Sharing Teaching Ideas: A Prop Is Worth Ten Thousand Words

1999 ◽  
Vol 92 (1) ◽  
pp. 27-28
Author(s):  
Carol M. Critchlow
Keyword(s):  
Cross Sections ◽  
Calculus Students ◽  
Teaching Ideas ◽  
Solids Of Revolution

I find that calculus students have great trouble visualizing solids of revolution and their cross sections. To help them, I resort to a wide variety of props.

Sharing Teaching Ideas: Edible Calculus

1989 ◽  
Vol 82 (5) ◽  
pp. 346-347
Keyword(s):  
The Other ◽  
Teaching Ideas ◽  
Solids Of Revolution

The other night while preparing supper, I was thinking of my calculus presentation of the day on volumes of solids of revolution and volumes by slicing. It occurred to me that I had the perfect equipment on hand to illustrate exactly what I had gestured and illustrated with some rough sketches. I admit I had also encountered some skeptical looks from my students.

Spatial Training for Calculus Students: Sex Differences in Achievement and in Visualization Ability

1987 ◽  
Vol 18 (2) ◽  
pp. 126-140
Author(s):  
Joan Ferrini-Mundy
Keyword(s):  
Sex Differences ◽  
Treatment Effect ◽  
Spatial Visualization ◽  
Control Treatment ◽  
Significant Treatment ◽  
Solid Of Revolution ◽  
Calculus Students ◽  
Spatial Training ◽  
Solids Of Revolution ◽  
Visualization Ability

This study investigated the effects of spatial training upon calculus achievement, spatial visualization ability, and the use of visualization in solving problems on solids of revolution. After pretesting, 250 college students participated in one of two spatial-training treatments or in a control treatment. Multivariate analyses of covariance revealed no treatment effect on calculus achievement or spatial visualization ability, but there were significant sex differences favoring women in calculus achievement and favoring men in spatial visualization ability. There were interaction effects for calculus achievement and the use of visualization in solving solid-of-revolution problems and a significant treatment effect for visualization of solids of revolution. Spatial training may benefit performance in certain areas of calculus for women more than for men.

Sharing Teaching Ideas: The Significance of the “Insignificant” Constants

1989 ◽  
Vol 82 (3) ◽  
pp. 186a-188
Keyword(s):  
Calculus Students ◽  
Teaching Ideas

My calculus students are often irritated when I deduct a point for the omission of the constant of integration. However, the following examples will usually convince them that the constants are not just another picky detail that they must remember.

Sharing Teaching Ideas: Why Not Three Dimensions?

1999 ◽  
Vol 92 (7) ◽  
pp. 560-567
Author(s):  
Steve Legé ◽  
Mark Fidler
Keyword(s):  
High School ◽  
School Curriculum ◽  
Three Dimensions ◽  
Spatial Skills ◽  
High School Curriculum ◽  
Calculus Students ◽  
Second Year ◽  
Teaching Ideas

When I reviewed our high school curriculum, I realized that my students did not have enough practice with situations that required analysis in three dimensions. Few situations that applied the threedimensional ideas studied in geometry were found in second-year algebra and precalculus, and calculus students faced with rotations that produced solids had very little experience to help them with the visualizations required. As a response, I developed several projects that I integrated into my courses at all three levels. What follows are descriptions of a three-year sequence of projects that help to develop students' spatial skills. The photographs are all examples of student-produced work.

Analysis of STEM micrographs of thick objects

1978 ◽  
Vol 36 (2) ◽  
pp. 106-107
Author(s):  
S. Golladay
Keyword(s):  
Inelastic Scattering ◽  
Multiple Scattering ◽  
Mass Distribution ◽  
Cross Sections ◽  
Phase Contrast ◽  
Image Point ◽  
Contrast Effects ◽  
Total Cross Sections ◽  
Elastic And Inelastic Scattering

The theory of multiple scattering has been worked out by Groves and comparisons have been made between predicted and observed signals for thick specimens observed in a STEM under conditions where phase contrast effects are unimportant. Independent measurements of the collection efficiencies of the two STEM detectors, calculations of the ratio σe/σi = R, where σe, σi are the total cross sections for elastic and inelastic scattering respectively, and a model of the unknown mass distribution are needed for these comparisons. In this paper an extension of this work will be described which allows the determination of the required efficiencies, R, and the unknown mass distribution from the data without additional measurements or models. Essential to the analysis is the fact that in a STEM two or more signal measurements can be made simultaneously at each image point.

