The effect of mathematical games on on-task behaviours in the primary classroom

A challenge for primary classroom teachers is to maintain students’ engagement with learning tasks while catering for their diverse needs, capabilities and interests. Multiple pedagogical approaches are employed to promote on-task behaviours in the mathematics classroom. There is a general assumption by educators that games ignite children’s on-task behaviours, but there is little systemically researched empirical data to support this claim. This paper compares students’ on-task behaviours during non-digital game-playing lessons compared with non-game-playing lessons. Six randomly selected grade 5 and 6 students (9–12 year olds) were observed during ten mathematics lessons. A total of 2,100 observations were recorded via an observational schedule and analysed by comparing the percentage of exhibited behaviours. The study found the children spent 93 % of the class-time exhibiting on-task engagement during the game-playing lessons compared with 72 % during the non-game-playing lessons. The game-playing lessons also promoted greater incidents of student talk related to the mathematical task (34 %) compared with the non-game playing lessons (11 %). These results support the argument that games serve to increase students’ time-on-task in mathematics lessons. Therefore, it is contended that use of games explicitly addressing the mathematical content being taught in a classroom is one way to increase engagement and, in turn, potential for learning.

Testing the effectiveness of mathematical games as a pedagogical tool for children's learning

In an effort to engage children in mathematics learning, many primary teachers use mathematical games and activities. Games have been employed for drill and practice, warm-up activities and rewards. The effectiveness of games as a pedagogical tool requires further examination if games are to be employed for the teaching of mathematical concepts. This paper reports research that compared the effectiveness of non-digital games with non-game but engaging activities as pedagogical tools for promoting mathematical learning. In the classrooms that played games, the effects of adding teacher-led whole class discussion was explored. The research was conducted with 10–12-year-old children in eight classrooms in three Australian primary schools, using differing instructional approaches to teach multiplication and division of decimals. A quasi-experimental design with pre-test, post-test and delayed post-test was employed, and the effects of the interventions were measured by the children’s written test performance. Test results indicated lesser gains in learning in game playing situations versus non-game activities and that teacher-led discussions during and following the game playing did not improve children’s learning. The finding that these games did not help children demonstrate a mathematical understanding of concepts under test conditions suggests that educators should carefully consider the application and appropriateness of games before employing them as a vehicle for introducing mathematical concepts.

Towards mathematical literacy in the 21st century : perspectives from Indonesia

The notion of mathematical literacy advocated by PISA (OECD, 2006) offers a broader conception for assessing mathematical competences and processes with the main focus on the relevant use of mathematics in life. This notion of mathematical literacy is closely connected to the notion of mathematical modelling whereby mathematics is put to solving real world problems. Indonesia has participated as a partner country in PISA since 2000. The PISA trends in mathematics from 2003 to 2009 revealed unsatisfactory mathematical literacy among 15-year-old students from Indonesia who lagged behind the average of OCED countries. In this paper, exemplary cases will be discussed to examine and promote mathematical literacy at teacher education level. Lesson ideas and instruments were adapted from PISA 2006 released items. The potential of such tasks will be discussed based on case studies of implementing these instruments with samples of pre-service teachers in Yogyakarta. 

Building awareness of mathematical modelling at teacher education: a case study in Indonesia

A growing interest to teach mathematics closely connected to its use in daily life has taken place in Indonesia for over a decade (Sembiring, Hadi, and Dolk 2008). This chapter  reports an exploratory case study of  the building of an awareness of mathematical modelling in teacher education in Indonesia. A modelling task, re-designing a parking lot (Ang 2009), was assigned to groups of pre-service secondary mathematics teachers. All groups undertook the stages of collecting data on a parking lot, identifying limitations in the current design of the parking lot, and proposing a new design based on their observations and analyses. The nature of the mathematical models elicited by pre-service teachers during various stages of completing the modelling task will be examined. Implications of this study suggest the need to encourage pre-service teachers to state the assumptions and real-world considerations and link them to the mathematical model in order to validate their models.

A review of mathematical equations to assign individual marks from a team mark

BACKGROUND : Team-based learning is an integral part of engineering education today. Development of team skills is now a part of the curriculum at universities as employers demand these skills on graduates. Higher education institutions enforce academic staff to teach, practise and assess team skills, and at the same time, they ask academic staff to supply individual marks and/or grades. Allocating individual marks from a team mark is a very complex and sensitive task that may adversely affect both individual and team performance. A number of both qualitative and quantitative methods are available to address this issue. Quantitative mathematical methods are favoured over qualitative subjective methods as they are more straightforward to explain to the students and they may help minimise conflicts between assessors and students. PURPOSE : This study presents a review of commonly used mathematical equations to allocate individual marks from a team mark. Quantitative analytical equations are favoured over qualitative subjective methods because they are more straightforward to explain to the students and if explained to the students in advance, they may help minimise conflicts between assessors and students. Some of these analytical equations focus primarily on the assessment of the quality of teamwork product (product assessment) while the others put greater emphasis on the assessment of teamwork performance (process assessment). The remaining equations try to strike a balance between product assessment and process assessment. The primary purpose of this study is to discuss the qualitative aspects of quantitative equations. DESIGN/METHOD : This study simulates a set of scenarios of team marks and individual contributions that collectively cover all possible teamwork assessment environments. The available analytical equations are then applied to each case to examine their relative merits with respect to a set of evaluation criteria with exhaustive graphical plots. RESULTS : Although each analytical equations discussed and analysed in this study has its own merits for a particular application scenario, the recent methods such as knee formula in SPARKPLUS and cap formula, are relatively better in terms of a number of evaluation criteria such as fairness, teamwork attitude, balance between process and product assessments etc. In addition to having all favourable properties of knee formula, cap formula explicitly considers the quality of teamwork (i.e., team mark) while allocating individual marks. Cap formula may, however, be difficult to explain to the students due to relatively complex mathematical equations involved. CONCLUSIONS : Not all existing analytical equations that allocate individual marks from a team mark have similar characteristics. Recent methods, knee formula and cap formula, are advantageous in terms of a number of evaluation criteria and are recommended to apply in practice. However, it is important to examine these equations with respect to enhancing students’ learning achievements rather than the students and academic staff’s preferences.

