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  • 1.
    Abrahamsson, Emma
    et al.
    Jönköping University.
    Edlund, Rebecca
    Jönköping University.
    Tal i bråkform och tallinjen som hjälpmedel: En litteraturstudie om elevers svårigheter med tal i bråkform och en jämförelse av tallinjen och areamodeller2023Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
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  • 2.
    Abrahamsson, Fredrik
    Jönköping University, School of Engineering, JTH, Mathematics.
    Strong L1 convergence to equilibrium without entropy conditions for the Boltzmann equation1999In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 24, no 7-8, p. 1501-1535Article in journal (Refereed)
    Abstract [en]

    The main result of this paper is that for the har dsphere kernel, the solution of the spatially homogenous Boltzmann equation converges strongly in L1 to equilibrium given that the initial data f0 belongs to L1(R3,(1+v^2)dv). This was previously known to be true with the additional assumption that f0logf0 belonged to L1(R3), which corresponds to bounded initial entropy.

  • 3.
    Abrahamsson, Gustav
    Jönköping University, School of Education and Communication.
    Elevers statistiska slutsatser: En kvalitativ studie som undersöker hur elever utan formell statistisk träning drar slutsatser utifrån statistiska data2022Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    This study examines how students without formal statistics draw conclusions based on statistical data. The study refers to how pupil draw conclusions based on existing data, reason within the subject statistics and which aspects pupil may have difficulty in perceiving. To investigate this, the following research question were used: How do Swedish students without formal statistical training express informal statistical inferences? 

      

    This study is based on informal statistical inference which means that how to draw conclusions based on already existing data about what will happen in the next step. To collect data for this study, the data collection method focusgroup interviews with students in year 5 was used. The collected data were compiled, analyzed and compared with previous research. The results showed that students have difficulty drawing conclusions based on the existing data because they do not see it in a larger context.

     

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  • 4. Abrahamsson, Gustav
    et al.
    Säleby, William
    Att utveckla elevers statistikkunskaper: En litteraturstudie om undervisningsstrategier i statistik2021Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
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  • 5.
    Abramsson, Matilda
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Elevers förståelse av likhetstecknet: En studie i årskurs 32016Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The aim of the study is to explore the understanding of the equal sign and how the teaching about the equal sign among third grade students can be varied to be as effective as possible.  The aim will be answered trough the questions: what patterns of variation can the studied students meet and what critical aspects have the students identified. Patterns of variation means that what is critical in the teaching should be varied to become visible. Critical aspects is what students need to identify to understand what should be learned. The foundation of the study is the Variation Theory, where patterns of variation and critical aspects are central concepts.

    The observations were accomplished during a third grade lesson and six students were selected for interviews about the equal sign. The result of the study shows that the students met six critical aspects during the lesson. For every critical aspect there were one or several patterns of variation that was exposed to the students. The result also states that the students who were interviewed have a relational and instrumental understanding of the equal sign. The students also have understanding of a critical aspect that they did not meet in the observed lesson, namely that all numbers have to enter in a task. Four out of six students have understanding of the critical aspect that there should be equivalence in a chain of similarities. The result also show that the students understanding of the equal sign is not dependent of that they meet patterns of variation in the teaching, but that they meet the critical aspects somehow.

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  • 6.
    Akram, Muhammad N.
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Amin, Muhammad
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Economics, Finance and Statistics.
    A new biased estimator for the gamma regression model: Some applications in medical sciences2023In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 52, no 11, p. 3612-3632Article in journal (Refereed)
    Abstract [en]

    The Gamma Regression Model (GRM) has a variety of applications in medical sciences and other disciplines. The results of the GRM may be misleading in the presence of multicollinearity. In this article, a new biased estimator called James-Stein estimator is proposed to reduce the impact of correlated regressors for the GRM. The mean squared error (MSE) properties of the proposed estimator are derived and compared with the existing estimators. We conducted a simulation study and employed the MSE and bias evaluation criterion to judge the proposed estimator’s performance. Finally, two medical dataset are considered to show the benefit of the proposed estimator over existing estimators.

  • 7.
    Akram, Muhammad Nauman
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Amin, Muhammad
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    A new Liu-type estimator for the Inverse Gaussian Regression Model2020In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 90, no 7, p. 1153-1172Article in journal (Refereed)
    Abstract [en]

    The Inverse Gaussian Regression Model (IGRM) is used when the response variable is positively skewed and follows the inverse Gaussian distribution. In this article, we propose a Liu-type estimator to combat multicollinearity in the IGRM. The variance of the Maximum Likelihood Estimator (MLE) is overstated due to the presence of severe multicollinearity. Moreover, some estimation methods are suggested to estimate the optimal value of the shrinkage parameter. The performance of the proposed estimator is compared with the MLE and some other existing estimators in the sense of mean squared error through Monte Carlo simulation and different real-life applications. Under certain conditions, it is concluded that the proposed estimator is superior to the MLE, ridge, and Liu estimator.

  • 8.
    Alheety, M. I.
    et al.
    Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Ramadi, Iraq.
    Månsson, Kristofer
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Kibria, B. M. Golam
    Department of Mathematics and Statistics, Florida International University, Miami, FL, United States.
    A new kind of stochastic restricted biased estimator for logistic regression model2021In: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 48, no 9, p. 1559-1578Article in journal (Refereed)
    Abstract [en]

    In the logistic regression model, the variance of the maximum likelihood estimator is inflated and unstable when the multicollinearity exists in the data. There are several methods available in literature to overcome this problem. We propose a new stochastic restricted biased estimator. We study the statistical properties of the proposed estimator and compare its performance with some existing estimators in the sense of scalar mean squared criterion. An example and a simulation study are provided to illustrate the performance of the proposed estimator. 

  • 9.
    Alheety, Mustafa I.
    et al.
    Univ Anbar, Dept Math, Coll Educ Pure Sci, Ramadi, Iraq..
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Månsson, Kristofer
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Kibria, B. M. Golam
    Florida Int Univ, Dept Math & Stat, Miami, FL 33199 USA..
    Modifed almost unbiased two-parameter estimator for the Poisson regression model with an application to accident data2021In: SORT - Statistics and Operations Research Transactions, ISSN 1696-2281, E-ISSN 2013-8830, Vol. 45, no 2, p. 121-142Article in journal (Refereed)
    Abstract [en]

    Due to the large amount of accidents negatively affecting the wellbeing of the survivors and their families, a substantial amount of research is conducted to determine the causes of road accidents. This type of data come in the form of non-negative integers and may be modelled using the Poisson regression model. Unfortunately, the commonly used maximum likelihood estimator is unstable when the explanatory variables of the Poisson regression model are highly correlated. Therefore, this paper proposes a new almost unbiased estimator which reduces the instability of the maximum likelihood estimator and at the same time produce smaller mean squared error. We study the sta-tistical properties of the proposed estimator and a simulation study has been conducted to compare the performance of the estimators in the smaller mean squared error sense. Finally, Swedish traffic fatality data are analyzed to show the beneft of the proposed method.

