Making sense by measuring arcs: a teaching experiment in angle measure

Moore, Kevin C.

doi:10.1007/s10649-012-9450-6

Cited by 50 publications

(66 citation statements)

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“…Research has documented the role of units coordination in fractions concepts (see Hackenberg & Tillema, 2009;Izsák, Jacobson, de Araujo, & Orrill, 2012) as well as algebraic reasoning (e.g., Hackenberg, 2013 Thompson, 1994), with the process of quantification referring to how one assigns-or imagines assigning-numerical values to such measurable attributes (Thompson, 2011). As Thompson and others indicate (e.g., Moore, 2013;Moore & Carlson, 2012;Thompson & Carlson, 2017), values are a particular category of number that reference the result of an executed or imagined measurement process. In fact, when students do not attend to numbers as values in real world problems, their problem solving may become an "ungrounded debate" (Smith & Thompson, 2008, p. 110) about choosing numbers rather than reasoning about the relationships among quantities (Sowder, 1988).…”

Section: Skip Counting and Units Coordination -Students' Competence Wmentioning

confidence: 99%

“…Consider a study focusing on precalculus students' angle measure understandings. Moore (2013) argued that instruction that treats angle measure as a set of procedures for calculating or reading a protractor "fails to address the quantitative structure behind the process of determining an angle's measure" (p. 227, emphasis in original). Thus, the rich web of mathematical connections that led to the use of these calculations may be absent.…”

Section: Skip Counting and Units Coordination -Students' Competence Wmentioning

confidence: 99%

“…Instead, the answer is merely a number on the protractor found through a procedure. Considering Moore's (2013) findings in relation to time on an analog clock, individuals may construct or interpret the clock based on procedures of clock reading rather than as a measure of or as a relationship between quantities. Rather than an individual treating numerals on a clock as reflecting values, one may treat them as numbers absent of any attribute of the real world.…”

Section: Time As a Measure 194mentioning

confidence: 99%

“…Time may be a part of routinized activity across a day, but the clock that indicates the time is a complex measuring tool featuring multiple related units. Prior calls have challenged an instructional focus on procedural uses of measurement tools (like rulers or protractors) without highlighting the quantitative referents underlying their procedural uses (Kamii & Clark, 1997;Moore, 2013;Stephan & Clements, 2003). Nonetheless, despite everyday applications of time, research on how students come to understand standard tools for and concepts related to time as a measure remains minimal.…”

mentioning

confidence: 99%

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Time as a measure: Elementary students positioning the hands of an analog clock

2018

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Elementary students have difficulty with the topic of time. The present study investigated students' actions to position hour and minute hands on an analog clock to indicate particular times of the day. Using one-on-one interviews with students in Grades 2 and 4 (n = 48), we analyzed whether students were more accurate for one hand indicator (hour or minute) versus the other as well as their solution approaches as they positioned each hand. We first present a quantitative analysis of student performance to document whether hour and minute hands posed differential challenges for students as they positioned hands to indicate particular times. Results indicate the hour hand is significantly more challenging to position accurately than the minute hand. Students' solutions reflected varied approaches, including consideration of the quantitative hour-minute multiplicative relationship, attention to part-whole relations, and matching numbers from the provided time to numerals on the clock. We discuss implications for theory and instruction, including the relationship of time to length measure learning trajectories and the current treatment of time in K-12 mathematics standards for the United States.

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Section: Skip Counting and Units Coordination -Students' Competence Wmentioning

confidence: 99%

Section: Skip Counting and Units Coordination -Students' Competence Wmentioning

confidence: 99%

Section: Time As a Measure 194mentioning

confidence: 99%

mentioning

confidence: 99%

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Time as a measure: Elementary students positioning the hands of an analog clock

2018

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“…Connected with these issues, it was found in the study of Çetin and Dane (2004) that university level students defined the geometric concepts which are connected to each other such as angle, angle in circles and angle measurement as if they are independent topics from each other. Then, letting students know these concepts by developing a conceptual understanding of trigonometric functions appropriately to the content constructs seems the best way in teaching them (Moore, 2013). In addition, strong relationships between these concepts should be considered in the conceptual development process (Moore, 2013;Thompson, 2008).…”

Section: Introductionmentioning

confidence: 99%

Students perceptions and development of conceptual understanding regarding trigonometry and trigonometric function

Çetin¹

2015

Educ. Res. Rev.

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This study aims to analyse university level mathematics education students' perceptions on conceptual understanding of trigonometry and trigonometric functions and their content development of these concepts. A case study was conducted with 90 freshman students of Elementary Mathematics Department. The data were gathered via a scale; they included ten questions related to perceptions of concept knowledge and a knowledge test with five open ended questions related to the mathematical content that students use. Descriptive and content analyses were applied within the frame of the research goal. Findings showed that though students had a high level of perception about the fundamental concepts of trigonometry and trigonometric functions, specifically angle-angle measurement and arc-arc measurement, they were not successful in understanding their conceptual development. But, they were aware of this issue. In addition, though the students had the visual images of these concepts, their mathematical content usage in the development of conceptual understanding of these concepts were far from the original issues of content development of these concepts. Based on the findings, some suggestions were given about angle, arc and their measurements to lessen the problems hindering the teaching of trigonometry and trigonometric functions in Mathematics education.

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