Arla Westenskow

A study comparing virtual manipulatives with other instructional treatments in third- and fourth-grade classrooms

The study reported here examined virtual manipulatives as an instructional treatment in 17 third- and fourth-grade classrooms. Students were randomly assigned to two treatment groups: texts and physical manipulatives (PM), and virtual manipulatives (VM). Results revealed no significant differences in achievement between the treatments. Additional results showed that objective ability predicted fraction achievement; virtual manipulative use can be modulated by test question type (e.g., symbolic vs. pictorial); percentage of class time using representations differed between VM and PM classrooms; and percentage of class time spent using representation types differed, potentially providing differential opportunities to learn.

Teaching anxieties revealed: pre-service elementary teachers’ reflections on their mathematics teaching experiences

Over the last 50 years, there has been ample research dedicated to mathematics anxiety in contexts of teaching and learning. However, there has been less attention focused on pre-service teachers’ anxieties about teaching mathematics in classroom settings. This study analyzed pre-service teachers’ reflections at the conclusion of an elementary mathematics field experience in order to determine common themes surrounding anxiety-related events based on mathematics practice-teaching experiences. Through qualitative analysis of pre-service teachers’ reflections using open and axial coding, three categories and ten themes surrounding elementary pre-service teachers’ anxiety-related events based on mathematics practice-teaching experiences emerged. Some of the themes presented were ones that increased pre-service teachers’ anxieties for teaching mathematics, whereas other themes reflected aspects of the field experience that decreased anxiety for teaching mathematics. Based on the themes revealed in this study, suggestions for strategies and materials that could be developed for university mathematics methods courses are discussed. Novel perspectives for considering mathematics teaching anxiety, such as locus of control and future time perspective, are shared.

An Examination of Children’s Learning Progression Shifts While Using Touch Screen Virtual Manipulative Mathematics Apps

The purpose of this study was to examine shifts in young childrens learning progression levels while they interacted with virtual manipulative mathematics apps on touch-screen devices. A total of 100 children participated in six mathematics learning sequences while using 18 virtual manipulative mathematics touch-screen apps during clinical interviews. Researchers developed a micro-scoring tool to analyze video data from two camera sources (i.e., GoPro camera, wall-mounted camera). Our results showed that it is possible to document evidence of shifts in childrens learning progressions while they are interacting with mathematics apps on touch-screen devices. Our results also indicated patterns in the childrens interactions that were related to the shifts in their learning progression levels. These results suggest that an open-ended number of tasks with a variety of representations and tasks at varying levels of difficulty led to children refining their understanding and shaping their concept image of mathematical ideas resulting in incremental shifts in learning. The results of this study have important implications about how mathematical tasks in touch-screen apps may prompt childrens incremental learning progression shifts to occur, and thereby promote opportunities for learning. We propose that design features in mathematics apps can be created to support and encourage these learning shifts.

Evolution of Unit Fraction Conceptions in Two Fifth-Graders with a Learning Disability: An Exploratory Study.

ABSTRACT The literature seems limited in what is known about conceptual processes that underlie evolution of students with learning disabilities (SLD) conceptions of fractions. This exploratory study examines how a foundational scheme of unit fractions (1/n) may evolve through the mathematical activity of two fifth grade girls. We analyze data segments from episodes conducted during a teaching experiment grounded in the activity of iterating estimates of one persons equal share. Our findings include four distinct conceptual stages: (1) No Conception of the Nature of Adjustment to the Magnitude of a Unit Fraction, (2) Evolving Anticipation of the Nature of Adjustment but not of its Relative Amount, (3) Anticipation of the Nature of Adjustment with an Evolving Partial Amount, and (4) a Dual Anticipation of the Nature and Amount of Adjustment. Findings demonstrate each girl was able to use her constructed scheme to successfully solve and reason about novel problems. We discuss the need for more research to confirm the findings from this study, while offering a conjecture of the possibilities for more SLDs to advance their conceptions of fractions in future interventions.

An Iceberg Model for Improving Mathematical Understanding and Mindset or Disposition: An Individualized Summer Intervention Program.

