Developing mathematical fluency: comparing exercises and rich tasks

Achieving fluency in important mathematical procedures is fundamental to students’ mathematical development. The usual way to develop procedural fluency is to practise repetitive exercises, but is this the only effective way?This paper reports three quasi experimental studies carried out in a total of 11 secondary schools involving altogether 528 students aged 12–15. In each study, parallel classes were taught the same mathematical procedure before one class undertook traditional exercises while the other worked on a "mathematical etude" (Foster International Journal of Mathematical Education in Science and Technology, 44(5), 765–774, 2013b), designed to be a richer task involving extensive opportunities for practice of the relevant procedure. Bayesian t tests on the gain scores between pre- and post-tests in each study provided evidence of no difference between the two conditions. A Bayesian meta-analysis of the three studies gave a combined Bayes factor of 5.83, constituting Bsubstantial^ evidence (Jeffreys, 1961) in favour of the null hypothesis that etudes and exercises were equally effective, relative to the alternative hypothesis that they were not. These data support the conclusion that the mathematical etudes trialled are comparable to traditional exercises in their effects on procedural fluency. This could make etudes a viable alternative to exercises, since they offer the possibility of richer, more creative problem-solving activity, with comparable effectiveness in developing procedural fluency

Small group interventions for children aged 5-9 years old with mathematical learning difficulties

The research related to educational interventions for children with mathematical learning difficulties has been increasing steadily. In this chapter I focus on small group interventions for children aged 5–9 years old with learning difficulties in mathematics. First, I describe the important issues: (1) who are the children having problems in mathematics, (2) what do we mean with (special) education intervention, (3) what does Responsiveness to Intervention mean, and (4) what intervention features have been found effective for children aged 5–9 years with learning difficulties in mathematics. Then, I describe the research and developmental work that has been done in Finland on designing web services which provide evidence-based information and materials for educators. The two web services are LukiMat and ThinkMath. Together, these two web services include the knowledge base, assessment batteries and intervention tools to be used in relation to mathematical learning difficulties in the age group 5–9 years.Peer reviewe

The effects of precision teaching and self-regulation learning on early multiplication fluency

Fluent recall of basic facts is essential to the development of more complex math skills. Therefore, failure to develop fluency with basic facts may impede the development of these skills. The present study used a between groups experimental design to investigate whether a basic facts fluency program, implemented within a self-regulated learner (SRL) framework, could lead to increased fluency with multiplication facts for Year 5 and Year 6 New Zealand students (9–10 years old). This study also investigated the extent to which the SRL program altered students’ basic facts practice behavior outside of school hours. The study found that the SRL program resulted in rapid fluency development that was maintained over time. Nomothetic and idiographic analysis confirmed that the program was suitable for use within Tier 1 of the response to intervention framework. In addition, the study also found that students who received the program altered their practice behavior outside school hours. The results from this study show how elements of self-regulated learning and precision teaching can be successfully combined to enhance students’ mathematics achievement

A brief primary care intervention to reduce fear of movement in chronic low back pain patients

Fear avoidance model of chronic pain-based interventions are effective, but have not been successfully implemented into primary care. It was hypothesized that speed walking times and key measures of the fear avoidance model would improve following the brief intervention delivered in primary care. A brief primary care-based intervention (PCB) that included a single educational session, speed walking (an in vivo desensitization exposure task), and visual performance feedback was designed to reduce fear avoidance beliefs and improve function in 4 patients with chronic low back pain. A multiple baseline across subjects with a changing criterion design indicated that speed walking times improved from baseline only after the PCB intervention was delivered. Six fear avoidance model outcome measures improved from baseline to end of study and five of six outcome measures improved from end of study to follow-up. This study provides evidence for the efficacy of a brief PCB fear avoidance intervention that was successfully implemented into a busy clinic for the treatment of chronic pain