Using internet-based problem-solving activities to enhance students' understanding of 3-dimensional spatial relationships

Planet ◽  
2011 ◽  
Vol 24 (1) ◽  
pp. 68-75
Author(s):  
Maggie Williams ◽  
Peter Williams ◽  
Alan Boyle
Keyword(s):  
Problem Solving ◽  
Spatial Relationships ◽  
3 Dimensional

Ideas

1988 ◽  
Vol 35 (8) ◽  
pp. 27-36
Author(s):  
Alan Barson ◽  
Lois Barson
Keyword(s):  
Problem Solving ◽  
Spatial Relationships ◽  
Area Measure ◽  
Problem Solving Skills ◽  
Whole Number

Ideas for this month is a set of activities based in geometry. Through geometry students can practice area measure, work with whole-number and fractional computation, and develop problem-solving skills in spatial relationships. The activities that follow will offer such experiences.

Cognitive Perspectives on Map Displays for Helicopter Flight

1989 ◽  
Vol 33 (2) ◽  
pp. 13-17 ◽  
Author(s):  
Kelly Harwood
Keyword(s):  
Problem Solving ◽  
Spatial Cognition ◽  
Large Scale ◽  
Human Performance ◽  
The Other ◽  
Spatial Relationships ◽  
Low Level ◽  
Helicopter Flight ◽  
The Earth ◽  
Cognitive Perspectives

Currently accessible technologies are providing entirely new display concepts for enhancing helicopter navigation. Yet the effectiveness of such displays depends on the extent to which they are configured according to principles from research on human performance. Computer generated map displays in the present study were configured according to previous research on maps, navigational problem solving, and spatial cognition in large scale environments. Interest centered on the representation of different spatial relationships that would best support helicopter navigational problem solving. One map display emphasized the global relationships between objects in the environment. The other map showed the pilot's relationship to objects as he travelled through the environment Twenty skilled pilots used the maps to complete several navigational tasks that occurred within a realistic simulation program tailored for helicopter navigation. Findings indicate that the type of task and mode of flight (low level or Nap of the Earth (NOE)) are important determinants of map display effectiveness.

scholarly journals Development of Learning Tools using Maples for Engineering Mathematics Subject

2018 ◽  
Vol 9 (1) ◽  
pp. 131
Author(s):  
Norlenda Mohd Noor ◽  
Hanifah Sulaiman ◽  
Zuraida Alwadood ◽  
Suhaila Abd Halim ◽  
Nurul Filzah Syamimi Wahid ◽  
...  
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Engineering Students ◽  
Dimensional Space ◽  
Mathematical Problem ◽  
Learning Tools ◽  
Problem Solving Skills ◽  
3 Dimensional ◽  
Engineering Mathematics ◽  
The Subject

<p>Mathematics is one of the basic and core subject for engineering students. Learning mathematics helps in developing problem solving skills as the subject requires critical thinking. However, many students perceive mathematics as a difficult subject and eventually get poor result for the subject. In the institution under study, there were increases in failure rate for the subject for the past few semesters. Based on a preliminary study, it was found that 55 percent of engineering student claimed that they encountered difficulties in visualizing functions in 3-dimensional space, which is the main content for engineering calculus subject. This fact is very unsatisfactory as engineering students are expected to possess strong mathematical problem solving skills. In light of this, the objective of this research is to develop an interactive teaching and learning tools, so as to assist students in visualizing 3-dimensional space functions. The tool is intended to be used in teaching and learning process in classrooms and it is expected that the students’ understanding in the subject could be improved.</p>

Geometry all around us—K–12

1969 ◽  
Vol 16 (6) ◽  
pp. 437-445
Author(s):  
John C. Egsgard
Keyword(s):  
Dimensional Space ◽  
Spatial Relationships ◽  
3 Dimensional ◽  
Space Rocket ◽  
The World ◽  
Mathematics Educators ◽  
Polaroid Camera ◽  
Different Shapes ◽  
The Many ◽  
K 12