This study describes 3 years of mathematics intervention research examining the effectiveness of a summer individualized tutoring program for rising fourth-, fifth-, and sixth-grade students with low mathematics achievement. Based on an iceberg model of learning, an instructional framework was developed that identified and targeted students’ specific mathematical needs, developed number sense flexibility, and encouraged positive mindset or disposition. Students participated in eight one-on-one tutoring intervention sessions. Pre- and posttest results indicated that students made moderate to large effect size gains in each targeted area of instruction. Additionally, the intervention proved to produce positive results across three different contexts for delivering tutoring instruction.

A Window Into Mathematical Support: How Parents’ Perceptions Change Following Observations of Mathematics Tutoring

This research study examined the perceptions of 24 parents of rising 5th-grade students with mathematics learning difficulties as part of a 10-week summer mathematics tutoring experience. During the summer tutoring program, parents observed their children participating in mathematics learning experiences during one-to-one tutoring sessions. At the conclusion of the summer tutoring services, parents reflected on observations of their own children in surveys and interviews. Results indicated that parents’ observations of the tutoring impacted their perceptions and changed the support they provided to their children during and after the tutoring program. Parents reported changes in attitudes and beliefs about mathematics, gaining insights into their child’s mathematical understanding, and changes in their methods and practices as mathematics supporters outside of the tutoring sessions.

How design features in digital math games support learning and mathematics connections

Abstract Current research shows that digital games can significantly enhance childrens learning. The purpose of this study was to examine how design features in 12 digital math games influenced childrens learning. The participants in this study were 193 children in Grades 2 through 6 (ages 8–12). During clinical interviews, children in the study completed pre-tests, interacted with digital math games, responded to questions about the digital math games, and completed post-tests. We recorded the interactions using two video perspectives that recorded childrens gameplay and responses to interviewers. We employed mixed methods to analyze the data and identify salient patterns in childrens experiences with the digital math games. The analysis revealed significant gains for 9 of the 12 digital games and most children were aware of the design features in the games. There were eight prominent categories of design features in the video data that supported learning and mathematics connections. Six categories focused on how the design features supported learning in the digital games. These categories included: accuracy feedback, unlimited/multiple attempts, information tutorials and hints, focused constraint, progressive levels, and game efficiency. Two categories were more specific to embodied cognition and action with the mathematics, and focused on how design features promoted mathematics connections. These categories included: linked representations and linked physical actions. The digital games in this study that did not include linked representations and opportunities for linked physical actions as design features did not produce significant gains. These results suggest the key role of mathematics-specific design features in the design of digital math games.

Components of place value understanding: Targeting mathematical difficulties when providing interventions. School Science and Mathematics

Place value understanding requires the same activity that students use when developing fractional and algebraic reasoning, making this understanding foundational to mathematics learning. However, many students engage successfully in mathematics classrooms without having a conceptual understanding of place value, preventing them from accessing mathematics that is more sophisticated later. The purpose of this exploratory study is to investigate how upper elementary students’ unit coordination related to difficulties they experience when engaging in place value tasks. Understanding place value requires that students coordinate units recursively to construct multi-digit numbers from their single-digit number understandings through forms of unit development and strategic counting. Findings suggest that students identified as low-achieving were capable of only one or two levels of unit coordination. Furthermore, these students relied on inaccurate procedures to solve problems with millennial numbers. These findings indicate that upper elementary students identified as low-achieving are not to yet able to (de)compose numbers effectively, regroup tens and hundreds when operating on numbers, and transition between millennial numbers. Implications of this study suggest that curricula designers and statewide standards should adopt nuances in unit coordination when developing tasks that promote or assess students’ place value understanding.

Theory and educational research: toward critical social explanation

Taylor and Francis QSE_A_444033.sgm 10.1080/09518390903436724 International Journal of Qualitative Studies in Education 0951398 (pri t)/1366-5898 (online) Original Article 2 09 & Francis 0002 09 Sh ryMarx sher y.m @usu.edu Theory and educational research: toward critical social explanation, edited by Jean Anyon, New York/London, Routledge, 2009, 216 pp., US

Effects of Virtual Manipulatives on Student Achievement and Mathematics Learning

32.95 (paperback), ISBN 978-0-415-99042-4