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

Using game-based learning to enhance adaptive number knowledge

The aim of this dissertation was to explore how game-based learning can be used to develop primary school students’ adaptive number knowledge. The dissertation comprises five studies that explore the Number Navigation Game’s (NNG) development, testing and effects in enhancing primary school students’ adaptive number knowledge and related mathematical skills and knowledge. The studies use different methodologies and ask varying questions through the process of development and testing of the NNG. However, as a common thread, each study explores the relationship between game mechanics and mathematical content, and the relationship between game-based training and learning-outcome measures. Study I tested the NNG’s first working prototype from a user experience point of view and investigated instances of adaptive number knowledge in the game’s context. The game was tested in two sessions, with one student (age 11) playing individually and two students (ages 9 and 11) using the game collaboratively. Data were collected using video-recorded observations, gameplay screen capture and open-ended interview questions regarding the game experience. Results showed that already, the NNG prototype triggered players’ active engagement with different number combinations and numerical relations as well as reflection and discussion about these numerical relations. This suggested that gameplay with the NNG could trigger the type of mathematical thinking and problem solving which was expected to help enhance students’ development of adaptive number knowledge. Study II comprised three sub-studies (fifth-graders, n = 55; university students, n = 55; and sixth-graders, n = 22) and aimed to develop and test the Arithmetic Production Task, a paper-and-pencil measure of adaptive number knowledge. Individual differences in the Arithmetic Production Task and the relation between adaptive number knowledge and other mathematical skills and knowledge were explored. Results showed similar patterns of individual differences across the different samples and age groups. Adaptive number knowledge was found to be related to arithmetic fluency and conceptual knowledge of arithmetic. Results suggest that the Arithmetic Production Task was able to capture how participants recognise opportunities to use numerical features in their arithmetic problem solving, which can be used as an indicator of their adaptive number knowledge. Study III was the first attempt to test the NNG’s effects and examine the relationship between game performance and adaptive number knowledge. The study used a quasi-experimental pre-test/post-test design. Participants were 11 pairs of sixth-grade students (11 females, age range: 11-13) from one classroom who played the NNG over a seven-week period. Results showed improvement in participants’ performance in adaptive number knowledge and math fluency. Game performance was found to be a predictor of students’ post-test performance on the multi-operational aspect of adaptive number knowledge. Study IV provides a detailed overview of game design decisions in the NNG, which are based on theory and the results from previous pilot studies using the NNG (Studies I and III). Another game-development phase followed Study IV, resulting in the final NNG prototype used in Study V. After the initial pilot and development stages, Study V aimed to test the NNG’s effects in the classroom and on a larger scale across different grade levels. Study V explored how training with the NNG affects the development of primary school students’ adaptive number knowledge, arithmetic fluency and pre-algebra knowledge at different grade levels; and how students’ performance on the NNG affects the development of the mathematical learning outcomes. A pre-test/post-test randomised control design was used, in which the experimental group played the NNG for 10 weeks during math class, and the control group received regular math instruction. Results showed significant overall improvement in the experimental group compared with the control group on all measured mathematical learning outcomes. Game performance was related to the experimental group’s post-test scores even after controlling for pre-test scores and grade. Additionally, results showed that the NNG develops different aspects of adaptive number knowledge, math fluency and pre-algebra knowledge across grade levels. Overall, the present dissertation’s findings show that the NNG can provide efficient and novel training opportunities for developing primary school students’ adaptive number knowledge and related mathematical skills and knowledge. The game-based format allowed for a large amount of open-ended practice with various number-operation combinations, which usually is difficult to achieve in regular mathematics classrooms. The dissertation’s results provide empirical evidence for the theoretical model of adaptive number knowledge as a component of adaptivity with arithmetic. Additionally, a new and scalable measurement and novel training of adaptive number knowledge were developed. The results also highlight the importance of an iterative design process in educational game development, with the following guiding principles: integration of educational content and game features, measurement questions and application of trainin

Partnering with Principals Through Formal and Informal Professional Development

Mathematics Specialists and administrators need to define what they should see students and teachers doing in classrooms that promote proficiency and understanding in mathematics. Formal, divisionwide professional development on this topic can quickly guide and inform a large group of administrators in one setting. However, potentially more powerful professional development can occur on a small scale one building at a time through mathematics department learning walks

Mathematical difficulties as decoupling of expectation and developmental trajectories

Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science

Using iPad applications to promote fluency in mathematics and improve attitudes toward studying

This study monitored four third grade students who used iPad games to study multiplication facts for seven weeks. They took a survey at the beginning and end of the study to assess their attitude toward school, studying, and math in order to determine whether an attitude change took place throughout the course of events. The students also participated in a timed multiplication test with eighty-one questions at the beginning and took the same test at the end of the seven-week period. I met with the group twice weekly during the school day to play multiplication practice games. The group consisted of two boys and two girls at a private school in Fayetteville, Arkansas. They were chosen to participate in this study by their classroom teacher because of they demonstrated need in the areas of study skills and multiplication

