Toward a theoretical structure to characterize early probabilistic thinking

Groth, Randall E.; Austin, Jathan; Naumann, Madeline; Rickards, Megan

doi:10.1007/s13394-019-00287-w

Cited by 16 publications

(30 citation statements)

References 33 publications

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“…The needs for student identification in solving the probabilistic problems have various categories [14]. In solving the probabilistic problems, initial probabilistic thinking is needed for drawing differences between thoughts [39]. Self-efficacy will affect the learning of mathematics [32].…”

Section: Discussionmentioning

confidence: 99%

Mathematical Communication Profile in Solving Probability Problems Reviewed by Self-efficacy of Prospective Mathematics Teachers

Shodiqin¹,

Sukestiyarno²,

Wardono³

et al. 2020

ujer

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Mathematical communication plays a very important role in learning mathematics, so it needs to be developed in mathematics learning. Mathematical communication is the process of conveying mathematical ideas to obtain a shared understanding between those who give and receive information. This study aims to describe the mathematical communication profile of prospective mathematics teachers based on self-efficacy in solving probabilistic problems. By solving probabilistic problems, it can improve probabilistic thinking, so that probabilistic problem solving can improve the ability to think at a higher level or Higher Order Thinking Skill, which is urgently needed today. This qualitative research is a study case. Subjects in this study were prospective mathematics teachers selected based on self-efficacy. The instruments used in this study were written tests and guided interviews based on probabilistic problems. Then the subjects were interviewed based on their work on the assignment. Data collection techniques are done through observation, interviewing, and documentation, while the data analysis technique used by researchers uses the Miles and Huberman model, namely by the process of (1) reduction data, (2) presentation data, and (3) drawing conclusions and verification. The results showed that prospective mathematics teachers who had different self-efficacy in solving probabilistic problems had different mathematical communication skills.

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Section: Discussionmentioning

confidence: 99%

Mathematical Communication Profile in Solving Probability Problems Reviewed by Self-efficacy of Prospective Mathematics Teachers

Shodiqin¹,

Sukestiyarno²,

Wardono³

et al. 2020

ujer

View full text Add to dashboard Cite

show abstract

“…The coding of responses to workbook questions focused on variation and the student generated TinkerPlots representations was carried out using the coding method shown in Table 1. The coding mirrored the three levels of the modes of the SOLO model (Biggs & Collis, 1982 extended for the IK mode as suggested by Groth et al (2021). There are U, M, or R level IK responses that are potentially normative inconsistent with the task or normative consistent with the task (Figure 2).…”

Section: Data Coding and Analysismentioning

confidence: 96%

“…Recent work by Groth et al (2021), describing young students' probabilistic thinking, extended the characterization of the IK mode by specifically suggesting two parallel U-M-R cycles in the mode and providing labels for the two potential types of thinking involved. One is termed normative incompatible, characterized by myths, superstitions, and subjective or deterministic beliefs.…”

Section: Theoretical Perspectivementioning

confidence: 99%

“…Because the aims reported here relate to the practice of statistics rather than the detailed description of development of a science concept, informal comments made about the physical experiences of the activity were considered to be contextual intuitions and images in the IK mode (Collis & Romberg, 1991). The normative compatibility or incompatibility of the IK responses (Groth et al, 2021) was considered during coding, but given the ages and experiences of the students, it was not expected there would be very many incompatible responses. The assumption in Table 1 and later tables is that reported IK responses are normative compatible.…”

Section: Data Coding and Analysismentioning

confidence: 99%

“…This research takes heed of Green's (1993) and Shaughnessy's (1997) pleas for the study of what students "are capable of doing" when experiencing variation. Exploring students' explanations of their experiences of variation in a context was accomplished by building on the recent developmental work of Groth et al (2021) in the Ikonic mode (IK) of functioning, as well as further exploring the Concrete Symbolic mode (CS) of functioning (Biggs & Collis, 1982 and the relationship of the two via Multimodal functioning (Collis & Romberg, 1991;Watson et al, 1995;Watson & Collis, 1994). The link between the normative compatible IK mode and the CS mode is seen to provide considerable support for many of the CS responses, as shown in the detailed analyses of the responses to workbook questions and the summary in Table 9.…”

Section: Characterizing the Understanding Of Variation Within A Stem ...mentioning

confidence: 99%

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Characterizing Student Experience of Variation Within a Stem Context: Improving Catapults

Watson

Fitzallen

Wright

et al. 2022

SERJ

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STEM learning experiences at the school level provide both opportunities and challenges for exploring students’ understanding of statistical concepts. This report focuses on data handling and informal inference embedded in a STEM context, that is, of testing, adjusting, and retesting catapults. In particular, the learning goal was for Grade 4 (aged 9–10 years) students to build on their developing understanding of variation while learning about the science topic of force as demonstrated by two configurations of catapults causing ping pong balls to be launched different distances. This report focuses on the students’ experiences of variation that were associated with the activity from a structural perspective during implementation. The analysis, employing various aspects of the Structure of Observed Learning Outcomes, points to the potential contribution of multimodal functioning in identifying and characterizing understanding of variation in a new context. The activity took place with 50 students in two classes with data collected from student workbooks. Results suggest that meaningful engagement with context can provide support for developing understanding of the concept of variation.

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A method for assessing students’ interpretations of contextualized data

Groth

Choi

2023

Educ Stud Math

Self Cite

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Learning to interpret data in context is an important educational outcome. To assess students’ attainment of this outcome, it is necessary to examine the interplay between their contextual and statistical reasoning. We describe a research method designed to do so. The method draws upon Toulmin’s ( 1958 , 2003 ) model of argumentation for the first stage of qualitative data analysis and the Structure of the Observed Learning Outcome (SOLO) (Biggs & Collis, 1991 ) model for the second stage. Toulmin analyses help identify the justifications and expressions of uncertainty students provide in their interpretive arguments. Subsequent analyses based on the multi-modal conceptualization of SOLO help characterize the quality of student arguments relative to one another. Existing literature and an empirical example are drawn upon to explain how the Toulmin and SOLO models can be used in tandem to analyze students’ interpretations of contextualized data. We also explain how pairing Toulmin and SOLO can address theoretical and practical limitations that arise when using just one of the two models on its own.

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Toward a theoretical structure to characterize early probabilistic thinking

Cited by 16 publications

References 33 publications

Mathematical Communication Profile in Solving Probability Problems Reviewed by Self-efficacy of Prospective Mathematics Teachers

Mathematical Communication Profile in Solving Probability Problems Reviewed by Self-efficacy of Prospective Mathematics Teachers

Characterizing Student Experience of Variation Within a Stem Context: Improving Catapults

A method for assessing students’ interpretations of contextualized data

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