Knowledge used for teaching counting: A case study of the treatment of counting by two Grade 3 teachers situated in schools serving working class communities in the Western Cape Province of South Africa

Knowing how to correctly count, is fundamental to the future mathematics success of young children. Earlier studies show that many South African primary school students underperform in mathematics even when evaluated with task below grade level. Reports suggest that this is a problem stemming from the poor pedagogic, and or content knowledge of classroom mathematics teachers. Shulman (1986; 1987) refers to this area of knowledge as Pedagogic Content Knowledge (PCK). In the field of mathematics teaching and learning, Ball, Thames and Phelps (2008) refer to it as Mathematics Knowledge for Teaching (MKfT). Teachers' mathematics PCK, comprises of three core knowledge domain: (i) Teacher's Knowledge of Content and Teaching (KCT); (ii) Teacher's Knowledge of Content and Student (KCS); and (iii) teacher's Knowledge of Content and Curriculum (KCC). Teachers' KCS was considered in this study as it concerns what teachers know about what learners know and how they learn. The general interest of this project was to study the construction of experience of mathematics (non-core domain knowledge) by genetic endowment on the basis of contextual data. More specifically, the particular interest of the study is on the construction of the experience of counting in the pedagogic situations of Grade 3 schooling. For that purpose, video records of mathematics teaching in two schools situated in working-class communities were analysed. The study adopted an Integrated Causal Model approach which drew on resources from different disciplines such as mathematics education, cognitive science, evolutionary psychology and mathematics. The study was partly framed by Bernstein's pedagogic device, particularly with respect to his notion of evaluation, as well as the inter-related constructs of PCK, MKfT and KCS. The theoretical resources used to describe computations were drawn largely from Davis (2001, 2010b, 2011a, 2012, 2013a, 2015, 2018) and related work on the use of morphisms as elaborated in Baker et al. (1971), Gallistel & King, (2010), Krause (1969) and Open University (1970). These resources were used to produce the analytic framework for the production of and analysis of data. The analysis describes the computational activities of teachers and learners during the recorded lessons, specifically the computational domains made available pedagogically. In so doing, I was able to provide more illumination on what is described as teacher's KCS for teaching counting at the Grade 3 level. From the generated data, the study finds that counting proper was restricted to the constitution and identification of very small ordered discrete aggregates which can be handled by human core domain object tracking system and approximate number system, and that an implicit reliance on numerical order derived from computations on aggregates was central to the teaching and learning of counting

PRODUCTION AND EVALUATION OF FLAVORED YOGHURT FROM GRADED LEVELS OD SOURSOP (ANNONA MURICATA) PULP

Yoghurt was produced and flavoured with graded levels of soursop pulp. Soursop pulp was used to substitute 0, 10, 20, 30, 40 and 50% of yoghurt. The chemical, sensory and microbiological properties of the yoghurts were determined. The results showed that the pH of the yoghurt ranged from 4.30 to 4.60. The protein content varied from 2.68%-5.83% and the ash content ranged from 1.21% - 1.38%. The fat and moisture contents decreased and the values varied from 2.21% - 4.12% and 74.57%- 79.26% respectively. However, the carbohydrate and micro-nutrient (Ca and Vitamin C) content increased with increased level of soursop in the yoghurt. The total viable count and lactic acid bacteria count values were also inversely proportional to the concentration of soursop. The values for Total viable count (TVC) ranged from 2.0×105-4.5×105 while the values for Lactic acid bacteria (LAB) varied from1.3×105-3.9×105. There was no significant difference (p < 0.05) in the overall acceptability of all the products. The most acceptable flavoured yoghurt contained 60% yoghurt and 40% soursop pulp and had a general acceptability of 7.15. Soursop could be used to produce acceptable beverage.Key words: Flavoured yoghurt, Micro-organisms, Micro-nutrient, Soursop pulp, Sensory evaluatio

Foreign Direct Investment and Economic Development in Nigeria

This study examined the Foreign Direct Investment (FDI) trends and their influence on the Nigerian Economy over the time frame of 1986 to 2018. Secondary data were sourced from the Central Bank of Nigeria statistical bulletin of various issues and CBN annual reports. This study utilized the Error Correction Model Granger Causality and other diagnostic tests in capturing the long-run and short-run dynamics of the variables used in the model. The result revealed the existence of a positive and significant long-run relationship between Foreign direct investment on the human development index proxy for Economic development. Due to the influence of foreign direct investment, the study recommends that the government should foster its appropriation of capital and recurrent expenditure towards improving the productive dominance of the nation, and eliminate room for insecurity and political turmoil

Microbiological evaluation of sachet water and street-vended yoghurt and “Zobo” drinks sold in Nsukka metropolis

