Groupwork

While we often read about the advantages of groupwork, it is always a helpful reminded that just places students in close proximity to each other does not always promote healthy groupwork. There is a difference between groupwork and cooperative learning. "The Dilemma of Groupwork" brought up some interesting ideas that I had not spent much time reading about before. The first time Mrs. Todd put her groups together without any prior planning I wasn't entirely surprised that it didn't work out, but I was surprised at all the different dynamics in a group that group members probably are not even consciously aware of. After reading the article it left me wondering how to solve the issue though. Cohen wrote that even when teachers tried to place students of similar abilities together they were still able to fine tune who they thought were the higher level students among themselves. If this is the case, what can teachers do to get all students involved? One thing that comes to my mind is giving each student a specific task within the group. This ensures that they have to get involved, especially if the tasks are integral to the groupwork. But about if students are just gathering to talk about an idea? Can you always structure groupwork so each student has a specific task? I wondered about the application of groupwork in math. In my field my CT always has the students in pairs. They are arranged so they have the same partners for a month or two at a time and students are paired with uneven levels of ability. Is this a good method of bypassing the internal ranking of groupwork? I wondered how it would apply to the work being done in the students in the DMI text this week. When Eleanor gave her lesson to the students it seems like they worked by themselves to come up with different methods of solving the problem. Would this many different methods have emerged if students had worked in groups? Would some of the students voices been ignored, thus losing valuable contributions? But perhaps even more refined ideas would have emerged. This is something that has really left me wondering. In Lauren's case she had a handful of students that were very confused about keeping place value in their head. Lauren was working with them but if they were all in a group together would they have stayed confused because they all had similar abilities? Maybe in a mixed ability group they could have solved the problem. Much of math has to do with making sense of how numbers work. It seems like groupwork would be ideal for this. I think group size is very important. For small problems like this I would think more than 3 would be too many. This limits the group dynamic issues that were brought up in Cohen. It is hard for one persons ideas to be ignored if there is only one other person in the group. Many students might think of math as a subject they don't enjoy because they see it as a solitary subject. If teachers really think of ways to integrate cooperative learning in a way that does not disadvantage some group members, all students could benefit from the activity.

Groupwork

After reading the article, The Dilemma of Groupwork, I could not help but find myself relating the information conveyed to my own, personal experiences within academic settings. The article construed the various problems coinciding with the act of group work within a classroom setting. These problems correlate with an array of statuses that are assigned to children inclusive of academic statuses, peer statuses, and societal statuses. When describing the concept of an academic status, the book states, "In the classroom it is impossible to compose groups where all members have equal status. Students generally have an idea of the relative competence of each of their classmates in important subjects like reading and math acquired from listening to their classmates perform, from hearing the teacher's evaluation of that performance, and from finding out each other's marks and grades" (28). In essence, when working in groups the children whom are highly respected academically and perform well on a plethora of given tasks are usually in a hierarchical position in which their opinions are more respected and thoughts and ideas taken to be truth. On the contrary, students who are known by their peers as being incompetent and unable to complete tasks with accuracy have few opportunities to offer their ideas and, when those thoughts are conveyed, are rarely taken seriously. Peer status is one that arises due to social hierarchies based on level of attractiveness, popularity, or athletic ability. Students seen as having a high peer status generally tend to dominate the conversations existing within group work while students possessing a low peer status have little opportunity to speak. Lastly, societal status's arise as a direct result of what culture is more valued within the community, school district, etc. For example, in the hypothetical situation depicted of Ms. Todd's class, there were only three African American students within her classroom and two of the three were non-participatory during group discussion and failed to convey their thoughts and ideas. This suggests that because there are so few individuals deriving from this culture (within this particular classroom) they maintain a low societal status. Overall, it is extremely important to consider and recognize these existing status's within a classroom. As Cohen states, "Those who do not participate because they are of low status will learn less than they might have if they had interacted more. In addition, those who are of high status will have more access to the interaction and will therefore learn more. It is a case of the rich getting richer" (36). He goes on to say, "If status characteristics are allowed to operate unchecked, the interaction of the children will only reinforce the prejudices they entered school with" (37). Because these outcomes are both extremely problematic and not only hinder children's academic learning but also socio-political mindset, it is increasingly important to make yourself away of these existing hierarchies and intervene as much as possible. In reflecting on my own experiences within the school system, I have routinely been one of the students who sits quietly during discussion and listens to the opinions of the rest of the group. This is not a result of my own incompetence nor of my inability to think of something constructive to say, rather just my own feelings of inferiority and shyness within a group. I now understand that in doing this I am essentially encouraging other individuals to view me as uneducated and assume I have nothing worthy to offer them within a group situation. This is certainly not how I wish to be interpreted by my peers and it is disheartening to think that, through my own actions, I have essentially perpetuated and encouraged this thinking. Because of the negative feelings that I have developed as a result of other's opinions of me, I know how important it is to intervene when these situations are occurring. In my own classroom, while I do intend to promote group work, I now have the insight to do so with a critical eye.

