After reading the Effective Questioning reading, I felt like I had gained a valuable resource in becoming a prepared future math teacher. Overall, the piece explicitly lays out various types of questions that can be used to help teachers act as facilitators in many different aspects of mathematical processes. I feel as if this is an aspect of teaching many pre-service teachers are uncomfortable with, yet this reading practically provides a “how to guide” for developing the exact type of language and question types that are necessary in the classroom. The questions fell within six topics, including: Promoting Classroom Discourse and Student Efficacy, Problem Solving, Reasoning and Proof, Connections, Communication, and Representation. (Nurnberger-Haag)
In the Wilkins article, a focus is placed on differentiating curriculum for gifted students. I found some common lines between this article and the effective questioning article in many aspects, as the article also provided guidelines for teachers, in the form of different activities for students. One of the activity types included integrating across the curriculum, (for example: asking students to write a letter to the President discussing which measurement system is best and why (Wilkins, Wilkins, & Oliver, 2006)) which may be tied to the connections aspect of the questioning reading, specifically in the form of asking the sample question, “Explain a situation in social studies/science/language arts, etc when this math topic could help you understand that situation.” Many of the activity types can be directly related to the various question types- demonstrating a link between the ways structuring a classroom can work to benefit in forms of differentiation as well.
As brought up in the Problem Solving and At Risk Students article, the structure of a classroom is crucially dependant to the students who make up the classroom. Ideal classroom structures as represented in the other two articles are almost equally brought to the forefront in a form of criticism, as the author states, “I agreed philosophically that this method was an ideal method to teach mathematics, yet I also knew that the same task given to my group would bring tears and anger.” (Robert, 2002). And so, the teacher had to learn how to adapt to her classroom in a way that still challenged the students in the way the previous articles suggested, but in a more “custom-tailored” format in order to build students’ confidence to continue to reach toward more advanced tasks. Overall, the articles I read all dealt with effectively structuring one’s classroom, but also considering ways in which one must consider the individual aspects of a classroom to determine the most effective structure rather than a “fit-all” mentality.
In the Wilkins article, a focus is placed on differentiating curriculum for gifted students. I found some common lines between this article and the effective questioning article in many aspects, as the article also provided guidelines for teachers, in the form of different activities for students. One of the activity types included integrating across the curriculum, (for example: asking students to write a letter to the President discussing which measurement system is best and why (Wilkins, Wilkins, & Oliver, 2006)) which may be tied to the connections aspect of the questioning reading, specifically in the form of asking the sample question, “Explain a situation in social studies/science/language arts, etc when this math topic could help you understand that situation.” Many of the activity types can be directly related to the various question types- demonstrating a link between the ways structuring a classroom can work to benefit in forms of differentiation as well.
As brought up in the Problem Solving and At Risk Students article, the structure of a classroom is crucially dependant to the students who make up the classroom. Ideal classroom structures as represented in the other two articles are almost equally brought to the forefront in a form of criticism, as the author states, “I agreed philosophically that this method was an ideal method to teach mathematics, yet I also knew that the same task given to my group would bring tears and anger.” (Robert, 2002). And so, the teacher had to learn how to adapt to her classroom in a way that still challenged the students in the way the previous articles suggested, but in a more “custom-tailored” format in order to build students’ confidence to continue to reach toward more advanced tasks. Overall, the articles I read all dealt with effectively structuring one’s classroom, but also considering ways in which one must consider the individual aspects of a classroom to determine the most effective structure rather than a “fit-all” mentality.
Similar to the article you discussed about At Risk Students and the importance of structure in the classroom, one of the articles I read this week focused on the steps that a teacher should take to help students with disabilities understand math. The authors outlined five basic guidelines that should be followed in every classroom- not just for students with disabilities, but to benefit all students. These ideas included things like using multiple models of representation, starting with concrete and eventually reaching abstract (Miller & Hudson, 2006). The authors suggested that students should use many different forms of representation to solve a task in order to gain a deeper understanding of its meaning. Like the reading you mentioned, this article also stressed the importance of having a specific structure in mind when planning and teaching, as it is the initial foundation for a successful lesson.
ReplyDeleteThe other reading I did this week also dealt with math instruction for students with learning disabilities. This article made a lot of great points and was full of specific examples of how to help struggling students work through problem solving methods. The basis of the article was around two specific students and the progress they made over the course of instruction. The authors were adamant that the key to helping them grow was not to “fix” their skill deficits, but to build on the knowledge & strengths they already had (Behrend, 2003). Several dialogues were written out detailing the way a teacher worked with the pair to get them to think critically and challenge each other’s ideas. By seeing the way the other boy solved the task and what his though process was, each student was able to realize their own correct and incorrect responses and figure out ways to re-think them. This article is a very useful tool in showing how to work with more than one student at a time in a way that will benefit them both.
My articles were similar to both of yours with the only difference being that mine focused on English Language Learners. My two articles focused on the problems that ELL's face during math lessons and one of the most common problems was happening during word problems and problem solving problems. One suggestion that I really liked from the "Problem Solving For English Language Learners" article was that when given a word problem the teacher should first have a discussion about the various aspects of the problem (like what a chicken is if a chicken is in the problem). They should also have them clarify what the problem is asking so the ELL's have a good idea of what is being asked of them. One thing that really stuck out to me in the article is that it said ELL's are not only learning subject content but language acquisiton as well and the teachers need to be aware of this otherwise the students may fall behind because they do not understand what is being asked of them.
DeleteI actually think this type of suggestion can go along with students with other disabilities as well. Clarifying can never be a bad thing and will help ensure that EVERY student understands. Also, as for "gifted students" which Jessie focused on, I think that while ELL's may not fit the definition of "gifted" I think that their academic talents may only be hindered by their language and therefore they may be considered gifted once they overcome the language hurdle. Going along with this, I think it is important to not hinder their learning by not pushing them like a teacher would for a gifted student. I think the actual math portion of the problems should push students and make them think but the teacher just needs to keep in mind that the wording or some parts of the problem may be unclear to certain students and may need clarification.