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Impact Of Covid-19 Pandemic On Mathematics Achievement And Problem-Solving Ability: Insights From Secondary Schools In India, Laishram Nirtish Singh, Anand Jyoti Sanasam, Jocyline Thokchom, Ningombam Cha Cogent, Laisom Sharmeswar Singh

Journal of Humanistic Mathematics

The COVID-19 pandemic disrupted students’ engagement with mathematics. This study aims to contribute to our understanding of the extent of this disrupting by examining differences in mathematics achievement and problem-solving ability between adjacent cohorts who learned Class 8 under different schooling conditions in India: Group A (pandemic-exposed Class 8 cohort) and Group B (post-reopening Class 8 cohort). Using a descriptive design in a natural setting, we selected a stratified sample of 1,200 students from Class 9 and Class 10 across 21 secondary schools in Manipur, India. The sample was stratified by gender, family type, school type, and locality to ensure …

"Math Is Like A Rollercoaster": Exploring Math Similes And Metaphors, Carmen M. Latterell, Janelle L. Wilson

Journal of Humanistic Mathematics

In this article we explore the metaphors and similes that pre-service elementary teachers use to describe mathematics. Employing qualitative content analysis, we separately coded the metaphors and similes into conceptual categories and analyzed themes that emerged. This grounded theory approach led to the creation of seven categories of metaphors and similes and three overarching themes. Math was viewed as a journey, a puzzle, a personal experience, a creative process, an algorithm, infinite, and an embodied process. Pre-service elementary teachers viewed mathematics as a process that takes effort. Overall, mathematics is a positive experience for them. In addition, mathematics involves fitting …

Cultivating Mathematics Teacher Educators’ Hearts, Critical Consciousness, And Professional Praxis Through Book Study, Mary Raygoza, Missy D. Cosby, Sheila Orr, Barbara King, Justin T. Burris, Siddhi Soni

Journal of Humanistic Mathematics

At a time when executive orders and state legislation are attempting to ban practices promoting equity, belonging, and social justice from education, specifically STEM education, in the United States, mathematics teacher educators (MTEs) remain committed to humanizing mathematics teaching and learning practices and seek opportunities to learn how to adhere to their convictions while preparing mathematics teachers for the classroom. This paper offers reflections and considerations for how the authors engaged interested MTEs to shift or strengthen their individual and collective professional praxis through a book study. Specifically, we examine the design (the what) and process (the how) of a …

Piracy, Terrorism, And The Law: Differential Equations In Hostage Situations, Gabriel Hallevy

Journal of Humanistic Mathematics

Pirates have taken the crew of an American ship hostage. They promise to release the hostages only if another pirate who is held in an American prison for commission of piracy crimes against American citizens, is released. Should the U.S. government enter into negotiations with them? Should they send armed forces and risk the hostages? Should they release the prisoner immediately and unconditionally? The article models and analyzes possible policies regarding sensitive situations involving hostages and other related risks using differential equations. The solutions are surprisingly simple, but not necessarily intuitive. Our analysis aims to demonstrate how powerful mathematics is …

Grationality, With A Spoon, L. Jeneva Clark

Journal of Humanistic Mathematics

I introduced grationality at a 2025 sectional meeting of the Mathematical Association of America to install a handle on a concept akin to rationality of numbers, but in a geometric context. More specifically, we define a nice n-gon to be a regular n-gon with side lengths that are natural numbers; then a number n is grational if and only if there exists a nice n-gon such that its area equals the sum of areas of n congruent nice n-gons. In this paper I offer several examples of grational and non-grational numbers, followed by theorems about how the grationality of a …

A Method For Folding Origami Rectilinear Polygon Extrusions, Everett L. Jin

Journal of Humanistic Mathematics

We present a method for generating crease patterns for folding any rectilinear polygon extrusion with a specified uniform minimum edge-to-edge distance, using a rectangular sheet of paper. We demonstrate that the resulting models are efficient and watertight. In addition, they achieve optimal efficiency, meaning they attain the smallest possible scale factor from the original sheet of paper to the folded rectilinear polygon extrusion. Finally, we provide a code implementation of the method. Our study not only facilitates crease pattern design for origami artists but also offers an innovative, art-driven pedagogical tool for inspiring interest in mathematics.

The Set Card Game And Partitions Into Maximal Caps: A Partial Difference Sets Approach, John Polhill

Journal of Humanistic Mathematics

More specifically, we revisit the problem of determining the maximum number of cards that can be dealt in the SET® card game without any matches, which is well known to be equivalent to the problem of determining the size of a maximal cap in the affine space AG(4,3). We present a new approach to the problem by using partial difference sets, a method that is equivalent to using strongly regular graphs with a regular automorphism group. The paper includes several possible avenues for future investigations on how partial difference sets might be used in related problems.