  • 10.
    Ali, Abdul Aziz
    et al.
    Linnéuniversitetet, Institutionen för nationalekonomi och statistik (NS).
    Månsson, Kristofer
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Shukur, Ghazi
    Linnéuniversitetet, Institutionen för nationalekonomi och statistik (NS).
    A wavelet-based variance ratio unit root test for a system of equations2020In: Studies in Nonlinear Dynamics and Econometrics, ISSN 1081-1826, E-ISSN 1558-3708, Vol. 24, no 3, p. 1-16, article id 20180005Article in journal (Refereed)
    Abstract [en]

    In this paper, we suggest a unit root test for a system of equations using a spectral variance decomposition method based on the Maximal Overlap Discrete Wavelet Transform. We obtain the limiting distribution of the test statistic and study its small sample properties using Monte Carlo simulations. We find that, for multiple time series of small lengths, the wavelet-based method is robust to size distortions in the presence of cross-sectional dependence. The wavelet-based test is also more powerful than the Cross-sectionally Augmented Im et al. unit root test (Pesaran, M. H. 2007. "A Simple Panel Unit Root Test in the Presence of Cross-section Dependence." Journal of Applied Econometrics 22 (2): 265-312.) for time series with between 20 and 100 observations, using systems of 5 and 10 equations. We demonstrate the usefulness of the test through an application on evaluating the Purchasing Power Parity theory for the Group of 7 countries and find support for the theory, whereas the test by Pesaran (Pesaran, M. H. 2007. "A Simple Panel Unit Root Test in the Presence of Cross-section Dependence." Journal of Applied Econometrics 22 (2): 265-312.) finds no such support. 

  • 11.
    Alka,
    et al.
    Department of Mathematics and Statistics, Banasthali University, Jaipur, Rajasthan, India.
    Rai, Piyush Kant
    Department of Statistics, Banaras Hindu University, Varanasi, Uttar Pradesh, India.
    Qasim, Muhammad
    Department of Statistics & Computer Science, University of Veterinary & Animal Sciences, Lahore, Pakistan.
    Two-step calibration of design weights under two auxiliary variables in sample survey2019In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 89, no 12, p. 2316-2327Article in journal (Refereed)
    Abstract [en]

    Calibration on the available auxiliary variables is widely used to increase the precision of the estimates of parameters. Singh and Sedory [Two-step calibration of design weights in survey sampling. Commun Stat Theory Methods. 2016;45(12):3510–3523.] considered the problem of calibration of design weights under two-step for single auxiliary variable. For a given sample, design weights and calibrated weights are set proportional to each other, in the first step. While, in the second step, the value of proportionality constant is determined on the basis of objectives of individual investigator/user for, for example, to get minimum mean squared error or reduction of bias. In this paper, we have suggested to use two auxiliary variables for two-step calibration of the design weights and compared the results with single auxiliary variable for different sample sizes based on simulated and real-life data set. The simulated and real-life application results show that two-auxiliary variables based two-step calibration estimator outperforms the estimator under single auxiliary variable in terms of minimum mean squared error. 

  • 12.
    Alka, Singh
    et al.
    Banasthali Univ, Dept Math & Stat, Jaipur 304022, Rajasthan, India..
    Rai, Piyush Kant
    Banaras Hindu Univ, Dept Stat, Varanasi 221005, Uttar Pradesh, India..
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Two-Step Calibration Estimator with Double Use of Auxiliary Variable: Method and Application2022In: Journal of the Iranian Statistical Society, ISSN 1726-4057, Vol. 21, no 1, p. 37-54Article in journal (Refereed)
    Abstract [en]

    This article introduces a two-step calibration technique for the inverse relationship between study variable and auxiliary variable along with the double use of the auxiliary variable. In the first step, the calibration weights and design weights are set proportional to each other for a given sample. While in the second step, the constant of proportionality is to be obtained on the basis of some different objectives of the investigation viz. bias reduction or minimum Mean Squared Error (MSE) of the proposed estimator. Many estimators based on inverse relationship between x and y have been already developed and are considered to be special cases of the proposed estimator. Properties of the proposed estimator is discussed in details. Moreover, a simulation study has also been conducted to compare the performance of the proposed estimator under Simple Random Sampling Without Replacement (SRSWOR) and Lahiri-Midzuno (L-M) sampling design in terms of percent relative bias and MSE. The benefits of two-step calibration estimator are also demonstrated using real life data.

  • 13.
    Al-khafaji, Aea
    et al.
    Jönköping University, School of Education and Communication.
    Mutmain, Sonia
    Jönköping University, School of Education and Communication.
    En litteraturstudie om vad forskning pekar ut som möjliga orsaker till elevers missuppfattningar inom algebra: – bokstavssymboler, operationssymboler och prioriteringsregler.2023Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Aritmetik handlar om de fyra räknesätten och innefattar beräkningar och operationer på tal. Algebra är däremot matematikområdet där elever räknar med bokstäver istället för med bara tal. Forskning har visat att när elever arbetar med algebra uppstår vissa missuppfattningar. Syftet med studien var att undersöka vad den matematiska forskningen pekar på som kan vara orsak till att elever har problem med områden av algebra. Denna litteraturstudie baserar sig på matematikdidaktisk forskning. Materialet har analyserats och bearbetats både enskilt och gemensamt utifrån förbestämda urvalskriterier. Det analyserade materialet består av åtta vetenskapliga artiklar, en review-artikel och ett konferensbidrag.

    I den forskning som har analyserats i studien beskrivs det olika anledningar till missuppfattningar med bokstavssymboler, operationssymboler och prioriteringsregler inom algebra. De två oftast nämnda anledningar är att elever saknar väsentliga kunskaper inom aritmetik och saknar en konceptuell kunskap. Några enstaka texter pekade ut läromedel och lärarens förklaringar som möjliga orsaker till elevers missuppfattningar.

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  • 14.
    Almasri, Abdullah
    et al.
    Department of Economics and Statistics, Karlstad University, Karlstad, Sweden.
    Månsson, Kristofer
    Jönköping University, Jönköping International Business School, JIBS, Statistics. Department of Economics and Statistics, Göteborg University, Göteborg, Sweden.
    Sjölander, Pär
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Shukur, Ghazi
    Jönköping University, Jönköping International Business School, JIBS, Statistics. Department of Economics and Statistics, Linnaeus University, Växjö, Sweden.
    A wavelet-based panel unit-root test in the presence of an unknown structural break and cross-sectional dependency, with an application of purchasing power parity theory in developing countries2017In: Applied Economics, ISSN 0003-6846, E-ISSN 1466-4283, Vol. 49, no 21, p. 2096-2105Article in journal (Refereed)
    Abstract [en]

    This article introduces two different non-parametric wavelet-based panel unit-root tests in the presence of unknown structural breaks and cross-sectional dependencies in the data. These tests are compared with a previously suggested non-parametric wavelet test, the parameteric Im-Pesaran and Shin (IPS) test and a Wald type of test. The results from the Monte Carlo simulations clearly show that the new wavelet-ratio tests are superior to the traditional tests both in terms of size and power in panel unit-root tests because of its robustness to cross-section dependency and structural breaks. Based on an empirical Central American panel application, we can, in contrast to previous research (where bias due to structural breaks is simply disregarded), find strong, clear-cut support for purchasing power parity (PPP) in this developing region.

