The article is Shifting Mathematical Authority
from Mathematics Teacher Vol. 104, No. 4, November 2010 pp 315-318.
- What is an example of a challenge you have had as a teacher related to whether or not to answer a student's question?
- What are your beliefs and reactions to the author's comment that..."If mathematics cannot be understood, only copied, then students have locked themselves out of any mathematical situation in which they do not already know exactly what to do..."
- What can teachers do to shift the audience for mathematical talk and establish mathematical legitimacy as a communal concern?
- With which teacher in the article, Mr. Neal and Ms. Crawford did you most closely connect? Why?
Casey Rurode
ReplyDelete•What is an example of a challenge you have had as a teacher related to whether or not to answer a student's question?
Often times students ask questions about things they experience in their daily lives that are related to key topics that we have discussed in class. Most of the time I feel that the students should be able to answer the questions that they ask me since they have learned all of the scientific information they need to solve their question. While I appreciate these questions because it makes me aware of how much, or how little, the students took away from the lesson or activity, I hate to answer such questions because I want the students to challenge themselves and critically think to figure out the answer on their own. Recently I have started throwing students’ questions out to the class instead of answering them. Sometimes the students impress me with their recall and ability to connect abstract scientific concepts to events they observe and their personal experiences. Other times I feel frustrated that the students are unable to explain what they experience or wonder about on their own. I am unsure whether that is an indication that the students have not learned, cannot recall material, do not know how to think critically, are not confident in themselves, or are too lazy to think of an answer on their own.
•What are your beliefs and reactions to the author's comment that..."If mathematics cannot be understood, only copied, then students have locked themselves out of any mathematical situation in which they do not already know exactly what to do..."
I think that statement is sad but even worse true. I have noticed that a majority of my students do not challenge themselves to creatively solve a problem; they just look at the question and assume they can’t do it because it is new. This is definitely something that I have noticed while discussing both scientific concepts in addition to the math that we use in science class. When students have to manipulate equations many say right away they have no idea what to do, that math is dumb, and that we should not be doing math in science. This takes me back to a question that I think about often: Do our students know how to think critically? If not, then why? How can we teach them to think critically and be problem solvers?
Casey Rurode
ReplyDelete•What can teachers do to shift the audience for mathematical talk and establish mathematical legitimacy as a communal concern?
It seems that teachers can help this shift along by building up the students’ confidence in their ability to answer different types of questions. I loved the suggestion of putting the students in groups to do work but chunking the amount of team time the students have to complete each problem or a certain set of problems. The chunking makes the work seems less daunting for one, but also provides an opportunity for students who are confused to understand how to work the problems or what to do if they get stuck. Therefore when the students have to complete the next chunk of problems they will feel better about their ability to solve the problem. Another strategy to increase communal concern about mathematical legitimacy is to let many students share not just their answers but their reasoning as well, have other students interpret the work of their classmates, and have students constructively critique each other.
•With which teacher in the article, Mr. Neal and Ms. Crawford did you most closely connect? Why?
I hate to say it but I think I identify most with Ms. Crawford; however, I wish I could be more like Mr. Neal! I feel this way because Ms. Crawford was described as being a “quality controller ” who always wanted her students to give correct and well supported answers. When the students are working in groups I do constantly listen in a have a terrible habit of answers the students’ questions when they ask me to instead of requiring the students’ to sort out an answer together. Ms. Crawford would also direct class discussions and confirm or deny the correctness of students’ response. This is also something that I believe I do. I never realized that me taking control of class discussions would make students dependent on what I say and make them feel as if they couldn’t solve their own curiosities. Now that I am aware of what I do I want to make an effort to stop!
Challenge: I like to share ideas and thoughts of my own. I tend to do so, not in the "know it all sense" but in the sense that in doing so, I feel my thoughts provoked, inspiration flowing and professional connections. I do realize, however, that this is mostly selfish. It does exactly what the article is commenting on...makes ME appear to be the end source for answers and ideas. This is not my intent as I would hope that I empower versus enable thinkers within my students. It is definitely something that I am and will continue to work on. It's also sometimes easier and feels more "responsible" to answer a student's question. After all, were were trained as students that teachers should have the answers. In doing this as teachers, though, we perpetuate the cycle. Could it be a goal/challenge for tomorrow that I don't answer one single question of my students? I will give it a try!
ReplyDeleteAs you mentioned, Casey, I think it's all of the above reasons as to why students don't "chew" on their thoughts more and question/debate the thinking of others. This is something that I am used to but am realizing that not everyone has had experience with. I'm thinking more input on how to "occasion" vs. "cause" these situations in the classroom would be helpful (p.316)
We have, to some extent, created the situation we are in in education/society that is mentioned here... We have always provided the answers and been positioned as the experts on a given topic simply because we are teachers. I know this is the image/impression that I had as a student and, sometimes even now, continue to feel throughout some of my graduate work. Thankfully, this is slowly beginning to change. As we realize (both in society and in education) an answer and/or the correct answer is not usually enough. The understanding of what it means is equally, if not more, important. As is being able to explain it, convince others by supporting it with evidence, adjust it as needed in certain situations, etc...
ReplyDeleteThe comment about using group chunks to LISTEN instead of to help/fix misconceptions is vital to remember. It's hard for me to not discuss, especially about something that is so very interesting to me (mathematics). However, keeping in mind the purpose of the collaboration chunk as a time for students to grapple with topics and a time for me to absorb their ideas, thoughts and their questions without "rescuing" them is key to remember. As the author states, the slight change in timing and pacing of this work could make all of the difference in executing this well. I plan to use the author's quote on pg 317 that Mr. Neal shared with his class..."opportunity for students to 'discuss what we have learned...extend(ing) our knowledge...through talking and listening to one another". He also provides some great points and questions to use in self-assessing my facilitation that I think might make a good rubric/checklist for me to use as a tool.
ReplyDeleteI am trying to be more like Mr. Neal. I am, however, still challenged by how much and how little structure I provide for a given learning opportunity. It is surprising to me, although entirely understandable, that many of my students (adults...teachers) come to meetings, workshops, discussion with little to no pre-thought as to what the session should/would entail. Even when some do have their own ideas/thoughts, they don't know how to contribute and share them professionally. I see the same challenges here as I do within high school student classrooms. I do think the key is this idea of the facilitator creating the "occasion" vs. "causing" discourse and that this is not a straightforward skill. It also seems to take some flexiblity and creativity in planning and implementation of lessons. I'm definitely going to work on this more throughout my planning and co-planning work this year and would be interested in working together on this if anyone is interested.
ReplyDelete