Auditory and haptic feedback to train basic mathematical skills of children with visual impairments

Physical manipulatives, such as rods or tiles, are widely used for mathematics learning, as they support embodied cognition, enable the execution of epistemic actions, and foster conceptual metaphors. Counting them, children explore, rearrange, and reinterpret the environment through the haptic channel. Vision generally complements physical actions, which makes using traditional manipulatives limited for children with visual impairments (VIs). Digitally augmenting manipulatives with feedback through alternative modalities might improve them. We specifically discuss conveying number representations to children with VIs using haptic and auditory channels within an environment encouraging exploration and supporting active touch counting strategies while promoting reflection. This paper presents LETSMath, a tangible system for training basic mathematical skills of children with VIs, developed through Design-Based Research with three iterations in which we involved 19 children with VIs and their educators. We discuss how the system may support training skills in the composition of numbers and the impact that the different system features have on slowing down the interaction pace to trigger reflection, in understanding, and in incorporation.Universitat Pompeu Fabra (Spain) through MIREGAMIS: 2018 LLAV 00009Agencia Nacional de Investigación e Innovación - ANIIFundación CeibalCentro Interdisciplinario en Cognición para la Enseñanza y el Aprendizaje - CICEA, Universidad de la RepúblicaUniversitat Oberta de Catalunya (Spain) through Ministry of Science, Innovation, and Universities IJCI-2017-32162LASIGE Research Unit (Portugal) through FCT project mIDR (AAC02/SAICT/-2017, project 30347, cofunded by COMPETE/FEDER/FNR), the LASIGE Research Unit, ref. UIDB/00408/2020 and ref. UIDP/00408/2020

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

The effects of a grouping by tens manipulative on children's strategy use, base ten understanding and mathematical knowledge

Manipulatives have the potential to be powerful tools in helping children improve their number sense, develop advanced mathematical strategies, and build an understanding of the base ten number system. Physical manipulatives used in classrooms, however, are often not designed to promote efficient strategy use, such as counting on, and typically do not encourage children to perceive higher-order units in multi-digit numbers. The aim of this study was to closely examine the affordances of a novel grouping by tens virtual manipulative. Seventy-nine first grade students were randomly assigned to one of two math software comparison groups or a reading software control group. In the math comparison groups, children received scaffolding and feedback while playing a computerized enumeration game that required them to use the novel grouping by tens manipulative. Children in the Transformation group used a manipulative that transformed from a unitized to a continuous model, while children in the Unitized group used a manipulative that remained discrete. Researchers recorded children's strategy use and accuracy when determining how many objects appeared on the screen, and the data were examined microgenetically. Children's counting on abilities, base ten understanding, and number sense were tested at posttest to examine group differences. The results showed that using the transforming manipulative significantly improved children's ability to count on at posttest. The math software also improved girls' base ten understanding at posttest. Children who used the math software in both conditions improved in their advanced strategy use and accuracy over time. These findings suggest that virtual manipulatives have the potential to improve children's strategy use and base ten understanding in ways that physical manipulatives may not. Suggestions for future research are discussed

Effects of Family, Child, and Teacher Demographics on Prekindergarten Children\u27s Access to and Use of Numeracy and Spatial Materials in the Early Education Setting

Florida’s Voluntary Pre-Kindergarten program (VPK) aims to ensure that all 4-year-olds are prepared to excel in K-12 mathematics. Early numeracy/spatial skills are predictive of success in K–12 mathematics. No research has examined whether VPK classrooms are equipped with the materials necessary to teach numeracy/spatial skill. The Pre-Kindergarten Numeracy and Spatial Environment Survey was created to examine the frequency of access to and use of numeracy/spatial materials in VPK classrooms. The 69-item survey was completed by the lead educator from a sample of 62 pre-kindergarten classrooms in Miami-Dade County. Regression analysis results suggest the location of the pre-kindergarten center, the sex distribution of the children in the classrooms or the number of years of experience that the educator has as a lead teacher along with the extra training courses undertaken by the teachers does not affect the access to or the use of, numeracy and spatial materials in the classrooms

Promoting the Development of an Integrated Numerical Representation through the Coordination of Physical Materials