  • 15.
    Almén, Oscar
    et al.
    Jönköping University, School of Education and Communication.
    Thörnow, Johan
    Jönköping University, School of Education and Communication.
    Interaktiva skrivtavlor: Erfarenheter från matematiklärare i Jönköping med omnejd.2010Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Studien har  undersökt matematiklärare på gymnasiet och deras erfarenheter från att använda interaktiva skrivtavlor (Smartboard, Activboard & Teamboard). Åtta lärare har blivit intervjuade i en kvalitativ undersökning med fenomenografiskt fokus.

    Det blir idag allt mer populärt med interaktiva skrivtavlor i svenska skolor. Många skolor har valt att satsa mycket pengar på att installera interaktiva skrivtavlor, trots att det råder delade meningar om huruvida det finns något samband mellan tavlorna och förhöjda elevprestationer. Skolan har under många år haft en hög förväntan på IT. Trots att flera av de undersökta lärarna i studien är positiva så finns det också många negativa erfarenheter att ta lärdom av. Inte minst ifrågasätts hur man infört tekniken på de olika skolorna och vilka intressen som ligger bakom. I studien kan du läsa om goda användningsexempel i matematikundervisningen. Du kan också ta del av de begränsningar som lärare upplever att tavlan har då den används i matematiken. Lärare diskuterar bland annat följande teman; förberedelse, spara och publicera, motivation och skriv- och rithjälp.

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  • 16. Al-Sultani, Zahraa
    Matematikens tal: En kvalitativ intervjustudie om lärarens metoder för att främja elevers muntliga kommunikation i matematikundervisningen2023Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Syftet med studien är att bidra med kunskap kring hur lärare beskriver hur de arbetar med muntlig kommunikation i matematikundervisningen. Vidare består syftet också i att belysa hur lärare upplever att den muntliga kommunikationsförmågan påverkar elevernas lärande i matematikundervisningen. För att komma fram till studiens syfte skall följande frågor besvaras: 

    Vilka metoder använder lärare för att utveckla elevernas kommunikationsförmåga?Hur upplever lärare att den muntliga kommunikationsförmågan påverkar elevernas lärande i matematikundervisning?För att få svar på frågeställningar används en kvalitativ metod med semistrukturerade intervjuer. I studien intervjuades sex behöriga lärare som undervisar i matematikämnet i förskoleklass, låg- och mellanstadiet som har minst fyra års yrkeserfarenhet inom matematikområdet.

    Resultatet visar att lärare använder olika metoder och arbetssätt för att skapa muntlig kommunikation i matematikundervisningen. Alla lärare som deltog i undersökning använder formativt arbetssätt såsom feedback, uppmuntra eleverna att vara resurs för varandra samt att genomföra kamratbedömning som ett sätt att skapa muntlig kommunikation i matematikundervisningen. Resultatet visar också att muntlig kommunikation har en viktig roll för elevernas lärande, där elevernas har möjlighet att utveckla sin förståelse av begrepp och resonemang. Alla lärare i undersökningen betonade att muntlig kommunikation är ett användbart verktyg för att identifiera elevernas individuella behov samt som en grund för att anpassa och utveckla undervisningens metoder.

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  • 17.
    Amin, Muhammad
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Amanullah, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Aslam, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Qasim, Muhammad
    Department of Statistics and Computer Science, University of Veterinary and Animal Sciences, Lahore, Pakistan.
    Influence diagnostics in gamma ridge regression model2019In: Journal of Statistical Computation and Simulation, ISSN 0094-9655, E-ISSN 1563-5163, Vol. 89, no 3, p. 536-556Article in journal (Refereed)
    Abstract [en]

    In this article, we proposed some influence diagnostics for the gamma regression model (GRM) and the gamma ridge regression model (GRRM). We assess the impact of influential observations on the GRM and GRRM estimates by extending the work of Pregibon [Logistic regression diagnostics. Ann Stat. 1981;9:705–724] and Walker and Birch [Influence measures in ridge regression. Technometrics. 1988;30:221–227]. Comparison of both models is made and demonstrated with the help of a simulation study and a real data set. We report some momentous results in detecting the influential observations and their effects on the GRM and GRRM estimates. 

  • 18.
    Amin, Muhammad
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Punjab, Pakistan.
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Afzal, Saima
    Department of Statistics, Bahauddin Zakariya University, Multan, Punjab, Pakistan.
    Naveed, Khalid
    Department of Statistics, Bahauddin Zakariya University, Multan, Punjab, Pakistan.
    New ridge estimators in the inverse Gaussian regression: Monte Carlo simulation and application to chemical data2022In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 51, no 10, p. 6170-6187Article in journal (Refereed)
    Abstract [en]

    In numerous application areas, when the response variable is continuous, positively skewed, and well fitted to the inverse Gaussian distribution, the inverse Gaussian regression model (IGRM) is an effective approach in such scenarios. The problem of multicollinearity is very common in several application areas like chemometrics, biology, finance, and so forth. The effects of multicollinearity can be reduced using the ridge estimator. This research proposes new ridge estimators to address the issue of multicollinearity in the IGRM. The performance of the new estimators is compared with the maximum likelihood estimator and some other existing estimators. The mean square error is used as a performance evaluation criterion. A Monte Carlo simulation study is conducted to assess the performance of the new ridge estimators based on the minimum mean square error criterion. The Monte Carlo simulation results show that the performance of the proposed estimators is better than the available methods. The comparison of proposed ridge estimators is also evaluated using two real chemometrics applications. The results of Monte Carlo simulation and real applications confirmed the superiority of the proposed ridge estimators to other competitor methods.

  • 19.
    Amin, Muhammad
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Statistics. Department of Statistics and Computer Science, University of Veterinary and Animal Sciences, Lahore, Pakistan.
    Amanullah, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Performance of Asar and Genç and Huang and Yang’s Two-Parameter Estimation Methods for the Gamma Regression Model2019In: Iranian Journal of Science and Technology, Transactions A: Science, ISSN 1028-6276, Vol. 43, no 6, p. 2951-2963Article in journal (Refereed)
    Abstract [en]

    This study assesses the performance of two-parameter estimation methods to combat multicollinearity in the Gamma regression model. We derived optimal values for two-parameter estimation methods in the Gamma regression model. Furthermore, we proposed some estimation methods to estimate the shrinkage parameters and these methods improve the efficiency of the two-parameter estimator. We compare the performance of these estimators by means of Monte Carlo simulation study where the mean squared error (MSE) is considered as a performance criterion. Finally, consider a reaction rate data to evaluate the performance of the estimators. The simulation and numerical example results showed that the two-parameter biased estimators have smaller MSE than the maximum likelihood estimator under certain conditions.

