The study investigated the effects of two generative learning activities on students’ academic achievement of the part-whole representation of rational numbers while using virtual manipulatives. Third-grade students were divided randomly in two groups to evaluate the effects of two generative learning activities: answering-questions and generating-examples while using two virtual manipulatives related to part-whole representation of rational numbers. The study employed an experimental design with pre- and post-tests. A 2x2 mixed analysis of variance (ANOVA) was used to determine any significant interaction between the two groups (answering questions and generating-examples) and between two tests (pre-test and immediate post-test). In addition, a 2x3 mixed analysis of variance (ANOVA) and a Bonferroni post-hoc analysis were used to determine the effects of the generative strategies on fostering comprehension, and to determine any significant differences between the two groups (answering-questions and generating-examples) and among the three tests (pre-test, immediate post-test, and delayed posttest). Results showed that an answering-questions strategy had a significantly greater effect than a generating-examples strategy on an immediate comprehension posttest. In addition, no significant interaction was found between the generative strategies on a delayed comprehension tests. However a difference score analysis between the immediate posttest scores and the delayed posttest scores revealed a significant difference between the answering-questions and the generating-examples groups suggesting that students who used generating-examples strategy tended to remember relatively more information than students who used the answering-questions strategy. The findings are discussed in the context of the related literature and directions for future research are suggested. / Ph. D.

Students with emotional or behavioral disorders (EBD) are more likely than other students with disabilities to drop out of school (Blackorby & Wagner, 1996) and suffer societal consequences that include higher probabilities and rates of incarceration, poverty, drug abuse, homelessness, low wages, and unemployment (Bradley, Doolittle, & Bartolotta, 2008; Wagner, 1995). High school graduation is a critical factor to improve post-secondary outcomes for students with EBD; yet it is often mathematics, specifically algebra, that stands in the way of graduation (Blackorby & Wagner). Students with EBD often enter middle school lacking foundational mathematics skills, such as fractions, which sets them up to struggle with pre-algebra and ultimately fail algebra (U.S. Department of Education, 2008). The purpose of this study was to improve the ability of middle school students with EBD to access online grade-level mathematics content by providing fraction remediation to improve conceptual fraction knowledge and procedural fluency. The intervention consisted of Initial Fraction Ideas, an intervention curriculum from the Rational Number Project (RNP; Cramer, Behr, Post, & Lesh, 2009), in conjunction with three online virtual manipulatives (VM). The unique blended learning environment of this study provided the opportunity to evaluate the use of an evidence-based fraction intervention, in conjunction with VMs, in a single subject, multiple baseline across subjects design. Fluency data was gathered from daily fraction addition assessments (FAA) administered after each intervention session. A second component of the study featured a non-experimental repeated measures design that assessed student conceptual understanding of fraction equivalency through the administration of pre, post, and delayed-post Equivalent Fraction Tests (EFT). The intervention was effective in producing increases in median group fluency with high effect sizes, across three replications, establishing a functional relationship between the intervention and the dependent variable for these groups of students with EBD. In addition, all groups posted mean gains in equivalent fraction knowledge from pre to post-EFT, and maintained those gains for at least 15 days after the intervention concluded.

published_or_final_version / abstract / Education / Master / Master of Education

The primary purpose of this study was to determine if the implementation of an intervention involving teachers' use of children's literature, related storybook manipulatives, and a scaffolding (LMS) approach to learning would improve preschool children's mathematics test scores. Additionally, the LMS approach was examined to determine whether teachers' perceptions of their effectiveness in mathematics instruction changed from the beginning to the end of the study. The subjects of the study included 60 preschool-aged children and six teachers from two child care centers. The preschool teachers participated in either a control or experimental condition (the LMS approach) in their daily mathematics instruction with their preschool children. The researcher tested the children using the Test of Early Mathematics Ability and an abbreviated version of the Stanford-Binet Intelligence Scale. The study was based on two main research questions. The first question asked if there was a difference in the Test of Early Mathematics Ability total posttest scores between children in the literature-manipulatives-scaffolding intervention group and children in the control group after assuring equivalency of the two groups. The second question addressed if preschool teachers believed they were more effective in their mathematics instruction after implementing the LMS approach with young children. The answer to the first research question was that there was no statistically significant difference in the Test of Early Mathematics Ability total posttest scores between children in the literature-manipulatives-scaffolding group and children in the control group. However, the answer to the second question was that preschool teachers believed they were more effective in their mathematics instruction after implementing the LMS approach with young children. Recommendations for future research on early childhood mathematics include the investigation of preschool children's ability, achievement, and interest in mathematics; teachers' use of mathematics scaffolding techniques; and longitudinal mathematics interventions beginning during the preschool years.

Syftet med den empiriska studien är att undersöka lärares användning av konkret material i matematikundervisningen. I studien undersöks vilket konkret material som läraren använder, hur det konkreta materialet används och i vilka undervisningssituationer som läraren hänvisar till konkret material. Genom observationer av fyra olika lärare, i fyra olika klassrum har vi fått svar på studiens frågeställningar. Med hjälp av rational number projekt och Heddens teori har resultatet analyserats. Resultatet visar att konkret material är framgångsrikt för elever när det ska gå från konkret till abstrakt förståelse inom matematik. Resultatet visar även att det är viktigt att variera mellan olika representationer i undervisningen. De olika representationerna som framgick i observationerna är bilder, verkliga situationer samt talade och skrivna symboler.