How do children use physical and virtual tools to develop new numerical knowledge? While concrete instructional materials may support the delivery of novel information to learners, they may also over-simplify the task, unintentionally reducing learners' performance in recall and transfer tasks. This reduction in testing performance may be mitigated by embedding physical incongruencies in the design of instructional materials. The effort of resolving this incongruency can foster a richer understanding of the underlying concept. In two experiments children were trained on a computerized number line estimation task, with a novel scale (0-180), and then asked to perform a series of posttest number line estimation tasks that varied spatial features of the training number line. In experiment 1, during training with feedback, children either received a ruler depicting endpoint and quartile magnitudes (i.e., 0, 45, 90, 135, 180) that physically matched the on-screen number line (congruent ruler), a proportionally-similar ruler scaled 33% larger than the on-screen number line (incongruent ruler), or no ruler. Children were trained to criterion before proceeding to posttest. Results indicated that while children who used the congruent ruler performed well during training, their performance at posttest was less accurate than the other two conditions. On the other hand, by increasing the difficulty of the learning task, while providing relevant landmark information, children in the incongruent ruler condition produced the highest accuracy at posttest. In experiment 2, controlling for learning task duration, the incongruent ruler and congruent ruler conditions were compared directly. Posttest results confirmed an advantage for children in the more complex, incongruent ruler condition. These results are interpreted to suggest that landmarks representations are an important and accessible means of developing a mature numerical representation of the number line. Furthermore, the results confirm that desirable difficulties are an essential component of the learning process. Potential implications for the design of learning activities that balance instructional support with conceptual challenge are discussed

Preschoolers and multi-digit numbers: A path to mathematics through the symbols themselves

Numerous studies from developmental psychology have suggested that human symbolic representation of numbers is built upon the evolutionally old capacity for representing quantities that is shared with other species. Substantial research from mathematics education also supports the idea that mathematical concepts are best learned through their corresponding physical representations. We argue for an independent pathway to learning “big” multi-digit symbolic numbers that focuses on the symbol system itself. Across five experiments using both between- and within-subject designs, we asked preschoolers to identify written multi-digit numbers with their spoken names in a two-alternative-choice-test or to indicate the larger quantity between two written numbers. Results showed that preschoolers could reliably map spoken number names to written forms and compare the magnitudes of two written multi-digit numbers. Importantly, these abilities were not related to their non-symbolic representation of quantities. These findings have important implications for numerical cognition, symbolic development, teaching, and education

Children\u27s Mathematical Engagement Based on Their Awareness of Different Coding Toys\u27 Design Features

Tangible coding toys have been promulgated as useful learning tools for young children to learn computer science and mathematics concepts and skills. Although research shows coding toys can support mathematics for early childhood aged children, little is known about the specific design features of coding toys that afford mathematical thinking concepts and skills to young children. The purpose of this study was to examine kindergarten-aged children’s awareness of the design features in coding toys and to understand how those design features afford children’s engagement with mathematics. The dataset used for this study was collected as part of design-based research NSF project (award #DRL-1842116). I used a multi-phased qualitative analysis with a total of 42 hours of video data of 106, 5- to 6-year-old children engaging in coding toy tasks with four coding to answer the three research questions which were focused on perception of design features, mathematical engagement, and how different design features could afford mathematics. Results indicated that (a) children used and perceived the grid square and command arrow design features frequently, while other design features were used moderately or rarely; (b) children engaged in a variety of mathematical concepts and skills in five main categories of mathematical topics: spatial reasoning, geometry, comparison, measurement, and number; and (c) the relationship between design features affording mathematics varied depending on the coding toy. This research highlights the importance of specific design features to afford certain mathematical concepts and skills. These findings have important implications as early childhood educators explore ways to implement coding toys to support mathematics and computer science concepts, researchers conduct studies to better understanding how coding toys support mathematics and computer science learning, and commercial companies design new coding toys to fill the needs of educators and parents

Investigating the Effects of the MathemAntics Number Line Activity on Children's Number Sense

