An Investigation of African American Students' Mathematical Problem Solving

Students’ use of technological tools for verification purposes in geometry problem solving

“…Working with ninth grade algebra students, Pugalee (2001Pugalee ( , 2004 found that there were few instances of verifying computations and that the frequency of verification activities was not related to success with the problem-solving task. But other studies provide evidence that the use of verification is related somewhat to problem solving success (Cai, 1994;Eizenberg & Zaslavsky, 2002, 2004Malloy & Jones, 1998). For example, Zaslavsky (2002, 2004), focused on identifying undergraduate students' tendencies to verify their solutions to combinatorial problems and the verification strategies they employed solving these problems.…”

Investigation of Preservice Teachers’ Problem Solving Strategies in Computer Algebra Systems Environments

“…Pólya"nın belirttiği stratejilerin yanında, alanyazında da çeşitli problem çözme stratejileri tanımlanmıştır: (1) Bir önceki aşamada yapılanların, mevcut aşamada yapılacakların kontrolünü sağladığı, böylece bir önceki aşamaya dönmeyi engelleyen, döngüsel olmayan strateji (anti looping heuristic) (Davies, 2000); (2) Mevcut durumla, problemin amacı arasındaki farkı en aza indirme stratejilerini içeren araç-amaç analizi (Reed, 2007); (3) Bir resim veya şekil çimek, tablo veya liste oluşturmak (Malloy, Jones, 1998) (4) Problemin parçaları yerine bütününe odaklanılan holistik strateji ile sonuca ulaşmaya çalışırken, problemin birbirinden farklı parçalarını düşünülmesini içeren analitik strateji (Boulter & Kirby, 1994;Malloy & Jones, 1998); (5) Benzer problemleri kullanarak çözme (Reed, 2007); (6) Birdenbire ortaya çıkan sonucu doğrulama (pop-upverify) (Hammouri,2003); (7) Bireylerin, tamamıyla tanıdık olmayan bir problem durumuyla birdenbire karşılaştıklarında ve çözüme dair herhangi bir planları olmadığında probleme başlamak için kullandıkları deneme yanılma stratejisi. (Brunning, Schraw &Ronnig,1995); (8) Olası çözümleri üretme ve doğruluğunu test etme (Jonassen, 1997), (9) Ayrıştırma ve sadeleştirme (Jonassen, 1997).…”

Student engagement and college readiness in mathematics.

“…In this classroom environment the teacher scaffolds instruction to insure all students make connections between what they know and the new topic being learned (Bell & Pape, 2012). Students utilize work space in ways that encourage cooperative learning (Malloy & Jones, 1998). The teacher provides opportunities for students to express what they know and to receive immediate feedback from the teacher as well as their peers (Russell, 2012).…”

“…The teacher provides opportunities for students to express what they know and to receive immediate feedback from the teacher as well as their peers (Russell, 2012). Students also feel comfortable taking risks, understanding that problem solving is part of the learning process (Malloy & Jones, 1998). Effective mathematics teaching should be in student centered classrooms where the teaching consistently contributes to achieving the goals of the mathematics instruction reform.…”

“…Social constructivism theorists argue that successful performance in mathematics is related to the needs, aspirations, and perspectives of the class of individuals where, the collective emphasis of group learning remains through all interactions (Von Glasersfeld, 1991). Students' attitudes about themselves, their needs, and motivation for learning mathematics in constructivist classrooms all influence their cognitive development, their work, their thinking, and therefore their cultures of learning (Malloy & Jones, 1998). In a constructivist mathematics classroom, students negotiate shared meanings of mathematics concepts while working together in engaged learning groups (Ross & Wilson, 2007).…”