Will we ever teach mathematics again in the way we used to before the pandemic?

After about two years of emergency remote teaching during the pandemic, the teaching of mathematics is slowly returning to (what used to be called) normal. However, after the period of mostly teaching online, there is uncertainty about the extent to which we will return to the way we were teaching before. In this survey paper we attempt to give some background to the impact that emergency remote teaching may have had on teaching mathematics. We examine the possible social implications and then focus on the changing mathematics classroom, focusing on the actual mathematics curriculum, learning design and assessment, the role of collaborative activities and social media, educational videos, and the role of family and parents in future. There are indicators from the literature that educators may not return to the traditional way of teaching entirely, especially in secondary and higher education. We conclude with describing some possible new research areas that have developed through emergency remote teaching, including online education for younger learners, local learning ecosystems, the role of family and parents, instructional design, and the mathematics content of curricula.

The impact of COVID-19 on the format and nature of academic conferences in mathematics education.

The global COVID-19 pandemic has provided an opportunity to re-examine the possibility of organising virtual conferences in mathematics education, in which the social needs of participants can also be addressed. In this study we investigated the future impact that this change may have on the format and nature of mathematics education conferences. The study was conducted in two phases. We used an online questionnaire in which we asked participants to give us some input on the issues above. In the second phase of the project, focus group interviews were conducted with international mathematics education researchers. This study is an exploratory study, in which the sample was not developed in a way that could generate comparisons. The aim of the study was to raise possibilities about what may be the future of mathematics education conferences. Findings indicate that although academics are pro-actively thinking about alternative conference formats, the proven value of face-to-face conferences is still very real, showing that it is too early for us to have a clear vision of the future format of academic conferences.

Using enaction to evolve from pre-Covid to post-Covid pedagogy: a case study with South African mathematics teachers.

The Covid-19 pandemic and subsequent national lockdown in South Africa induced a rapid, albeit challenging, implementation of blended learning (with a strong online focus) at all educational levels. During this time, a group of teachers were involved in a specialised computer integrated education course, preparing them for the design and implementation of technologically enhanced modes of teaching. In this research we considered the positive impact of the situation during the pandemic on these mathematics teachers' practice, as well as their conceptualisation of the way forward for technology enhanced mathematics education. We conducted an explorative survey study, employing an enactivist approach, to investigate their experiences of addressing procedural and conceptual aspects of mathematics education, as well as their observations of learners' reactions to these changed practices. Our findings show that participants experienced their exposure to technology as creating an environment they foresee will have a lasting impact on their teaching practice. Participants emphasised the importance of using educational technology meaningfully as a cognitive tool that allows for learners to learn with the technology and not from the technology, which impacts on the importance of learner-centred teaching strategies and the development of high cognitive level interactive learning activities.

Transformation of the mathematics classroom with the internet.

Growing use of the internet in educational contexts has been prominent in recent years. In this survey paper, we describe how the internet is transforming the mathematics classroom and mathematics teacher education. We use as references several reviews of use of the internet in mathematics education settings made in recent years to determine how the field has evolved. We identify three domains in which new approaches are being generated by mathematic educators: principles of design of new settings; social interaction and construction knowledge; and tools and resources. The papers in this issue reflect different perspectives developed in the last decade in these three domains, providing evidence of the advances in theoretical frameworks and support in the generation of new meanings for old constructs such as 'tool', 'resources' or 'learning setting'. We firstly highlight the different ways in which the use of digital technologies generates new ways of thinking about mathematics and the settings in which it is learnt, and how mathematics teacher educators frame the new initiatives of initial training and professional development. In this survey paper, we identify trends for future research regarding theoretical and methodological aspects, and recognise new opportunities requiring further engagement.

Saharan dust and the impact on adult and elderly allergic patients: the effect of threshold values in the northern sector of Gran Canaria, Spain.

Gran Canaria Island is frequently impacted by Saharan dust, a health hazard of particular concern to the island population and health agencies. Airborne mineral dust has the severest impact on the higher age groups of the population, and those with respiratory conditions; despite that, on average, the ambient particulate matter (PM) concentrations fall within international PM guidelines. During 2010 and 2011, an epidemiological survey, in parallel with an air quality study, was conducted at the Dr Negrín hospital in Gran Canaria. This included the quarterly monitoring of outpatients and recording of emergency patients with respiratory diseases, together with the measurement of aerosol, meteorological, and PM-related air quality levels. The finer more toxic particles were collected with PM2.5 (particulate matter with aerodynamic diameter less than 2.5 µm) aerosol samplers. The filter samples were gravimetrically and chemically analyzed for their elemental, water-soluble ions, carbon, and mineralogical contents. Individual particle morphology was measured by Scanning Electron Microscopy. Statistical analysis of the chemical and clinical data included the analysis of variance and calculation of Spearman correlation coefficients. No statistically significant relations were found between the allergic control group, the emergency room admissions, pulmonary conditions, medication, and elevated Saharan dust levels. However, changing environmental conditions, such as an increase in humidity or a reduction in ambient air temperature made a significant difference to the outcomes recorded on the health statements of the allergic and respiratory illness groups of the Gran Canary population.

