Technology Solutions for Developmental Math: An Overview of Current and Emerging Practices

Reviews current practices in and strategies for incorporating innovative technology into the teaching of remedial math at the college level. Outlines challenges, emerging trends, and ways to combine technology with new concepts of instructional strategy

Teaching mathematics : self-knowledge, pupil knowledge and content knowledge

Mathematical learning is significantly influenced by the quality of mathematics teaching (Hiebert and Grouws 2007). In spite of the evidence for teachers seeking to do what they believe to be in the best interests of their learners (Schuck 2009; Gholami and Husu 2010), research and policy reports (within the UK and beyond) draw attention to insufficient mathematical attainment (Williams 2008; Eurydice 2011). Why is there this discrepancy? On the one hand, teachers are open to improving their professional practices (Escudero and S´anchez 2007), and on the other, the findings of mathematical education research make little or no impact on teachers’ practice (Wiliam 2003), even although teachers themselves think that they are enacting new or revised practices (Speer 2005)

Building Conceptual Understandings of Equivalence

The equal sign is prevalent at all levels of mathematics however many students misunderstand the meaning of the equal sign and consider it an operational symbol for the completion of an algorithm (Baroody & Ginsburg, 1983; Rittle-Johnson & Alibali, 1999). Three constructs were studied through the lens of the Developing Mathematical Thinking (Brendefur, 2008), Relational Thinking, Spatial Reasoning and Modes of Representation. A review of literature was conducted to examine the effects of mathematics instruction on the development of students’ conceptual understanding of equivalence through the integration of spatial reasoning and relational thinking. The Developing Mathematical Thinking (DMT) curricular resources integrate Bruner’s enactive, iconic, and symbolic modes of representations (1966), using tasks designed to strengthen students’ spatial reasoning and relational thinking to develop mathematical equivalence. The research question “What is the effect of integrating iconic teaching methodology into mathematics instruction on first grade students’ relational thinking and spatial reasoning performance?” was analyzed to determine whether there was a significant difference in pre-and posttest scores for the two groups. Students were found to have a better opportunity to develop conceptual understanding of mathematics in their early years of school when taught with the progression of EIS, relational thinking and spatial reasoning

The Effects of Digital Game-Based Learning on Algebraic Procedural and Conceptual Understanding and Motivation Towards Mathematics

This study examined the impact of digital game-based learning (DGBL) on procedural and conceptual understanding of algebraic expressions and equations and the motivation of students towards classroom mathematics. The mixed-methods sequential explanatory design was used in this study to collect data to determine the effectiveness of DGBL in a 7th grade STEM class. Following a pre-test and pre-motivation survey, students were assigned to either the DGBL group or the non-gaming computer applications as supplemental to mathematics instruction. In order to address both procedural targets and conceptual targets students would be using the technology interventions in addition to traditional math instruction as part of their daily math class, and a problem-based unit taught as part of their STEM class. Following the treatment, a post-test, post-motivation survey, and a conceptual assessment were administered, as well as a digital questionnaire. No significant differences were detected between their understanding of procedural or conceptual problems, nor was there a significant impact to their motivation towards mathematics based on the quantitative data gathered. Students displayed an enthusiastic response to the DGBL environment based on their transcripts from the follow-up questionnaire. The results of the study imply that there is a need for further development of DGBL systems and scaffolded supports to assist students in making connections from the digital environment to classroom mathematics. It further indicates that enjoyment of the DGBL environment does not necessarily transfer to motivation to learn the subject matter in the non-digital environment

Taking Stock of Common Core Math Implementation: Supporting Teachers to Shift Instruction: Insights from the Math in Common 2015 Baseline Survey of Teachers and Administrators

In spring 2015, WestEd administered surveys to understand the perspectives on Common Core State Standards-Mathematics (CCSS-M) implementation of teachers and administrators in eight California school districts participating in the Math in Common (MiC) initiative. From this survey effort, we were able to learn from over 1,000 respondents about some of the initial successes and challenges facing California educators attempting to put in place and support new -- and what some consider revolutionary -- ideas in U.S. mathematics education

