Unit Fractions as Superheroes for Instruction

2020 ◽  
Vol 113 (4) ◽  
pp. 278-286
Author(s):  
Susan Baker Empson ◽  
Victoria R. Jacobs ◽  
Naomi A. Jessup ◽  
Amy Hewitt ◽  
D'Anna Pynes ◽  
...  
Keyword(s):  
Unit Fractions ◽  
Unit Fraction ◽  
Children's Strategies

The complexity of understanding unit fractions is often underappreciated in instruction. We introduce a continuum of children's understanding of unit fractions to explore this complexity and to help teachers make sense of children's strategies and recognize milestones in the development of unit-fraction understanding. Suggestions for developing this understanding are provided.

Iteration: Unit Fraction Knowledge and the French Fry Tasks

2015 ◽  
Vol 22 (3) ◽  
pp. 148-157 ◽  
Author(s):  
Ron Tzur ◽  
Jessica Hunt
Keyword(s):  
French Fry ◽  
Unit Fractions ◽  
Unit Fraction

Using these tasks can help nurture children's multiplicative notions of unit fractions beyond part-whole understanding.

scholarly journals Dynamic Windows Scheduling with Reallocation

2021 ◽  
Vol 26 ◽  
pp. 1-19
Author(s):  
Martín Farach-Colton ◽  
Katia Leal ◽  
Miguel A. Mosteiro ◽  
Christopher Thraves Caro
Keyword(s):  
Supply Chain ◽  
Bin Packing ◽  
Time Slot ◽  
Peak Load ◽  
Communication Channels ◽  
Current Load ◽  
Constant Amount ◽  
Unit Fractions ◽  
Consecutive Time ◽  
Multiple Variants

We consider the Windows Scheduling (WS) problem, which is a restricted version of Unit-Fractions Bin Packing, and it is also called Inventory Replenishment in the context of Supply Chain. In brief, WS problem is to schedule the use of communication channels to clients. Each client c i is characterized by an active cycle and a window w i . During the period of time that any given client c i is active, there must be at least one transmission from c i scheduled in any w i consecutive time slots, but at most one transmission can be carried out in each channel per time slot. The goal is to minimize the number of channels used. We extend previous online models, where decisions are permanent, assuming that clients may be reallocated at some cost. We assume that such cost is a constant amount paid per reallocation. That is, we aim to minimize also the number of reallocations. We present three online reallocation algorithms for Windows Scheduling. We evaluate experimentally multiple variants of these protocols showing that, in practice, all three achieve constant amortized reallocations with close to optimal channel usage. Our simulations also expose interesting tradeoffs between reallocations and channel usage. We introduce a new objective function for WS with reallocations that can be also applied to models where reallocations are not possible. We analyze this metric for one of the algorithms that, to the best of our knowledge, is the first online WS protocol with theoretical guarantees that applies to scenarios where clients may leave and the analysis is against current load rather than peak load. Using previous results, we also observe bounds on channel usage for one of the algorithms.

scholarly journals Food-Choice Values of Elementary School Children and Strategies Used to Influence Mothers’ Food Purchasing Decisions

2020 ◽  
Vol 4 (Supplement_2) ◽  
pp. 720-720
Author(s):  
Nazratun Monalisa ◽  
Edward Frongillo ◽  
Christine Blake ◽  
Susan Steck ◽  
Robin DiPietro
Keyword(s):  
Elementary School ◽  
South Carolina ◽  
School Children ◽  
Food Choice ◽  
Elementary School Children ◽  
Healthy Foods ◽  
Purchasing Decisions ◽  
Food Purchasing ◽  
Food Purchases ◽  
Children's Strategies

Abstract Objectives This study aimed to understand the values held by elementary school children in constructing food choices and the strategies they used to influence their mothers’ food purchasing decisions. Methods Semi-structured qualitative interviews were conducted with 40 elementary school children (aged 6–11 years) and their mothers living in South Carolina. Food choice information was collected only from children and strategies to influence mothers’ food purchases were collected from both children and mothers. The interviews were audio-recorded, transcribed verbatim, and open-coded. Coding matrices were used to compare children's and mothers’ responses on the children's strategies to influence mothers’ food purchasing decisions. Results Children most valued taste, texture, and flavor of the food items, followed by perceived benefits, happiness, craving, following family and friends, the items’ healthfulness, preparation, and presentation when they made food choice decisions. Children reported 157 strategies that they used to influence mothers’ purchasing decisions. Mothers had concordance with 80 strategies that children mentioned. In mother-child dyads, more concordance was observed between mothers and sons than between mothers and daughters. The most common and successful strategies from both the children's and mothers’ perspectives were reasoned requests, repeated polite requests, and referencing friends. Other strategies included offers to contribute money or service, teaming up with siblings, writing a shopping list, and grabbing desired items. Mothers perceived that children had a lot of influence on their food purchasing decisions. Conclusions Children were aware of the strategies that would get positive reactions from their mothers. Mothers’ acknowledgement of children's influence on their food purchase decisions suggests that children can serve as change agents for improving mothers’ food purchases if children prefer healthy foods. Interventions are needed for mothers to help address children's strategies to influence mothers to purchase unhealthy foods and make healthy foods more appealing to children instead of yielding to children's requests for unhealthy items. Funding Sources SPARC grant and Ogoussan Doctoral Research Award from the University of South Carolina.