Direct Observation of Heat Exchanger Deposits by Cross Sectioning

1967 ◽  
Vol 25 ◽  
pp. 364-365
Author(s):  
R. W. Anderson ◽  
D. L. Senecal
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Heat Exchanger ◽  
Direct Observation ◽  
Cross Sections ◽  
Preparation Method ◽  
Specimen Preparation ◽  
Flowing Water ◽  
Transmission Electron ◽  
Deposit Layer

A problem was presented to observe the packing densities of deposits of sub-micron corrosion product particles. The deposits were 5-100 mils thick and had formed on the inside surfaces of 3/8 inch diameter Zircaloy-2 heat exchanger tubes. The particles were iron oxides deposited from flowing water and consequently were only weakly bonded. Particular care was required during handling to preserve the original formations of the deposits. The specimen preparation method described below allowed direct observation of cross sections of the deposit layers by transmission electron microscopy.The specimens were short sections of the tubes (about 3 inches long) that were carefully cut from the systems. The insides of the tube sections were first coated with a thin layer of a fluid epoxy resin by dipping. This coating served to impregnate the deposit layer as well as to protect the layer if subsequent handling were required.

An Analysis of Dissociation of Molecules in a High Resolution Electron Microscope

1973 ◽  
Vol 31 ◽  
pp. 486-487
Author(s):  
Mihir Parikh
Keyword(s):  
Electron Microscope ◽  
High Resolution ◽  
Cross Sections ◽  
Resolving Power ◽  
Peak Intensity ◽  
Molecular Film ◽  
Resolution Electron ◽  
Dissociation Cross Section ◽  
High Resolution Electron Microscope ◽  
The Stability

It is well known that the resolution of bio-molecules in a high resolution electron microscope depends not just on the physical resolving power of the instrument, but also on the stability of these molecules under the electron beam. Experimentally, the damage to the bio-molecules is commo ly monitored by the decrease in the intensity of the diffraction pattern, or more quantitatively by the decrease in the peaks of an energy loss spectrum. In the latter case the exposure, EC, to decrease the peak intensity from IO to I’O can be related to the molecular dissociation cross-section, σD, by EC = ℓn(IO /I’O) /ℓD. Qu ntitative data on damage cross-sections are just being reported, However, the microscopist needs to know the explicit dependence of damage on: (1) the molecular properties, (2) the density and characteristics of the molecular film and that of the support film, if any, (3) the temperature of the molecular film and (4) certain characteristics of the electron microscope used

Surface ultrastructure of danazol treated rat endometrium: A SEM study

1983 ◽  
Vol 41 ◽  
pp. 556-557
Author(s):  
R.P. Apkarian ◽  
J.S. Sanfilippo
Keyword(s):  
Cross Sections ◽  
Reproductive Tract ◽  
Preliminary Investigation ◽  
Breast Disease ◽  
Distal Segment ◽  
Uterine Horn ◽  
Female Reproductive Tract ◽  
Ultrastructural Changes ◽  
Cycle Phase ◽  
Sprague Dawley

The synthetic androgen danazol, is an isoxazol derivative of ethisterone. It is utilized in the treatment of endometriosis, fibrocystic breast disease, and has a potential use as a contraceptive. A study was designed to evaluate the ultrastructural changes associated with danazol therapy in a rat model. The preliminary investigation of the distal segment of the rat uterine horn was undertaken as part of a larger study intended to elucidate the effects of danazol on the female reproductive tract.Cross-sections (2-3 mm in length) of the distal segment of the uterine horn from sixteen Sprague-Dawley rats were prepared for SEM. Ten rats in estrus served as controls and six danazol treated rats were noted to have alterations of the estrus cycle i.e. a lag in cycle phase or noncycling patterns. Specimens were fixed in 3% glutaraldehyde in 0.05M phosphate buffer containing CaCl2 at pH 7.0-7.4 and chilled to 4°C. After a brief wash in distilled water, specimens were passed through a graded series of ethanol, critical point dryed in CO2 from absolute ethanol, and coated with 6nm Au. Observations were made with an IS1-40 SEM operated at 15kV.

Electron Irradiation Effects in Polyoxymethylene Crystals Grown Inside Trioxane Crystals

1971 ◽  
Vol 29 ◽  
pp. 78-79
Author(s):  
J. P. Colson ◽  
D. H. Reneker
Keyword(s):  
Cross Section ◽  
Cross Sections ◽  
Detailed Examination ◽  
The Other ◽  
Electron Micrograph ◽  
Irradiation Effects ◽  
Threefold Axis ◽  
Typical Sample ◽  
Polymer Crystals ◽  
Chain Axis

Polyoxymethylene (POM) crystals grow inside trioxane crystals which have been irradiated and heated to a temperature slightly below their melting point. Figure 1 shows a low magnification electron micrograph of a group of such POM crystals. Detailed examination at higher magnification showed that three distinct types of POM crystals grew in a typical sample. The three types of POM crystals were distinguished by the direction that the polymer chain axis in each crystal made with respect to the threefold axis of the trioxane crystal. These polyoxymethylene crystals were described previously.At low magnifications the three types of polymer crystals appeared as slender rods. One type had a hexagonal cross section and the other two types had rectangular cross sections, that is, they were ribbonlike.

Sign in / Sign up

Export Citation Format

Share Document