Manipulating Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Technological Behaviour Of Pellets Containing Dried Green Crop, Christian Furll

IGC Proceedings (1977-2023)

Pelleted dried green crop presents essential advantages compared to chaff and meal as processing forms. Normally, the solidity of the pellets does not exceed the values required by animal feeding. Abrasion resulting from turnover processes is at present too high, particularly for the discharge of bins. Belt conveyors, vibrating conveyors, and bucket elevators are suitable to convey pellets. Storage of pellets over long periods has to be done by respecting prescribed climate conditions. Zones with excessive portion of abraded par­ticles in the storing pile are a preferred cause for self-heating. Slit-type dosing units as well as dosing units equipped with …

Results Of Comparative Investigations Into The Chevving And Ruminating Activities Of The Dairy Cow Fed Dried Forage From Grass And Leguminous Crops, B Piatkowski, S Nagel

IGC Proceedings (1977-2023)

The chewing and ruminating activities were studied of dairy cows fed grass, alfalfa, and straw of different physical forms. An electronic­ally controlled measuring device was applied. When feeding 8 kg of grass hay (32 % crude fibre in dry matter), the ruminating time was 5: 24 and 1 :49 hours (20,712 and 6,982 ruminat­ing movements) for chopped and ground + pelleted forages, respectively. It declined from 1 : 49 to 0: 0 l hours (from 6,929 to 70 move­ments) when hot-air dried alfalfa (23 % crude fibre) was fed in chopped and ground + pelleted forms, respectively. The ruminating time …

Feed Efficiency In Dairy Cows Of Roughages Preserved And Treated In Different Ways, M Zausch, E Boldt

IGC Proceedings (1977-2023)

Trials were conducted with dairy cows to investigate the feed efficiency of grass-clover mixture (wilted silage, silage made of fresh material with addition of foDTiic acid, artifi­cially dried forage, pellets with varying portions of straw). The results obtained allow to draw the following conclusions:

As regards dry matter intake, digestibility, and feed efficiency, grass-dover for wilted silage should be wilted to give a OM content not exceeding 40 %.

Pelleting artificially dried grass-clover mix­ture and its use in mixed rations together with other separately pelleted components should be avoided.

The best feed efficiency is reached when dried grass-clover is converted …

The Influence Of Dried And Ensiled Grass On Rumen Fermen­Tation, J Voigt, B Piatkowski

IGC Proceedings (1977-2023)

Rumen-fistulated cows were used to study the influence of the forage preservation technique on rumen fermentation and holdup time of the feed in the rumen. Cocksfoot (Dactylis glomerata) preserved as wilted silage or dried green crop was fed in the following variants: wilted silage alone; wilted silage + sugar beet + protein supplement; dried green crop alone; dried green crop + sugar beet + protein supplement. As compared with dried green crop, the shares of true protein and sugar in wilted silage were reduced from 9.8 • to 6.4 '.'I􀉧 and from 7.7 to 1.8 %in DM, respectively. In comparison …

Changes In Feeding Value Of Preserved Grass And Legumes By The Action Of High Temperatures, R Prym, F Weissbach

IGC Proceedings (1977-2023)

High temperatures acting on grass and legumes during preservation and storage, cause nutrient digestibility to deteriorate. Protein digestibility is likely to be most strongly affected. Digest­ibility measurements were performed on sheep to estimate the extent of heat damage suffered by dried green forage and silages. Various laboratory methods were applied for record­ing. such damage. The detennination of the acid-detergent insoluble crude protein portion proved a very suitable approach.

Growth And Nitrogen Retention Of Lambs Fed Alfalfa Dehy­Drated At Different Temperatures, H K. Goering

IGC Proceedings (1977-2023)

Alfalfa was dried at four temperatures ranging from 60 to 180 °C in two experiments to evaluate the effect on composition, diet di­gestibility, and growth by lambs. In Experi­ment I, the alfalfa was supplemented with 0.6 % salt and pelleted. In Experiment 2, alfalfa was supplemented with 24.4 % starch, 18.5% straw, 6% cane molasses, 0.5% sodium phosphate, and 0.6 % salt so that total nitrogen intake was not in excess of the protein require­ment for growth of the lambs. Cell wall, acid­detergent fiber, lignin, acid-detergent insoluble nitrogen, and pepsin insoluble nitrogen in­creased in the alfalfa dried at 180 °C. …

Non-Mechanical Field Losses In Wilting Grasses As Influenced By Different Factors, G Rucker, O Knabe

IGC Proceedings (1977-2023)

When wilting grasses, non-mechanical field losses of different extent may occur. The main factors influencing the extent of losses were: water content at cutting time, drying rate, temperature, amount of rain, swath den­sity, and content of water-soluble carbohy­drates in the crop.