There is growing evidence among mathematics educators that geometry should be experienced in each year of schooling from kindergarten through grade 12. Geometry is the study of spatial relationships of all kinds, relationships that can be found in the 3-dimensional space we live in and on any 2-dimensional surface in this 3-dimensional space. These relationships can be discovered all around us. Observe the many different shapes in your environment. This is geometry. Listen to the description of the path of the latest space rocket. This is geometry. Compare the photograph taken with a polaroid camera to the object that it pictures. This is geometry. Notice the symmetry to be found in a spherical or cubical shape and the lack of symmetry in some modern works of sculpture. This is geometry. AU of these involve spatial relationships. Children are aware of spatial relationships from their earliest days. Introducing them to the idea of geometry as being concerned with shape and size in the material world will help them to realize and appreciate that mathematics is something that plays an important role in the world in which we live.

Making Cute Count

2007 ◽  
Vol 14 (3) ◽  
pp. 153-159
Author(s):  
Denise Dark
Keyword(s):  
Problem Solving ◽  
Cooperative Learning ◽  
Small Group ◽  
Group Work ◽  
Number Sense ◽  
Spatial Relationships ◽  
Small Group Work ◽  
Mathematical Ideas ◽  
Kindergarten Classroom

A holiday quilt project in a kindergarten classroom becomes a focus for exploring patterns, shapes, measurement, spatial relationships, and number sense. Cooperative learning, small group work, problem solving, and communication of mathematical ideas enhance the completion of the project.

Three-Dimensional Reconstruction Using Stereo Pairs from Serial Thick Sections

1977 ◽  
Vol 35 ◽  
pp. 562-563
Author(s):  
Robert Glaeser ◽  
Thomas Bauer ◽  
David Grano
Keyword(s):  
Three Dimensional ◽  
Dimensional Structure ◽  
Serial Sections ◽  
Thin Sections ◽  
3 Dimensional ◽  
Transmission Electron ◽  
Freeze Dried ◽  
Dimensional Reconstruction ◽  
Stereo Imagery ◽  
Whole Mounts

In transmission electron microscopy, the 3-dimensional structure of an object is usually obtained in one of two ways. For objects which can be included in one specimen, as for example with elements included in freeze- dried whole mounts and examined with a high voltage microscope, stereo pairs can be obtained which exhibit the 3-D structure of the element. For objects which can not be included in one specimen, the 3-D shape is obtained by reconstruction from serial sections. However, without stereo imagery, only detail which remains constant within the thickness of the section can be used in the reconstruction; consequently, the choice is between a low resolution reconstruction using a few thick sections and a better resolution reconstruction using many thin sections, generally a tedious chore. This paper describes an approach to 3-D reconstruction which uses stereo images of serial thick sections to reconstruct an object including detail which changes within the depth of an individual thick section.

Structural preservation and absolute contrast of catalase crystal sections prepared with tannic acid

1983 ◽  
Vol 41 ◽  
pp. 448-449
Author(s):  
C.W. Akey ◽  
M. Szalay ◽  
S.J. Edelstein
Keyword(s):  
Tannic Acid ◽  
Beef Heart ◽  
X Rays ◽  
Screw Axis ◽  
General Applicability ◽  
Thin Sections ◽  
Beef Liver ◽  
3 Dimensional ◽  
Dimensional Reconstruction ◽  
Structural Preservation