Microbial, physical and chemical characteristics of six brands of sachet water and street-vended yoghurt (two) and “Zobo” drinks (three) sold in Nsukka metropolis were studied. Parameters such pH, total dissolvedsolids, copper, iron, alkalinity, appearance, taste, colour, aerobic mesophilic count, coliform counts were evaluated. Data obtained from the study showed that the yoghurt and “Zobo” drinks sold at the moment arebacteriologically safe. “Zobo” drink samples had total plate count of 9.9×101 CFU/ml to 1.48×102 CFU/ml, negative to coliform, Salmonella, and E. coli. Yoghurt samples had total plate count of 9.9×101 CFU/ml to1.59×102 CFU/ml, negative to coliform, Salmonella and E. coli. Sachet water samples had pH of 7.25 to 7.50, total dissolved solids of 2.66ppm to 15.03ppm, hardness of 0.24ppm to 15.00ppm, iron, nitrate and nitrite were not detected. A total plate count of 1.41×102 to 3.19×102 , negative to Salmonella spp and some positive to Pseudomonas spp, coliform and E. coli. Thus the need for improved water treatment methods and storagebefore drinking and use for food drink processing

A Review on Natural Gas Utilization and Cutting Carbon Emissions: How viable is Compressed Natural Gas for Road Vehicle Fuel?

As the world grows and economies develop, global demand for energy will continue to grow dramatically. Demand for natural gas is likely to overtake other fossil fuels due to its availability, accessibility, versatility and cleanliness. For instance, the International Energy Agency (IEA) proposed in May 2012 that global demand for natural gas could rise more than 50% by 2035, from 2010 levels. According to the Intergovernmental Panel on Climate Change (IPCC), global greenhouse gas (GHG) emissions must be reduced by 50 to 80 percent by 2050 to avoid dramatic consequences of global warming. In order to meet this growing energy demand and GHG reduction, we must develop all commercially-viable energy sources. As we know that no single energy source can meet the world's growing energy needs. We also need a more diverse energy mix which will enable energy security and help tackle the issue of climate change. Meeting this growing long-term societal demand requires that we develop all economic and environmentally-sound energy sources. Natural gas which is the cleanest compared to other fossil fuels is available to provide the world with a viable alternative. Its abundance, reliability, versatility and accessibility, will be a huge factor.  This paper considers the value of compressed natural gas (CNG) to be used for natural gas vehicles (NGV), and how it could  serve as a long-term emission-reducing energy source. Such uptake would also improve utilisation of natural gas instead of flaring it, thereby minimizing environmental harm and improving public safety. Keywords: Compressed Natural Gas (CNG), Natural Gas Vehicles (NGV), Green House Gas (GHG), Cash Flow Analysis of CN

Analysing the Effect of Deep and Shallow Water Depth on the Motion of a Floating Offshore Pontoon

This research is intended to analyse the effect of seawater depth on sea seakeeping analyses. So it's crucial to understand ship motion on waves. As a result, precise hydrodynamic/motion force forecasts in constrained waterways is essential. The goal of this research is to look into how water depth affects ship heave motion. It is quite important to understand how floating offshore pontoon behave in deep and shallow water due to renewed interest of Nigeria Energy company in offshore exploration. Therefore accurate prediction of heave force will be analysed in this research. This study uses the linear wave theorem, Response Amplitude Operator, to estimate the hydrodynamic forces that occur in deep and shallow water. Bonny Island, Nigeria tidal wave using a depth of 500 and 5 meters. The results obtained in this research reveal a rapid decrease in heave response displacement from 0 to 0.2 wave frequency. According to the data, FOP operation is optimum at 500m seawater depth, where the effect of heave motion is less noticeable as shown in this research as at when compared to a 5m depth

FINANCIAL DEEPENING AND COMMERCIAL BANKS PERFORMNCE: EVIDENCE FROM NIGERIA

The work was aimed at determining the financial deepening impact on commercial bank performance in Nigeria. Financial deepening was decomposed into credit allocation to private sector as a ratio of GDP, money supply as a ratio of gross domestic product and total loan to deposit ratio while net interest margin was used as proxy for commercial bank performance. Data was sourced from the CBN statistical bulletin and the world bank data base from 2000 to 2022. The Augmented Dickey Fuller unit root test was used in determining stationarity of the data which were not stationary after first differencing hence giving room for the application of the ARDL bond test to determine the short and long run relationship between the implicated variables while the Granger causality test was used to determine the causality between financial deepening and commercial bank performance. The results revealed nonexistence of short run relation but existence of long run relationship was observed while a unidirectional relation between credit allocated to private sector ratio to GDP and net interest margin why no causality was recorded between other variables studied. The work recommends need for commercial banks to improve on their financial deepening activities so as to broaden their financial services operations and more so, policy makers should step in and ensure commercial banking broaden their financial deepening to accommodate individuals and the business world entirely