  • 20.
    Amin, Muhammad
    et al.
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Qasim, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Amanullah, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Afzal, Saima
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Performance of some ridge estimators for the gamma regression model2020In: Statistical papers, ISSN 0932-5026, E-ISSN 1613-9798, Vol. 61, no 3, p. 997-1026Article in journal (Refereed)
    Abstract [en]

    In this study, we proposed some ridge estimators by considering the work of Månsson (Econ Model 29(2):178–184, 2012), Dorugade (J Assoc Arab Univ Basic Appl Sci 15:94–99, 2014) and some others for the gamma regression model (GRM). The GRM is a special form of the generalized linear model (GLM), where the response variable is positively skewed and well fitted to the gamma distribution. The commonly used method for estimation of the GRM coefficients is the maximum likelihood (ML) estimation method. The ML estimation method perform better, if the explanatory variables are uncorrelated. There are the situations, where the explanatory variables are correlated, then the ML estimation method is incapable to estimate the GRM coefficients. In this situation, some biased estimation methods are proposed and the most popular one is the ridge estimation method. The ridge estimators for the GRM are proposed and compared on the basis of mean squared error (MSE). Moreover, the outperforms of proposed ridge estimators are also calculated. The comparison has done using a Monte Carlo simulation study and two real data sets. Results show that Kibria’s and Månsson and Shukur’s methods are preferred over the ML method. 

  • 21.
    Amin, Muhammad
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Yasin, Ahad
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Amanullah, Muhammad
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Almost unbiased ridge estimator in the gamma regression model2022In: Communications in statistics. Simulation and computation, ISSN 0361-0918, E-ISSN 1532-4141, Vol. 51, no 7, p. 3830-3850Article in journal (Refereed)
    Abstract [en]

    This article introduces the almost unbiased gamma ridge regression estimator (AUGRRE) estimator based on the gamma ridge regression estimator (GRRE). Furthermore, some shrinkage parameters are proposed for the AUGRRE. The performance of the AUGRRE by using different shrinkage parameters is compared with the existing GRRE and maximum likelihood estimator. A Monte Carlo simulation is carried out to assess the performance of the estimators where the bias and mean squared error performance criteria are used. We also used a real-life dataset to demonstrate the benefit of the proposed estimators. The simulation and real-life example results show the superiority of AUGRRE over the GRRE and the maximum likelihood estimator for the gamma regression model with collinear explanatory variables.

  • 22.
    Amin, Muhammad
    et al.
    Department of Statistics, University of Sargodha, Sargodha, Pakistan.
    Ullah, Muhammad Aman
    Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
    Qasim, Muhammad
    Jönköping University, Jönköping International Business School, JIBS, Statistics.
    Diagnostic techniques for the inverse Gaussian regression model2022In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 51, no 8, p. 2552-2564Article in journal (Refereed)
    Abstract [en]

    In this article, we propose some diagnostic techniques for the inverse Gaussian regression model (IGRM), which are appropriate for modeling the response variable that undertakes positively skewed continuous dataset. Moreover, two new diagnostic methods are mainly proposed for the IGRM, which named as covariance ratio (CVR) and Welsch?s distance (WD). The comparison of our proposed methods of influence diagnostics with the existing approaches has been made through Monte Carlo simulation under different factors. In addition, the benefit of the proposed methods is assessed using a real application. Based on the simulation and empirical application results, we observed that the performance of the proposed method is better than the existing methods for detection of influential observations.

  • 23.
    Anderfelt, Filip
    et al.
    Jönköping University, School of Engineering, JTH, Industrial Product Development, Production and Design, JTH, Product design and development (PDD).
    Svensson, Filip
    Jönköping University, School of Engineering, JTH, Industrial Product Development, Production and Design, JTH, Product design and development (PDD).
    Stopp För Mekansiskt vevbord2020Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    ROL Ergo is a company that manufactures and develops height-adjustable tables. Their product line-up consists mainly of electrically operated tables, but also a small-scale of tables where the height is determined by a hand-driven crank.

    One problem with ROL Ergos hand-operated crank table, PR25 2-column 2-stage crank, is the function of stopping the table after 470 mm which is the tables desired stroke. The solution the existing table have, to prevent this from happening, is a plastic stop mounted on top of the table’s outer legs.

    This plastic stop is intended to stop the table when the leg reaches its highest position. The hand crank used to change the height of the table have an integrated torque clutch which is used to prevent that the torque applied to the crank exceeds 4.3 Nm. However, the force applied to the plastic part that is generated by the hand crank is greater than what the plastic part is constructed for. This results in the stop being pushed out of its position and must be mounted back by hand, or in worst case, breaks.

    This report covers the steps taken to find a solution to this problem. Initially, the forces generated by the hand crank in the tables height adjustable system is needed. When these forces were calculated the process of finding concepts and solutions could begin. When a final concept was defined, the solution was verified with simulations and physical tests to ensure the concept’s stop function.

    Through this process the work resulted in a concept where a C formed ring is mounted onto the table’s thread bars. This ensures that the thread bars are prevented to thread further than the desired height. By using results from calculations, simulations and physical tests, the developed concept could be verified to withstand the forces generated by the hand crank in order to stop the table at the desired stroke.

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  • 24.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    A modified Schwarz-Christoffel mapping for regions with piecewise smooth boundaries2008In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 213, no 1, p. 56-70Article in journal (Refereed)
    Abstract [en]

    A method where polygon corners in Schwarz-Christoffel mappings are rounded, is used to construct mappings from the upper half-plane to regions bounded by arbitrary piecewise smooth curves. From a given curve, a polygon is constructed by taking tangents to the curve in a number of carefully chosen so called tangent points. The Schwarz-Christoffel mapping for that polygon is then constructed and modified to round the corners.Since such a modification causes effects on the polygon outside the rounded corners, the parameters in the mapping have to be re-determined. This is done by comparing side-lengths in tangent polygons to the given curve and the curve produced by the modified Schwarz-Christoffel mapping. The set of equations that this comparison gives, can normally be solved using a quasi--Newton method.The resulting function maps the upper half--plane on a region bounded by a curve that apart from possible vertices is smooth, i.e., one time continuously differentiable, that passes through the tangent points on the given curve, has the same direction as the given curve in these points and changes direction monotonically between them. Furthermore, where the original curve has a vertex, the constructed curve has a vertex with the same inner angle.The method is especially useful for unbounded regions with smooth boundary curves that pass infinity as straight lines, such as channels with parallel walls at the ends. These properties are kept in the region produced by the constructed mapping.

  • 25.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Modified Schwarz-Christoffel mappings using approximate curve factors2009In: Journal of Computational and Applied Mathematics, ISSN 0377-0427, E-ISSN 1879-1778, Vol. 233, no 4, p. 1117-1127Article in journal (Refereed)
    Abstract [en]

    The Schwarz–Christoffel mapping from the upper half-plane to a polygonal region in the complex plane is an integral of a product with several factors, where each factor corresponds to a certain vertex in the polygon. Different modifications of the Schwarz–Christoffel mapping in which factors are replaced with the so-called curve factors to achieve polygons with rounded corners are known since long times. Among other requisites, the arguments of a curve factor and its correspondent scl factor must be equal outside some closed interval on the real axis.