Characterizing mineral dusts and other aerosols from the Middle East--Part 1: ambient sampling.

The purpose of the Enhanced Particulate Matter Surveillance Program was to provide scientifically founded information on the chemical and physical properties of dust collected over a period of approximately 1 year in Djibouti, Afghanistan (Bagram, Khowst), Qatar, United Arab Emirates, Iraq (Balad, Baghdad, Tallil, Tikrit, Taji, Al Asad), and Kuwait (northern, central, coastal, and southern regions). Three collocated low-volume particulate samplers, one each for the total suspended particulate matter, < 10 micro m in aerodynamic diameter (PM(10)) particulate matter, and < 2.5 micro m in aerodynamic diameter (PM(2.5)) particulate matter, were deployed at each of the 15 sites, operating on a '1 in 6' day sampling schedule. Trace-element analysis was performed to measure levels of potentially harmful metals, while major-element and ion-chemistry analyses provided an estimate of mineral components. Scanning electron microscopy with energy dispersive spectroscopy was used to analyze the chemical composition of small individual particles. Secondary electron images provided information on particle size and shape. This study shows the three main air pollutant types to be geological dust, smoke from burn pits, and heavy metal condensates (possibly from metals smelting and battery manufacturing facilities). Non-dust storm events resulted in elevated trace metal concentrations in Baghdad, Balad, and Taji in Iraq. Scanning-electron-microscopy secondary electron images of individual particles revealed no evidence of freshly fractured quartz grains. In all instances, quartz grains had rounded edges and mineral grains were generally coated by clay minerals and iron oxides.

Characterizing mineral dusts and other aerosols from the Middle East--Part 2: grab samples and re-suspensions.

The purpose of the Enhanced Particulate Matter Surveillance Program was to provide scientifically founded information on the chemical and physical properties of dust collected during a period of approximately 1 year in Djibouti, Afghanistan (Bagram, Khowst), Qatar, United Arab Emirates, Iraq (Balad, Baghdad, Tallil, Tikrit, Taji, Al Asad), and Kuwait (northern, central, coastal, and southern regions). To fully understand mineral dusts, their chemical and physical properties, as well as mineralogical inter-relationships, were accurately established. In addition to the ambient samples, bulk soil samples were collected at each of the 15 sites. In each case, approximately 1 kg of soil from the top 10 mm at a previously undisturbed area near the aerosol sampling site was collected. The samples were air-dried and sample splits taken for soil analysis. Further sample splits were sieved to separate the < 38 micro m particle fractions for mineralogical analysis. Examples of major-element and trace-element chemistry, mineralogy, and other physical properties of the 15 grab samples are presented. The purpose of the trace-element analysis was to measure levels of potentially harmful metals while the major-element and ion-chemistry analyses provided an estimate of mineral components. X-ray diffractometry provided a measure of the mineral content of the dust. Scanning electron microscopy with energy dispersive spectroscopy was used to analyze chemical composition of small individual particles. From similarities in the chemistry and mineralogy of re-suspended and ambient sample sets, it is evident that portions of the ambient dust are from local soils.

Particulate emissions from U.S. Department of Defense artillery backblast testing.

There is a dearth of information on dust emissions from sources that are unique to the U.S. Department of Defense testing and training activities. However, accurate emissions factors are needed for these sources so that military installations can prepare accurate particulate matter (PM) emission inventories. One such source, coarse and fine PM (PM10 and PM2.5) emissions from artillery backblast testing on improved gun positions, was characterized at the Yuma Proving Ground near Yuma, AZ, in October 2005. Fugitive emissions are created by the shockwave from artillery pieces, which ejects dust from the surface on which the artillery is resting. Other contributions of PM can be attributed to the combustion of the propellants. For a 155-mm howitzer firing a range of propellant charges or zones, amounts of emitted PM10 ranged from -19 g of PM10 per firing event for a zone 1 charge to 92 g of PM10 per firing event for a zone 5. The corresponding rates for PM2.5 were approximately 9 g of PM2.5 and 49 g of PM2.5 per firing. The average measured emission rates for PM1o and PM2.5 appear to scale with the zone charge value. The measurements show that the estimated annual contributions of PM10 (52.2 t) and PM2.5 (28.5 t) from artillery backblast are insignificant in the context of the 2002 U.S. Environment Protection Agency (EPA) PM emission inventory. Using national-level activity data for artillery fire, the most conservative estimate is that backblast would contribute the equivalent of 5 x 10(-4) % and 1.6 x 10(-3)% of the annual total PM10 and PM2.5 fugitive dust contributions, respectively, based on 2002 EPA inventory data.

Source profiles for industrial, mobile, and area sources in the Big Bend Regional Aerosol Visibility and Observational study.

