The effect of calculators on the numerical problem-solving skills and attitudes of primary students towards mathematics /

The purpose of this study was to determine the effect that calculators have on the attitudes and numerical problem-solving skills of primary students. The sample used for this research was one of convenience. The sample consisted of two grade 3 classes within the York Region District School Board. The students in the experimental group used calculators for this problem-solving unit. The students in the control group completed the same numerical problem-solving unit without the use of calculators. The pretest-posttest control group design was used for this study. All students involved in this study completed a computational pretest and an attitude pretest. At the end of the study, the students completed a computational posttest. Five students from the experimental group and five students from the control group received their posttests in the form of a taped interview. At the end of the unit, all students completed the attitude scale that they had received before the numerical problem-solving unit once again. Data for qualitative analysis included anecdotal observations, journal entries, and transcribed interviews. The constant comparative method was used to analyze the qualitative data. A t test was also performed on the data to determine whether there were changes in test and attitude scores between the control and experimental group. Overall, the findings of this study support the hypothesis that calculators improve the attitudes of primary students toward mathematics. Also, there is some evidence to suggest that calculators improve the computational skills of grade 3 students.

Assessment in tertiary mathematics

There is a growing consensus among many educators that the goals of teaching and learning mathematics are to help students solve real-life problems, participate intelligently in daily affairs, and prepare them for jobs (Gardiner, 1994; Roeber, 1995). These goals suggest that the role of routine procedural skills should be diminished while more emphasis ought to be placed on learners gaining conceptual insights and analytical skills that appear essential in real-life mathematical problem solving (Schoenfeld, 1993; Stenmark, 1989).

Recognising and respecting Torres Strait Islander mathematics knowledges and home languages through mainstream mathematics education [Abstract]

This abstract provides a preliminary discussion of the importance of recognising Torres Strait Islander knowledges and home languages of mathematics education. It stems from a project involving Torres Strait Islander Teachers and Teacher Aides and university based researchers who are working together to enhance the mathematics learning of students from Years 4-9. A key focus of the project is that mathematics is relevant and provides students with opportunities for further education, training and employment. Veronica Arbon (2008) questions the assumptions underpinning Western mainstream education as beneficial for Aboriginal and Torres Strait Islander people which assumes that it enables them to better participate in Australian society. She asks “how de we best achieve outcomes for and with Indigenous people conducive to our cultural, physical and economic sustainability as defined by us from Indigenous knowledge positions?” (p. 118). How does a mainstream education written to English conventions provide students with the knowledge and skills to participate in daily life, if it does not recognise the cultural identity of Indigenous students as it should (Priest, 2005; cf. Schnukal, 2003)? Arbon (2008) states that this view is now brought into question with calls for both ways education where mainstream knowledge and practices is blended with Indigenous cultural knowledges of learning. This project considers as crucial that cultural knowledges and experiences of Indigenous people to be valued and respected and given the currency in the same way that non Indigenous knowledge is (Taylor, 2003) for both ways education to work.

