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## Investigation of Eighth-Grade Students’ Understanding of the Slope of the Linear Function

### Citations

4262 | Basics of qualitative research: Grounded theory procedures and techniques - Strauss, Corbin - 1990 |

587 | A Coefficient of Agreement for Nominal Scales Educ Psychol Meas - Cohen |

106 |
Functions, Graphs, and Graphing: Tasks, Learning and Teaching
- Leinhardt, Zaslavsky, et al.
- 1990
(Show Context)
Citation Context ...key. Research has noted that students had difficulties and misconceptions associated with the concept of slope. Some studies have focused on students’ understanding of slope within abstract contexts (=-=LEINHARDT et al., 1990-=-; ZASLAVSKY et al., 2002) and others on real-world contexts (NEMIROVSKY, 1997; STUMP, 2001). There are misconceptions associated with the calculation of slope, and when it is represented in decimal fo... |

66 |
Learning: the microgenetic analysis of one student’s evolving understanding of a complex subject matter domain
- Schoenfeld, Smith, et al.
- 1993
(Show Context)
Citation Context ...change (BELL; JANVIER, 1981; LEINHARDT et al., 1990; ORTON, 1984). The concept of slope can pose challenges for students when they must translate between different representations (MOSCHKOVICH, 1996; =-=SCHOENFELD et al., 1993-=-; SMITH; ARCAVI; SCHOENFELD, 1989). There is confusion between the role of m and b when a function is written in the form y = mx + b. It may be difficult for students to consider the slope as ratio if... |

48 | Children's understanding of mathematics - Hart, ed - 1981 |

42 | Supporting innovation: The impact of a teacher's conceptions of functions on his implementation of a reform curriculum - Lloyd, Wilson - 1998 |

22 | Standards for School Mathematics - Principles - 1992 |

19 |
Student understanding of the Cartesian Connection: An exploratory study
- Knuth
- 2000
(Show Context)
Citation Context ...ch has investigated students’ errors, conceptions, and misconceptions in linear functions and their graphs (ACUNA, 2007; BIRGIN, 2006; CHIU et al., 2001; DAVIS, 2007; HITT, 1998; GRAHAM; SHARP, 1999; =-=KNUTH, 2000-=-; LEINHARDT; ZASLAVSKY; STEIN, 1990; MEVARECH; KRAMARSKY, 1997; MOSCHKOVICH, 1996; 1999; NATHAN; KIM, 2007; STUMP, 1996; 2001; ZASLAVSKY; SELA; LERON, 2002). Many of these research studies have shown ... |

18 | Results from the second mathematics assessment - Carpenter, Corbitt, et al. - 1981 |

18 |
Difficulties in the articulation of different representations linked to the concept of function
- Hitt
- 1998
(Show Context)
Citation Context ...ntertwined. Thus, previous research has investigated students’ errors, conceptions, and misconceptions in linear functions and their graphs (ACUNA, 2007; BIRGIN, 2006; CHIU et al., 2001; DAVIS, 2007; =-=HITT, 1998-=-; GRAHAM; SHARP, 1999; KNUTH, 2000; LEINHARDT; ZASLAVSKY; STEIN, 1990; MEVARECH; KRAMARSKY, 1997; MOSCHKOVICH, 1996; 1999; NATHAN; KIM, 2007; STUMP, 1996; 2001; ZASLAVSKY; SELA; LERON, 2002). Many of ... |

18 | The effect of spreadsheet and dynamic geometry software on the achievement and self-efficacy of 7th-grade students - Isiksal, Askar - 2005 |

14 | An examination of the line graphing ability of students in grades seven through twelve - Padilla, McKenzie, et al. - 1986 |

13 |
Use of situations in mathematics education
- Janvier
- 1981
(Show Context)
Citation Context ...n. 42A, p. 139-162, abr. 2012 not necessarily correspond to that in another representation, but the ability to translate among varied formats is necessary to effectively interpret problem situations (=-=JANVIER, 1981-=-; MOSCHKOVICH, 1996). Today, the students are expected to learn functions and their graphs with single procedural knowledge, and they are supposed to have a conceptual level of understanding and to ca... |

11 |
Appropriating mathematical practices: A case study of learning to use and explore functions through interaction with a tutor
- Moschkovich
- 2004
(Show Context)
Citation Context .... In this context, many studies stated that computer technology could be used for translations between graphical and algebraic representations (BAKI, 2002; BIRGIN; KUTLUCA, 2006; LLOYD; WILSON, 1998; =-=MOSCHKOVICH, 2004-=-). Because many computer technologies, software programs, and graphical calculators open up the possibility of more visual constructions, and linking the graphical and algebraic representations of fun... |

11 |
Understanding rate of change
- Orton
- 1984
(Show Context)
Citation Context ...CHOENFELD; SMITH; ARCAVI, 1993), connecting graphs to linear equations (Acuna, 2007; Birgin, 2006), and connecting graphs to the notion of rate of change (BELL; JANVIER, 1981; LEINHARDT et al., 1990; =-=ORTON, 1984-=-). The concept of slope can pose challenges for students when they must translate between different representations (MOSCHKOVICH, 1996; SCHOENFELD et al., 1993; SMITH; ARCAVI; SCHOENFELD, 1989). There... |