Teachers\u27 Perceptions of Manipulatives During Middle School Math Instruction

In a Colorado school district, school personnel and parents were concerned that middle school math proficiency levels were low for 2011-2014 and math teachers were not using manipulatives in their classes to increase math performance. The district\u27s math coordinator did not foresee providing specific professional development (PD) for math manipulative use to address these concerns. Without this PD, math teachers may be ill-quipped to teach math concepts when using manipulatives, which, in turn, could lead to further poor math performance. The purpose of this qualitative bounded collective case study was to explore middle school teachers\u27 perceptions of PD and perceived self-efficacy regading the implementation of manipulatives. Knowles\u27s andragogy and Piaget\u27s cognitive development theories framed this study. A homogeneous sample of 12 voluntary participants with more than 5 years teaching middle school math, both with and without access to manipulatives, volunteered to participate in this study. Data from observations, interviews, and archival documents were analyzed using comparative and inductive analyses and were analytically coded. Participants reported a need for PD that focused on physical and virtual manipulatives (PM and VM) and a low perceived self-efficacy regarding manipulatives use during math instruction. A blended PD using face-to-face and distance learning formats was designed to increase math teachers\u27 knowledge of and perceived self-efficacy with PM and VM for math instruction. This endeavor may contribute to positive social change by reforming PD opportunities to support teachers\u27 practice and self-efficacy using manipulatives during math instruction, ultimately increasing student performance

The effects of the integration of mathematics within children\u27s literature on early numeracy skills of young children with disabilities

Math skills are critical for future success in school (Eccles, 1997), as school-entry math knowledge is the strongest predictor of later academic achievement (Claessens, Duncan, & Engel, 2009). Researchers have found that teachers of young children spend less time teaching mathematics than other subject areas (Phillips & Meloy, 2012), and there is a lack of formal early mathematics instruction for young children’s understanding of early numeracy (Chard et al., 2008). However, preschoolers are developmentally ready for mathematics and are more able to learn math concepts than previously believed (Balfanz, Ginsburg, & Greenes, 2003). While there is a recent increase of literature on math with young children, there is a scarcity of research related to young children with disabilities in the field of mathematics, particularly utilizing evidence based interventions. The current study investigates one intervention integrating mathematics within children’s literature for preschoolers with disabilities. This study was a quasi-experimental group design, with one treatment group and one comparison group (N = 50 participants). Targeted early numeracy skills included: (1) one-to-one correspondence, (2) quantity comparison, and (3) numeral identification. The 20-minute intervention was conducted three days per week for six weeks; the comparison group received a typical small group storybook reading of the same literature book with no elaborations. The Test of Early Mathematics Ability, Third Edition (TEMA-3; Ginsburg & Baroody, 2003) was used as a pre and post standardized assessment, and analyzed using one-way ANCOVAs controlling for pretest scores. The Preschool Numeracy Indicators (PNI; Floyd, Hojnoski, & Key, 2006) was used as a weekly curriculum based measurement and analyzed by one-way ANCOVAS and by individual and group means for descriptive data. After the intervention, the children in the treatment group scored significantly higher in the areas of total math ability, quantity comparison, and one-to-one counting fluency than the comparison group. Implications include possibilities for further integrating mathematics within literature for preschoolers with disabilities, the benefits of intentional storybook selection for this type of intervention, and the recognition of the importance of introducing mathematical topics to preschoolers with disabilities in order of developmental cognitive readiness

Struggling learners of mathematics: An investigation of their learning through reform-based instruction