    In this paper, the term approximate curve factor is defined such that many of the already known curve factors are included as special cases. Additionally, by alleviating the requisite on the argument from exact to asymptotic equality, new types of curve factors are introduced. While traditional curve factors have a C1 regularity, C regular approximate curve factors can be constructed, resulting in smooth boundary curves when used in conformal mappings.

    Applications include modelling of wave scattering in waveguides. When using approximate curve factors in modified Schwarz–Christoffel mappings, numerical conformal mappings can be constructed that preserve two important properties in the waveguides. First, the direction of the boundary curve can be well controlled, especially towards infinity, where the application requires two straight parallel walls. Second, a smooth (C) boundary curve can be achieved.

  • 26.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Numerical Conformal Mappings for Regions Bounded by Smooth Curves2006Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In many applications, conformal mappings are used to transform twodimensional regions into simpler ones. One such region for which conformal mappings are needed is a channel bounded by continuously differentiable curves. In the applications that have motivated this work, it is important that the region an approximate conformal mapping produces, has this property, but also that the direction of the curve can be controlled, especially in the ends of the channel.

    This thesis treats three different methods for numerically constructing conformal mappings between the upper half–plane or unit circle and a region bounded by a continuously differentiable curve, where the direction of the curve in a number of control points is controlled, exact or approximately.

    The first method is built on an idea by Peter Henrici, where a modified Schwarz–Christoffel mapping maps the upper half–plane conformally on a polygon with rounded corners. His idea is used in an algorithm by which mappings for arbitrary regions, bounded by smooth curves are constructed.

    The second method uses the fact that a Schwarz–Christoffel mapping from the upper half–plane or unit circle to a polygon maps a region Q inside the half–plane or circle, for example a circle with radius less than 1 or a sector in the half–plane, on a region Ω inside the polygon bounded by a smooth curve. Given such a region Ω, we develop methods to find a suitable outer polygon and corresponding Schwarz–Christoffel mapping that gives a mapping from Q to Ω.

    Both these methods use the concept of tangent polygons to numerically determine the coefficients in the mappings.

    Finally, we use one of Don Marshall’s zipper algorithms to construct conformal mappings from the upper half–plane to channels bounded by arbitrary smooth curves, with the additional property that they are parallel straight lines when approaching infinity.

  • 27.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Numerical conformal mappings for waveguides2009Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Acoustic or electro-magnetic scattering in a waveguide with varying direction and cross-section can be re-formulated as a two-dimensional scattering problem, provided that the variations take place in only one dimension at a time. By using the so-called Building Block Method, it is possible to construct the scattering properties of a combination of scatterers when the properties of each scatterer are known. Hence, variations in the waveguide geometry or in the boundary conditions can be treated one at a time.

    Using the Building Block Method, the problem takes the form of the Helmholtz equation for stationary waves in a waveguide of infinite length and with smoothly varying geometry and boundary conditions. A conformal mapping is used to transform the problem into a corresponding problem in a straight horizontal waveguide, and by expanding the field in Fourier trigonometric series, the problem can be reformulated as an infinite-dimensional ordinary differential equation. From this, numerically solvable differential equations for the reflection and transmission operators are derived.

    To be applicable in the Building Block Method, the numerical conformal mapping must be constructed such that the direction of the boundary curve can be controlled. At the channel ends, it is an indispensable requirement, that the two boundary curves are (at least) asymptotically parallel and straight. Furthermore, to achieve bounded operators in the differential equations, the boundary curves must satisfy different regularity conditions, depending on the boundary conditions.

    In this work, several methods to accomplish such conformal mappings are presented. The Schwarz–Christoffel mapping, which is a natural starting point and for which also efficient numerical software exists, can be modified in different ways in order to achieve polygons with rounded corners. We present algorithms by which the parameters in the mappings can be determined after such modifications. We show also how the unmodified Schwarz–Christoffel mapping can be used for regions with a smooth boundary. This is done by constructing an appropriate outer polygon to the considered region.

    Finally, we introduce one method that is not Schwarz–Christoffel-related, by showing how one of the so-called zipper algorithms can be used for waveguides.

  • 28.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Numerical Conformal Mappings for Waveguides2010In: Computational Mathematics: Theory, Methods and Applications, Hauppauge NY, USA: Nova Science Publishers , 2010Chapter in book (Other (popular science, discussion, etc.))
    Abstract [en]

    Acoustic or electro-magnetic scattering in a waveguide with  varying direction and cross-section can, if the variations takes  place in only one dimension at a time be re-formulated as a  two-dimensional scattering problem. By using the so-called  Building Block Method, it is possible to construct the  scattering properties of a combination of scatterers when the  properties of each scatterer are known. Hence, variations in the  waveguide geometry or in the boundary conditions can be treated   one at a time.  We consider in this work acoustic scattering, but the same  techniques can be used for both electro-magnetic and some quantum  scattering problems.  By suppressing the time dependence and by using the Building Block  Method, the problem takes the form of the Helmholtz equation in a  waveguide of infinite length and with smoothly varying geometry and  boundary conditions.  A conformal mapping is used to transform the  problem into a corresponding problem in a straight horizontal  channel, and by expanding the field in Fourier trigonometric series,  the problem can be reformulated as an infinite-dimensional ordinary  differential equation. From this, numerically solvable differential  equations for the reflection and transmission operators are  derived.  To be applicable in the Building Block Method, the numerical  conformal mapping must be constructed such that the direction of the  boundary curve can be controlled. At the channel ends, it is an  indispensable requirement, that the two boundary curves are (at least)  asymptotically parallel and straight. Furthermore, to achieve  bounded operators in the differential equations, the boundary curves  must satisfy different regularity conditions, depending on the  properties of the boundary.  Several methods to accomplish such conformal mappings are  presented. The Schwarz-Christoffel mapping, which is a natural starting point and for which  also efficient numerical software exists, can be modified in  different ways to round the polygon corners, and we show algorithms  by which the parameter problem can be solved after such  modifications. It is also possible to use the unmodified Schwarz-Christoffel mapping for  regions with smooth boundary, by constructing an appropriate outer  polygon to the considered region.  Finally, we show how a so-called  zipper algorithm can be used for waveguides.

  • 29.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    On the curvature of an inner curve in a Schwarz--Christoffel mapping2009In: Further Progress in Analysis: Proceedings of the 6th International ISAAC Congress, Ankara, Turkey, 2007, World Scientific , 2009, p. 281-290Conference paper (Refereed)
    Abstract [en]

    In the so called outer polygon method, an approximative conformal mapping for a given simply connected region Ω is constructed using a Schwarz–Christoffel mapping for an outer polygon, a polygonal region of which Ω is a subset. The resulting region is then bounded by a C-curve, which among other things means that its curvature is bounded.In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz–Christoffel mapping from R, the unit disk or upper half–plane, to a polygonal region P of a curve inside R. From the Schwarz–Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.

