Factors Associated with the Utilization of Mathematics Manipulatives in Grades Kindergarten Through Four

Since the publication of Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics in 1989, mathematics pedagogy has shifted from the standard memorization of facts and processes to concept development and application. Teachers have been encouraged to utilize manipulatives to help students bridge the gap between concrete and abstract mathematical concepts. This study was conducted to determine if grade level impacted the frequency with which manipulatives were used, to examine teacher perceptions of eleven factors associated with the frequency of utilization of math manipulatives, and to assess the perceived effect of teaching with manipulatives on the mathematics achievement of public school students in grades kindergarten through four. The study took place during the 1997-98 school year, using a survey of kindergarten through fourth grade teachers whose schools were located in Area IV of the Regional Offices of Education, which covers east-central Illinois. Of 187 teachers who were sent a survey, 113 returned it for a response rate of 60%. Kindergarten and first grade teachers reported using manipulatives more frequently than teachers in grades two, three, and four. Every respondent in grades kindergarten, one, and two reported using manipulatives at least once a week. Frequency of usage fell dramatically after second grade. Ninety-eight percent of teachers indicated that the use of math manipulatives had a positive impact on increasing student achievement, while 97% indicated they believed the use of manipulatives was vital to student understanding. Of the eleven factors examined, teachers perceived the following to impact the frequency with which they utilized manipulatives: the amount of time involved in teaching the lesson, the amount of time in planning the lesson, class size, classroom management issues, and the need for additional assistance during manipulative-based instruction. Seventy-five percent of teachers perceived that manipulatives were integrated into their current curriculum. Fifty-seven percent of teachers indicated that their districts provided all of the manipulatives they needed, while 54% indicated that the personal expense of providing manipulative materials did not limit their use. Ninety-two percent of administrators and 75% of parents were perceived by teachers as being supportive. Eighty-five percent of teachers indicated their level of training in using manipulatives was adequate. Recommendations as a result of the study included establishing teacher committees to determine a minimum level of manipulatives required at each grade level, and a district commitment to provide financial resources for the basic supply; enlisting parent volunteers to assist during manipulative-based instruction; and establishing a procedure in each district by which teachers could choose to utilize a manipulative-based approach in place of the district textbook adoption. It was also recommended that further research be conducted to assess the impact of class size on the frequency of utilization, and that a study be undertaken which compares academic achievement of students who receive mathematics instruction through a manipulative-based approach to that of students instructed through the traditional, textbook driven curriculum

Factors Associated with the Utilization of Mathematics Manipulatives in Grades Kindergarten Through Four

Since the publication of Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics in 1989, mathematics pedagogy has shifted from the standard memorization of facts and processes to concept development and application. Teachers have been encouraged to utilize manipulatives to help students bridge the gap between concrete and abstract mathematical concepts. This study was conducted to determine if grade level impacted the frequency with which manipulatives were used, to examine teacher perceptions of eleven factors associated with the frequency of utilization of math manipulatives, and to assess the perceived effect of teaching with manipulatives on the mathematics achievement of public school students in grades kindergarten through four. The study took place during the 1997-98 school year, using a survey of kindergarten through fourth grade teachers whose schools were located in Area IV of the Regional Offices of Education, which covers east-central Illinois. Of 187 teachers who were sent a survey, 113 returned it for a response rate of 60%. Kindergarten and first grade teachers reported using manipulatives more frequently than teachers in grades two, three, and four. Every respondent in grades kindergarten, one, and two reported using manipulatives at least once a week. Frequency of usage fell dramatically after second grade. Ninety-eight percent of teachers indicated that the use of math manipulatives had a positive impact on increasing student achievement, while 97% indicated they believed the use of manipulatives was vital to student understanding. Of the eleven factors examined, teachers perceived the following to impact the frequency with which they utilized manipulatives: the amount of time involved in teaching the lesson, the amount of time in planning the lesson, class size, classroom management issues, and the need for additional assistance during manipulative-based instruction. Seventy-five percent of teachers perceived that manipulatives were integrated into their current curriculum. Fifty-seven percent of teachers indicated that their districts provided all of the manipulatives they needed, while 54% indicated that the personal expense of providing manipulative materials did not limit their use. Ninety-two percent of administrators and 75% of parents were perceived by teachers as being supportive. Eighty-five percent of teachers indicated their level of training in using manipulatives was adequate. Recommendations as a result of the study included establishing teacher committees to determine a minimum level of manipulatives required at each grade level, and a district commitment to provide financial resources for the basic supply; enlisting parent volunteers to assist during manipulative-based instruction; and establishing a procedure in each district by which teachers could choose to utilize a manipulative-based approach in place of the district textbook adoption. It was also recommended that further research be conducted to assess the impact of class size on the frequency of utilization, and that a study be undertaken which compares academic achievement of students who receive mathematics instruction through a manipulative-based approach to that of students instructed through the traditional, textbook driven curriculum

Potential impact of iodine on tropospheric levels of ozone and other critical oxidants