Representative PM2.5 and PM10 source emissions were sampled in Texas during the Big Bend Regional Aerosol Visibility and Observa (BRAVO) study. Chemical source profiles for elements, ions, and carbon fractions of 145 samples are reported for paved and unpaved road dust, soil dust, motor vehicle exhaust, vegetative burning, four coal-fired power stations, an oil refinery catalytic cracker, two cement kilns, and residential meat cooking. Several samples were taken from each emitter and source type, and these were averaged by source type, and in source subgroups based on commonality of chemical composition. The standard deviation represents the variability of the chemical mass fractions. BRAVO profiles differed in some respects from profiles measured elsewhere. High calcium abundances in geological dust, high selenium abundances in coal-fired power stations, and high antimony abundances in oil refinery catalytic cracker emissions were found. Abundances of eight thermally evolved carbon fractions [Atmos. Environ. 28 (15) (1994) 2493] differ among combustion sources, and a Monte Carlo simulation demonstrates that these differences are sufficient to differentiate among several carbon-emitters.

Chapter one: exposure measurements.

Determining human exposure to suspended particulate concentrations requires measurements that quantify different particle properties in microenvironments where people live, work, and play. Particle mass, size, and chemical composition are important exposure variables, and these are typically measured with time-integrated samples on filters that are later submitted to laboratory analyses. This requires substantial sample handling, quality assurance, and data reduction. Newer technologies are being developed that allow in-situ, time-resolved measurements for mass, carbon, sulfate, nitrate, particle size, and other variables. These are large measurement systems that are more suitable for fixed monitoring sites than for personal applications. Human exposure studies need to be designed to accomplish specific objectives rather than to serve too many purposes. Resources need to be divided among study design, field sampling, laboratory analysis, quality assurance, data management, and data analysis phases. Many exposure projects allocated too little to the non-measurement activities.

Designing monitoring networks to represent outdoor human exposure.

Measurements of outdoor human exposure to suspended particulate matter (PM) are always constrained by available resources. An effective network design requires tradeoffs between variables measured, the number of sampling locations, sample duration, and sampling frequency. Sampling sites are needed to represent neighborhood and urban spatial scales with minimal influences from nearby sources. Although most PM measurements for determining compliance with standards are taken over 24-h periods every third to sixth day, outdoor human exposure assessment requires measurements taken continuously throughout the day, preferably over durations of 1 h or less. More detailed particle size and chemistry data are also desirable, as smaller size fractions and specific chemicals may be better indicators of adverse health effects than total mass samples.

Monitoring of particulate matter outdoors.

Recent studies of the size and composition of atmospheric particulate matter (PM) have demonstrated the usefulness of separating atmospheric PM into its fine and coarse components. The need to measure the mass and composition of fine and coarse PM separately has been emphasized by research in exposure, epidemiology, and toxicology of atmospheric PM. This paper provides a background on the size distribution and properties of PM relevant to the differences between fine and coarse particles. Various decisions that must be made when deciding how to separate, collect, and measure PM are discussed. Techniques for monitoring fine and coarse particles, including the US Federal Reference Method for PM2.5 and several techniques for PM10-2.5, are presented. Problems encountered in collecting semivolatile PM and in weighing atmospheric PM collected on a filter are described. Continuous monitoring methods for PM mass and for PM components (carbon, nitrate, and sulfate) are described and brief descriptions are given of analytical techniques for the chemical characterization of collected PM. This information should be especially useful for environmental workers familiar with monitoring methods for total suspended particles or PM10 but who will need to measure PM2, and PM10-2.5 in the future.

Receptor modeling application framework for particle source apportionment.

Receptor models infer contributions from particulate matter (PM) source types using multivariate measurements of particle chemical and physical properties. Receptor models complement source models that estimate concentrations from emissions inventories and transport meteorology. Enrichment factor, chemical mass balance, multiple linear regression, eigenvector. edge detection, neural network, aerosol evolution, and aerosol equilibrium models have all been used to solve particulate air quality problems, and more than 500 citations of their theory and application document these uses. While elements, ions, and carbons were often used to apportion TSP, PM10, and PM2.5 among many source types, many of these components have been reduced in source emissions such that more complex measurements of carbon fractions, specific organic compounds, single particle characteristics, and isotopic abundances now need to be measured in source and receptor samples. Compliance monitoring networks are not usually designed to obtain data for the observables, locations, and time periods that allow receptor models to be applied. Measurements from existing networks can be used to form conceptual models that allow the needed monitoring network to be optimized. The framework for using receptor models to solve air quality problems consists of: (1) formulating a conceptual model; (2) identifying potential sources; (3) characterizing source emissions; (4) obtaining and analyzing ambient PM samples for major components and source markers; (5) confirming source types with multivariate receptor models; (6) quantifying source contributions with the chemical mass balance; (7) estimating profile changes and the limiting precursor gases for secondary aerosols; and (8) reconciling receptor modeling results with source models, emissions inventories, and receptor data analyses.