Den här studien syftade till att undersöka hur undervisning med respektive utan konkret material kan påverka vad elever i årskurs 2 kan lära sig om rektanglar, kvadrater och trianglar. För att besvara ovanstående syfte har Learning Study varit en inspirationskälla för genomförandet av den här studien. Studien har genomförts i årskurs 2 där 18 elever delades in i två grupper, elevgrupp A och elevgrupp B. I varje grupp har tre moment genomförts: förtest, lektion och eftertest. Lektionerna hade samma syfte och innehåll, med den skillnaden att konkret material endast skulle användas i en av dem. Utifrån resultatet av eftertestet visar det sig att många elever i båda grupperna har utvecklat sina kunskaper att särskilja rektanglar, kvadrater och trianglar. Men när det gäller elevernas kompetens att använda begrepp och beskriva egenskaper hos dessa figurer så visar det sig att lektionen med konkret material har gett bättre resultat. Dock är det några elever i båda grupperna som inte uppvisat någon förbättring efter lektionerna. / <p>Matematik</p>

This study analyzes the preservice elementary mathematics teachers&rsquo / self efficacy beliefs and outcome expectancies about using manipulatives and investigates whether, or not, university and gender differences have any significant effect on their self efficacy and outcome expectancies. In mathematics education, students&rsquo / conceptions about abstract mathematical ideas and being able to convert them into concrete ideas are very important. For this reason, it is very beneficial to use manipulative materials in the mathematics lessons. However, most of the preservice mathematics teachers in Turkey lack knowledge about using manipulatives. The sample of present study consisted of 77 senior undergraduate students studying in Elementary Mathematics Teacher Education programs at 2 different universities located in Ankara and Izmir. Data were collected in spring term of 2006-2007 academic years. The survey items were adopted from previously developed teacher efficacy instrument, which partly ensures the items to be parallel with the existing theory about the construct. The survey consisted of three parts / demographic information, knowledge about the manipulatives, and &lsquo / The Instrument of Preservice Mathematics Teachers&rsquo / Efficacy Beliefs about Using Manipulatives&rsquo / (EBMU). The present study demonstrated that the gender differences did not effect preservice elementary mathematics teachers&rsquo / personal manipulative use teaching efficacy whereas the university differences had a significant effect on their personal manipulative use teaching efficacy. In addition, the gender and university attended produced statistically significant main effect on preservice elementary mathematics teachers&rsquo / outcome expectancies.

The purpose of the study was to investigate the impact of 5E learning cycle on sixth grade students&rsquo / mathematics achievement on and attitudes toward mathematics. The study was carried out in a public school in one of the towns of the Central Anatolia Region with 28 sixth-grade elementary school students. One group pretest-posttest design was used. Mathematics Achievement Test and Mathematics Attitude Scale were administered to collect the necessary data. The instruction will be applied by the researcher five hours per week in a 15-week. The data were analyzed by using one-way repeated measures analysis of variance and a paired-samples t-test. According to the results of the study it was found that there was a statistically significant change in mathematics achievement of sixth grade students who participated in the instruction based on 5E learning cycle over three time periods (pre-intervention, post-intervention, and follow-up). There was only no statistically significant mean difference between post-intervention and follow-up mathematics achievement. Furthermore, there was a statistically significant decrease in mean scores of attitudes toward mathematics from prior intervention to after intervention.

A concern for the Swedish students’ knowledge of mathematics, especially in algebra, is formulated in the PISA –rapport (Skolverket, 2012). From this conclusion, an interest was formed to investigate how practicing teachers in Sweden use manipulatives to support students in developing a better understanding of algebra. An interview-based study is presented in this degree project. This study focus on four Swedish teacher’s perspectives on using manipulatives when working with the equality sign in algebra. The purpose of this study is through interviews highlight these teachers' perceptions of manipulatives and ways of working with the material. The result of this study presents a generally positive view on using manipulatives in teaching mathematics, especially working with the equality sign in algebra. The result also presents how the teachers address the importance of developing an understanding of the equality sign.  The teacher’s answers and perspectives on using manipulatives is also confirmed by research and literature. Finally this study marks the significant role of the teacher when students learn and develop an understanding for mathematics. This degree project is analyzed by following questions: -What experience and skills do teachers have with the use of manipulatives when it comes to working with the concepts of the equal sign in algebra?- In which way does the teachers believe that working with manipulatives facilitates an understanding of the equal sign?- What importance do teachers lay on manipulatives regardingthesignificance of the equal sign?

Dissertation (Ph.D.)--Texas A&M University, 2004. / Title from PDF t.p. (viewed on Sept. 9, 2008). "Major subject: Educational Psychology." Includes bibliographical references (p. 119-136).