Is There Something to be Gained from Guessing? Middle School Students' Use of Systematic Guess and Check

Johanning, Debra I.

doi:10.1111/j.1949-8594.2007.tb17927.x

Cited by 9 publications

(4 citation statements)

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“…The important and, sometimes, crucial stage in the process of planning the problem solution is that of finding an internal representation of the problem. This is the stage whereby the problem data are translated into a form, which materializes the situation; from this form it is convenient to begin the solution [11].…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Effect of difference in word formulation and mathematical characteristics of story problems on mathematics preservice teachers and practising teachers

Patkin

Gazit

2011

International Journal of Mathematical Education in Science and

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This article aims to present the findings of a research which investigated the effect of a difference in word formulation and mathematical characteristics of story problems on their successful solution by preservice mathematics teachers (students) and practising mathematics teachers. The findings show that in the case of a problem with a difference in word formulation of one of its components, but that difference does not entail a difference in the mathematical characteristics and the solution process, the percentage of correct answers to the two versions did not vary significantly. However, when there is a difference in the word formulation of one of the problem's components, leading to difference in the mathematical characteristics and the problem solution, there is a wide gap in the percentage of correct answers between the two versions. These findings were relevant to the preservice mathematics teachers as well as to the practising mathematics teachers. Moreover, the findings illustrate that the students displayed greater originality in the solution process than did the practising teachers. Consequently, during in-service courses and teacher education, it is recommended that we need to focus also on story problems with different word formulations in order to facilitate the thinking processes leading to their solutions.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Effect of difference in word formulation and mathematical characteristics of story problems on mathematics preservice teachers and practising teachers

Patkin

Gazit

2011

International Journal of Mathematical Education in Science and

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“…To overcome the random use of guessing and checking, Johanning (2007) proposed "systematic guess and check" (p. 123). Systematic guess and check highlighted the connections between previous guesses and next steps and required students to use the information gained from initial guesses to move toward a solution.…”

Section: Guess and Checkmentioning

confidence: 99%

“…Data included field notes, students' written and narrative solutions, and comments and questions, and interviews with students whose solutions were identified as unclear or interesting. Johanning (2007) noticed that when students engaged in systematic guess and check they focussed on the situational context of the problem, identified relationships between their guesses and their next steps, generalised from their guess to their next step, and applied relational reasoning to their guesses and checks. The guess itself became less significant and the thinking behind the guess was emphasised.…”

Section: Guess and Checkmentioning

confidence: 99%

“…They should be able to explain what makes their guess credible and generalise the mathematical concepts of their guess to new problems (Leinhardt & Schwarz, 1997). However, if the teacher or school culture does not sanction students' guesses they are less likely to occur, or if they do occur are less likely to be appropriated or valued (Guerrero, 2010;Johanning, 2007;Wong et al, 2002). Wong and colleagues (2002) asked 1216 students from Hong Kong in 3 rd , 6 th , 7 th , and 9 th grade (aged 9 to 15) to solve and explain three sets of non-routine computational, word, and open-ended mathematical problems.…”

Section: Teacher Influences On Student Judgementmentioning

confidence: 99%

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Teacher practice in primary mathematics classrooms: A story of positioning

Tait-McCutcheon¹

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<p>The past twenty-five years have seen a dramatic increase in the interest given to dialogue between teachers and students, and students and students during mathematics teaching and learning. This interest is evident within the growing body of research and the call for the increased quality and quantity of student discourse in curriculum and policy documents. Recent research in mathematics education is underpinned by the belief that students learn best when they have the opportunity to participate in their own and others’ mathematical talk, text, and actions in purposeful and meaningful ways. This study explores how teachers position themselves and students in their lowest and highest mathematics strategy groups and how that positioning influences the sharing of mathematical know-how. Mathematical know-how within this study comprises teacher and student independence, judgement, and creativity. Social-constructivist theories of teaching and learning underpin the focus of this study. The importance of teachers and students constructing and co-constructing individual and shared mathematical understandings through dialogically rich interactions with each other and the environment are considered. Positioning theory provides the theoretical lens through which mathematical know-how will be analysed and understood. The constructs of positioning theory important to this research were the teachers’ and students’ positions, enacted as their rights and duties, the storylines that develop through the positions, rights, and duties and the teachers’ and students’ social acts which come to have significance and be a social force within the teaching and learning. The decision to employ qualitative case study methodology arose naturally from the subjective social phenomenon of teaching and learning. The analysis of data generated through video and audio recordings, transcriptions, participant observations, and documents and archival records supported the development of the two cases: teacher affording positioning, and teacher constraining positioning. The particularised and investigative design of qualitative case study supported the development of an emerging taxonomy of teacher affording and constraining positioning. The taxonomy contributed to the growing body of knowledge regarding student participation by categorising new thinking in regards to the phenomenon of teachers and positioning in mathematics. Teachers in this study afforded the sharing of mathematical know-how from the position of appropriator, procurer, and provoker. The positions of controller, proprietor, and protector were found to constrain the sharing of mathematical know-how. Significant differences were revealed in how teachers positioned themselves and how their positioning influenced opportunities for student engagement. Higher levels of student talk, text, and actions were evident when teachers positioned themselves to ensure the mathematics was visible, fluid, and contestable. Collaboration between teachers and students, and students and students, was a strong feature of the emerging taxonomy.</p>

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A Study of Grade Two Students Solving a Non-Routine Problem with Access to Manipulatives

Leow,

Kaur

2024

Int J of Sci and Math Educ

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Is There Something to be Gained from Guessing? Middle School Students' Use of Systematic Guess and Check

Cited by 9 publications

References 10 publications

Effect of difference in word formulation and mathematical characteristics of story problems on mathematics preservice teachers and practising teachers

Effect of difference in word formulation and mathematical characteristics of story problems on mathematics preservice teachers and practising teachers

Teacher practice in primary mathematics classrooms: A story of positioning

A Study of Grade Two Students Solving a Non-Routine Problem with Access to Manipulatives

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