Dilemmas of Groupwork

I found the article “The Dilemma of Groupwork” by Cohen extremely interesting since I am a huge fan of using group work in my problems. I was well aware that group work could backfire considering students working with their friends were likely to fool around. I believed that if you assign groups made up of students with high ability levels and low ability levels, the high ability levels would be able to teach and help out those with low ability levels. After reading this article, I know that this is not necessarily all true and good. Like I had originally thought, there are students who are classified into different levels. I was not aware, though, that there was more to this classification. I found it interesting that they too had classified children with an academic status, but also an expert status. I liked that Cohen also went deeper to peer and societal status. I’ve seen multiple times in our classroom these classifications in play. During times of free time, the children automatically form their own groups. In these groups there is always a student who takes charge in the task at hand and one or two that sit back and usually observe. For example, there was a group of four students playing with blocks one day. One student who would not necessarily be classified as a high achieving student was taking the initiative and taking charge of the group. Although this child is not the one that the rest would normally see as being an expert or “high status member” in terms of academic level, this particular child is very popular with his peers because of his humorous personality. This shows that leaders are found all throughout school time and not only in assigned group work.
After reading this article, I found myself discouraged from wanting to use group work. I found myself analyzing and thinking about more examples from the classroom and my own experiences. The more I thought about it, the more I realized that Cohen had come to true conclusions. I have been involved in group work where these exact characters come to life. I have also watched group work where I have seen leaders, children being silly, children sitting back and not getting involved and students to shy or embarrassed to chime in. I have also been involved in group work where everyone truly worked together though. The more I thought about it the more I found similarities in all these instances. One was that there were no more than two or three involved. When you work in partners, it is necessary for both people to be involved. The other instances were when the activities were fun and all students were required to be involved. For example, last semester in my TE class, we did a lot of dramatic play in groups. In these instances everyone had to play a part so it was imperative that everyone became involved. The activities were also very fun and silly at times so everyone, even those who were naturally shy, enjoyed themselves and were more willing to put in effort.

A little late... but special needs students

I read the article called "Why Students with Special Needs Have Difficulty Learning Mathematics and What Teachers Can Do to Help" by David Allsopp. This article considered special need students to have one or more of four struggles. The first one was attention problems. These students have trouble focusing on one thing because they are constantly focusing on EVERYTHING making it difficult for them to catch the important details that the teacher may be saying.The second problems children sometimes face are cognitive processing problems. These children have trouble processing from what they see visually to what they are writing on paper. Metacognitive problems can also hinder children's mathematics learning. This means that the students me be unaware of other possible ways of learning. The fourth struggle is one that is extremely hindering in mathematics. Memory problems put students at a disadvantage because they have difficulty retrieving the information that the brain has successfully stored. In mathematics, children have a disadvantage because they require memory. For instance, in long division, it is necessary for the child to know addition, multiplication, subtraction and it takes memory to remember all the correct steps in the correct order.
In order to help these children, there are a number of ways we can plan and teach lessons. Allsopp explains some strategies to help with instruction with special need students. First, teach in authentic and meaningful contexts. It is helpful to directly model both general problem-solving strategies and specific learning strategies using multisensory techniques. This allows the teacher to cater to the different learners and show the children other ways to learn. Another strategy is to ensure that the sequence of instruction moves form the concrete, to the representational and then to the abstract. Teachers will find it helpful to allow the students opportunities to use their language to describe their mathematical understandings. It is also important to provide multiple practice opportunities to help students use their developing mathematical knowledge and build proficiency. Studies have also shown that using nemonic devices because they help retrieve problem solving steps from memory both independently and efficiently. For example, for the order of operations, we continually hear "please excuse my dear aunt sally". These "name games" are helpful for students. Most importantly, and I believe this is true for all students, is that we must continually monitor students performances and offer meaningful feedback.

Gifted Students ...

