Magic Circles in the Arbelos

In the arbelos three simple circles are constructed on which the tangency points for three circle chains, all with Archimedes’ circle as a common starting point, are situated. In relation to this setting, some algebraic formulae and remarks are presented. The development of the ideas and the relations that were “discovered” were strongly mediated by the use of dynamic geometry software

Conceptual and procedural approaches to mathematics in the engineering curriculum : student conceptions and performance

BACKGROUND : Demands by engineering faculties of mathematics departments have traditionally been for teaching computational skills while also expecting analytic and creative knowledge-based skills. We report on a project between two institutions, one in South Africa and one in Sweden, that investigated whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than the traditional more procedurally oriented way of teaching. PURPOSE (HYPOTHESIS) : We focus on how second-year engineering students respond to the conceptual-procedural distinction, comparing performance and confidence between Swedish and South African groups of students in answering conceptual and procedural mathematics problems. We also compare these students’ conceptions on the role of conceptual and procedural mathematics problems within and outside their mathematics studies. DESIGN/METHOD : An instrument consisting of procedural and conceptual items as well as items on student opinions on the roles of the different types of knowledge in their studies was conducted with groups of second-year engineering students at two universities, one in each country. RESULTS : Although differences between the two countries are small, Swedish students see procedural items to be more common in their mathematics studies while the South African students find both conceptual and procedural items common; the latter group see the conceptually oriented items as more common in their studies outside the mathematics courses. CONCLUSIONS : Students view mathematics as procedural. Conceptual mathematics is seen as relevant outside mathematics. The use of mathematics in other subjects within engineering education can be experienced differently by students from different institutions, indicating that the same type of education can handle the application of mathematics in different ways in different institutions.http://onlinelibrary.wiley.com/journal/10.1002/(ISSN)2168-9830hb201

Conceptual or procedural mathematics for engineering students – views of two qualified engineers from two countries

This study forms part of a collaboration project between universities in South Africa and Sweden in which we investigate whether the emphasis in undergraduate mathematics courses for engineering students would benefit from being more conceptually oriented than a traditional more procedurally oriented way of teaching. In this paper, we report in some detail from two interviews with professional engineers, selected to represent two different ‘poles’ of engineering work. The aim was to explore different kinds of arguments regarding the role of mathematics in engineering work, as well as some common across contexts. Both interviewees feel that conceptual mathematics is more important for engineering work, although the role of the procedural aspect was seen by one of the interviewees also to be important, but in a very intricate way.http://www.tandfonline.com/loi/tmes202016-11-30hb201

Conceptual and procedural approaches to mathematics in the engineering curriculum – comparing views of junior and senior engineering students in two countries

One challenge for an optimal design of the mathematical components in engineering education curricula is to understand how the procedural and conceptual dimensions of mathematical work can be matched with different demands and contexts from the education and practice of engineers. The focus in this paper is on how engineering students respond to the conceptual-procedural distinction, comparing performance and confidence between second and fourth year groups of students in their answers to a questionnaire comprising conceptually and procedurally focused mathematics problems. We also compare these students’ conceptions on the role of conceptual and procedural mathematics problems within and outside their mathematics studies. Our data suggest that when mathematical knowledge is being recontextualised to engineering subjects or engineering design, a conceptual approach to mathematics is more essential than a procedural approach; working within the mathematical domain, however, the procedural aspects of mathematics are as essential as the conceptual aspects.http://www.ejmste.com/am2017Mathematics and Applied Mathematic

An experimental model for studying claw lesions in growing female pigs

Problems with claw lesions leading to lameness are a growing concern in pig production. However, the causes and development of claw lesions are poorly understood and studies on prevention of claw lesion problems in gifts and sows are limited.This study tested a new experimental model which facilitates evaluation of the impact of different risk factors on pig feet lesions.The model consisted of using young gilts with a well-known background and promoting traumatic claw lesions for study purposes by increasing social and agonistic activity through regrouping on concrete flooring. Then claw lesions were assessed systematically and objectively on feet after slaughter. To test the model, two levels of exposure to concrete flooring were compared; normal activity in groups of gifts (no regrouping=NR) and increased activity in groups of gifts by performing several regroupings (repeated regrouping=RR).A total of 72 gilts (pairs of litter mates) in two batches, aged 4 months, were randomly distributed to the two treatments (NR and RR) in group pens (3 gilts per pen) with concrete flooring. The gilts were given approximately 200 g of straw per gilt every day. At 8, 9 and 10 months of age, half the gilts (36 animals) were regrouped with each other. At 11 months of age, all gifts in both treatments were slaughtered and the left rear foot from each was removed and collected for detailed studies of claw lesions. Lesions of the heel, transition heel/toe, white line, wall and toe and over-growth of the heel were assessed on the outer and inner digit. Blind scoring of claw lesions on a scale from 0 to 3 was carried out in laboratory conditions on cleaned claws. Body lesions were also blind-scored on a scale from 0 to 3 one week after the third regrouping.The results showed claw lesions on the soft and hard horn of the claws and significantly (p = 0.004) higher claw lesion score in RR gifts (0.40) than in NR gilts (0.23).It was concluded that as expected, regrouping gifts on concrete flooring resulted in both more numerous and more severe claw lesions than ungrouped gilts. Likewise, body lesion score was significantly (p < 0.001) higher in RR gilts (1.71) than NR gilts (0.46).It was also concluded that the proposed model could be a successful experimental design for challenging different risk factors, e.g. flooring and management, for development of claw lesions in pigs. (C) 2015 Elsevier B.V. All rights reserved

