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Abstract The purpose of this study was to develop mathematical games to assist children in learning addition and subtraction computation. The investigator designed games and experimented through four extra lessons, then studied children¡¦s mathematical learning after the lessons. Participants of this study were second grade children from two elementary schools in Kaohsiung. The experimentation was divided into three phases: pilot phase, first edition phase, and, second edition phase. Data collection and administration included pre-test and post-test; questionnaire of children¡¦s attitude towards mathematics; questionnaire of children¡¦s attitude towards games; record sheets for loan of games; children¡¦s worksheets; learning diaries; researcher¡¦s observation notes; and, researcher¡¦s reflections on design of games. The researcher referred to the above data source, later, evaluated according to the results of experimentation, and completed final revisions. Data analyses and results were three: Design, implementation, and revision. Design. When designing a game, the materials followed that of children¡¦s real life experiences. The characteristics of the four games were: Cooperation, challenge, education, and, chance and luck. Implementation. Children changed from ¡§individual responsibility¡¨ to ¡§co-ordination and cooperation in group¡¨, from ¡§assurance¡¨ to ¡§lack of confidence¡¨, from ¡§marginal participation¡¨ to ¡§eager to play with laughter¡¨, and ¡§no control of shouting¡¨. From the data analyses, children performed well in cognition, attitude, and skills. Revision. The principles of modification were to evaluate games¡¦ strengths and weaknesses, and adjusting games design. The respective revisions were tutoring play, children as key persons, formulating regulations, and, enriching contents. The findings of this study suggested that children benefit from mathematical games and constitute mathematical learning in two-digit number computation. If instructors try hard to design games, be keen in administration, and adjusted games, children will learn through games and result more effective mathematics learning. Finally, it is concluded that the goal of enhancing mathematics learning through games-based instruction as feasible. Key word¡Gmathematics games, addition and subtraction computation

Dissertation (Ph. D.)--University of Akron, Dept. of Polymer Science, 2009. / "May, 2009." Title from electronic dissertation title page (viewed 11/29/2009) Advisor, Judit E. Puskas; Committee members, Roderic P. Quirk, Joseph P. Kennedy, Li Jia, Chrys Wesdemiotis; Department Chair, Ali Dhinojwala; Dean of the College, Stephen Z. D. Cheng; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

Thesis (M. Phil.)--University of Hong Kong, 1984. / Caption title.

published_or_final_version / Chemistry / Master / Master of Philosophy

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AIM: The primary purpose of this thesis was to evaluate the pattern of changes to accommodation and phoria when pre-presbyopic individuals perform near work for 20 minutes with +2D lenses. In addition, the thesis also investigates the effect of the accommodative vergence cross-link (AV/A) and age on binocular adaptation to addition lenses. METHODS: Accommodation was measured using the PowerRefractor (Multichannel Systems, Germany) and phoria was measured using the modified Thorington Technique. Twenty four pre-presbyopic and emmetropic individuals (11 adults and 13 children) participated in the study. All participants fixated a near target at a distance of 33 cm for 20 minutes with +2D (lens condition) and without (no lens condition) +2D addition lenses. Binocular and monocular changes in accommodation and near phoria were measured at the outset and at 3, 6, 9, 15 and 20 minute intervals. RESULTS: Effect of +2D lenses on accommodation and phoria: The emmetropic adult participants exhibited lag of accommodation under the no lens condition (binocular: 0.51 ?? 0.12D; monocular: 0.64 ?? 0.15D) that were eliminated (under monocular viewing) and reversed (exceeded demand by 0.51 ?? 0.11 D under binocular viewing condition) with the addition of +2D lenses. The near phoria showed a significant increase towards exophoria by 6 ?? 0.56 ???D upon introduction of +2D lenses. Sustained near viewing with +2 D lenses resulted in significant reduction of the binocular focus alone (not monocular focus) after 3 minutes of binocular viewing (magnitude of reduction: 0.24D; P<0.01). The exophoria also showed a concomitant reduction after 3 minutes of fixation at the near task (Magnitude of reduction: 3.6 ?? 0.6 ???D; P<0.001). The magnitude and rate of vergence adaptation, determined using an exponential function, was found to be 4.6 ?? 0.21 ???D and 2.12 minutes respectively for the emmetropic adult participants. Effect of age on vergence adaptation: A pattern of significant reduction in phoria and binocular focus similar to the adult participants was observed in young children. Analysis of the vergence adaptation curves in the two age groups did not show any significant difference in both the magnitude as well as the rate of phoria adaptation within the age range tested (Magnitude of adaptation - Adults: 4.65 ???D; Children: 4.51 ???D; P > 0.05; Time constants -Adults: 2.12 minutes: Children: 1.53 minutes, P > 0.05). Effect of AV/A ratio on vergence adaptation: The stimulus (St-AV/A) and the response AV/A (R-AV/A) ratios were determined and the participants were divided into two groups (low and high AV/A ratio) under both the conditions. The result indicated that, under both testing conditions (stimulus and response AV/A), the individuals with higher AV/A ratios demonstrated greater magnitudes of vergence adaptation than those individuals with lower ratios (Magnitude of adaptation: Low St-AV/A = 4.12 ???D; Low R-AV/A= 4.25???D; High St-AV/A = 4.88 ???D; High R-AV/A = 4.65???D; P<0.05) CONCLUSIONS: Introduction of near addition lenses initiated an increase in exophoria and convergence driven accommodation. Vergence adaptation occurred after 3 minutes of binocular viewing thus reducing exophoria and convergence driven accommodation. The magnitude and completeness of phoria adaptation were seen to depend on an individuals AV/A ratio with greater magnitude and incomplete adaptation observed in participants with higher AV/A ratios. Age, within the limits of the study did not appear to influence phoria adaptation with near addition lenses.

Syftet med denna studie har varit att undersöka och jämföra vilka metoder inom addition och subtraktion som förekommer i två matematiklärobokserier. Vi har sökt svar på frågorna: vilka metoder för addition och subtraktion som läroböckerna ger, hur dessa behandlas och bygger vidare på varandra samt hur böckerna förhåller sig till gällande läro- och kursplaner. Den metod vi har använt oss av är en innehållslig idéanalys, eftersom vi tittat på dels vad, men också hur det tas upp. Materialet vi använt denna metod på är två matematiklärobokserier, som är reviderade till gällande läroplan, Lgr11. Som verktyg för att genomföra denna studie har vi utarbetat ett analysschema som har fokuserat på vilka metoder böckerna tar upp samt tre metaforer som beskriver hur det tas upp. Resultatet av denna studie har visat att det finns stora skillnader på hur böckerna arbetar med addition och subtraktion. Den ena boken tar upp metoderna flera gånger, börjar grundande och bygger vidare för att fördjupa och utveckla kunskaper. Den andra tar upp metoderna få gånger samt stannar på det grundande, det vill säga bygger aldrig vidare. Detta leder till att den första boken ger förutsättningar för påbyggnad och kunskap medan den andra snarare begränsar elevernas fortsatta kunskapsutveckling.