinhart’s classroom, students’ participation is anything but optional (5-1). He stresses that “the learning of one person is of little value unless it can be communicated to others” (5-5), and I completely support this.

As a student, I can see how this method could cause me to become frustrated and annoyed; I frequently prefer to know the “right answer” without understanding how to explain the mathematics behind it. Although allowing students to struggle to solve a problem (6-7) can be frustrating for them, the skill of being able to explain the reasoning behind a solution is very valuable.

This article resonated with me more than any of the other selections we have read so far. I found the author’s idea not only insightful, but also very valuable. In never saying anything a kid can say, it forces us as teachers to be more purposeful with our words in instruction and questioning. In addition, it forces the students to think for themselves and allows them to make their own mathematical discoveries, rather than being force-fed a jumble of mathematical ideas from the teacher in which they do not see connections or develop understandings.

Personally, I find it extremely challenging not to give too much guidance and let the //kids// make the discoveries. In my attempts to help (despite good intentions), I can see myself becoming a dispenser of answers rather than someone who truly makes a difference in the way my students learn. However, I believe Reinhart’s approach will produce results that are //far// more worthwhile than the traditional instructional method could ever generate.

Mandi Mills

“Never Say Anything a Kid Can Say!” has more to offer about why we should stay away from teacher-centered, direct-instruction (478-3). Some of the other readings have shown the importance of group work with cooperative learning, but “Never Say Anything a Kid Can Say!” has shown a lot questioning strategies that are very important to remember when teaching.

The first point that the author makes is to try to ask a question every time you are tempted to tell students something (480-2). This is a great way to help make students think more on their own. The biggest thing to remember with this one is to ask smart questions that will make them think and that they understand. Which leads into the next point of asking good question that are open ended, or more than one acceptable response may be possible (480-3). Yes and no questions do not require much thinking and can sometime be repetitive that don’t require much thinking. The fourth point made is replacing lecture with set of question (480-5). When I first read this, I thought of teachers that every other sentence that they say is in a question tone of voice and instead of it being a question it is more finish my sentence with what I was going to say or else it is wrong. The author defines lectures as the transfer of information from the notes of the lecturer to the notes of the student without passing through the minds of either (480-5). I have had numerous of classes that this is the case and how the class goes of the teacher lecturing or writing stuff on the board and the students just sitting their writing notes of pages after pages. After looking back through my notes I never fully understand them. Half of the time I don’t even get all of the notes since I am not a fast writer and the teacher never looks up or turns around from the board.

One thing that all of the articles have been saying is that these changes are not easy, and it will take time. The results are not going to happen right away and it will be a struggle with wanting to result back to the old way of teaching.

Bret Van Zanten

In Reinhart’s article, one teacher explores the value of asking questions versus giving answers. He felt that despite all his demonstrating and explaining, the students were not understanding the concepts. The flaw here is that is was //his// demonstrations and explanations; Reinhart finally came upon the idea that “if [his] students were to ever really learn mathematics, //they// would have to do the explaining, and [//he//], the listening.” (1-4) I agree with Reinhart in that students who can explain a concept in their own words demonstrate their understanding and, more importantly, their misunderstanding. If students are being vocal about their ideas in the classroom, it gives the teacher a window into the students’ thoughts. Once a teacher has a clear picture of what the class is thinking, he or she will be able to either move forward in the lesson or pause on one topic until the whole class understands. During such a pause, however, we cannot return to our own demonstrating and explaining, we must continue with well thought-out questions that allow for students to come to mathematical understanding on their own. I must admit that this makes me, as a future educator, nervous. How will I know which questions to ask? This is why Reinhart advocates for planning out our question techniques ahead of time, much as we would plan a lesson ahead of time (2-2).