A Comparison of Two Approaches To Promote Multiplication Fact Fluency In Fifth Grade

Fifth grade students are expected to be fluent in basic multiplication facts by the start of fifth grade, however many are not (Minnesota Department of Education, 2007). When fifth grade students are not fluent in basic multiplication facts, they struggle to understand and master grade level skills and standards (Allen-Lyall, 2018; Burns et al., 2012; Ok & Bryant, 2016; The Math Learning Center, 2017; Wong & Evans, 2007). This quantitative research study compared two classwide approaches to promote multiplication fact fluency in fifth grade. Throughout the research phase, one fifth grade math class practiced multiplication facts for ten minutes each day using computer-based multiplication fact practice and a second fifth grade math class practiced multiplication facts for ten minutes each day using game-based multiplication fact practice. A multiplication probe was given as a pretest before the research phase to determine the average digits correct for each fifth grade math class. Following the research phase, the same multiplication probe used as a pretest was administered for a second time as a posttest to determine the average digits correct for each fifth grade math class. The average increase in the digits correct from the pretest to the posttest for both classes was analyzed to determine which multiplication practice method is most effective in promoting multiplication fact fluency in fifth grade

The Evaluation of Enhanced Academic Instruction in After-School Programs: Findings After the First Year of Implementation

This report presents one-year implementation and impact findings on two supplemental academic instruction approaches developed for after-school settings -- one for math and one for reading. Compared with regular after-school programming, the supplemental math program had impacts on student SAT 10 test scores and the supplemental reading program did not --although the reading program had some effect on reading fluency

Exploring the use of known strategies for achieving fluency of multiplication and division facts in third grade.

In order to complete higher level math tasks, fluency of multiplication and division is crucial. Based on state standards, third grade students are expected to become fluent with multiplication and division facts from 0-100 by the end of the year. Throughout history many educators have relied on timed tests to teach and assess math fact fluency. Best practices for helping students become fluent with math facts is now highly debated. The purpose of this teacher action research study was to evaluate the effectiveness of using math fact games and visual math cards as means of distributed practice in order to achieve fluency with multiplication and division facts among a group of forty-seven, third-grade students in a suburban school district in Central Ohio. A mixed-method design was framed within a cycle of inquiry used in teacher action research, including a pre-assessment, student interviews, and summative assessments for data collection. The focus of the study was to implement research-based instructional strategies for boosting fluency of math facts, then assessing, student fluency. Data from the Post-Assessment, verbal assessment, rating scales, and interviews showed that students did in fact learn to multiply and divide when taught these strategies. Students reported that learning strategies were crucial, math games were helpful as well as enjoyable, and timed tests would cause anxiety. Moreover, the assessment used in this study was a more valid measure of what fluency in mathematics really encompasses. Regardless of the sequence in which the two strategies were introduced, all students demonstrated growth in strategy usage and efficiency over the two-week period

The effects of computer games on the mastery of multiplication facts for students with exceptional learning needs

The purpose of this study was to examine the effects of multiplication computer games on mastering multiplication facts for students with exceptional learning needs. Three students will be participating in this research study. There is one male student and two female students, in Grades 3 and 4. Each of the three students has an individualized education plan (IEP) and receives three hours of instruction outside the regular classroom in a resource room setting. Two of the students have been identified as having Specific Learning Disabilities and one as having multiple disabilities. The students were selected for the study due to a lack of mastery of multiplication facts. This study was utilized a pretest- posttest design and data was collected during the baseline, intervention, and post-intervention phases. The research study was designed to determine the increase of multiplication mastered by each student. The dependent variable was the student scores on the multiplication assessments. The independent variable was the multiplication computer games that the students were playing in this study. The computer games were used to improve mastery of multiplication facts. The data from this study suggests that multiplication computer games are an effective way to improve mastery of multiplication facts. This has led me to conclude that incorporating games, technology, and computer games is beneficial for skill development for students with and without disabilities. Technology is an effective means to master multiplication facts. Games and technology can increase motivation in math for all students. The results from this study parallel results from previous studies that technology and computer games are effective in improving math skills for students with disabilities. It should be incorporated into the math curriculums, not replace current curriculums. Technology and games can increase motivation in math. The findings suggest future investigations into the use of computer games in math

Play It Again Mathematics

This action research project focuses on implementing game-based learning into a first-grade math lesson, to help improve addition facts and fluency. The study was conducted over a ten-day period in one first grade classroom. Data was collected at the beginning of this study and at the end to determine if playing games in math increases a student\u27s addition fact fluency . After the initial one-minute addition pre-test, the students were divided into two groups according to ability. One of the groups was the control group who learned addition math facts through paper and pencil activities and the other group was the study group who learned addition by playing games. After the ten days of intervention, students who were in the study group showed significant growth after taking the one-minute addition post-test. The findings of this study found that when the students played math games, they were able to do better on the one-minute addition test and were more engaged and enjoyed math more than their counterparts