Children making sense of economic insecurity: Facework, fairness and belonging

2016 ◽  
Vol 53 (1) ◽  
pp. 94-109 ◽  
Author(s):  
Rose Butler
Keyword(s):  
Low Income ◽  
Recent Analysis ◽  
Economic Insecurity ◽  
Cultural Narratives ◽  
Making Sense ◽  
Research With Children ◽  
Low Income Families ◽  
Complex Forms ◽  
Regional Australia ◽  
Children's Strategies

This article contributes to our understanding of how children cope with economic insecurity in affluent nations. Based on research with children and adults in regional Australia, it argues for the importance of cultural narratives in making sense of children’s strategies to cope with financial hardship. Drawing on Goffman’s concept of ‘facework’, and recent analysis by Pugh, it analyses the complex forms of facework that children use to manage situations of economic insecurity and shows how such practices may be anchored in cultural narratives of ‘fairness’. Goffman’s ‘facework’ refers to the expressive order required to save face, a term used to signify how we participate in a social regime, particularly when we perform unexpected feelings. In this article, the author develops a theoretical framework to analyse three types of facework used by children from low-income families in this Australian context, and coins these practices ‘going without’, ‘cutting down’, and ‘staying within’. Through such facework, children sought to maintain inclusion and uphold dignity, practices which were increasingly difficult amidst rising inequality. This raised contradictions in belonging and acceptance among others, particularly for children from refugee backgrounds.

Children's Strategies for Gathering Information in Three Tasks

1986 ◽  
Vol 57 (6) ◽  
pp. 1429 ◽  
Author(s):  
Patricia H. Miller ◽  
Vernon F. Haynes ◽  
Darlene DeMarie-Dreblow ◽  
Janet Woody-Ramsey
Keyword(s):  
Children's Strategies

scholarly journals Monochromatic solutions to equations with unit fractions

1991 ◽  
Vol 43 (3) ◽  
pp. 387-392 ◽  
Author(s):  
Tom C. Brown ◽  
Voijtech Rödl
Keyword(s):  
Solutions To Equations ◽  
Unit Fractions ◽  
Image Position ◽  
Positive Integers

Our main result is that if G(x1, …, xn) = 0 is a system of homogeneous equations such that for every partition of the positive integers into finitely many classes there are distinct y1,…, yn in one class such that G(y1, …, yn) = 0, then, for every partition of the positive integers into finitely many classes there are distinct Z1, …, Zn in one class such thatIn particular, we show that if the positive integers are split into r classes, then for every n ≥ 2 there are distinct positive integers x1, x1, …, xn in one class such thatWe also show that if [1, n6 − (n2 − n)2] is partitioned into two classes, then some class contains x0, x1, …, xn such that(Here, x0, x2, …, xn are not necessarily distinct.)

Keeping the Teacher Happy

1980 ◽  
Vol 8 (4) ◽  
pp. 3-7 ◽  
Author(s):  
M. Christie
Keyword(s):  
The Other ◽  
Children’S Behaviour ◽  
Children's Strategies

In his book How Children Fail, John Holt talks about the strategies children have for coping with school. The strategies of most children, says Holt, have been consistently self-centred, protective and aimed above all else at avoiding trouble, embarrassment, punishment, disapproval or loss of status. This is particularly true of the ones who have had a tough time in school. When they get a problem, I can read the thoughts on their faces. I can almost hear them, ‘Am I going to get this right? Probably not. What’ll happen to me when I get it wrong? Will the teacher get mad? Will the other kids laugh at me?’I didn’t really get to thinking much about children’s strategies until I had stopped teaching and gone into a few classes to observe as a fly on the wall. Most of what went on in the classroom went completely unnoticed by the teacher. And what the teacher did notice, she seemed often to misunderstand. The children had an amazing variety of strategies which really had the teacher fooled. Some of them had fooled me too, for the years I had been teaching. I thought that if I were to point out some of the strategies which I saw, teachers may begin to look more carefully at their own and their children’s behaviour.

Children's Strategies for Displaying Anger and Sadness: What Works With Whom?

2003 ◽  
Vol 49 (1) ◽  
pp. 100-122 ◽  
Author(s):  
Kimberly L. Shipman ◽  
Janice Zeman ◽  
April E. Nesin ◽  
Monica Fitzgerald
Keyword(s):  
What Works ◽  
Children's Strategies
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