Three methods of obtaining 20 Å resolution in sectioned protein crystals have recently been described. They include tannic acid fixation, low temperature embedding and grid sectioning. To be useful for 3-dimensional reconstruction thin sections must possess suitable resolution, structural fidelity and a known contrast. Tannic acid fixation appears to satisfy the above criteria based on studies of crystals of Pseudomonas cytochrome oxidase, orthorhombic beef liver catalase and beef heart F1-ATPase. In order to develop methods with general applicability, we have concentrated our efforts on a trigonal modification of catalase which routinely demonstrated a resolution of 40 Å. The catalase system is particularly useful since a comparison with the structure recently solved with x-rays will permit evaluation of the accuracy of 3-D reconstructions of sectioned crystals.Initially, we re-evaluated the packing of trigonal catalase crystals studied by Longley. Images of the (001) plane are of particular interest since they give a projection down the 31-screw axis in space group P3121. Images obtained by the method of Longley or by tannic acid fixation are negatively contrasted since control experiments with orthorhombic catalase plates yield negatively stained specimens with conditions used for the larger trigonal crystals.

Deviations from Ideal Decagonal Symmetry in Electron Diffraction Patterns of the “Decagonal” Phase in the Al-Co-Cu Alloy System

1991 ◽  
Vol 49 ◽  
pp. 914-915
Author(s):  
Atul S. Ramani ◽  
Earle R. Ryba ◽  
Paul R. Howell
Keyword(s):  
Electron Microscope ◽  
Alloy System ◽  
Nominal Composition ◽  
Dimensional Lattice ◽  
3 Dimensional ◽  
Decagonal Phase ◽  
Cu Alloy ◽  
Transmission Electron ◽  
Lattice Periodicity ◽  
Diffraction Patterns

The “decagonal” phase in the Al-Co-Cu system of nominal composition Al65CO15Cu20 first discovered by He et al. is especially suitable as a topic of investigation since it has been claimed that it is thermodynamically stable and is reported to be periodic in the dimension perpendicular to the plane of quasiperiodic 10-fold symmetry. It can thus be expected that it is an important link between fully periodic and fully quasiperiodic phases. In the present paper, we report important findings of our transmission electron microscope (TEM) study that concern deviations from ideal decagonal symmetry of selected area diffraction patterns (SADPs) obtained from several “decagonal” phase crystals and also observation of a lattice of main reflections on the 10-fold and 2-fold SADPs that implies complete 3-dimensional lattice periodicity and the fundamentally incommensurate nature of the “decagonal” phase. We also present diffraction evidence for a new transition phase that can be classified as being one-dimensionally quasiperiodic if the lattice of main reflections is ignored.

A Novel Reconstitution Method for Inducing the Formation of Regular 2-Dimensional Arrays of Membrane Proteins and Lipids

1988 ◽  
Vol 46 ◽  
pp. 152-153 ◽  
Author(s):  
A. Engel ◽  
A. Holzenburg ◽  
K. Stauffer ◽  
J. Rosenbusch ◽  
U. Aebi
Keyword(s):  
Membrane Proteins ◽  
Flow Rate ◽  
Lipid Membranes ◽  
Functional Characterization ◽  
Dimensional Structure ◽  
Electron Crystallography ◽  
Peltier Element ◽  
Protein Ratio ◽  
Precise Control ◽  
3 Dimensional

Reconstitution of solubilized and purified membrane proteins in the presence of phospholipids into vesicles allows their functions to be studied by simple bulk measurements (e.g. diffusion of differently sized solutes) or by conductance measurements after transformation into planar membranes. On the other hand, reconstitution into regular protein-lipid arrays, usually forming at a specific lipid-to-protein ratio, provides the basis for determining the 3-dimensional structure of membrane proteins employing the tools of electron crystallography.To refine reconstitution conditions for reproducibly inducing formation of large and highly ordered protein-lipid membranes that are suitable for both electron crystallography and patch clamping experiments aimed at their functional characterization, we built a flow-dialysis device that allows precise control of temperature and flow-rate (Fig. 1). The flow rate is generated by a peristaltic pump and can be adjusted from 1 to 500 ml/h. The dialysis buffer is brought to a preselected temperature during its travel through a meandering path before it enters the dialysis reservoir. A Z-80 based computer controls a Peltier element allowing the temperature profile to be programmed as function of time.

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