Assessment of primary 5 students' mathematical modelling competencies

 Mathematical modelling is increasingly becoming part of an instructional approach deemed to develop students with competencies to function as 21st century learners and problem solvers. As mathematical modelling is a relatively new domain in the Singapore primary school mathematics curriculum, many teachers may not be aware of the learning outcomes and competencies needed to develop in their students during mathematical modelling. This paper reports on the assessment of two groups of Primary 5 students’ (aged 11) mathematical modelling competencies in their first attempt in completing a modelling task. The students’ competencies are assessed to be at levels 1 and 2 of a researcher-designed rubric. Findings appear to suggest that students faced particular challenges in formulating a mathematical problem from the real-world problem through making assumptions. Implications on teacher education on the facilitation of problem formulation and mathematisation during mathematical modelling at the primary level are drawn.

Fostering teacher competencies in incorporating mathematical modelling in Singapore primary mathematics classrooms

Until recently, the limited use of modelling activities in Singapore mathematics classrooms despite the incorporation of mathematical modelling in the curriculum since 2003 could be due to a lack of concerted efforts in teacher preparation. Explicit guidelines have recently been developed by the Ministry of Education (CPDD, 2012) with a view to harness the potentials of modelling activities for fostering 21st Century Competences in students. This paper illustrates how a multi-tiered teaching experiment using design research methodology was conducted to build teachers' capacity in facilitating and designing modelling tasks using a case study involving an experienced teacher in a primary 5 (aged 10-11) mathematics classroom. Implications on the identification of teacher competencies to be focused upon during teacher development in incorporating mathematical modelling in Singapore classrooms will be drawn.

Brief report: children with ADHA without co-morbid autism do not have impaired motor proficiency on the Movement Assessment Battery for Children

Motor proficiency was investigated in a sample of children with Attention Deficit Hyperactivity Disorder-Combined type (ADHD-CT) without autism. Accounting for the influence of co-morbid autistic symptoms in ADHD motor studies is vital given that motor impairment has been linked to social–communication symptoms in children who have co-morbid ADHD and autistic-like symptoms. Two groups of children aged between 7–14 years were recruited; children with ADHD-CT (n = 16; mean age 10 years, 7 months [SD = 1 year, 10 months]) and a typically developing (n = 16; mean age 10 years, 6 months [SD = 2 years, 6 months]) group. Motor proficiency was measured using the Movement Assessment Battery for Children-2nd Edition, ADHD symptoms were measured using the Conner’s Parent Rating Scale. Children with ADHD-CT who had been screened for co-morbid autism did not display motor difficulties on the MABC-2. Higher levels of inattention, but not hyperactivity or impulsivity were associated with poorer motor performance. These findings provide indirect evidence that the motor problems that children with ADHD experience may be related to co-occurring social responsiveness impairments.

A mathematical model of neuromuscular adaptation to resistance training and its application in a computer simulation of accommodating loads

A large corpus of data obtained by means of empirical study of neuromuscular adaptation is currently of limited use to athletes and their coaches. One of the reasons lies in the unclear direct practical utility of many individual trials. This paper introduces a mathematical model of adaptation to resistance training, which derives its elements from physiological fundamentals on the one side, and empirical findings on the other. The key element of the proposed model is what is here termed the athlete’s capability profile. This is a generalization of length and velocity dependent force production characteristics of individual muscles, to an exercise with arbitrary biomechanics. The capability profile, a two-dimensional function over the capability plane, plays the central role in the proposed model of the training-adaptation feedback loop. Together with a dynamic model of resistance the capability profile is used in the model’s predictive stage when exercise performance is simulated using a numerical approximation of differential equations of motion. Simulation results are used to infer the adaptational stimulus, which manifests itself through a fed back modification of the capability profile. It is shown how empirical evidence of exercise specificity can be formulated mathematically and integrated in this framework. A detailed description of the proposed model is followed by examples of its application—new insights into the effects of accommodating loading for powerlifting are demonstrated. This is followed by a discussion of the limitations of the proposed model and an overview of avenues for future work.