A new analysis of tropospheric iodine chemistry suggests that under certain conditions this chemistry could have a significant impact on the rate of destruction of tropospheric ozone. In addition, it suggests that modest shifts could result in the critical radical ratio HO2/OH. This analysis is based on the first ever observations of CH3I in the middle and upper free troposphere as recorded during the NASA Pacific Exploratory Mission in the western Pacific. Improved evaluations of several critical gas kinetic and photochemical rate coefficients have also been used. Three iodine source scenarios were explored in arriving at the above conclusions. These include: (1) the assumption that the release of CH3I from the marine environment was the only iodine source with boundary layer levels reflecting a low-productivity source region, (2) same as scenario 1 but with an additional marine iodine source in the form of higher molecular weight iodocarbons, and (3) source scenario 2 but with the release of all iodocarbons occurring in a region of high biological productivity. Based on one-dimensional model simulations, these three source scenarios resulted in estimated Ix (Ix =I + IO + HI + HOI + 2I2O2 +INOx) yields for the upper troposphere of 0.5, 1.5, and 7 parts per trillion by volume (pptv), respectively. Of these, only at the 1.5 and 7 pptv level were meaningful enhancements in O3 destruction estimated. Total column O3 destruction for these cases averaged 6 and 30%, respectively. At present we believe the 1.5 pptv Ix source scenario to be more typical of the tropical marine environment; however, for specific regions of the Pacific (i.e., marine upwelling regions) and for specific seasons of the year, much higher levels might be experienced. Even so, significant uncertainties still remain in the proposed iodine chemistry. In particular, much uncertainty remains in the magnitude of the marine iodine source. In addition, several rate coefficients for gas phase processes need further investigating, as does the efficiency for removal of iodine due to aerosol scavenging processes. Copyright 1996 by the American Geophysical Union

Opiate Written Behavioral Agreements: A Case for Abandonment

Written behavioral agreements (WBAs) are gaining popularity as part of the effort to manage the alarming increase in prescription drug abuse. The rationale for increased use of WBAs in managing patients with chronic pain is that they are believed to increase adherence to agreed-upon behaviors, reduce addiction to or diversion of prescription drugs, and satisfy informed consent requirements. However, there are no high-quality data to support their widespread use in any of these areas. The evidence used to support the use of WBAs is insufficient to justify their unfairness and the high risk of harm they pose to the doctor-patient relationship. Instead, we contend that WBAs are being used to provide leverage for severing relationships with some of our most challenging patients. We propose that physicians treating patients for chronic pain abandon the use of WBAs. Alternatives include open communication, detailed informed consent processes, carefully documented discussions, and most important, commitment to ongoing relationships even with difficult patients

Highlights of OH, H2SO4, and methane sulfonic acid measurements made aboard the NASA P-3B during Transport and Chemical Evolution over the Pacific

Measurements of hydroxyl radical (OH), sulfuric acid (H2SO4), and methane sulfonic acid (MSA) were performed aboard the NASA P-3B using the selected ion chemical ionization mass spectrometry technique during the Transport and Chemical Evolution over the Pacific (TRACE-P) study. Photochemical box model calculations of OH concentrations yielded generally good agreement with an overall tendency to overestimate the measured OH by ∼20%. Further analysis reveals that this overestimation is present only at altitudes greater than ∼1.5 km, with the model underestimating OH measurements at lower altitudes. Boundary layer H2SO4 measurements, performed in a volcanic plume off the southern coast of Japan, revealed some of the largest marine boundary layer H2SO4 concentrations ever observed and were accompanied by new particle formation. Nighttime measurements of OH, H2SO4, and MSA in the remote pacific off Midway Island revealed significant boundary layer concentrations of H2SO4 and MSA, indicating evidence of nighttime boundary layer oxidation processes but in the absence of OH. A cursory exploration of the sources of production of the H2SO4 and MSA observed at night is presented

Summary of ground water and surface water flow and contaminant transport computer codes used at the Idaho National Engineering Laboratory (INEL). Version 1.0

This report presents information on computer codes for numerical and analytical models that have been used at the Idaho National Engineering Laboratory (INEL) to model ground water and surface water flow and contaminant transport. Organizations conducting modeling at the INEL include: EG&G Idaho, Inc., US Geological Survey, and Westinghouse Idaho Nuclear Company. Information concerning computer codes included in this report are: agency responsible for the modeling effort, name of the computer code, proprietor of the code (copyright holder or original author), validation and verification studies, applications of the model at INEL, the prime user of the model, computer code description, computing environment requirements, and documentation and references for the computer code

Carbonyl sulfide and carbon disulfide: Large-scale distributions over the western Pacific and emissions from Asia during TRACE-P

An extensive set of carbonyl sulfide (OCS) and carbon disulfide (CS 2) observations were made as part of the NASA Transport and Chemical Evolution over the Pacific (TRACE-P) project, which took place in the early spring 2001. TRACE-P sampling focused on the western Pacific region but in total included the geographic region 110°E to 290°E longitude, 5°N to 50°N latitude, and 0-12 km altitude. Substantial OCS and CS2 enhancements were observed for a great many air masses of Chinese and Japanese origin during TRACE-P. Over the western Pacific, mean mixing ratios of long-lived OCS and shorter-lived CS2 showed a gradual decrease by about 10% and a factor of 5-10, respectively, from the surface to 8-10 km altitude, presumably because land-based sources dominated their distribution during February through April 2001. The highest mean OCS and CS 2 levels (580 and 20 pptv, respectively, based on 2.5° × 2.5° latitude bins) were observed below 2 km near the coast of Asia, at latitudes between 25°N and 35°N, where urban Asian outflow was strongest. Ratios of OCS versus CO for continental SE Asia were much lower compared to Chinese and Japanese signatures and were strongly associated with biomass burning/biofuel emissions. We present a new inventory of anthropogenic Asian emissions (including biomass burning) for OCS and CS2 and compare it to emission estimates based on regional relationships of OCS and CS 2 to CO and CO2. The OCS and CS2 results for the two methods compare well for continental SE Asia and Japan plus Korea and also for Chinese CS2 emissions. However, it appears that the inventory underestimates Chinese emissions of OCS by about 30-100%. This difference may be related to the fact that we did not include natural sources such as wetland emissions in our inventory, although the contributions from such sources are believed to be at a seasonal low during the study period. Uncertainties in OCS emissions from Chinese coal burning, which are poorly characterized, likely contribute to the discrepancy. Copyright 2004 by the American Geophysical Union