Teacher to Teacher: Playing around with Mono-pi-ly

2006 ◽  
Vol 11 (6) ◽  
pp. 294-297
Author(s):  
Cindy Kroon
Keyword(s):  
South Dakota ◽  
Three Dimensional ◽  
Department Of Education ◽  
School Mathematics ◽  
Mathematics Students ◽  
Measurement Standard ◽  
Three Dimensional Objects ◽  
Principles And Standards

According to the geometry standard in Principles and Standards for School Mathematics, “In grades 6–8, all students should precisely describe, classify, and understand relationships among types of two- and three- dimensional objects” (NCTM 2000, p. 232). The Measurement Standard goes on to state, “In grades 6–8, all students should develop and use formulas to determine the circumference of circles” (NCTM 2000, p. 240). In addition, South Dakota's Measurement Standard for Grade 7 delineates what mathematics students should know, such as “Given the formulas, find the circumference, perimeter, and area of circles” (South Dakota Department of Education 2004).

Writing Samples to Understand Mathematical Thinking

2002 ◽  
Vol 7 (9) ◽  
pp. 517-520
Author(s):  
Dianne S. Goldsby ◽  
Barbara Cozza
Keyword(s):  
Mathematical Thinking ◽  
School Mathematics ◽  
Mathematics Students ◽  
Principles And Standards

NCTM's Principles and Standards for School Mathematics emphasizes the need for all students to organize and consolidate their mathematical thinking through communication and to communicate their mathematical thinking coherently to others (NCTM 2000). Writing helps students focus on their own understandings of mathematics: “Students gain insights into their thinking when they present their methods for solving problems, when they justify their reasoning to a classmate or teacher, or when they formulate a question about something that is puzzling them” (NCTM 2000, pp. 60–61).

Geometric Conjectures: The Importance of Counterexamples

2003 ◽  
Vol 9 (4) ◽  
pp. 210-215
Author(s):  
Jeffery J. Boats ◽  
Nancy K. Dwyer ◽  
Sharon Laing ◽  
Mark P. Fratella
Keyword(s):  
Middle School ◽  
Pattern Recognition ◽  
Middle School Mathematics ◽  
School Mathematics ◽  
Mathematics Students ◽  
Reasoning Skills ◽  
Principles And Standards

TO DEVELOP STUDENTS' REASONING SKILLS, the NCTM's Principles and Standards for School Mathematics (2000) recommends that students make generalizations and evaluate conjectures. In particular, middle school mathematics students should be engaged in activities involving pattern recognition as a means of formulating such conjectures.

Quick Reads: Another Good Idea: A Yin and Yang Approach to Area and Irregular Shapes

2007 ◽  
Vol 13 (5) ◽  
pp. 296-297
Author(s):  
David Yopp ◽  
Zhou Jinyan
Keyword(s):  
United States ◽  
The United States ◽  
School Mathematics ◽  
Irregular Shape ◽  
Measurement Standard ◽  
Irregular Shapes ◽  
Complex Shapes ◽  
Yin And Yang ◽  
Principles And Standards ◽  
Different Cultures

The Measurement Standard for grades 6–8 in NCTM's Principles and Standards for School Mathematics (2000) emphasizes that students should develop formulas to find the areas of triangles, parallelograms, and trapezoids and develop strategies to find the areas of more complex shapes. “Developing formulas” often involves doubling or cutting and translating pieces of basic shapes, such as triangles, parallelograms, and trapezoids. Strategies for working with more complex shapes often include partitioning them into triangles, rectangles, or parallelograms. The yin and yang activity offers an irregular shape to investigate and extends and reinforces these strategies. Behind the name and the objects in the activity is the yin and yang story, which gives students the opportunity to reflect on different cultures and may help them remember the doubling strategy for finding area. This activity has been successfully implemented with students in China by Zhou Jinyan and with students in the United States by David Yopp.

Teaching Beginning Courses: Flower Power: Creating an Engaging Modeling Problem to Motivate Mathematics Students at an Alternative School

2003 ◽  
Vol 96 (6) ◽  
pp. 430-433
Author(s):  
Karen Koellner-Clark ◽  
Janice Newton
Keyword(s):  
Problem Solving ◽  
Alternative School ◽  
Mathematics Learning ◽  
School Mathematics ◽  
Mathematics Students ◽  
Modeling Problem ◽  
Principles And Standards

Using rich problem activities that require modeling can be engaging for students who struggle to understand the content in entrylevel courses. Further, they provide students with a forum in which communication and problem solving are expected. According to Principles and Standards for School Mathematics, “Interacting with others offers opportunities for exchanging and reflecting on ideas; hence, communication is a fundamental element of mathematics learning” (NCTM 2000, p. 348).

Measurement: What's the Big Idea?