Kinematic gait characteristics of straight line walk in clinically sound dairy cows

The aim of this study is to describe the kinematic gait characteristics of straight line walk in clinically sound dairy cows using body mounted Inertial Measurement Units (IMUs) at multiple anatomical locations. The temporal parameters used are speed and non-speed normalized stance duration, bipedal and tripedal support durations, maximal protraction and retraction angles of the distal limbs and vertical displacement curves of the upper body. Gait analysis was performed by letting 17 dairy cows walk in a straight line at their own chosen pace while equipped with IMU sensors on tubera sacrale, left and right tuber coxae (LTC and RTC), back, withers, head, neck and all four lower limbs. Data intervals with stride by stride regularity were selected based on video data. For temporal parameters, the median was calculated and 95% confidence intervals (CI) were estimated based on linear mixed model (LMM) analysis, while for limb and vertical displacement curves, the median and most typical curves were calculated. The temporal parameters and distal limb angles showed consistent results with low variance and LMM analysis showed non-overlapping CI for all temporal parameters. The distal limb angle curves showed a larger and steeper retraction angle range for the distal front limbs compared with the hind limbs. The vertical displacement curves of the sacrum, withers, LTC and RTC showed a consistent sinusoidal pattern while the head, back and collar curves were less consistent and showed more variation between and within cows. This kinematic description might allow to objectively differentiate between normal and lame gait in the future and determine the best anatomical location for sensor attachment for lameness detection purposes

Hur fungerar olika gummigolv i grisningsboxen praktiskt och hur är suggans liggbeteende på gummi- jämfört med betonggolv?

Gummigolv på den fasta betongytan installerades i ett antal grisningsboxar med syfte att förbättra djurhälsa och komfort för både smågrisar och suggor. I detta Fakta-blad presenteras erfarenheter från de testade gummigolven samt resultat från suggornas beteende i jämförelse med betonggolv. Totalt testades och jämfördes tre olika gummimaterial i grisningsboxarna under fem grisningsomgångar. Hur lång tid suggorna stod eller låg och var suggorna befann sig i grisningsboxen studerades med hjälp av dygnsvisa videoinspelningar ca 1 vecka respektive 3 veckor efter grisningen. Sammanfattningsvis konstaterades att suggornas liggbeteende inte påverkades negativt av gummimaterialen, snarare tvärtom. Den mjukare gummimattan bedömdes som bäst ur komfortsynpunkt. Hållbarheten hos gummimassabeläggningen var inte tillräckligt bra och den hårdare gummimattan upplevdes som hal vid grisningen för både sugga och personal

Fiberströ till mjölkkor – effekt på djurvälfärd, djurhälsa, mjölkkvalitet och kostnaden för strömedel

Genom att separera gödseln får man gödselfiber (fiberströ) som kan användas som strömedel till mjölkkorna. I denna studie jämförde vi 17 gårdar som använde fiberströ med 17 gårdar som använde såg-/kutterspån som strömedel i liggbås till mjölkkor. Fiberströ jämfört med såg-/kutterspån påverkade inte mjölkmängd, celltal i tankmjölk, djurvälfärd eller djurhälsa förutom att klövhälsan var bättre eftersom totala anmärkningar, klöveksem och klövsulesår var lägre. Totalantalet bakterier var högre i oanvänt fiberströ och i fiberströ från liggbåsen än för såg-/kutterspån men i tankmjölken var det ingen skillnad. Kostnaden för fiberströ varierade för gårdarna beroende på hur mycket fiberströ som producerades

An experimental model for studying claw lesions in growing female pigs

Problems with claw lesions leading to lameness are a growing concern in pig production. However, the causes and development of claw lesions are poorly understood and studies on prevention of claw lesion problems in gifts and sows are limited.This study tested a new experimental model which facilitates evaluation of the impact of different risk factors on pig feet lesions.The model consisted of using young gilts with a well-known background and promoting traumatic claw lesions for study purposes by increasing social and agonistic activity through regrouping on concrete flooring. Then claw lesions were assessed systematically and objectively on feet after slaughter. To test the model, two levels of exposure to concrete flooring were compared; normal activity in groups of gifts (no regrouping=NR) and increased activity in groups of gifts by performing several regroupings (repeated regrouping=RR).A total of 72 gilts (pairs of litter mates) in two batches, aged 4 months, were randomly distributed to the two treatments (NR and RR) in group pens (3 gilts per pen) with concrete flooring. The gilts were given approximately 200 g of straw per gilt every day. At 8, 9 and 10 months of age, half the gilts (36 animals) were regrouped with each other. At 11 months of age, all gifts in both treatments were slaughtered and the left rear foot from each was removed and collected for detailed studies of claw lesions. Lesions of the heel, transition heel/toe, white line, wall and toe and over-growth of the heel were assessed on the outer and inner digit. Blind scoring of claw lesions on a scale from 0 to 3 was carried out in laboratory conditions on cleaned claws. Body lesions were also blind-scored on a scale from 0 to 3 one week after the third regrouping.The results showed claw lesions on the soft and hard horn of the claws and significantly (p = 0.004) higher claw lesion score in RR gifts (0.40) than in NR gilts (0.23).It was concluded that as expected, regrouping gifts on concrete flooring resulted in both more numerous and more severe claw lesions than ungrouped gilts. Likewise, body lesion score was significantly (p < 0.001) higher in RR gilts (1.71) than NR gilts (0.46).It was also concluded that the proposed model could be a successful experimental design for challenging different risk factors, e.g. flooring and management, for development of claw lesions in pigs. (C) 2015 Elsevier B.V. All rights reserved