A significant portion of our reading has been about the benefit of group work in a classroom, as this set up gives students the opportunity to discuss math and reason things out for themselves. Which is why I was surprised at first to read Reinhart’s suggestion that students work independently before group work (5-3). I agree with his rationale, however, that if students don’t have time for themselves to collect their individual thoughts, one or two students in the group, who already understand, may just immediately take over. This reminded me of my own middle school group work experience, in which I would take over the group, explaining my answer to those with whom I was paired. This was beneficial to me, because I was getting lots of practice explaining and conversing about mathematical ideas, but it was not beneficial to my group-mates, who never had the opportunity to think for themselves, and would not be able to defend our solution, as Reinhart requires of his students (5-9). This is why individual thinking time is required before group work, so students can come together to share ideas, rather than one or two students controlling the process.

Another suggestion that Reinhart made that I felt would be really beneficial was his requirement that students or groups must contribute at least one thing to a group discussion, even if that is a question (5-6). This would require students who do not understand the problem to at least think about it in enough depth to ask a clarifying question. This way, a student who doesn’t understand is still exploring his or her own thoughts, clearing up a misunderstanding, and practicing communicating mathematical ideas.

By listening to students rather than lecturing, Reinhart makes a serious effort to understand his students’ thinking and students get a chance to do critical thinking about the concepts. Many of questioning techniques and suggestions that he made were really helpful for me in terms of thinking about how I, as a teacher, would like to run a classroom.

Valerie Gipper

This week’s reading and discussion is based off of Steven Reinhart’s article “Never Say Anything a Kid Can Say!” In this article Reinhart explains the same struggle that many new teachers face. He felt as if he was giving good mathematical instruction yet his students weren’t taking much away from his lessons. After doing research on teaching techniques bthrough books, seminars, extra college courses, he decided to change his teaching style by 10% each year. (1-2)

In the heart of the article Reinhart goes into depth about asking good questions and to keep asking questions. I really liked that idea of not giving the student the answer but to always ask them leading style questions to help them discover the idea. He states that when he gave out the answer directly thinking usually stopped at that point on the student’s part. (4-1) One way he promotes student led discussions was through the think-pair-share method. I really liked having the student first work on the problem individually as to not lose any students. Once they have all worked the problem individually then they would get into small groups to discuss what they found to each other then eventually the whole class.(4-4) Students where then expected to summarize other students thoughts meaning they are paying attention and contributing to the classroom atmosphere.

Reinhart goes on to state that being satisfied with one response can limit the potential of the student. When one student gives his or her response Reinhart states that it is critical to have others show alternate solutions or point out more efficient ways to solve a particular problem. During this time students will feel more comfortable and confident while defending their solutions because they have already discussed it with their smaller groups during the initial stages of the think-pair-share method. (4-4) When students are responding and questioning each other learning is being done that traditional methods might not have produced.

The main point of this article I think is to try and put the responsibility of learning back on the students. I agree with Reinhart that when students contribute to discussion with ideas or other thoughts a great deal of learning is going on. These students are learning how to solve problems rather than memorizing the way to do a specific problem. Although I agree that this method is superior I wonder how difficult it will actually be to apply.

Christopher Cardon

Author Steven Reinhart provides readers with background on how he ran his classroom vs. how he wanted it to be. He believed in improving his class little by little as each year passed. Reinhart listed five things which helped, including “Never say anything a kid can say!” Initially I thought the title suggested we were going to read about how to stay out of trouble, but what the author intended to imply was not to speak for students when it comes to their learning. One message of this article was not to repeat or paraphrase anything a student has said. By not repeating what someone says, you’re encouraging students to listen to their classmates better as well as learn to clarify their own thoughts. This could lead to a more open classroom: instead of the teacher talking to students and students talking back to the teacher, students begin to talk amongst each other while I observe their understanding.

That is an important aspect to the author’s classroom, student interaction. I like the definition of “lecture” Reinhart provides: “The transfer of information from the notes of the lecturer to the notes of the student without passing through the minds of either.” Rather than lecture students, I would prefer to apply the “think, pair, share.” model discussed: pose a question to the class and allow students to think for a while, individually. After time to think, partner students up into pairs or groups and have them share their thoughts with one another (this is a good time for the instructor to walk around and check for understanding). Once students have shared their ideas, bring the class together as a whole and have students share their group discussions/thoughts. This is a common practice in the education classes I take now and as a student it is a very comfortable atmosphere.

