
06520653
j
2016a.00257
Danielson, Christopher
They'll need it for calculus.
Math. Teach. Middle Sch. 20, No. 5, 260265 (2014).
2014
National Council of Teachers of Mathematics (NCTM), Reston, VA
EN
D23
I23
goals of mathematics education
learning objectives
lower secondary
curriculum
content selection
linear equations
polar coordinates
spirals
elementary algebra
calculus
previous knowledge
functions
slope
rate of change
graph of a function
nonlinear relationships
quadratic relationship
exponential relationship
finite differences
student activities
http://www.nctm.org/Publications/mathematicsteachinginmiddleschool/2014/Vol20/Issue5/They_llNeedItforCalculus/
From the text: Imagine a selfpropelled lawn mower that is tied to a stake by a rope. As the lawn mower runs, the rope wraps around the stake, pulling the mower closer with each revolution. My Calculus 2 students viewed a video of this scenario one recent semester. The lawn mower is already under way as the video begins, and the viewer sees only a few revolutions before the video ends. We worked to answer this question: How long will it take to complete the mowing? As my students undertook the challenge of answering this question, I came to understand that they were struggling to write an equation to describe the lawn mower's path. This surprised me, and it forced me to reflect on what it means to be ready for calculus. This article focuses on the big question of what it means to be ready for calculus; it also explores the role of the middle school curriculum in preparing students to study calculus later. This should not be construed as an endorsement of the pipeline to calculus or as an assignment of responsibility for these ideas to the middle school curriculum and to teachers exclusively. Instead, this article is written for an audience of middle school teachers from the perspective of a former middle school teacher and current college teacher.