The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions related to mathematical depth in preschool, spiral review in the upper elementary grades, ideas for differentiation in middle school, and projects for high school algebra.
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Asked & Answered
Asked & Answered
The Asked & Answered department shares excerpts from discussion threads on the online MyNCTM community. In this issue, featured threads highlight responses to members' questions regarding 1st grade number sense, multiplication and division of fractions, issues of definition and precision related to circles, and the value of rationalizing denominators.
Attending to Evidence of Students' Thinking during Instruction
Sherin Gamoran Miriam and James Lynn
This article explores three processes involved in attending to evidence of students' thinking, one of the Mathematics Teaching Practices in Principles to Actions: Ensuring Mathematical Success for All. These processes, explored during an activity on proportional relationships, are discussed in this article, another installment in the series.
Avoiding the Ineffective Keyword Strategy
Karen S. Karp, Sarah B. Bush, and Barbara J. Dougherty
Try these meaningful alternative approaches to helping students make sense of word problems.
A Better Tomorrow through Math
Christie Henderson
Math is so much more than numbers.
Danger! Animals in the Mathematics Classroom
Stefanie D. Livers, Kristin E. Harbour, and Lindsey Fowler
In our attempts to make a concept easier, we may hinder student learning.
Decomposing Rectangles
Annie Perkins and Christy Pettis
Students are given a problem to break down rectangles.
Designing for Voice and Agency
Laurie Speranzo and Erik Tillema
Specific teacher moves and lesson planning can facilitate student empowerment in the middle school classroom.
Emphasizing the M in STEAM activities
Emily Dardis and Megan H. Wickstrom
Modifications to a first- and second-grade STEAM activity, Elephant Toothpaste, highlight ways to emphasize mathematical thinking by running multiple experiments, posing mathematical questions, and having students make both qualitative and quantitative observations. Contributors to the iSTEM department share ideas and activities that stimulate student interest in the integrated fields of science, technology, engineering, and mathematics (STEM) in K–grade 5 classrooms.
Ferris Wheel Graphs
Wayne Nirode
To introduce sinusoidal functions, I use an animation of a Ferris wheel rotating for 60 seconds, with one seat labeled You (see fig. 1). Students draw a graph of their height above ground as a function of time with appropriate units and scales on both axes. Next a volunteer shares his or her graph. I then ask someone to share a different graph. I choose one student with a curved graph (see fig. 2a) and another with a piece-wise linear (sawtooth) graph (see fig. 2b).