This article also reiterates a theme from previous lessons, emphasizing the significance of process based questions over product based. We talked about this as a class, placing more importance on the process of math over just the right answer; this helps form a better understanding of material. One idea I was less familiar with was to be patient. Reinhart says that even when students have their hands raised, be patient and allow other students to ponder on the task at hand before selecting a student to answer. By selecting the first student with their hand up you chose the fastest thinker to provide an answer for the rest of the class. Eventually students might stop thinking because they know a classmate will shout it out soon anyway. Let everyone form a thought before choosing a student to answer out lout. I also like the idea of sharing with students reasons I ask questions. As teachers we should explain that we are continuously evaluating what the class knows or does not know. Their comments help us make decisions and plan the next activities. One reason we should never ask a question is to embarrass or punish a student. This has happened to me several times, usually when I wasn’t paying attention, my teacher would ask me a question he or she knew I didn’t know the answer to in order to call me out in front of the class. Every time that happened all I could think about for the rest of that class was the embarrassment I felt, and I held a resilient grudge against that teacher ever since. That does NOT encourage participation or learning the way I wish to in my classroom, so I like this point a lot.

Another really good point I liked was to avoid answering my own questions. I experienced this a lot as a student as well, a teacher would ask a few rhetorical questions they answer themselves then when they pose a question to the class, they receive silence and blank stares… “We’re waiting for YOU to answer that question!” is what we were pretty much telling the teacher. In order for students to think about our questions, we need to avoid answering our own questions like that.

- Tim H.

The article, “Never Say Anything a Kid Can Say,” discusses the fact that many teachers think they are doing a great job teaching their students but yet students are still not grasping material (478-1). I think this happens to a lot of teachers and I am not sure how to solve this problem. The author goes on to discuss on direct instruction did not fit his new style of teaching (478-3). Personally, I think the teaching style of direct instruction needs to be a thing of the past and from the articles we have been reading it seems things are moving to a more student centered approach. I think it is important for students to be involved and learn actively rather than passively.

In the section, “Questioning Strategies That Work for Me,” the author discusses the ability to ask the right questions (479-1). As teachers, we need to be able to ask the right questions that get students thinking and leading them in the right direction without giving them the answers. I think this is going to be a challenge but a challenge we can overcome with time and practice. (480-2) I agree that students should learn something from the questions we ask them, our questions should turn on the light bulb in their head and get their minds working.

The author goes on to discuss the importance of listening to students and valuing their input even if their thinking is flawed (480-7). I also believe it is extremely important for students to feel heard even if they are wrong. When they do show flawed logic it is our job to use questions to point them in the right direction and let them down easily.

The section, “Is this the right answer?” (481-2) I was not too impressed with. The author discusses that when students ask if an answer is correct he doesn’t tell them yes or no but instead asks them to explain it. I personally hated this approach in school, why can’t you just tell me if my answer is correct or not? I can see if it is incorrect to say no and then prompt the student with questions that will lead them in the correct direction but if their answer is right what is the harm in letting them know?

“Participation is not optional,” (482-1) I agree that we should hear every students input and I think that rests on the teacher making sure we give the quieter kids a chance to participate instead of always relying on the same students who always want to give the answers. Kaitlin Froehlke

In the article “Never Say Anything a Kid can Say!” a teacher talks about transforming his classroom after finding is teaching methods inadequate in producing the wanted results. The teacher claims that the biggest flaw in his system was he was explaining all of the mathematical material, but he needed his students to explain the material to be understood by their peers (1-4). He also mentions how are it is to get middle school students to be actively involved in classroom discussions. He then proceeds to give some steps to get these students involved with the discussion.

The first step he gives us is never say anything a kid can say (3-2). Basically instead of explaining different things to their students, teachers should ask questions that get kids to participate in the discussion. The next step he suggests is Ask good questions (3-3). This step basically says that the questions need to be open-ended that cause the student and the educator to learn.

