From research to design: Perspectives on early years and digital technologies

The three papers explore how we can use existing research traditions to create challenging new directions for design and development of technologies for the early years. The papers focus on literacy, numeracy and reflections on the design process

Learning by doing with shareable interfaces

New technologies, such as multi-touch tables, increasingly provide shareable interfaces where multiple people can simultaneously interact, enabling co-located groups to collaborate more flexibly than using single personal computers. Soon, these technologies will make their way into the classroom. However, little is known about what kinds of learning activities they will effectively support that other technologies, such as mobile devices, whiteboards, and personal computers, are currently unable to do. We suggest that one of the most promising uses of shareable interfaces is to support learning through exploration and creation. We present our work on DigiTile as a case study of how shareable interfaces can enable these forms of learning by doing. We demonstrate how DigiTile supports collaboration, present a field study on its learning benefits, and show how it can fit into a larger computing ecology

Informing the design of a multisensory learning environment for elementary mathematics learning

It is well known that primary school children may face difficulties in acquiring mathematical competence, possibly because teaching is generally based on formal lessons with little opportunity to exploit more multisensory-based activities within the classroom. To overcome such difficulties, we report here the exemplary design of a novel multisensory learning environment for teaching mathematical concepts based on meaningful inputs from elementary school teachers. First, we developed and administered a questionnaire to 101 teachers asking them to rate based on their experience the learning difficulty for specific arithmetical and geometrical concepts encountered by elementary school children. Additionally, the questionnaire investigated the feasibility to use multisensory information to teach mathematical concepts. Results show that challenging concepts differ depending on children school level, thus providing a guidance to improve teaching strategies and the design of new and emerging learning technologies accordingly. Second, we obtained specific and practical design inputs with workshops involving elementary school teachers and children. Altogether, these findings are used to inform the design of emerging multimodal technological applications, that take advantage not only of vision but also of other sensory modalities. In the present work, we describe in detail one exemplary multisensory environment design based on the questionnaire results and design ideas from the workshops: the Space Shapes game, which exploits visual and haptic/proprioceptive sensory information to support mental rotation, 2D–3D transformation and percentages. Corroborating research evidence in neuroscience and pedagogy, our work presents a functional approach to develop novel multimodal user interfaces to improve education in the classroom

The Anatomy of Virtual Manipulative Apps: Using Grounded Theory to Conceptualize and Evaluate Educational Apps that Contain Virtual Manipulatives

This exploratory qualitative study used grounded theory to investigate the anatomy of educational apps that contain virtual manipulatives. For this study 100 virtual manipulatives within educational apps designed for the iPad were observed by the researcher in order to expand the explanations of and build theory about virtual manipulatives within apps. Affordance theory was used to frame all six phases of the study in which the researcher identified virtual manipulatives situated within educational apps, conducted observer-as-participant structured and unstructured observations, analyzed component data including field notes and memos using open and axial coding, created a conceptual framework, developed an evaluation tool prototype to evaluate virtual manipulatives within educational apps, and used the evaluation tool prototype to evaluate additional virtual manipulatives within educational apps. The constant comparative method of open and axial coding was used to analyze the observation data that included field notes, memos, and video recordings. This indepth qualitative analysis led to the emergence of six study results concerning the components and relationships within educational apps that contain virtual manipulatives. The results revealed that: (1) virtual manipulatives within apps are comprised of two components: dynamic mathematical objects and features; (2) there are three distinct types of dynamic mathematical objects; (3) there are eight categories of features; (4) within one virtual manipulative there can be one or multiple objects; (5) varying relationships can exist among the dynamic object and the features within a virtual manipulative; and (6) varying relationships can exist among the virtual manipulatives within an education app in terms of the number, type, and ways the user proceeds. A conceptual framework was also developed during the study to illustrate the components and relationships that emerged from the analysis and to serve as the basis for the development of an evaluation tool prototype to evaluate educational apps that contain virtual manipulatives. The components, relationships, framework, and evaluation tool prototype developed during this study advance the literature on virtual manipulatives and provide researchers with a common language to evaluate these apps

Effectiveness of ST Math in College Remedial Mathematics Students of Learning Fraction Concepts

This study examined the extent to which the iPad app, Spatial Temporal Mathematics (ST Math), diminished college remedial mathematics students’ natural number bias and deepened their fraction conceptual understanding. In this quasi-experimental study one class played the ST Math fraction games for 8 weeks, and they were compared to a control class who were taught without technology. The frameworks for this study included the framework theory of conceptual change, the reorganization theory, the microworld and the Lesh Translation Model. Pre and post- tests were used to examine the fraction conceptual understanding of the students in the ST Math class and the non-ST Math class before and after the intervention. Also, interviews were conducted to investigate how the ST Math students developed their fraction conceptual understand before and after the game play, compared to the non-ST Math students. As a whole, the students in both classes exhibited the natural number bias in all three areas: magnitude, density, and computation at the pre-test stage. However at the post-test stage, they diminished the bias in magnitude but in the other two areas, the bias was persistent. Overall, the statistical result was not significant between the ST Math class and the non-ST Math class on the post-test. However, the ST Math class had more students who answered correctly regarding the fraction density concept on the post-test. Similarly, the post-interview results revealed that the ST Math students exhibited conceptual gain in fraction magnitude, the fraction addition concept, and the fraction multiplication concept. However, although they showed the conceptual gain in fraction multiplication, they had difficulty with the concept of fraction division. The students in both classes did not show any conceptual gain in fraction division

Teaching Preservice Teachers in the Time of COVID: What’s Worth Keeping?