2004 ◽  
Vol 9 (8) ◽  
pp. 430-431
Author(s):  
Sherri Martinie
Keyword(s):  
Three Dimensional ◽  
Learning Opportunities ◽  
School Mathematics ◽  
Actual Performance ◽  
Principles And Standards ◽  
K 12

The value of building a strong understanding of measurement must not be underestimated. The skills of measurement are frequently encountered in realworld situations, from measuring the size of a room to measuring the time it takes to run a mile in gym class to the amount of water used when a faucet drips. Instruction involving measurement should focus on teaching students, K–12, to 'understand measurable attributes of objects … and apply appropriate techniques, tools, and formulas to determine measurements' (NCTM's Principles and Standards for School Mathematics, p. 44). These measurements may be one, two, or three dimensional and involve length, weight, capacity, time, or temperature. However, research on measurement reports that this concept harbors the largest discrepancy between learning opportunities and actual performance, meaning that although students are instructed in measurement skills in school, they cannot show that they have learned the concept.

Prisms and Pyramids: Constructing Three-Dimensional Models to Build Understanding

2003 ◽  
Vol 9 (8) ◽  
pp. 436-442
Author(s):  
Beverly A. Koester
Keyword(s):  
Three Dimensional ◽  
School Mathematics ◽  
Plane Geometry ◽  
Elementary Grades ◽  
Two Dimensional ◽  
Rich Variety ◽  
Dimensional Models ◽  
Principles And Standards ◽  
Three Dimensional Models

The Geometry Standard of NCTM's Principles and Standards for School Mathematics (2000) describes the study of both two- and three-dimensional shapes. In the elementary grades, plane geometry often receives more emphasis than does three-dimensional geometry. In many classrooms, students actively explore two-dimensional shapes using a rich variety of materials, including tangrams, geoboards, and pattern blocks. Materials and lessons for exploring three-dimensional shapes are not as prevalent.

scholarly journals Fast Overlap Detection between Hard-Core Colloidal Cuboids and Spheres. The OCSI Algorithm

Algorithms ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 72
Author(s):  
Luca Tonti ◽  
Alessandro Patti
Keyword(s):  
Colloidal Particles ◽  
Dynamic Properties ◽  
Wide Spectrum ◽  
Three Dimensional ◽  
Hard Core ◽  
Detection Algorithm ◽  
Three Dimensional Objects ◽  
Aggregation Behaviour ◽  
Sphere Radius ◽  
User Friendly

Collision between rigid three-dimensional objects is a very common modelling problem in a wide spectrum of scientific disciplines, including Computer Science and Physics. It spans from realistic animation of polyhedral shapes for computer vision to the description of thermodynamic and dynamic properties in simple and complex fluids. For instance, colloidal particles of especially exotic shapes are commonly modelled as hard-core objects, whose collision test is key to correctly determine their phase and aggregation behaviour. In this work, we propose the Oriented Cuboid Sphere Intersection (OCSI) algorithm to detect collisions between prolate or oblate cuboids and spheres. We investigate OCSI’s performance by bench-marking it against a number of algorithms commonly employed in computer graphics and colloidal science: Quick Rejection First (QRI), Quick Rejection Intertwined (QRF) and a vectorized version of the OBB-sphere collision detection algorithm that explicitly uses SIMD Streaming Extension (SSE) intrinsics, here referred to as SSE-intr. We observed that QRI and QRF significantly depend on the specific cuboid anisotropy and sphere radius, while SSE-intr and OCSI maintain their speed independently of the objects’ geometry. While OCSI and SSE-intr, both based on SIMD parallelization, show excellent and very similar performance, the former provides a more accessible coding and user-friendly implementation as it exploits OpenMP directives for automatic vectorization.

scholarly journals The Effect of Material Properties on the Perceived Shape of Three-Dimensional Objects

i-Perception ◽  
2020 ◽  
Vol 11 (6) ◽  
pp. 204166952098231
Author(s):  
Masakazu Ohara ◽  
Juno Kim ◽  
Kowa Koida
Keyword(s):  
Material Properties ◽  
Regional Variation ◽  
Three Dimensional ◽  
Mean Square ◽  
Viewing Condition ◽  
Three Dimensional Objects ◽  
Transparent Objects ◽  
Dimensional Shape ◽  
Local Root ◽  
Three Dimensional Shape

Perceiving the shape of three-dimensional objects is essential for interacting with them in daily life. If objects are constructed from different materials, can the human visual system accurately estimate their three-dimensional shape? We varied the thickness, motion, opacity, and specularity of globally convex objects rendered in a photorealistic environment. These objects were presented under either dynamic or static viewing condition. Observers rated the overall convexity of these objects along the depth axis. Our results show that observers perceived solid transparent objects as flatter than the same objects rendered with opaque reflectance properties. Regional variation in local root-mean-square image contrast was shown to provide information that is predictive of perceived surface convexity.

Effects of prolonged weightlessness on mental rotation of three-dimensional objects

1993 ◽  
Vol 94 (1) ◽  
Author(s):  
Y. Matsakis ◽  
M. Lipshits ◽  
V. Gurfinkel ◽  
A. Berthoz
Keyword(s):  
Mental Rotation ◽  
Three Dimensional ◽  
Three Dimensional Objects
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