The Effect Of Mechanical, Thermal And Chemical Treatment On The Loss Of Water From Cut Leaves Of Grasses, Colin Edward Harris

IGC Proceedings (1977-2023)

Laboratory experiments have demonstrated that cut grass -leaves have a high resistance to water loss, probably largely due to the imper­meability of the surface cuticle to water vapour. This resistance can be reduced and drying rate increased by thermal and mechanical treatment, and by exposure to the vapour of boiling petroleum ether. The effectiveness of formic acid and tri-n-butyl phosphate suggests the possibility of using chemicals to increase the drying rate of grass crops cut for hay and dried in the field.

Measures For Increasing The Efficiency Of Hot-Air Drying Of Forage, Siegfried Prufer, Gerd Neubert

IGC Proceedings (1977-2023)

In the GDR, the drying of wilted green forage as well as of whole plants of cereals and grain maize considerably improves the effi­ciency of hot-air drying as a whole. The proc­essing of wilted crop and the inclusion of whole-plant drying in the drying pattern cause the throughput to increase by 30 to 50% and fuel consurnption per ton of dried crop to de­crease by up to 50 %, in comparison with drying of fresh green forage containing 15 to 18 % dry matter. Hot-air drying is particularly suitable for feed production along industrial lines. -Being but little dependent on …

Gdr Standard Plant For Producing Feed Pellets On Straw Basis, Gerheard Schmidt

IGC Proceedings (1977-2023)

Following the international trend, livestock production units are growing in size. Straw, a major feed reserve, must be effectively utilized to meet the growing roughage requirements, especially of ruminants. Therefore, in the GDR a standard feed pelleting plant (type GF A) was developed and put to commercial production. The various machines and equipment em­ployed in the different stages of the GFA pellet­ing technology are explained in detail. The use of that standard feed pelleting plant shows the advantages of processing straw for semi-finished and finished feeds.

The Efficiency Of Producing And Feeding Complete-Ration Feed Briquets Containing Forage Chop, G V. Blagoveshcheski, V M. Sokolov

IGC Proceedings (1977-2023)

Production of forage chop from a clover­timothy mixture is efficient when harvesting the forage between the shooting of clover (35 to 40 cm stand height) and mid-flowering. For high-temperature drying, each vegetative stage of the plants requires a clearly defined regime. When establishing formulas for com­plete-ration feed briquets containing clover­timoihy chop harvested before clover budding, the protein/carbohydrate ratio must be bal­anced by supplementing the ration with 30 p.c. barley meal and 29 p.c. straw; when the mix­ture was harvested during budding, phos­phorus supplementation (one p.c. monocal­cium phosphate) is necessary, whilst the mix­ture harvested during flowering has to be supplemented with …

The Production Of Dry Feeds From Straw And Green Forage In The Gdr, Fritz Berg

IGC Proceedings (1977-2023)

In the GDR, at present about 9% of the feed energy requirement of cattle is covered by dry feeds, above all mechanically processed and chemically treated straw as well as dried green forages. This share is expected to rise to 15 % in forthcoming years. On the basis of technological fundamentals devised by animal nutritionists, corresponding production processes are being developed and perfected. They allow to convert the feedstuffs into a physical and chemical form favourable to high intake; in addition, the feeding value of high-fibre feedstuffs is improved. In this way, the feedstuffs are fed in favourable com­bination as …

Evaluation And Determination Off Actors Defining The Length Of Thin-Stalked Green Forage Chop, Peter Szendro

IGC Proceedings (1977-2023)

A more exact analysis of the length distribution of chopped material from thin-stalked green forage crops provides more information for the further processing of this material and for comparing the quality of work of the different technologies. Material cut into longer and less homoge­neous chop with heavier destruction of the green plant particles shows properties more suitable for further processing than chop harvested with a self-propelled precision-chop forage harvester. In consideration of the special importance of the questions discussed it seems advisable to continue the experiments and to perform them under production conditions as well; the results thus obtained will …

Organization Of Wilted Silage Production Along Industrial Lines In The Selbelang Inter-Farm Cooperative Crop Produc­Tion Division, Hunter Watzke, Karl Bachmann

IGC Proceedings (1977-2023)