The purpose of this study was to explore mathematics instruction which implements reform-based problems within a traditionally taught classroom and its effect on struggling learners of mathematics. The reform-based problems implemented during the course of this study dealt with area and perimeter concepts at the fifth grade level. For this study, struggling learners of mathematics were defined as students scoring below the 40th percentile on the mathematics subtests of the Iowa Test of Basic Skills. The regular classroom teacher taught all lessons during the unit of instruction, while the researcher collected data from students using multiple methods: pretests and posttests, task-based interviews, standardized test scores, classroom observations, and pre and post attitude surveys. Through the pretest and posttests given during the course of this study, the researcher found evidence which connects reading comprehension to mathematical understanding. Students identified as struggling learners of mathematics were more likely to accurately calculate area and perimeter when the dimensions were given as numerals rather than words. Results from this research study show an increase in the struggling learners\u27 understanding of area and perimeter concepts when applied to problem-solving situations. The researcher conducted 10 observations of the fifth grade mathematics classroom. Through these observations, the researcher found the regular classroom teacher conducted mathematics instruction in a similar structure whether using the reform-based problems or a traditional lesson. The classroom teacher was deliberate in organizing each day\u27s instructional time beginning with a review of basic mathematics skills, whole-class discussion of problems and tasks, and individual work or small group exploration. The structure of instructional time, aligned with clear and consistent student expectations gave struggling learners of mathematics opportunities to be successful in learning the concepts of area and perimeter

Teachers\u27 Perceptions of Manipulatives During Middle School Math Instruction

In a Colorado school district, school personnel and parents were concerned that middle school math proficiency levels were low for 2011-2014 and math teachers were not using manipulatives in their classes to increase math performance. The district\u27s math coordinator did not foresee providing specific professional development (PD) for math manipulative use to address these concerns. Without this PD, math teachers may be ill-quipped to teach math concepts when using manipulatives, which, in turn, could lead to further poor math performance. The purpose of this qualitative bounded collective case study was to explore middle school teachers\u27 perceptions of PD and perceived self-efficacy regading the implementation of manipulatives. Knowles\u27s andragogy and Piaget\u27s cognitive development theories framed this study. A homogeneous sample of 12 voluntary participants with more than 5 years teaching middle school math, both with and without access to manipulatives, volunteered to participate in this study. Data from observations, interviews, and archival documents were analyzed using comparative and inductive analyses and were analytically coded. Participants reported a need for PD that focused on physical and virtual manipulatives (PM and VM) and a low perceived self-efficacy regarding manipulatives use during math instruction. A blended PD using face-to-face and distance learning formats was designed to increase math teachers\u27 knowledge of and perceived self-efficacy with PM and VM for math instruction. This endeavor may contribute to positive social change by reforming PD opportunities to support teachers\u27 practice and self-efficacy using manipulatives during math instruction, ultimately increasing student performance

Number sense : the underpinning understanding for early quantitative literacy

The fundamental meaning of Quantitative Literacy (QL) as the application of quantitative knowledge or reasoning in new/unfamiliar contexts is problematic because how we acquire knowledge, and transfer it to new situations, is not straightforward. This article argues that in the early development of QL, there is a specific corpus of numerical knowledge which learners need to integrate into their thinking, and to which teachers should attend. The paper is a rebuttal to historically prevalent (and simplistic) views that the terrain of early numerical understanding is little more than simple counting devoid of cognitive complexity. Rather, the knowledge upon which early QL develops comprises interdependent dimensions: Number Knowledge, Counting Skills and Principles, Nonverbal Calculation, Number Combinations and Story Problems - summarised as Number Sense. In order to derive the findings for this manuscript, a realist synthesis of recent Education and Psychology literature was conducted. The findings are of use not only when teaching very young children, but also when teaching learners who are experiencing learning difficulties through the absence of prerequisite numerical knowledge. As well distilling fundamental quantitative knowledge for teachers to integrate into practice, the review emphasises that improved pedagogy is less a function of literal applications of reported interventions, on the grounds of perceived efficacy elsewhere, but based in refinements of teachers' understandings. Because teachers need to adapt instructional sequences to the actual thinking and learning of learners in their charge, they need knowledge that allows them to develop their own theoretical understanding rather than didactic exhortations