Number sense, which can broadly thought of as the ability to quickly understand, approximate, and manipulate numerical quantities, can be a difficult construct for researchers to operationally define for empirical study. Regardless, many researchers agree it plays an important role in the development of the symbolic number system, which requires children to master many tasks such as counting, indentifying numerals, comparing magnitudes, transforming numbers and performing operations, estimating, and detecting number patterns, skills which are predictive of later math achievement. The number line is a powerful model of symbolic number consistent with researchers' hypotheses concerning the mental representation of number. The MathemAntics Number Line Activity (MANL) transforms the number line into a virtual manipulative, encourages estimation, provides multiple attempts, feedback, and scaffolding, and introduces a novel features where the user can define his own level of risk on the number line. The aim of the present study was to examine how these key features of MANL are best implemented to promote number sense in low-income second-graders. Sixty-six students from three schools were randomly assigned to one of three conditions; MANL User-Defined Range (UDR), and MANL Fixed Range (FR), and a Reading comparison condition and underwent a pretest session, four computer sessions, and a posttest session. During the computer sessions, researchers coded a child's observed strategy in placing targets on the number line. The results showed that children with higher number sense ability at pretest performed better on a posttest number line estimation measure when they were in the UDR condition than in the FR condition. Conversely, children with low number sense ability at pretest performed better on the number line estimation posttest measure when they were in the FR condition than UDR. Although in general, all children improved over time, children with low number sense ability at pretest were more likely to use the UDR tool ineffectively, thus negatively impacting performance. When children were not coded as responding quickly, target number significantly impacted performance in the computer sessions. Finally, children in the UDR condition utilized better expressed strategies on the number line estimation posttest than children in the Reading comparison group. These findings indicate that prior number sense ability plays a role in how children engage with MANL, which in turn affects the learning benefits the child receives. Implications for researchers, software designers, and math educators, as well as limitations are discussed

The role of perception in conceptual processing

Jedan od središnjih problema kognitivne znanosti je pitanje kako je pojmovno znanje reprezentirano u ljudskom umu. Teorija perceptivnih simboličkih sustava pretpostavlja da je znanje ukorijenjeno u modalno-specifičnim sustavima kao što su percepcija, motorika i emocije. Prema ovoj teoriji, perceptivna iskustva spremaju se u memorijske sustave koji se po potrebi mogu reaktivirati i oživjeti tijekom konceptualne obrade pomoću perceptivne simulacije. Važna kritika teorije je da ona može objasniti utjecaj perceptivnih varijabli na razumijevanje konkretnih pojmova, jer se objekti na koje se oni referiraju mogu lako predočiti, ali ne može objasniti kako razumijemo značenje apstraktnih pojmova te se postavlja pitanje imaju li perceptivne varijable utjecaj i na njihovu obradu. Cilj ovog istraživanja bio je ispitati je li razumijevanje značenja numeričkih pojmova utemeljeno u percepciji. Preciznije, u prvih šest eksperimenata cilj je bio ispitati jesu li elementarne aritmetičke operacije utemeljene u kretanju duž zajedničke prostorne reprezentacije veličina koja obuhvaća sve kvantitativne dimenzije kao što su prostor, vrijeme, brojevi i svjetlina. Osim toga, u sedmom i osmom eksperimentu ispitano je mogu li se mali brojevi utemeljiti u sustavu za subitizaciju odnosno sustavu za brzo i automatsko prebrojavanje malih skupova objekata u vidnom polju. U prvih šest eksperimenata ispitanici su rješavali aritmetičke zadatke koji su bili prikazani u crnoj ili bijeloj boji, a u sedmom i osmom eksperimentu ispitanici su uspoređivali rečenice i slike koje su varirale s obzirom na broj objekata spomenutih u rečenici i prikazanih na slici. U svim provedenim eksperimentima mjerena je i analizirana brzina i točnost rješavanja zadataka.One of the central issues in cognitive science is to understand how conceptual knowledge is represented in the mind. According to the theory of perceptual symbol systems, knowledge is grounded in modality-specific systems for perception, action and emotion. Perceptual experiences are stored in memory and they can be reactivated during conceptual processing via perceptual simulation. Important criticism of the theory is that it can explain understanding of concrete concepts because it is easy to visualize their referent objects but it is not clear how abstract concepts are processed and whether perceptual variables affect their understanding also. Aim of this research was to examine whether numerical concepts are grounded in perception