  • 30.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Schwarz-Christoffel Mappings for Nonpolygonal Regions2008In: SIAM Journal on Scientific Computing, ISSN 1064-8275, E-ISSN 1095-7197, Vol. 31, no 1, p. 94-111Article in journal (Refereed)
    Abstract [en]

    An approximate conformal mapping for an arbitrary region Ω bounded by a smooth curve Γ is constructed using the Schwarz–Christoffel mapping for a polygonal region in which Ω is embedded. An algorithm for finding this so-called outer polygon is presented. The resulting function is a conformal mapping from the upper half-plane or the unit disk to a region R, approximately equal to Ω. R is bounded by a C∞ curve, and since the mapping function originates from the Schwarz–Christoffel mapping and tangent polygons are used to determine it, important properties of Γ such as direction, linear asymptotes, and inflexion points are preserved in the boundary of R. The method makes extensive use of existing Schwarz–Christoffel software in both the determination of outer polygons and the calculation of function values. By the use suggested here, the capabilities of such well-written software are extended.

  • 31.
    Andersson, Anders
    Jönköping University, School of Engineering, JTH, Mathematics.
    Using a zipper algorithm to find a conformal map for a channel with smooth boundary2006In: Mathematical Modeling of Wave Phenomena: 2nd Conference, 2006, p. 378-Conference paper (Refereed)
    Abstract [en]

    The so called geodesic algorithm, which is one of the zipper algorithms for conformal mappings, is combined with a Schwarz–Christoffel mapping, in its original or in a modified form, to produce a conformal mapping function between the upper half-plane and an arbitrary channel with smooth boundary and parallel walls at the end.

  • 32.
    Andersson, Anders
    et al.
    Jönköping University, School of Engineering, JTH, Mathematics.
    Nilsson, Börje
    International Centre for Mathematical modelling, Växjö University.
    Acoustic Transmission in Ducts of Various Shapes with an Impedance Condition2008In: International Conference on Numerical Analysis and Applied Mathematics 2008, Melville: American Institute of Physics , 2008, p. 33-36Conference paper (Refereed)
    Abstract [en]

    Propagation of acoustic waves in a two-dimensional duct with an impedance condition at the boundary, is studied. The duct is assumed to have two ends at infinity being asymptotically straight, but otherwise to be arbitrarily shaped.The so called Building Block Method allows us to synthesize propagation properties for ducts with complicated geometries from results for simpler ducts. Conformal mappings can be used to transform these simple ducts to straight ducts with constant cross-sections.By using recently developed techniques for numerical conformal mappings, it is possible to construct a transformation between an infinite strip and an arbitrarily shaped duct with smooth or piecewise smooth boundary, keeping both smoothness and the well controlled boundary direction towards infinity that the above mentioned method requires.To accomplish a stable formulation of the problem, we express it in terms of scattering operators. The resulting differential equation is solved using wave splitting and invariant embedding techniques. We expand the involved functions in Fourier series, and hence, it is possible to give the operators a matrix representation. Numerical results are produced using truncated matrices.

  • 33.
    Andersson, Anders
    et al.
    Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.
    Nilsson, Börje
    Linnaeus university, Vaxjö, Sweden.
    Biro, Thomas
    Jönköping University, School of Engineering, JTH, Physics and Mathematics and Chemical Engineering.
    Fourier methods for harmonic scalar waves in general waveguides2016In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 98, no 1, p. 21-38Article in journal (Refereed)
    Abstract [en]

    A set of semi-analytic techniques based on Fourier analysis is used to solve wave-scattering problems in variously shaped waveguides with varying normal admittance boundary conditions. Key components are the newly developed conformal mapping methods, wave splitting, Fourier series expansions in eigenfunctions to non-normal operators, the building block method or the cascade technique, Dirichlet-to-Neumann operators, and reformulation in terms of stable differential equations for reflection and transmission matrices. For an example, the results show good correspondence with a finite element method solution to the same problem in the low- and medium-frequency domains. The Fourier method complements finite element analysis as a waveguide simulation tool. For inverse engineering involving tuning of straight waveguide parts joining complicated waveguide elements, the Fourier method is an attractive alternative including time aspects. The prime motivation for the Fourier method is its added physical understanding primarily at low frequencies.

  • 34.
    Andersson, Frida
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Hur matematikläroböcker presenterar räknelagar och räkneregler2016Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    In mathematics education textbooks to a large extent determine what is offered for students to be learnt. With this in mind, in this study, five Swedish textbooks series is reviewed in a latent and manifest content analysis approach where both quantitative and qualitative data is presented. The result of the quantitative data indicate that only a few textbooks series mentions the associative and distributive law in explicit manners. The result of the qualitative data shows that the basic laws of arithmetic is often described in other contexts. Many examples in the textbooks makes generalizations that may lead to limited understanding of the basic laws and rules of arithmetic.

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    Hur matematikläroböcker presenterar räknelagar och räkneregler
  • 35.
    Andersson, Frida
    et al.
    Jönköping University, School of Education and Communication.
    Englund Eriksson, Cathrine
    Jönköping University, School of Education and Communication.
    Associativa lagen i matematikdidaktisk forskning2015Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Matematiken är en vetenskap som är indelad i flera områden. Ett av dessa områden är aritmetik som betyder räknelära. Tillhörande aritmetiken finns ett antal egenskaper, räkneregler och räknelagar. Syftet med studien var att undersöka hur den associativa lagen beskrivs och uppfattas enligt matematikdidaktisk forskning. Arbetet är en litteraturstudie av matematikdidaktiska forskningspublikationer. Alla analyserade publikationer i studien är internationella och berör studiens forskningsområde inom en skolkontext. Materialet har med ett hermeneutiskt synsätt analyserats genom närläsning och med en komparativ metod. Det analyserade materialet består av nio vetenskapliga tidskriftsartiklar, två konferensbidrag samt ett kapitel ur en antologi.

    Den associativa lagen beskrivs inom flera olika områden och sammanhang i matematikdidaktisk forskning. Lagen beskrivs förutom som en egenskap med direkt tillhörighet i aritmetiken, dessutom som en del i ett relationellt tänkande och som en komponent i medvetenhet för matematisk struktur. Förståelse för lagen och dess egenskaper utgör ett viktigt element för elevers övergång från aritmetik till algebra. Den associativa lagen missuppfattas ofta och används på ett felaktigt sätt av såväl elever, lärarstudenter som lärare. Bristande förståelse för lagen och dess egenskaper leder till svårigheter i att generalisera de aritmetiska egenskaperna till att gälla även för algebra. 

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  • 36.
    Andersson, Sven
    et al.
    Jönköping University, School of Education and Communication, HLK, Disciplinary Research.
    Larsson, Peter
    Jönköping University, School of Education and Communication, HLK, Disciplinary Research.
    Läromedlets funktion i klassrummet, i matematik.2007Independent thesis Basic level (degree of Bachelor), 10 points / 15 hpStudent thesis
    Abstract [sv]

    Syftet med detta arbete var att undersöka och få grepp om de faktorer, som verkar mellan läromedlen och eleverna, respektive läromedlen och lärarna. Frågeställningarna var följande:

    - Vilka faktorer påverkar läromedlets funktion?

