Assessing Students' Understanding of Functions in a Graphing Calculator Environment

Beckmann, Charlene; Thompson, Denisse R.; Senk, Sharon L.

doi:10.1111/j.1949-8594.1999.tb17508.x

Cited by 7 publications

(5 citation statements)

References 3 publications

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“…Much more insight into student understanding needs to be collected by teachers; seeking written explanations from students has been suggested. Studies have recommended that having students justify their answers in writing can improve student understanding of transfers between representations (Anderson, Bloom, Mueller, & Pedler, 1997; Beckmann, Senk, & Thompson, 1999). This recommendation seems even more compelling, given that less than half the algebra teachers in this study reported even giving one problem requiring a written explanation to their students.…”

Section: Resultsmentioning

confidence: 99%

“…There is much debate about the central role functions play in the study of mathematics (Beckmann, Senk, & Thompson, 1999; Fererrini‐Mundy & Lauten, 1993; Schwartz, 1992), and there is increasing recognition that being able to move or transfer between their representations plays a key role in student understanding of them (Knuth, 2000; Porzio, 1999; Wilson & Krapfl, 1994). Representing functions in multiple ways is critical to student understanding of functions and success in mathematics.…”

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confidence: 99%

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Algebra Teachers' Utilization of Problems Requiring Transfer Between Algebraic, Numeric, and Graphic Representations

Cunningham

2005

School Sci & Mathematics

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For students to develop an understanding of functions, they must have opportunities to solve problems that require them to transfer between algebraic, numeric, and graphic representations (transfer problems). Research has confirmed student difficulties with certain types of transfer problems and has suggested instructional factors as a possible cause. Algebra teachers (n= 28) were surveyed to determine the amount of class time they devote to different types of transfer problems and how many times these problems appear on their teacher‐made assessments. Results suggest that teachers dedicate less class time to graphic to numeric transfer problems than to any other type of transfer problem and that these problems appear less frequently on assessments. These are exactly the types of transfer problems that pose the most difficulty for students. It is conjectured that teachers' familiarity with these problems, combined with assumed student mastery, contribute to this mismatch.

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Section: Resultsmentioning

confidence: 99%

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confidence: 99%

Algebra Teachers' Utilization of Problems Requiring Transfer Between Algebraic, Numeric, and Graphic Representations

Cunningham

2005

School Sci & Mathematics

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“…Function is an essential concept in mathematics and it affects the whole mathematics curriculum (Laughbaum, 2003;Knuth, 2000;Beckmann, Thompson & Senk, 1999;Cooney, 1999;Dossey, 1999;Hitt, 1998;Dreyfus & Eisenberg, 1982). NCTM (1989) standards also stress "one of the central themes of mathematics is the study of patterns and functions."…”

Section: Understanding Of Function Conceptmentioning

confidence: 99%

Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts

Dede

Soybaş

2011

EURASIA J MATH SCI T

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The purpose of this study is to determine the experience of mathematics preservice teachers related to function and equation concepts and the relations between them. Determining preservice mathematics teachers' understanding of function and equation concepts has great importance since it directly affects their future teaching careers. Data were collected by a questionnaire and semi-structured interviews and analyzed using existential-phenomenology. The results show that the experiences of preservice math teachers related to these concepts can be summarized under six different titles, namely, confusion of the definition of function with one-to-one and onto properties, relating it with daily life (exampling), failure to take the functioning conditions into account, the relation between the values which make the function zero and roots of the equation, multiple representations of functions and taking the defining set of functions and equations into account .

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“…Students can then integrate symbolic, numeric, tabular, graphical, and visual modes to create their mathematical knowledge. The use of such digital tools can thus provide teachers with different options to be adapted or adopted to tailor the teaching to the needs of individual students (Beckmann et al, 1999;Birgin & Acar, 2022;Murphy, 2016;Nicaise & Barnes, 1996;Waits & Demana, 1999).…”

Section: Contribution To the Literaturementioning

confidence: 99%

Effect of using Desmos on high school students’ understanding and learning of functions

Chechan

Ampadu

Pears

2023

EURASIA J Math Sci Tech Ed

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This study examines the effect of using Desmos on students’ performance in learning functions. An embedded mixed methods design was applied and involved 98 students from an upper secondary school in Sweden. Students’ assessments (pre- and post-test) and opinion polls were the two main data collection instruments. The results show that both groups (experimental and control) experienced a significant improvement in their post-test scores. However, the experimental group had a statistically significant improvement in comparison with that of the control group across the five constructs used in this study. The qualitative data revealed that the majority of the students ascribed a positive effect of the use of Desmos on their general understanding of function concepts, their ability to analyze functions and check their answers through visualization, which are difficult when working using paper and pencil.

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Assessing Students' Understanding of Functions in a Graphing Calculator Environment

Cited by 7 publications

References 3 publications

Algebra Teachers' Utilization of Problems Requiring Transfer Between Algebraic, Numeric, and Graphic Representations

Algebra Teachers' Utilization of Problems Requiring Transfer Between Algebraic, Numeric, and Graphic Representations

Preservice Mathematics Teachers’ Experiences about Function and Equation Concepts

Effect of using Desmos on high school students’ understanding and learning of functions

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