Making Sense of Integers through Storytelling

Wessman-Enzinger, Nicole M.; Mooney, Edward S.

doi:10.5951/mathteacmiddscho.20.4.0202

Cited by 19 publications

(13 citation statements)

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“…These are descriptions of the CMIAS that students used with the integers emerged from my previous study (Wessman-Enzinger & Mooney, 2014. This dissertation study suggests the need for the development and refinement of more robust descriptions of these conceptual models and for the investigation into other possible conceptual models.…”

Section: Rulementioning

confidence: 93%

“…Other researchers have pointed to other contexts being suitable for helping students grow conceptually with respect to negative integers in rich contexts (Stephan & Akyuz, 2012). Additionally, recent research conducted by this author has shown that students often make sense of negative integers in unconventional and unexpected ways (Wessman-Enzinger & Mooney, 2014). This dissertation study recognizes the complexity of the use of context with learning the integers and it directs attention to investigating the conceptions that students have and need about integers.…”

Section: A Focus On Student Thinkingmentioning

confidence: 94%

“…Contexts can illustrate important mathematical ideas and uses of the integers that are often lost in modern curriculum and standards (Wessman-Enzinger, 2015). Contexts used with integers promote ways of thinking that are more comprehensive than the context itself (Wessman-Enzinger & Mooney, 2014. Although the ideas about the role of context are complicated, it is important to look more broadly about what the thoughts or conceptions of contexts are promoting.…”

Section: Context As More Than a Pedagogical Toolmentioning

confidence: 99%

“…The suggested contexts promote ideas of thinking about the negative integers as counterbalance, bookkeeping, translation, and relativity. In fact, these mathematical ways of thinking, as well as some others, emerged as Conceptual Models for Integers that students used to make sense of the integers (Wessman-Enzinger & Mooney, 2014. These conceptual models are described in detail next.…”

Section: Context As More Than a Pedagogical Toolmentioning

confidence: 99%

“…In my first research study about student thinking, I investigated how experienced learners connected contexts to integer addition and subtraction open number sentences (Wessman-Enzinger & Mooney, 2014. I initially worked with six Grade 8 students.…”

Section: Discovering the Conceptual Models For Integer Addition And Smentioning

confidence: 99%

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Developing & Describing the Use & Learning of Conceptual Models for Integer Addition and Subtraction of Grade 5 Students

Wessman-Enzinger¹

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This dissertation reports the results of a teaching experiment, which explored student thinking about integer addition and subtraction. Through the lens of commognitive theory (Sfard, 2008), interpreting negative integers as secondary intuitions (Fischbein, 1987), and employing teaching experiment methodology (Steffe & Thompson, 2000), this study was a first step in developing more robust descriptions of students' conceptual models for integer addition and subtraction. I investigated: (a) the conceptual models that students exhibited, (b) the various ways that students utilized conceptual models while learning about the addition and subtraction of integers, and (c), the ways that students' conceptions evolved over the course of a teaching experiment. This study of students' conceptual models led to the modification and refinement of the CMIAS descriptions (Wessman-Enzinger & Mooney, 2014, 2015). Three Grade 5 students were selected based on results of a pilot study and students' responses to a written assessment. Data for this study was used from the Open Number Sentence and Context Individual Sessions of the 12-week teaching experiment. All of the Individual Sessions were videotaped and transcribed. The transcripts paired with all of the drawings produced by the students for stories for open number sentences generated and open number sentences solved during all Individual Sessions constituted the unit of analysis. A constant comparative method (Merriam, 1998) was used to modify the previous descriptions and develop new descriptions of the CMIAS (Wessman-Enzinger & Mooney, 2014). A description of the changes in mathematical discourse (i.e., word use, visual mediators, narratives, routines) was used to highlight the learning of integer addition and subtraction across the Individual Sessions.

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Section: Rulementioning

confidence: 93%

Section: A Focus On Student Thinkingmentioning

confidence: 94%

Section: Context As More Than a Pedagogical Toolmentioning

confidence: 99%

Section: Context As More Than a Pedagogical Toolmentioning

confidence: 99%

Section: Discovering the Conceptual Models For Integer Addition And Smentioning

confidence: 99%

See 3 more Smart Citations