I was interested in spending some time reading about working with gifted students because in my experience, it seems to be an area that slips through the cracks more than ever. Chval and Davis raised the point that with an increased emphasis on passing standardized tests and making AYP teachers feel more pressure to raise up their lower students while not putting as much effort into challenging their gifted students. While I feel my CT works hard to create differentiated assignments, I still see quite a few behavioral problems coming from one student in my class that is probably the most gifted in math and quite a few other subjects that is stemming from boredom. In the same article, I felt very bad for Craig because I know I have seen many of those scenes repeated in many different classrooms.

The Wilkin's piece talks extensively about the Mathematics Investigation Center. I thought a lot of the guidelines they put down for using this piece would make it very useful in the classroom. The MIC is a set of about nine activities modeled around different areas of math that are kept in the classroom for students that need more challenging work to do. Some of the problems are easier so most of the class can work on them but some are designed to be less accessible to lower students in the class. I liked the idea that students were not asked to work at the MIC outside of math time so they did not feel like they were being forced to do extra work. The activities in the MIC are supposed to be designed to be integrated into the math unit the class is working on at the time so gifted students aren't just working on drop-in lessons. This seemed like a great solution to some of the problems that students complained about in the Chval and Davis piece where they did not like that they finished far before other students in the class and had nothing to do, or that the teacher did not want them working ahead of other students in the class. This instruction method is a great way to keep everyone on the same topic, but different students can work on the problems at different levels.

Chval and Davis bring up a similar idea when they discuss differentiated tasks. These tasks usually have several different "levels" that students can work on according to ability. Students that considered high level can work on more advanced parts of the problem but all students should be able to access the problem at some level. This is another good way to challenge gifted students without making them feel like they have been singled out to do more work.

I found some relevance within the "Behavioral" piece as well. Some teachers might make the assumption that since a student misbehaves and does not do his work that means he is not smart. When Carter was given the chance to do "real world problems," something that the gifted students interviewed in Chval requested, he responded well and really began to show interest in math class. While home issues that were out of his control disrupted his math learning, it shows how much effect trying to really get students to problem solve with different problems can have on students in the classroom. The cranium crackers got Carter more interested in staying engaged in class and gifted students need the same effort from teachers to keep them engaged when they already know the content their classmates are working on.

At-Risk Students

After doing this week's readings and, more specifically, completing my chosen article titled "Problem Solving and At-Risk Students: Making Mathematics for All a Classroom Reality", I found myself left with more questions than answers. This article was a personal narrative written by a fifth grade mathematics instructor who found herself teaching in an impoverished rural elementary school that performed significantly below both grade level content expectations and those expectations formerly met by students in her previous teaching position within a prestigious suburban school. On the first day of class, she implemented an activity that had been loved and admired by her former students. However, within the context of her new classroom, this task was deemed as much too difficult and the students became easily frustrated, angry, and humiliated for being proven incompetent. While I understand that this teacher was simply trying to confront her students with an exciting, challenging, and competitive new problem solving task, I cannot help but question her logic and reasons for assuming this activity would be appropriate. Did she not review the student's prior academic records to gain a feel for what the students are capable of doing? Does she not have access to school wide standardized test results? Had she not conversed with the children's prior mathematics instructor to obtain an understanding of the curriculum that they had been exposed to? While all of these sources of information inevitably must be taken with a grain of salt, they can still provide guidance and significant understanding regarding the children's current capabilities. I feel that had the teacher invested the time and energy to perform this research, this entire situation could have been prevented and the students' pride kept in tact. I do, however, think that this teacher took appropriate and helpful measures in order to remedy the situation and establish a classroom of "problem solvers". The teacher quoted a text titled Teaching for Thinking as saying, "If we are to think, we must dare to think. Daring implies confidence in ourselves and in our abilities. When we have confidence, we often succeed in doing tasks far beyond our expectations. When confidence is missing, we fail at tasks that seem well within our grasp. Confidence grows largely as a result of experience" (292). Through rereading this passage, the teacher was able to realize that in order for the students to perform academically, they first needed to feel confident in their ability to do so. The way that she decided to build this confidence was to reevaluate her original lesson plans and break them down into more simplistic tasks. In essence, she decided that it would be most effective to take baby steps in order to gradually build the children's self confidence vs. bombarding them with one large task. I think that these strategies are quite profound and would be especially useful within special education classrooms. So often, students labeled "special ed." begin to associate negative connotations to this term and perceive themselves as incapable of learning or "stupid". When working with these students in the future, it will be so important that I counteract these common stereotypes and build their self esteem so that they are both motivated to complete tasks and confident in their ability to do so. Overall, the most important piece of information that I took away from this article was that " If the activity does not work, if the papers get crumpled, if arguments begin or materials get abused, I may give up on the activity, but I never give up on my students" (295).