The production of high-quality wilted silages on the basis of highly efficient machines and facilities for harvesting and preservation in the Selbelang inter-farm cooperative crop pro­duction division (KAP) is determined by the use of industrial methods of production. Ob­servance of optimum spans for harvesting forage to be used for the production of wilted silage, and the full utilization of machinery and facilities at rising levels of labour pro­ductivity and declining cost are achieved by way of complex and shift employment of machines, facilities, and workers. The size of machine complexes and their performance are dependent on the shape, equipment and …

Possibilities Of Ensiling Meadow Grass With Different Water Content, Roman Moraczewski, Helena Jurkiewicz

IGC Proceedings (1977-2023)

The paper involves results of investigations into the influence of various methods of grass preservation, different cutting times, and dif­Jerent water contents on the nutrient and min­eral levels in the silage. These results show good possibilities of preserving meadow grass by ensiling. Silage fodder has higher contents of crude protein, crude fibre, crude fat, and ash constituents than are found in hay dried under optimum conditions.

Material And Processing Characteristics Of Grasses And Grass Silages, Manfred Muller, Georg Otto

IGC Proceedings (1977-2023)

Material and processing characteristics are essential initial values for planning of proce­dures in industrialized crop production. From the technological stages and process sequences from grass mowing to removing the silage, the following key operations can be derived: chop­ping,. compressing, storing, and removing. For adequate planning of procedures it is necessary to determine the quantitative relations between the essential factors: chopper throughput, pro­portion of short chop, crude fibre content, and relative final density. A relation suitable for practical application and providing sufficient accuracy is established for estimating the mean dry matter content of a trailer load. If high­quality silage is to …

Comparison Of Three Techniques Of Forage Conservation, Tereza Kotapska, Tadeusz Olszewski

IGC Proceedings (1977-2023)

At the Instytut Mechanizacji i Elektryfikacji Rolnictwa technological trials have been per­formed on green forage conservation under plastic sheeting using round formers from the Italian manufacturers Frigieri, a silage press from the French firm Kuhn, and portable seg­ments of Polish production for the erection clamp silos. The trials covered the operating quality of the equipment and the evaluation of silage quality. During the trials, the performance of the equipment on erecting the silos and specific labour expenditure were established. In addi­tion, an economic rating was made of the ensiling process and of the general suitability of the above methods for …

Losses And Stability Of Silage In Dependence On The Degree Of Air Influence, G Weise, H Rettig, G Suckow

IGC Proceedings (1977-2023)

On the basis of model concepts of physical gas exchange, a method has been developed for studying the complex relations existing be­tween the parameters indicating ensilability and the specific local conditions for silage making (degree of anaerobiosis). Conclusions are drawn as to quantitative relations between the depth of the peripheral layers of a silage stock that are endangered by air, the initial density of the silage material, and the sealing of the silage top during the filling and storage periods. Therefrom, certain thresh­olds can be derived for minimum filling height per day as depending on the initial density of the …

Factors Influencing The Formation Of Effluent In Forage Ensiling, G Peters, F Weissbach

IGC Proceedings (1977-2023)

The amount of effluent formed in ensiling forage crops depends, above all, on the dry matter content of the initial material, on the pressure exerted on the feed stock, and on the kind of crop ensiled. Expected values of effluent a­mount were derived from model experiments and calculations. Adequate wilting of suitable forage crops will allow to reduce or prevent effluent formation. The degree of wilting re­quired depends on the height of the feed stock and on the kind of silo used. The limit of 30 % DM in initial material, so far generally accepted for effluent formation, only applies …

Wilted Silage Production For The Supply Of Large Cattle Populations, Wilhelm Schwandt

IGC Proceedings (1977-2023)

For supplying large cattle populations with high-quality roughage it is necessary to make available big forage batches of good and large­ly uniform quality. From 4,675 hectares of seed­ed grassland, the ZBE Pflanzenproduktion Ferdinandshof(Ferdinandshofinter-farmestab­lishment for crop production) every year pro­duce in good quality more than 80,000 tons of wilted silage. The material and technical basis of this forage production along industrial lines consists of powerful machine systems that are operated in multi-machine complexes, the oper­ators doing shift work.

Fundamentals Of Technique For The Employment Of Formic Acid In Ensiling Of Green Forage, O Knabe, E Muller

IGC Proceedings (1977-2023)

A model was used to work out fundamentals of technique for the employment of formic acid in ensiling of wilted green· forage under industry-like conditions of production. From the parameters: result of preservation, ex­tent of dry matter losses, costs, and profit, the optimum length of the wilting phase in the field and the usefulness of combining the ensil­ing of wilted green forage with the employment of formic acid have been determined. The following practice is recommended for optimum planning of the technique: field curing of green forage for two days followed by preservation either as wilted silage or with admixture …