As we begin to transition from online instruction to in-person, we (four mathematics teacher educators) reflect on how COVID-19 impacted our instruction and address the question: what will we take back to in-person instruction? This article includes our individual reflections and an analytical synthesis of them. Findings reveal that there were unanticipated ways that human connection and consideration arose from teaching online, much of which we want to maintain in some form when returning to brick and mortar classrooms. We conclude by highlighting the value and importance of reflection for our own well-being

Connecting the Points: An Investigation into Student Learning about Decimal Numbers

The purpose of this research project was to investigate the effects of a short-term teaching experiment on the learning of decimal numbers by primary students. The literature describes this area of mathematics as highly problematic for students. The content first covered student understanding of decimal symbols, and how this impacted upon their ability to order decimal numbers and carry out additive operations. It was then extended to cover the density of number property, and the application of multiplicative operations to situations involving decimals. In doing so, three areas of cognitive conflict were encountered by students, the belief that longer decimal numbers are larger than shorter ones (irrespective of the actual digits), that multiplication always makes numbers bigger, and that division always makes numbers smaller. The use of a microgenetic approach yielded data was able to be presented that provides details of the environment surrounding the moments where new learning was constructed. The characteristics of this environment include the use of physical artifacts and situational contexts involving measurement that precipitate student discussion and reflection. The methodology allowed for the collection of evidence regarding the highly complex nature of the learning, with evidence of 'folding back' to earlier schema and the co-existence of competing schema. The discussion presents reasons as to why the pedagogical approach that was employed facilitated learning. One of the main findings was that the use of challenging problems situated in measurement contexts that involved direct student participation promoted the extension and/or re-organization of student schema with regard to decimal numbers. The study has important implications for teachers at the upper primary level wanting to support student learning about the decimal numbers system

The role of co-construction of the clock model in the development of fractional understanding in a grade 4/5 classroom

The focus of this case study was to determine the impact of the co-construction and use of the clock model in the development of fractional understanding in a Grade 4/5 classroom. A pretest, instruction, midtest, intervention, posttest, retention test sequence was used. The teaching unit was developed to address six areas of student difficulty with fractions identified in the literature: factional parts are equal size portions, fraction symbols, improper fractions, size of unit fractions, estimation and comparison, and equivalent fractions. The clock model was co-constructed by the students with the teacher in the second half of the unit. Students used the clock model in four different forms: as an area model, as whole numbers of minutes, as equivalent fractions, and as an open clock. Although some students did not adopt the clock model, others used it with great success. Most students moved beyond using only landmark fractions of an hour to being able to work with thirds and sixths of an hour. The clock model helped some students to better understand the relationship between equivalent fractions. Recommendations are discussed

The effectiveness of using manipulatives to teach fractions

The current study will focus on the effectiveness of using manipulatives when teaching fractions to elementary school students. Learning the concepts of fractions can be one of the most difficult skills to master for elementary level students. With so many different ways to expose students to manipulatives and enhance their fraction learning experience, it is important to examine how effective these teaching tools can be with respect to student achievement. The current study will discuss the effectiveness on student achievement when manipulatives are used during the teaching process. The main focus will be on student growth after being taught concepts of fractions including addition and subtraction while using manipulatives to engage them in their lessons. The students involved in this study are in one fourth grade class. This class includes 18 students that are performing at various achievement levels. Some of the participants have specific learning disabilities which hinder their ability to retain mathematical concepts without repetition over a longer period of time. The lessons being taught are included in the Everyday Mathematics fourth grade curriculum for fraction concepts. This curriculum is the Vineland Public Schools district wide mathematics curriculum. The teachers are responsible for teaching this curriculum using manipulatives for specific lessons. The study is taking place of a time span of four weeks. They will be tested prior to being taught the unit on fractions. They will be divided into two groups: one group will be instructed using integration of manipulatives and the other group will be instructed using worksheets and direct instruction including teacher modeling. Both groups will be given a post test to determine if the use of manipulatives was effective. This study will consist of comparing students\u27 assessment scores when being taught the concepts of fractions while using manipulatives and students\u27 assessment scores when they are taught without the use of manipulatives. An independent sample T-test revealed that students working with manipulatives during instructional time, small group time, and independent tasks demonstrated a significant amount of growth as compared to their peers that did not use manipulatives during any time of the learning process