### Abstract

What is the slope of a (linear) function? Due to the ubiquitous use of mathematical software, this seemingly simple question is shown to lead to some subtle issues that are not usually addressed in the school curriculum. In particular, we present evidence that there exists much confusion regarding the connection between the algebraic and geometric aspects of slope, scale and angle. The confusion arises when some common but undeclared default assumptions, concerning the isomorphism between the algebraic and geometric systems, are undermined. The participants in the study were 11^{th}-grade students, prospective and in-service secondary mathematics teachers, mathematics educators and mathematicians-a total of 124 people. All participants responded to a simple but nonstandard task, concerning the behavior of slope under a non-homogeneous change of scale. Analysis of the responses reveals two main approaches, which we have termed 'analytic' and 'visual', as well as some combinations of the two.

Original language | English (US) |
---|---|

Pages (from-to) | 119-140 |

Number of pages | 22 |

Journal | Educational Studies in Mathematics |

Volume | 49 |

Issue number | 1 |

State | Published - 2002 |

### Fingerprint

### Keywords

- Cartesian coordinate system
- Cognitive conflict
- Computers
- Function
- Graph
- Graphic software
- Representation
- Scale
- Slope

### ASJC Scopus subject areas

- Mathematics(all)
- Social Sciences(all)

### Cite this

*Educational Studies in Mathematics*,

*49*(1), 119-140.

**Being sloppy about slope : The effect of changing the scale.** / Zaslavsky, Orit; Sela, Hagit; Leron, Uri.

Research output: Contribution to journal › Article

*Educational Studies in Mathematics*, vol. 49, no. 1, pp. 119-140.

}

TY - JOUR

T1 - Being sloppy about slope

T2 - The effect of changing the scale

AU - Zaslavsky, Orit

AU - Sela, Hagit

AU - Leron, Uri

PY - 2002

Y1 - 2002

N2 - What is the slope of a (linear) function? Due to the ubiquitous use of mathematical software, this seemingly simple question is shown to lead to some subtle issues that are not usually addressed in the school curriculum. In particular, we present evidence that there exists much confusion regarding the connection between the algebraic and geometric aspects of slope, scale and angle. The confusion arises when some common but undeclared default assumptions, concerning the isomorphism between the algebraic and geometric systems, are undermined. The participants in the study were 11th-grade students, prospective and in-service secondary mathematics teachers, mathematics educators and mathematicians-a total of 124 people. All participants responded to a simple but nonstandard task, concerning the behavior of slope under a non-homogeneous change of scale. Analysis of the responses reveals two main approaches, which we have termed 'analytic' and 'visual', as well as some combinations of the two.

AB - What is the slope of a (linear) function? Due to the ubiquitous use of mathematical software, this seemingly simple question is shown to lead to some subtle issues that are not usually addressed in the school curriculum. In particular, we present evidence that there exists much confusion regarding the connection between the algebraic and geometric aspects of slope, scale and angle. The confusion arises when some common but undeclared default assumptions, concerning the isomorphism between the algebraic and geometric systems, are undermined. The participants in the study were 11th-grade students, prospective and in-service secondary mathematics teachers, mathematics educators and mathematicians-a total of 124 people. All participants responded to a simple but nonstandard task, concerning the behavior of slope under a non-homogeneous change of scale. Analysis of the responses reveals two main approaches, which we have termed 'analytic' and 'visual', as well as some combinations of the two.

KW - Cartesian coordinate system

KW - Cognitive conflict

KW - Computers

KW - Function

KW - Graph

KW - Graphic software

KW - Representation

KW - Scale

KW - Slope

UR - http://www.scopus.com/inward/record.url?scp=10044266880&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=10044266880&partnerID=8YFLogxK

M3 - Article

VL - 49

SP - 119

EP - 140

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

SN - 0013-1954

IS - 1

ER -