The effect of Amblyopia on motor and psychosocial skills in children

Background/Aims: In an investigation of the functional impact of amblyopia on children, the fine motor skills, perceived self-esteem and eye movements of amblyopic children were compared with that of age-matched controls. The influence of amblyogenic condition or treatment factors that might predict any decrement in outcome measures was investigated. The relationship between indirect measures of eye movements that are used clinically and eye movement characteristics recorded during reading was examined and the relevance of proficiency in fine motor skills to performance on standardised educational tests was explored in a sub-group of the control children. Methods: Children with amblyopia (n=82; age 8.2 ± 1.3 years) from differing causes (infantile esotropia n=17, acquired strabismus n=28, anisometropia n=15, mixed n=13 and deprivation n=9), and a control group of children (n=106; age 9.5 ± 1.2 years) participated in this study. Measures of visual function included monocular logMAR visual acuity (VA) and stereopsis assessed with the Randot Preschool Stereoacuity test, while fine motor skills were measured using the Visual-Motor Control (VMC) and Upper Limb Speed and Dexterity (ULSD) subtests of the Brunicks-Oseretsky Test of Motor Proficiency. Perceived self esteem was assessed for those children from grade 3 school level with the Harter Self Perception Profile for Children and for those in younger grades (preschool to grade 2) with the Pictorial Scale of Perceived Competence and Acceptance for Young Children. A clinical measure of eye movements was made with the Developmental Eye Movement (DEM) test for those children aged eight years and above. For appropriate case-control comparison of data, the results from amblyopic children were compared with age-matched sub-samples drawn from the group of children with normal vision who completed the tests. Eye movements during reading for comprehension were recorded by the Visagraph infra-red recording system and results of standardised tests of educational performance were also obtained for a sub-set of the control group. Results Amblyopic children (n=82; age 8.2 ± 1.7 years) performed significantly poorer than age-matched control children (n=37; age 8.3 ± 1.3 years) on 9 of 16 fine motor skills sub-items and for the overall age-standardised scores for both VMC and ULSD items (p<0.05); differences were most evident on timed manual dexterity tasks. The underlying aetiology of amblyopia and level of stereoacuity significantly affected fine motor skill performance on both items. However, when examined in a multiple regression model that took into account the inter-correlation between visual characteristics, poorer fine motor skills performance was only associated with strabismus (F1,75 = 5.428; p =0. 022), and not with the level of stereoacuity, refractive error or visual acuity in either eye. Amblyopic children from grade 3 school level and above (n=47; age 9.2 ± 1.3 years), particularly those with acquired strabismus, had significantly lower social acceptance scores than age-matched control children (n=52; age 9.4 ± 0.5 years) (F(5,93) = 3.14; p = 0.012). However, the scores of the amblyopic children were not significantly different to controls for other areas related to self-esteem, including scholastic competence, physical appearance, athletic competence, behavioural conduct and global self worth. A lower social acceptance score was independently associated with a history of treatment with patching but not with a history of strabismus or wearing glasses. Amblyopic children from pre-school to grade 2 school level (n=29; age = 6.6 ± 0.6 years) had similar self-perception scores to their age-matched peers (n=20; age = 6.4 ± 0.5 years). There were no significant differences between the amblyopic (n=39; age 9.1 ± 0.9 years) and age-matched control (n = 42; age = 9.3 ± 0.38 years) groups for any of the DEM outcome measures (Vertical Time, Horizontal Time, Number of Errors and Ratio (Horizontal time/Vertical time)). Performance on the DEM did not significantly relate to measures of VA in either eye, level of binocular function, history of strabismus or refractive error. Developmental Eye Movement test outcome measures Horizontal Time and Vertical Time were significantly correlated with reading rates measured by the Visagraph for both reading for comprehension and naming numbers (r>0.5). Some moderate correlations were also seen between the DEM Ratio and word reading rates as recorded by Visagraph (r=0.37). In children with normal vision, academic scores in mathematics, spelling and reading were associated with measures of fine motor skills. Strongest effect sizes were seen with the timed manual dexterity domain, Upper Limb Speed and Dexterity. Conclusions Amblyopia may have a negative impact on a child’s fine motor skills and an older child’s sense of acceptance by their peers may be influenced by treatment that includes eye patching. Clinical measures of eye movements were not affected in amblyopic children. A number of the outcome measures of the DEM are associated with objective recordings of reading rates, supporting its clinical use for identification of children with slower reading rates. In children with normal vision, proficiency on clinical measures of fine motor skill are associated with outcomes on standardised measures of educational performance. Scores on timed manual dexterity tasks had the strongest association with educational performance. Collectively, the results of this study indicate that, in addition to the reduction in visual acuity and binocular function that define the condition, amblyopes have functional impairment in childhood development skills that underlie proficiency in everyday activities. The study provides support for strategies aimed at early identification and remediation of amblyopia and the co-morbidities that arise from abnormal visual neurodevelopment.

Thai students' engagement with cooperative learning in mathematics classrooms

Over the past decade, Thai schools have been encouraged by the Thai Ministry of Education to introduce more student-centred pedagogies such as cooperative learning into their classrooms (Carter, 2006). However, prior research has indicated that the implementation of cooperative learning into Thai schools has been confounded by cultural traditions endemic within Thai schools (Deveney, 2005). The purpose of the study was to investigate how 32 Grade 3 and 32 Grade 4 students enrolled in a Thai school engaged with cooperative learning in mathematics classrooms after they had been taught cooperative learning strategies and skills. These strategies and skills were derived from a conceptual framework that was the outcome of an analysis and synthesis of social learning, behaviourist and socio-cognitive theories found in the research literature. The intervention began with a two week program during which the students were introduced to and engaged in practicing a set of cooperative learning strategies and skills (3 times a week). Then during the next four weeks (3 times a week), these cooperative learning strategies and skills were applied in the contexts of two units of mathematics lessons. A survey of student attitudes with respect to their engagement in cooperative learning was conducted at the conclusion of the six-week intervention. The results from the analysis of the survey data were triangulated with the results derived from the analysis of data from classroom observations and teacher interviews. The analysis of data identified four complementary processes that need to be considered by Thai teachers attempting to implement cooperative learning into their mathematics classrooms. The paper concludes with a set of criteria derived from the results of the study to guide Thai teachers intending to implement cooperative learning strategies and skills in their classrooms.