Fuzzy Cost Modelling of Diving Chamber Control Measures under Uncertainties

The diving chamber is an important system needed for diving operations in the oil and gas industry. Divers use it for various purposes. Thus, the safety level of the diving chamber needs to be very high at all times and the system needs to be in a good state. To achieve this, various control measures such as control measures 1 and 2 can be adopted in preventing failures/hazards or mitigate their consequences. In this study, fuzzy cost algorithm is used to estimate the cost of using control measures 1 and 2 in ensuring optimal operational level for the diving chamber, while the preference degree approach is adopted in prioritizing the aforementioned cost of control measures 1 and 2. The result of the analysis indicated that control measure 2 is the most cost effective approach

Facilitating Improvement of Design for Safety and Operations of a Seaweed Harvester: A Hybrid Traditional Safety Method

Sea harvester is a vital marine vessel needed in sea safety and cleanliness. Reliability and safety of the operations of the vessel need to be ensured via identification of hazards/failures that tends to affect the system and prevent them from occurring and also mitigate their consequences. In this research, a traditional hybrid methodology is employed in ensuring the reliability and safety of a sea harvester. The methodology is a logical combination of preliminary hazard analysis (PHA), risk matrix approach (RMA) and event tree analysis (ETA). Fire, flood, machinery failure and capsize that pose to affect optimal operations of a sea harvester are identified using a PHA method. RMA is incorporated in application of the PHA method to estimate the risks associated with them. Due the fact that risks associated with fire, flood, machinery failure and capsize are classified as very high, identifying preventing measures becomes necessary. Furthermore, systems which by means of their operability and non-operability can mitigate fire, flood, machinery failure, capsize and grounding consequences are captured using an ETA method. Therefore, the traditional hybrid methodology developed is successfully applied in design for safety, construction and operation of a sea harveste

Effect of types of packaging materials on the physiochemical and microbiological characteristics of African bush mango - soursop fruit bar during storage

AbstractThis study evaluated fruit bar produced from the blends of African bush mango (Irvingia spp) and soursop (Annona muricata) in the ratio of 100:0, 0:100, 90:10, 80:20, 80:20, 70:30, 60:40, 50:50. The blends were properly mixed with the ingredients (citric acid and honey), heated at a temperature of 70 – 80 0C in a water bath until it formed solid. It was then poured into a greased tray and oven dried at a temperature of 55 – 60 0C for 8 hours in an oven dryer. The formulated fruit bar were allowed to cool, then packaged in three different packaging materials (low density polyethylene, high density polyethylene and foil). The different formulated fruit bars were subjected to sensory evaluation, proximate composition, micronutrient (vitamin C, phosphorus and calcium), microbial (total viable and mould counts) and physicochemical properties (brix, pH, and titrable acidity). Result showed that the overall acceptability of the formulated fruit bars differed significantly (p<0.05). In the proximate composition of the fruit bar, the moisture (2.56 % to 11.85 %), protein (2.17 % to 2.98 %), fiber (5,48 % to 13.63 %), crude fat (0.14 % to 1.07 %) and carbohydrate (71.41 % to 86.32 %) content of the fruit bar were not significantly different (p>0.05) among some samples while there was no significant different (p<0.05) among some other samples. The micronutrient composition of the fruit bar differs significantly (p<0.05) from each other. Also, the phosphorus (0.54 to 0.84 mg/100g) and calcium (11.20 to 20.12 mg/100g) content were high, while the vitamin C (48.50 to 84.50 mg/100g) content increased with the increase in the proportion of the blends. The microbial count of the products increased during storage. The total viable count of the sample showed that majority of the samples stored in high density polyethylene had high growth of microorganisms (2.7 × 109 cfu/ml) and the least from the low density polyethylene (1.4×105 cfu/ml). Based on the mould count, majority of the samples stored in the foil had values ranging from 1.0×10 to 7.0×102 cfu/ml and the least from the low density polyethylene (no growth). During the 4 weeks storage, the titrable acidity of the samples increased progressively, with the samples stored in the low density polyethylene having the highest value (1.50 %) and the high density polyethylene having the least value (1.43 %). The pH of the stored samples decreased, with samples stored in the low density polyethylene having the highest value (3.57 %) and least value obtain from the high density polyethylene (3.69 %). The sugar level of the stored sample increased with the samples stored in the low density polyethylene having the highest value (9.40 %) and the high density polyethylene has the least value (9.90 %).Key words: African bush mango (Irvingia spp), Fruit bar, Microbes, Packaging materials, Soursop (Annona muricata