Sunday, October 16, 2011

Literature Review

Fernandes, A, Keohler, J, & Reiter, H. (2011). Mathematics teachers circle around problem solving.  Mathematics Teaching in the Middle School. 17(2), 109-115.
The National Council of Teachers of Mathematics Standards  “recommend that students should have frequent opportunities to formulate, grapple with, and solve complex problems that require a significant amount of effort and should be encouraged to reflect on their thinking” (NCTM, 2000, p. 52)  My action research last year focused on my own instruction of problem solving.  Some of the challenges that I encountered came from my limited experience teaching problem solving in a constructivist way.  Fernandez, Keohler, & Reiter (2011) state that “making problem solving a central part of teaching may be challenging to teachers who have limited experiences in learning and teaching mathematics in this way” (p. 109).  From my experiences the last two summers at Bank Street, I believe that by collaborating with other math teachers at my school, I can bring richer problem solving experiences into my own classroom. 
In their article, they examine the key features of Math Teachers’ Circles, which “were developed with the aim of establishing a “culture of problem solving” among middle school mathematics teachers” (p. 109).  The authors use a vignette of a Math Teachers’ Circle as they attempt to work on the Frogs and Toad problem, to describe how teachers coming together to do math can be an enriching and inspiring experience.  “By making problem solving the central focus of the Circles, the teachers are provided with opportunities to engage in nonroutine problems and get firsthand experience of the challenge and thrill of finding a solution (Fernandez, Keohler, & Reiter, 2011, p 114).   I hope to use their article as a framework for my own collaboration with math teachers at JBA. 

Hiebert, J., et al. (1997). Making sense: Teaching and learning mathematics with understanding.  New Hampshire: Heinmann.
In this book, Hiebert emphasizes the importance of teaching and learning mathematics with understanding.  He uses one definition of understanding that “says that we understand something if we see how it is related or connected to other things we know” (Brownell 1935; Heibert and Carpenter 1992).  Heibert (1997) states that “To help think about how people make connections in mathematics and how they make connections that are useful, it is helpful to consider two processes that play an important role in the making of connections: reflection and communication” (p. 5).  I believe that getting together with math colleagues and doing math problems together will give teachers an opportunity to reflect and communicate on the math.   

Little, J. W. (1993). Teachers’ professional development in a climate of education reform, Educational Evaluation and Policy Analysis.  15, 129 – 151.
“Collaboration is increasingly identified as a key aspect in teachers’ professional growth.  Education reformers have recommended placing more attention on collegial relations of teachers for the purpose of professional growth” (Little, 1992, as cited in Syn-Jong, 2006, p. 178).  This article describes how teacher collaboration is an essential part of their professional development practice and school reform.  What I hope to learn from this experience of getting together with math colleagues and doing math problems together, I am curious about what I will learn about collaborative professional development. 

National Council of Teachers of Mathematics (NCTM). 2000.  Principles and Standards for School Mathematics.  Reston, VA: NCTM
According to the Professional Standards for Teaching Mathematics (National Council of Teachers of Mathematics, 1991), an essential factor in teachers’ professional development is the degree to which they “reflect on learning and teaching individually and with colleagues” (p. 168).  Unfortunately JBA does not have weekly or even monthly departmental math team meeting, therefore there was very limited collaboration between the teachers.  According to Professional Standards for Teaching Mathematics (NCTM 1991, p. 128), teachers need opportunities to experience mathematics instruction that will “enable all learners to experience mathematics as a dynamic engagement in solving problems.  These experiences should be designed deliberately to help teachers rethink their conceptions of what mathematics is, what a mathematics class is like, and how mathematics is learned.”  I believe that in order to be a stronger department, we need a space for the math teachers to come together to learn more about big math ideas and reflect on how their own mathematical understandings influence their practice.  I am interested in how doing math problems together will influence my own thoughts of collaboration and professional development.

Smith, M. S. (2001). Practice-based professional development for teachers of mathematics.  Reston, VA: NCTM
Smith (2001) states that “Professional development must provide teachers with the opportunity to improve their understanding of mathematics content and to reflect critically on their learning experiences” (p. 42).  Math teachers need the opportunity to not just reflect on what they want their students to know, but what they themselves know about math.  “Teachers must begin by making sense of mathematics.  In considering how students solved the problems, teachers must engage with the mathematical ideas that are at the heart of the tasks (Smith 2001, p. 43)  I believe that by doing math problems together with my colleagues, I will get a better understanding of the mathematical ideas that are at the heart of the tasks that I give my students and will result in a deeper mathematical understanding.

1 comment:

  1. Hi Anna.

    I believe I already read your literature review and gave you feedback. I think that going through those comments will help you with any technical errors.
    And remember that the references need to be single-spaced.

    Your voice and the personal connections are excellent, though. Remember to work on integrating the literature as you blog.