The next step this teacher prescribes is using process questions (3-4). The questions coming from the teacher need to require more than a yes or no response. The question should help the teacher determine what the students understand. They require that the student “reflect, analyze and explain his or her thinking or reasoning,” (3-5). The next step requires that the teacher replaces his or her lecture with sets of questions (3-6). For most of us lectures led by teachers are the staple of most classes, this approach encourages more student involvement in the lecture. The teacher asks questions that lead to student led discussion.

Later in the article the author talks about ensuring class participation (5-2). This article was very focused on the teachers’ ability to foster discussions that would lead to students’ ability to explain and communicate their understanding of mathematics. This approach seems to be in line with the standards we have been reading about, it most directly addresses the communication standards.

Mike Freeland

In “Never Say Anything a Kid Can Say!”, Steven Reinhart explains the importance of student-centered teaching, and how it not only allows for better learning, but also leads to student enjoyment. By implementing small changes to his curriculum each year, Reinhart was able to completely change his teaching style for the better (1-3). He noticed a flaw in our education system, and that is direct-instruction benefits the teacher more so than the students (1-4). The ultimate goal though is for the students to do the explaining and the teacher to do the listening. Doesn’t sound too hard? Well to achieve student understanding, a lot of careful planning is integrated into each lesson. The classroom environment needs to be ideal, and that consists of students feeling comfortable with sharing their ideas with the whole class.

Reinhart provides techniques that worked for him when transforming his classroom, such as creating a plan, sharing with students, teaching for success, being nonjudgmental, and mandatory participation. The plan should consist of questioning students instead of telling them, asking good/process questions, questioning instead of lecturing, and being patient (3-2). I feel that patience is the most important aspect of the plan. Providing students with a little more time to think will increase quality of answers and also decrease student anxiety. The paragraph on teaching for success reminded me of the article on student confidence. Allowing a quiet student the opportunity to share his/her response with the class builds confidence (3-9). Also, informing the student ahead of time that they will be sharing his answer prevents the anxiety of on-the-spot questions. Reinhart expects participation from every student in his classroom. When students participate, they get more out of a lesson.

As future teachers, we all want our students to succeed, but giving answers freely deprives them of understanding on their own. It is hard to watch children struggle, but that struggle is necessary when it comes to developing independent thinkers and learners. Reinhart’s techniques can be adapted to any subject to increase student learning. Why just stop with mathematics? By incorporating student-centered learning throughout grade-school curriculum, we can feel secure about sending our confident, well-rounded students out into the real world.

Hailey McDonell

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The article written by Steven Reinhart talks about introducing questioning and discussion strategies into the classroom. Reinhart early on, realized that no matter how good of teacher he was, how much planning, preparation and implementation he attempted to employ, the students were not learning. Instead of him doing the explaining and the students listening, Reinhart realized, he needed to let the students do the explaining and him the listening (1-4).

There needs to be a shift from my own tendency to answer my own questions and guide students to a desired result, to a question driven, student-oriented approach to learning. When students are asked to explain their ideas, they must feel comfortable sharing with the rest of the class or with the teacher, and it allows them to engage with the learning of mathematics (2-1).

Students that are expected to give justifications for their findings are more likely to come to a better understanding of the material through peer and teacher interactions. When an atmosphere is created where students are praised for their participation and respect for others, a teachable environment is achieved. The teacher is not the source for understanding but rather a mediator or monitor. Students learn by interacting with the content and wrestling with it on their own, in small groups, and with the entire class (5-3). Participation is required for every student to be able to contribute to the learning of others and themselves. Sometimes a teacher needs to prompt a shy student into submitting their own ideas into discussion.

The teacher needs to be aware of certain student's comfort levels and abilities, but also needs to take a firm stance as the leader of the class, modeling good ways to listen and learn from the students, and also justifying and explaining findings. Learning is not the responsibility of the teacher but of the students (6-7). A teacher can help facilitate this process but should never be a dictator running at their own pace and by their own firm agenda. Goals should be in place as far as material covered, but recognizing a unique classroom's needs and pace is very important in getting the most out of a mathematics course.