    - Vad kommunicerar dessa faktorer till lärare, respektive elever?

    För att få svar på dessa frågor, genomfördes kvalitativa intervjuer bland lärare och elever i gymnasiet, i ämnet matematik.

    I vårt arbete såg vi en röd tråd som löpte genom litteratur och artiklar. Tråden var vikten av det matematiska språket, och hur viktig den var för ett utvecklande av den matematiska förståelsen. Vi har skärskådat olika faktorer som vi fått fram genom en amerikansk utvärderingsprocedur. Faktorerna har undersökts och vi har tagit reda på vad dessa innebär. I intervjuerna med elever och lärare i gymnasieskolan har vi sett att våra antaganden blivit bekräftade.

    Det som har framhållits i debatten, är att man skall ta bort läroböckerna, men med detta menar man inte alltid att de skall tas bort helt, utan att deras dominans skall minska. Detta bör ske till förmån för en dialog i klassrummen, i grupparbeten eller i dialoger mellan eleverna och lärarna. I vårt arbete har åsikter kommit fram som stödjer dessa tankar, att kommunikationen är viktig för att bygga upp den matematiska förståelsen.

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  • 37.
    Askew, Mike
    et al.
    Univ Witwatersrand, Wits Sch Educ, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Univ Witwatersrand, Wits Sch Educ, Johannesburg, South Africa.
    Deconstructing South African Grade 1 learners’ awareness of number in terms of cardinality, ordinality and relational understandings2020In: ZDM - the International Journal on Mathematics Education, ISSN 1863-9690, E-ISSN 1863-9704, Vol. 52, p. 793-804Article in journal (Refereed)
    Abstract [en]

    The cardinal and ordinal aspects of number have been widely written about as key constructs that need to be brought together in children’s understanding in order for them to appreciate the idea of numerosity. In this paper, we discuss similarities and differences in the ways in which understandings not only of ordinality, cardinality but also additive and multiplicative relations have been theorized. We examine how the connections between these can be considered through a focus on number line representations and children positioning and comparing numbers. The responses of a cohort of South African Grade 1 learners’ (6- and 7-year-olds) to a numerical magnitude estimation task and to a numerical comparison task are analysed and the findings compared to those in the international literature, some of which argue that children’s early, informal, understandings of cardinality and ordinality are underpinned by an intuitive logarithmic model relating number order and size. A main finding presented here is that the responses from learners in this study exhibited a better fit with an exponential model of the relationship between cardinality and ordinality. These findings raise questions about whether some of the findings in previous research are as universal as sometimes claimed.

  • 38.
    Askew, Mike
    et al.
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Venkat, Hamsa
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Abdulhamid, Lawan
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Mathews, Corin
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Morrison, Samantha
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Ramdhany, Viren
    University of Johannesburg, South Africa.
    Tshesane, Herman
    Wits School of Education, University of the Witwatersrand, Johannesburg, South Africa.
    Teaching for structure and generality: Assessing changes in teachers mediating primary mathematics2019In: Proceedings of the 43rd Conference of the International Group for the Psychology of Mathematics Education, Pretoria, South Africa, 7-12 July 2019: Volume 2, Research reports (A-K) / [ed] M. Graven, H. Venkat, A. A. Essien & P. Vale, Pretoria, South Africa: PME , 2019, p. 41-48Conference paper (Refereed)
    Abstract [en]

    From a sociocultural perspective that a teacher’s use of mediational means is central to student learning, this paper presents an analysis of six teachers and their mediating, across a two-three year time gap. Drawing on the Mediating Primary Mathematics framework – developed to examine the type and quality of mediational means – we propose two composite assessments of quality of mediation – extent and depth – that indicate the extent to which teaching addresses mathematical structure and generality. The findings reveal a range of differences in these two assessments for each of the six teachers, but that all six teachers were more coherent in their use of mediational means in the later lesson than in the earlier one. These findings have implications for other schooling systems and researchers seeking to improve the quality of mathematics instruction.

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  • 39.
    Avery, Helen
    Jönköping University, School of Education and Communication, HLK, Praktiknära utbildningsforskning (PUF), Mathematics Education Research. Centre for Middle Eastern Studies, Lund University, Sweden.
    Acquérir les gestes qu’il faut: les mathématiques scolaires comme interaction et savoir-faire2019In: AREF 2019: Livret des résumés, 2019, p. 286-287Conference paper (Refereed)
    Abstract [en]

    The paper presents the synthesis of a series of studies on support measures for pupils with additional languages in Sweden, with a particular focus on the consequences of language support measures for teaching and learning school mathematics. The analysis identifies several critical aspects in mathematics teaching when the pupils transition from one school system to another, and particularly when they do not yet have a shared language to communicate among each other or with their teachers. Three aspects with relevance to language support will be discussed and illustrated with examples from the studies: the notion of mathematics as a formal language; the notion of levels and absolute progression in mathematics; the notion that learning mathematics means understanding "concepts".

  • 40.
    Ax, Malin
    et al.
    Jönköping University, School of Education and Communication.
    Selent, Johanna
    Jönköping University, School of Education and Communication.
    Elevers förståelse för tal i bråkform.: Vad gynnar elevers förståelse för tal i bråkform?2020Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    I matematikundervisningen i årskurs 1–3 lär sig elever grundläggande kunskaper för att förstå tal i bråkform. Förståelsen för tal i bråkform är viktig för fortsatt kunskapsutveckling inom tal i decimalform, algebra och procent. Litteraturstudiens syfte är att belysa hur matematikdidaktisk forskning beskriver hur elever möter svårigheter för tal i bråkform samt vilken undervisning som kan förebygga att svårigheter uppkommer för tal i bråkform.

    Genom litteratur och databassökningar framkom att de vanligaste svårigheterna för tal i bråkform är förståelsen för täljare och nämnare, storleksordning av tal i bråkform och samband mellan olika representationsformer. Litteraturstudien grundar sig i vetenskapliga artiklar, sökta genom olika söktjänster. De granskade artiklarna är eniga om att digitala verktyg, tal i bråkform kopplat till vardagen, aktiviteter och konkret material kan främja elevers förståelse för tal i bråkform. I litteraturstudien framkommer det att förståelse för täljare och nämnare, stambråk, del av helhet och del av antal är grunden till att förstå tal i bråkform. Resultatet visar också att undervisning om tal i bråkform kan vara en problematisk del i matematiken. Det krävs därför en välplanerad och varierad undervisning för att gynna elevers förståelse för tal i bråkform.