10 |
Moving up and getting steeper: Negotiating shared descriptions of linear graphs
- Moschkovich
- 1996
(Show Context)
Citation Context ...162, abr. 2012 not necessarily correspond to that in another representation, but the ability to translate among varied formats is necessary to effectively interpret problem situations (JANVIER, 1981; =-=MOSCHKOVICH, 1996-=-). Today, the students are expected to learn functions and their graphs with single procedural knowledge, and they are supposed to have a conceptual level of understanding and to carry out broader tas... |

9 |
Learning to graph linear functions: A case study of conceptual change
- Chiu, Kessel, et al.
- 2001
(Show Context)
Citation Context ...e. Conceptual understanding of the domain of linear functions, including much more the procedural learning, involves understanding the connections between the graphical and algebraic representations (=-=CHIU et al., 2001-=-). A main characteristic that makes a linear function interesting for research in mathematics education is that several representations are intertwined. Thus, previous research has investigated studen... |

8 | The interpretation of graphs representing situations. For the learning of mathematics - Bell, Janvier - 1981 |

5 | Functions: Linearity unconstrained - MARKOVITZ, EYLON, et al. - 1983 |

5 | Students’ use of the x-intercept as an instance of a transitional conception - Moschkovich - 1999 |

5 | When teaching becomes learning. Cognition and Instruction - SHERIN - 1989 |

4 |
Graphs, gradients and intercepts
- Barr
- 1980
(Show Context)
Citation Context ...xts (NEMIROVSKY, 1997; STUMP, 2001). There are misconceptions associated with the calculation of slope, and when it is represented in decimal form, students have trouble considering slope as a ratio (=-=BARR, 1980-=-; STUMP, 1996; 2001). They also have difficulty interpreting linear functions and their graphs (BARR, 1980, MOSCHKOVICH, 1996; NATHAN; KIM, 2007; SCHOENFELD; SMITH; ARCAVI, 1993), connecting graphs to... |

4 | Pattern generalization with graphs and words: a crosssectional and longitudinal analysis of middle school students’ representational fluency - NATHAN, KIM - 2007 |

3 | On the development of a sense for functions. In - EISENBURG - 1992 |

3 | Fostering Connections Between the Verbal, Algebraic, and Geometric Representations of Basic Planar Curves for - Kondratieva, Radu - 2009 |

3 | Liberating school mathematics from procedural view - Noss, A - 1996 |

2 |
Use of slope and y-intercept in prediction and description, as seen from students’ perspective
- ACUNA
- 2007
(Show Context)
Citation Context ...mathematics education is that several representations are intertwined. Thus, previous research has investigated students’ errors, conceptions, and misconceptions in linear functions and their graphs (=-=ACUNA, 2007-=-; BIRGIN, 2006; CHIU et al., 2001; DAVIS, 2007; HITT, 1998; GRAHAM; SHARP, 1999; KNUTH, 2000; LEINHARDT; ZASLAVSKY; STEIN, 1990; MEVARECH; KRAMARSKY, 1997; MOSCHKOVICH, 1996; 1999; NATHAN; KIM, 2007; ... |

2 |
Bilgisayar destekli matematik . Ankara: Ceren
- BAKI
- 2002
(Show Context)
Citation Context ...tween graphical representations and algebraic parameters. In this context, many studies stated that computer technology could be used for translations between graphical and algebraic representations (=-=BAKI, 2002-=-; BIRGIN; KUTLUCA, 2006; LLOYD; WILSON, 1998; MOSCHKOVICH, 2004). Because many computer technologies, software programs, and graphical calculators open up the possibility of more visual constructions,... |

2 | Teaching functions through Excel - BAKI, ÖZTEKIN - 2003 |

2 | The effects of computer-assisted instruction on the students’ achievement in mathematics at seventh grade - BIRGIN, KUTLUCA, et al. |

2 | An investigation into able students’ understanding of motion graphs. Teaching Mathematics and its Applications - GRAHAM, SAHARP - 1999 |

2 |
The development of function concept in different levels of students
- GÜVEN
- 2004
(Show Context)
Citation Context ...ning parameter of a linear function. Although many research studies have investigated secondary students’ and mathematic teachers’ knowledge of functions (ZAZLAVSKY et al., 2002; STUMP, 1996; 2001; ; =-=GÜVEN, 2004-=-), a search of literature reveals no evidence regarding eighthgrade students’ knowledge of the concept of slope. The misconceptions and deficiencies of the students in linear functions also may lead t... |

2 |
Using the SOLO taxonomy to evaluate student learning of function concepts in developmental algebra
- RIDER
- 2004
(Show Context)
Citation Context .... 2012 156 BIRGIN, O. perceived slope mostly in geometric means and had a scarce understanding of algebraic, trigonometric, and functional representations. Therefore, some studies (NATHAN; KIM, 2007; =-=RIDER, 2004-=-) stated that students’ understandings may be raised to the conceptual learning level by making reference to different types of representations. When using different types of representations, no singl... |

2 | Students’ conceptualizations of mathematics functions: the effect of a pedagogical approach involving multiple representations.1991 - RIZZITU - 1991 |

2 |
Thesis (Doctoral in… area of doctoral
- STUMP
- 1996
(Show Context)
Citation Context ...he derivatives in calculus (DAVIS, 2007). They also represent linear combinations of quantities, situations of constant increase or decrease, lines as shortest distances, and approximations to curve (=-=STUMP, 1996-=-). An understanding of linear functions in one representation will 141 Bolema, Rio Claro (SP), v. 26, n. 42A, p. 139-162, abr. 2012 not necessarily correspond to that in another representation, but th... |

2 | Being sloppy about slope: the effect of changing the scale - unknown authors |