-kyle d.
As I read through this article I realized that we as teachers like to have the control of the classroom because for the most part this is what we’ve seen in the classroom itself. I realize that if we want our students to grow we cannot do everything for them as teachers in the past have done for students. In the article Reinhart gives us a short list of things that he has observed and learned over the years from other teachers as well. Not only that but he also mentions how he came to his realizations. I feel like they have been extremely insightful for me as well.

In Rinehart’s article he says that he realized that at first he did a great deal of explaining and learning of the materials on his behalf but if the students were to learn then he would have to have the students do the explaining (1- 4). This is true because even as college students I hear students say I understand a subject better if I explain it to someone else. Now that I think about it for half of my high school career I was explaining to other students how to do the math and thus understood it better in the end. This leads me to affirm that because I was doing that explaining that I understood that material almost better than most of my peers. I also noticed that he says he changed his class gradually because he knows that too much change can be disastrous to students, especially if it happens too fast (2-3).

The idea of changing your classroom slowly seems to be a theme in these articles, which also provokes the idea that it must work, and work well. Next he goes into a discussion of what has worked for him and other teachers as well. He gives out his first list which is on the topic of what has worked he only credits the first on the list as his personal contribution. The list is as follows: 1. Never say what a student can say themselves - if you know a student in your class understands and can tell another student what it means and how to make sense of the problem then by all means allow the student to do so.

2. Ask good questions- you should ask student’s questions that allow you to see what they have been thinking or what they know or don’t know.

3. Use more process questions than product questions- ask questions that question how they got the answer not just what the answer is.

4. Replace lectures with a set of questions- instead of just standing in front of the class and transferring mindless notes use questions that allow the students to think

5. Be patient- if we always allow the first student who raises their hand, which is usually the same student anyhow, then we are robbing all other students of their thinking time.

Throughout the next page of the article he discusses a few scenarios of what to do with wrong responses and how to get students to be more involved and respect the activity in the classroom. I especially liked how he said that we should explain why we do what we do to our students (3-7). I like the idea of giving the students responsibility just the same as we have our own responsibilities. Bringing us to the next list that he makes which is the topic of participation.

He says that participation is not an optional item in his class. He gives us another list that somewhat serves as a guideline for what good participation should look like. The list is as follows:


 * 1) 1. Use the Think-Pair-Share strategy- I learned about this strategy a lot while I was in the SPED 4290 class that was held in the second summer semester. This strategy allows students to work independently, then with a partner, and then share their findings with the class. It also allows some of the pressure to be taken off of each student knowing that he/she has had time to discuss it with someone else and somewhat check for a common understanding.
 * 2) 2. If the students can not contribute anything to the discussion or are confused they must pose a question to the class.
 * 3) 3. Always require students to ask a question if they need help- a simple I don’t get it is unacceptable.
 * 4) 4. Require several responses to the same questions – don’t think of problems as just having one answer or just one process.
 * 5) 5. No one in a group is done until everyone in the group can explain/ defend their process/ solution.
 * 6) 6. Use hand signals often- this allows for you to observe if students are on task and find out which are having difficulties.
 * 7) 7. Never carry a pencil because you will be tempted to work the problem out for your students.
 * 8) 8. Avoid answering your own questions- this also robs a student from doing their own thinking.
 * 9) 9. Ask questions of the whole group
 * 10) 10. Limit the use of group responses.
 * 11) 11. Don’t allow students to blurt out answers.

I find that whenever I am helping students with their work I often tend to work out the solutions for them and or explain it to them and talk it out to them instead of letting them figure it out on their own. I hope that now knowing what I know I can take the steps to change and make it so that students think about the processes of doing math instead of just getting an answer. Denise S

