Mathematical Habits of the Mind for Preservice Teachers

Abstract

This article provides an overview of mathematical habits of the mind and discusses how the concept relates to Polya's problem solving principles as well as exemplification. Specific problems are discussed as a means to assist preservice elementary school teachers' in their development of mathematical habits of the mind. Without a technique to begin solving these rich problems, preservice teachers may have difficulty getting started. The process of preservice teachers outlining their thinking as they progress through Polya's process is discussed. Students' reflections from this technique are discussed to explore the outcomes that may be expected from establishing an environment where students are encouraged to develop mathematical habits of the mind.

Construction Process of the Length of 3√2 by Paper Folding

“…Because, especially during the accomplishing P6, they sometimes stopped and they couldn"t be sure whether they were on the right direction or not. Correspondingly with Jacobbe and Millman"s (2009) statements, MHM is related to problem solving principles. While accomplishing P6, teachers acted like that they were solving a problem and their actions referred to Polya"s problem solving principles which are (i) understand the problem, (ii) devise a plan, (iii) carry out the plan and (iv) look back.…”

“…According to her, solving problems in different ways is a MHM which requires and fosters advanced mathematical thinking. Jacobbe and Millman (2009) associated MHM with Polya"s problem solving principles. They stated that rich problems would help preservice elementary teachers develop their MHM.…”

Examining the Relationship between Geometric Habits of Mind and the Mathematics Achievement: The case of Mathematics Preservice Teachers

“…Literatürde genelde matematiksel düşünme alışkanlıklarına özelde ise geometrik düşünme alışkanlıklarına yön veren çalışmalara rastlanmaktadır (Gordon, 2011;Harel & Sowder, 2005;Herbst, 2006;Jacobbe & Millman, 2009;Marshall, 2004;Marzano ve ark., 1993). Bu çalışmalardan biri Jacobbe ve Millman (2009) tarafından yürütülen çalışmadır.…”

“…Bu kapsamda Driscoll ve arkadaşları (2007), Goldenberg (1996) İlgili literatürde matematik ve geometrik düşünme alışkanlıklarının problem çözme ile iç içe olduğu görülmektedir. Yani geometrik düşünme alışkanlıkları bireylerin problem çözme stratejilerine yön vermektedir (Costa & Kallick, 2000;Driscoll ve ark., 2007;Driscoll ve ark., 2008;Jacobbe & Millman, 2009). Bunun dışında literatürde öğrencilerin matematik derslerindeki başarılarının problem çözme stratejileri ile matematiksel ve geometrik düşünme alışkanlıklarını kullanma düzeyleri ile ilişkili olduğu görülmektedir (Gordon, 2011;Marshall, 2004).…”

Habits of Mind Calon Guru Matematika dalam Pemecahan Masalah Matematis

“…Skala habits of mind dalam pemecahan masalah matematis dikembangkan berdasarkan adaptasi dari indikator habits of mind yang dikembangkan oleh Costa & Kallick 2008; Jacobbe & Millman (2009); dan Johnson (2012). Tes pemecahan masalah matematis dan pedoman wawancara menjadi instrumen pendukung untuk menganalisis habits of mind calon guru matematika dalam pemecahan masalah matematis.…”