Functions, Graphs, and Graphing: Tasks, Learning, and Teaching

@article{Leinhardt1990FunctionsGA,
  title={Functions, Graphs, and Graphing: Tasks, Learning, and Teaching},
  author={Gaea Leinhardt and Orit Zaslavsky and Mary Kay Stein},
  journal={Review of Educational Research},
  year={1990},
  volume={60},
  pages={1 - 64}
}
This review of the introductory instructional substance of functions and graphs analyzes research on the interpretation and construction tasks associated with functions and some of their representations: algebraic, tabular, and graphical. The review also analyzes the nature of learning in terms of intuitions and misconceptions, and the plausible approaches to teaching through sequences, explanations, and examples. The topic is significant because of (a) the increased recognition of the… 

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References

SHOWING 1-10 OF 197 REFERENCES

Subject-Matter Knowledge and Elementary Instruction: A Case from Functions and Graphing

The purpose of the present investigation was to describe the relationship between teachers’ knowledge of mathematics and their instructional practice. An experienced fifth grade teacher was

The Interpretation of Graphs Representing Situations.

The present article attempts to give an outline of the work as a whole and its main outcomes, including the incidence of graphical wmk in current British school courses, and the outcomes of previous general surveys of graphical understanding.

The impact of microcomputer‐based labs on children's ability to interpret graphs

Graphing represents a key symbol system for scientific communication. Widely-reported low graphing skills notwithstanding, middle school students can learn to communicate with graphs in the context

Points, Lines, and Their Representations.

Students come to mathematics lessons with some exisiting concepts about the topics being presented. These concepts have been constructed by the students from information encountered in everyday

Student difficulties in connecting graphs and physics: Examples from kinematics

Some common errors exhibited by students in interpreting graphs in physics are illustrated by examples from kinematics. These are taken from the results of a descriptive study extending over a period

Research Issues in the Learning and Teaching of Algebra

This chapter discusses research agendas for research on the learning and teaching of Algebra from a Cognitive Science Perspective and discusses the role of representation system theory in the learning of algebra.

Intuitions on Functions.

A theoretical model is presented for commencing a systematic assessment of students’ intuitions on the mathematical notion of functions. This model considers functions in terms of a three-dimensional

Green Globs: A Microcomputer Application for Graphing of Equations.

An activity that uses the bomputergs unique capabilities to provide students with a meaningful and highly motivating experience with the graphing of equations is outlined, including descriptions of techniqaes used by some of the more advanced students.

Knowing, Learning, and Instruction

Contents. L.B. Resnick, Introduction. W. Kintsch, Learning from Text. I.L. Beck, M.G. McKeown, Expository Text for Young Readers: The Issue of Coherence. G. Leinhardt, Development of an Expert
...