194 research outputs found
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Number Representations: Improper Fractions, Squares, Square Roots
No full textMany years of K-12 math education are dedicated to the learning of numbers (e.g., counting, different number forms: whole numbers, decimals, fractions). A common challenge is the integration of learned number forms (e.g., whole numbers) with new number forms (e.g., decimals) as children tend to carry the “rules” they learned to the next number concept. Research on number representation has covered numbers up to proper fractions (e.g., magnitudes less than 1), but little research has been conducted looking at number forms beyond this point, like improper fractions (e.g., magnitudes more than 1, 5/3), squares and square roots. In my dissertation, I ask the question of whether adults also rely on more familiar/known number forms when processing these more complex number forms. The overarching hypothesis is that people use more familiar/known number forms as references for assessing magnitude of these complex number forms because the number representation of the former is more precise and reliable than the latter. I use a combination of cognitive and perceptual tasks such as magnitude comparison of numbers and visuals, and magnitude estimation across four chapters. People were better at assessing the magnitudes of improper fractions when they used mixed fractions and decimals as reference points rather than improper fractions (Chapter 1). Performance on magnitude comparison of improper fractions worsened as (whole number) magnitude increased for both symbolic/numerical and non-symbolic/visual tasks (Chapter 2). The reference numerical range for squaring numbers anchored and restricted people’s estimates of squares (Chapter 3). Finally, the natural numbers within the square root sign predicted magnitude estimation of square roots better than its actual magnitudes (i.e., mental number line hypothesis) and distance from perfect-squares predicted magnitude estimation as well. Altogether, we found that people use more familiar numbers – whole numbers, proper fractions, decimals (Chapter 1); multiples (Chapter 2); numerical range (Chapter 3); and natural numbers and perfect-squares – when processing more complex numbers – improper fractions (Chapters 1-2), squares (Chapter 3) and square roots (Chapter 4). My dissertation fills in major gaps in the numerical cognition literature and its chosen number forms have implications for algebra and calculus readiness in students
São Paulo Cycling Network Development Design: A Minimum Spanning Tree Approach
No full textCycling is a heated topic in social media and a political hotspot in São Paulo. The implementation of bicycles took place in the city after the cooperation agreement signed by the Municipal Bureau of International and the Institute for Transportation and development policy in 2009. The recent 10-year development of the cycling infrastructure resulted in an unconnected and scattered network throughout the city. To improve the accessibility and increase the service coverage, the study proposed the minimum spanning tree to design a well-connected cycling network. A case study of 4 center districts has been researched. The new plan aims to serve 94.49% inhabitants within 350 m of the walking distance and create links to the daily trip destinations in the regions, such as public transport stations, schools, shopping malls, hospitals, etc.Accepted Author ManuscriptTransport and Plannin
Perfezionamento e caratterizzazione sperimentale di un sistema di localizzazione UWB passivo
No full textIn questo elaborato si è presentato il miglioramento e la validazione di un sistema di localizzazione basato sulla combinazione della tecnologia UWB e quella dei sistemi RFID. In particolare, è stato implementato un algoritmo di localizzazione Least Mean Square, più robusto del metodo geometrico di trilaterazione, andandolo ad integrare in un contesto reale con più configurazioni basate sulla posizione dei nodi riceventi. Per il set-up del sistema, è stata necessaria una calibrazione dovuta ai ritardi di propagazione introdotti dal cablaggio, con un successivo test per validare l'affidabilità della localizzazione in tempo reale. Con la creazione di una griglia fittizia in cui posizionare un Tag UWB passivo progettato ad hoc, è stata eseguita un'analisi delle posizioni stimate con un successivo studio delle potenze ricevute, ipotizzando così un'eventuale correlazione tra stima e qualità del segnale. Il tutto è stato riproposto anche con l'aggiunta di un terzo nodo ricevente affinché si visualizzasse il miglioramento dal punto di vista prestazionale. Infine, è stato esteso l'algoritmo anche alla terza dimensione per verificare come il sistema si adattasse ad un nuovo scenario più complesso e realistico
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Magnitude Comparisons of Improper Fractions
No full textPrevious studies examining the mental representations of fractions have focused on fractions with magnitudes less thanone (e.g., 2/3). In the current study, we examine the mental representations of fractions with magnitudes greater than one,specifically those of improper fractions. Participants were asked to make magnitude comparisons of these improper frac-tions to a reference that was in an improper fraction, a mixed fraction, or a decimal format. Results show that magnitudesof improper fractions were more accurately accessed when they were compared to mixed fractions and decimals. Thissuggests that the reinterpretation of these improper fractions benefited magnitude processing. Distance effects on errorrate and response time were observed for all three reference formats and more consistently took the form of a Welfordfunction, which predicts worse performance above rather than below the reference. Possible explanations of these resultsare discussed
Discounted Prices Are Not Processed the Same as Fractions
No full textThe present study examines whether people’s mental representation of discounted prices, which have a part-whole relationship of the current price to original price, is similar to that of fractions. Participants performed a fraction comparison task and a deal comparison task on the same set of fractional magnitudes. In two experiments, we observed worse performance (error rate, RT of correct trials) on the deal comparison task. The distance effect, where magnitude comparisons are made more slowly and less accurately the closer two magnitudes are, observed in the two tasks was best modeled using logarithmic distance between the fractional magnitudes as a predictor of performance
Comparing Processing of Bundle Deal Formats to Fraction Formats
No full textPeople encounter improper fractions in real life contexts on a regular basis. One such example is with bundling at the grocery store (2/4). The present study seeks to understand how people process these bundle prices compared to improper fractions. Participants completed a magnitude comparison task with different bundling formats (2/4/2) and their fractional equivalents. We found a reliable difference between the bundle format (2/$4) seen in grocery stores and the most visually similar fraction (2/4). This difference shows that participants are not using a heuristic (larger fraction means cheaper per item) when comparing these bundle deals and instead do need to process them like improper fractions. Overall, we found that participants were better at comparing fractional magnitudes in a math context than in a financial context and that this effect of context also depended on format (2/4 vs. 4/2)
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Magnitude Comparisons of Discounted Prices: Are They Similar to Fractions?
No full textThe present study examines whether peoples mental representation of discounted prices, which have a part-whole relation-ship of the current price to the original price, is similar to that of fractions. Participants performed a fraction comparisontask and a deal comparison task on the same set of fractional magnitudes. In two experiments, we observed worse perfor-mance (error rate, RT of correct trials) on the deal comparison task. The distance effect, where magnitude comparisons aremade more slowly and less accurately the closer two magnitudes are, observed in the two tasks was best modeled usinglogarithmic distance between the fractional magnitudes as a predictor of performance
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Magnitude Processing of Improper Fractions When Comparing Bundle Deals
No full textPeople encounter improper fractions in real life contexts on a regular basis. One such example is with bundling at thegrocery store (2/4). The present study seeks to understand how people process these bundle prices comparedto improper fractions. Participants completed a magnitude comparison task with different bundling formats (2/4/2)and their fractional equivalents. We found a reliable difference between the bundle format (2/$4) seen in grocery storesand the most visually similar fraction (2/4). This difference shows that participants are not using a heuristic (larger fractionmeans cheaper per item) when comparing these bundle deals and instead do need to process them like improper fractions.Overall, we found that participants were better at comparing fractional magnitudes in a math context than in a financialcontext and that this effect of context also depended on format (2/4 vs. 4/2)
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