“Never Say Anything” is an article about a teacher changing his ways from familiar teacher-centered, direct instruction models to a more student-centered, problem-base approaches. The reason for his change was the question of the low levels of achievement many of his students had. For me as an educator I must know when to change gears in order for my students to grasp content for a good performance in the class. In order to be an effective educator the teacher concluded that if his students were to ever really learn mathematics they would have to do the explaining and he would have to do the listening. 478-3 The problem is getting middle school students to participate in classroom discussions can be a challenge because students can sometimes be self-conscious and insecure. This insecurity and the effects of negative peer pressure tend to discourage involvement. 479-1 In order to get beyond these roadblocks teachers must ask questions that require all students to participate in discussions and then you can create a classroom atmosphere in which students are actively engaged in mathematics and feel comfortable in sharing and discussing ideas, asking questions, and taking risks. 479-1. On 480-1 the teacher lists strategies that helps him orchestrate classroom discussion, they are never say anything a kid can say, ask good questions, use more process questions than product questions, replace lectures with sets of questions and be patient. These strategies are very useful for me to know how to guide a classroom that would lead them to think on their own more often. Another big problem is getting students to participate. The teacher lists eleven techniques to follow to apply to the classroom starting on 482-3 I will however just go over the ones that I feel are really important. In the think-pair-share strategy all students must think and work independently first, then they are paired with partners or join small groups. After working in the groups and the students come up with a strategy the kids share their answers to the class. This strategy forces the students to know what the problem is about, then when the students come together they can ask questions with each other to gain a better understanding which allows for a better solution when presenting to the class. Another strategy I found useful was not letting students blurt out answers. A students blurted out answer is a signal to the rest of the class to stop thinking. Students who develop this habit must realize that they are cheating other students of the right to think about the question. 483-6 I remember when I was in grade school and the teacher would ask us to solve a problem. There was always someone who knew the answer before anybody else did and that hindered the thought process of other students by not letting them find the answer on their own. In order for teachers to help students engage in real learning, we must ask good questions and allow students to struggle. We can’t tell them answers directly or do things for them or show them shortcuts for you relieve the students of their responsibilities and you cheat them of their responsibilities to make sense of mathematics. As a secondary educator I must know how to operate a classroom. I can’t let students sit back and let others take over. Requiring students to work alone places the responsibility for learning on each student which is the reason why students come to together in groups to clarify each other’s findings and hence forms mathematical knowledge.

Fredrick Martin

//Never Say Anything// is about a teacher who was unable to effectively teach his class using direct instruction and decided he needed to change in order to more effectively teach his students (1-3). A big deal of this came from the fact that while he could tell students how to solve mathematical problems, students would rarely have to think on their own and as a result, did not learn (1-4). The author, Steven Reinhart, goes on to describe what thought processes and techniques he uses to make his classes discuss and truly understand mathematics. An integral step in Reinhart’s teaching is around his principle of “Never say anything a kid can say!” (3-6) He allows his students to drive discussion and use their thinking and understanding. Overall, Reinhart puts all of the thinking onto the students. Another principle that Reinhart follows is that he will allow for a discussion to take a life of its own with the teacher answering as few of problems as he can (4-2). If he answers the questions for the students, they know that they are no longer responsible for thinking their own way through problems. This means that he must allow for the students to work through their difficulties. There is also required participation in discussion (5-2). He does this by splitting the class into smaller groups that must contribute to the classes assigned problem by having the smaller groups either to contribute to the understanding of a problem, or allowing a group to ask a question so that they may further understand the problem (5-7). I find the most important of Reinhart’s teaching style is when he talks about how he does not move on from a problem until everyone in a group understands the concept (5-10). This seems to be a constantly overlooked point in any of the readings we have done and any readings I have done in the past. While what I have read has never explicitly stated to leave children behind, none of them made a point of having a unanimous understanding. I also believe that classes I have taken part in have moved along before everyone understands, but this is usually for the sake of keeping a class moving forward. It would be interesting to see how much time is dedicated to whole classroom understanding. Reinhart concludes his paper by reinforcing his teaching’s most important points. Mostly, he wants his students to think in his classroom (6-7). His responsibilities in a classroom are to “ask good questions, allow students to struggle, and place the responsibility for learning on [his students] shoulders.” (6-7) It is interesting to see the focus of student-oriented thinking. Does direct instruction rob students of thinking? I believe it does as I loved not having to think throughout my mathematical courses, but I now realized I could have benefitted from a deeper understanding of mathematics.

-Marcus Edgette