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  • 41.
    Axelsson, Alexander
    Jönköping University, School of Education and Communication.
    Kan elevers koncentration och matematiska prestation förbättras med fysisk aktivitet?: En kvantitativ studie med elever i årskurs 42021Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    The aim of this study is to test the hypothesis that physical activity has positive effects on concentration and mathematical ability among students. The hypothesis was tested qualitatively through a quasi-experimental design in 4:th grade. Data was collected from a control group of 17 students, and an experimental group of 20 students. The experiment was conducted for two weeks with a total of six lessons in each group. In this study, two metrics were measured: concentration via self-assessment, and mathematical ability through two-minute-long multiplication exercises conducted by the students. The measurements were conducted at the very beginning and the very end of the lesson. Before each lesson, the experimental group performed physical activity by following a dance video. The results from this study show that students assessed their concentration higher at the end of the lesson compared to the beginning of the lecture. Concentration and mathematical ability increased in both of the groups, but the experimental group showed the largest increase in both metrics. However, the reported difference between the groups is very small. Students in the experimental group were on average able to correctly solve slightly less than one-half more exercises in the two-minute test, compared to the control group. The increase in the metrics between the groups was tested using statistical methods (t-test), which concluded that the increase is not statistically significant. Some possible factors contributing to the result of the study are discussed in the Discussion section. 

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  • 42.
    Axelsson, Johanna
    Jönköping University, School of Education and Communication, HLK, School Based Research, Mathematics Education Research.
    Geometriska mönster i Favorit matematik: En läromedelsgranskning av Favorit matematik i årskurserna 1-32017Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [en]

    Algebra in mathematics is so much more than just equations and calculations. Through the primary grades in school, geometric patterns are a part of the Swedish curriculum. By working with patterns we prepare the students for the more difficult algebra to come, and they learn to express themselves generally. Many studies show the benefits with the work with patterns in the primary grades, for example students learn how to see connections and how to generalise.

     

    This study is a teaching material study of the material Favorit matematik in the primary grades. The aim is to contribute knowledge about which mathematical abilities students are given chance to develop by working with patterns in Favorit matematik. Focus is also to study what type of pattern, of repeating patterns and growing patterns, that are more processed in the material. The method that has been used is a chart where the patterns and the abilities were written into.

     

    The result shows flaws when it comes to patterns in Favorit matematik. The teacher has to work with this along with the material to give the students chance to explore every mathematical ability. Nor is it shown that patterns are something within the algebra, it is mostly linked to other areas from the curriculum. Mostly the exercises were about completing a pattern that was repeating, and therefore the majority of the exercises was connected to the first ability, which is about solving problems and evaluate your strategies and methods. The result also shows that growing geometric patterns is not presented as much as repeating patterns.

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  • 43.
    Axelsson, Johanna
    et al.
    Jönköping University.
    Debreceni, Hanna
    Jönköping University.
    Mönster inom algebra: Med inriktning mot årskurs F-32016Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Mönsterarbete i lågstadiet är en bra start för inlärning av algebra, detta ger en grund för den kommande mer avancerade algebraundervisningen. Studiens övergripande syfte är att undersöka hur arbetet med mönster inom åldrarna 6-10 år kan se ut, och vilka fördelar mönsterarbetet har för elevers kommande lärande inom matematik. Uppsatsen är baserad på nationell och internationell vetenskapligt granskad forskning. Olika undervisningsexempel, som kan tillämpas i lågstadiet, belyses och vikten av mönsterarbetet tas upp. Studien berör arbete med tre typer av mönster: upprepade mönster, växande mönster och talföljder. Vår analys av forskning visar att mönsterarbete är en viktig del i matematiken och att det kan komma till nytta i elevers fortsatta matematikinlärning. Den visar också att upprepade mönster är den vanligaste sorten av mönster att arbeta med i de yngre åldrarna, men forskarna menar att lärarna bör vidga undervisningen och även arbeta med andra mönster. Studien riktar sig främst till lärare som undervisar i F-3 men även till andra som är intresserade av hur arbetet med mönster kan se ut i de lägre åldrarna. Exemplen som tas upp i uppsatsen kan lärare använda i sin undervisning.

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    Mönster inom algebra - Med inriktning mot årskurs F-3
  • 44. Axelsson, Linda
    Huvudräkningsstrategier inom addition: En kvalitativ studie av elevers val av huvudräkningsstrategier i årskurs sex2021Independent thesis Advanced level (professional degree), 10 credits / 15 HE creditsStudent thesis
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  • 45.
    Axelsson, Linda
    et al.
    Jönköping University.
    Mattsson, Ellinore
    Jönköping University.
    Huvudräkning och standardalgoritmer: En litteraturstudie om hur matematikdidaktisk forskning ser på huvudräkning jämfört med standardalgoritmer2020Independent thesis Basic level (professional degree), 10 credits / 15 HE creditsStudent thesis
    Abstract [sv]

    Inom matematikämnet är metoden standardalgoritmer en stor del av undervisningen, vilket ibland leder till att huvudräkning inte prioriteras. Syftet med denna litteraturstudie är att beskriva hur matematikdidaktisk forskning beskriver huvudräkning respektive standardalgoritmer. Vi har även granskat vad forskningen hävdar att lärare har för betydelse i dessa undervisningsmoment. Litteraturstudien innehåller forskning från 11 olika länder, där det valda materialet har granskats genom noggrann läsning och en jämförande analys av våra gemensamma tolkningar. Det analyserade materialet pekar på att när elever använder sig av skriftliga beräkningar resulterar det i noggrannare svar. Skriftliga beräkningar medför även att eleverna lättare kan följa sin egen tankegång, vilket leder till en ökad förståelse för sitt tillvägagångssätt. Resultatet visar att lärare bör besitta djupa kunskaper om vanligt förekommande svårigheter inom huvudräkning och standardalgoritmer. Anledningen till det är att de ska kunna uppmärksamma svårigheter i undervisningen. Resultatet av våra valda forskningsstudier visar att standardalgoritmer är effektiva, automatiska och generaliserbara. Standardalgoritmer kan leda till att beräkningar som innehåller flersiffriga tal och tal i decimalform underlättas. Analysen av de valda forskningsartiklarna indikerar att båda metoderna bör användas och att den ena inte utesluter den andra. 

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  • 46.
    Belov, I.
    et al.
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology.
    Alavizadeh, Z.
    Lindgren, M.
    Application of engineering optimization to evaluate heating-based humidity management in electronics enclosures2011In: Electronic Environment Konferens & Mässa 2011, Stockholm Älvsjö,5-6 April 2011, Invited speech, 2011, p. 161-162Conference paper (Other academic)
  • 47.
    Belov, Ilja
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Anti-Moisture Methodology for Electronics Enclosures in Harsh Storage Environments2008Conference paper (Other academic)
  • 48.
    Belov, Ilja
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Evaluation of Anti-Moisture Measures in Electronics Enclosure: Application of CFD Modelling2009Conference paper (Other academic)
  • 49.
    Belov, Ilja
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Humidity Management in Electronics Enclosure under Severe Climatic Conditions2008Conference paper (Other academic)
  • 50.
    Belov, Ilja
    Jönköping University, School of Engineering, JTH. Research area Materials and manufacturing - Surface technology. Jönköping University, School of Engineering, JTH. Research area Robust Embedded Systems.
    Optimization of PCB Heater Heating Profile for Power-efficient Humidity Management in Electronics Enclosures: OPTIMUS Worldwide User Meeting 2010, Antwerp, Belgium, November 22-23, 20102010Other (Other academic)
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