Mathematics funds of knowledge : sotmaute and sermaute fish in a Torres Strait Islander community

The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents’ funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based on the premise that people are competent and have knowledge that has been historically and culturally accumulated into a body of knowledge and skills essential for their functioning and well-being. This knowledge is then practised throughout their lives and passed onto the next generation of children. Through adopting a community research approach, funds of knowledge that can be used to validate the community’s identities as knowledgeable people, can also be used as foundations for future learnings for teachers, parents and children in the early years of school. They can be the bridge that joins a community’s funds of knowledge with schools validating that knowledge.

Retooling Chinese primary school teachers to use technology creatively to promote innovation and problem solving skills in science classrooms

This paper reports on the initial phase of a Professional Learning Program (PLP) undertaken by 100 primary school teachers in China that aimed to facilitate the development of adaptive expertise in using technology to facilitate innovative science teaching and learning such as that envisaged by the Chinese Ministry of Education’s (2010-2020) education reforms. Key principles derived from literature about professional learning and scaffolding of learning informed the design of the PLP. The analysis of data revealed that the participants had made substantial progress towards the development of adaptive expertise. This was manifested not only by advances in the participants’ repertoires of Subject Matter Knowledge and Pedagogical Content Knowledge but also in changes to their levels of confidence and identities as teachers. By the end of the initial phase of the PLP, the participants had coalesced into a professional learning community that readily engaged in the sharing, peer review, reuse and adaption, and collaborative design of innovative science learning and assessment activities. The findings from the study indicate that those engaged in the development of PLPs for teachers in China need to take cognizance of certain cultural factors and traditions idiosyncratic to the Chinese educational system. A set of revised principles is then presented to inform the future design and implementation of PLPs for teachers in China.

Building the science and innovation base: work, skills and employment issues

This Special Issue of New Technology, Work and Employment has been prompted by the increasing awareness in many countries of the need to maintain and grow their science and innovation base. The development of science, engineering, technology and mathematics (STEM) skills and capacity is seen as vital for economic development and prosperity through its impact on national and regional research and development (R&D), technological advancement, and innovation potential.

Early mathematical learning: Number processing skills and executive function at 5 and 8 years of age

This research investigated differences and associations in performance in number processing and executive function for children attending primary school in a large Australian metropolitan city. In a cross-sectional study, performance of 25 children in the first full-time year of school, (Prep; mean age = 5.5 years) and 21 children in Year 3 (mean age = 8.5 years) completed three number processing tasks and three executive function tasks. Year 3 children consistently outperformed the Prep year children on measures of accuracy and reaction time, on the tasks of number comparison, calculation, shifting, and inhibition but not on number line estimation. The components of executive function (shifting, inhibition, and working memory) showed different patterns of correlation to performance on number processing tasks across the early years of school. Findings could be used to enhance teachers’ understanding about the role of the cognitive processes employed by children in numeracy learning, and so inform teachers’ classroom practices.

Problem solving in a 21st century mathematics curriculum

Research on problem solving in the mathematics curriculum has spanned many decades, yielding pendulum-like swings in recommendations on various issues. Ongoing debates concern the effectiveness of teaching general strategies and heuristics, the role of mathematical content (as the means versus the learning goal of problem solving), the role of context, and the proper emphasis on the social and affective dimensions of problem solving (e.g., Lesh & Zawojewski, 2007; Lester, 2013; Lester & Kehle, 2003; Schoenfeld, 1985, 2008; Silver, 1985). Various scholarly perspectives—including cognitive and behavioral science, neuroscience, the discipline of mathematics, educational philosophy, and sociocultural stances—have informed these debates, often generating divergent resolutions. Perhaps due to this uncertainty, educators’ efforts over the years to improve students’ mathematical problem-solving skills have had disappointing results. Qualitative and quantitative studies consistently reveal mathematics students’ struggles to solve problems more significant than routine exercises (OECD, 2014; Boaler, 2009)...

Tutoring with higher mathematics and the use of technology

We discuss three approaches to the use of technology as a teaching and learning tool that we are currently implementing for a target group of about one hundred second level engineering mathematics students. Central to these approaches is the underlying theme of motivating relatively poorly motivated students to learn, with the aim of improving learning outcomes. The approaches to be discussed have been used to replace, in part, more traditional mathematics tutorial sessions and lecture presentations. In brief, the first approach involves the application of constructivist thinking in the tertiary education arena, using technology as a computational and visual tool to create motivational knowledge conflicts or crises. The central idea is to model a realistic process of how scientific theory is actually developed, as proposed by Kuhn (1962), in contrast to more standard lecture and tutorial presentations. The second approach involves replacing procedural or algorithmic pencil-and-paper skills-consolidation exercises by software based tasks. Finally, the third approach aims at creating opportunities for higher order thinking via "on-line" exploratory or discovery mode tasks. The latter incorporates the incubation period method, as originally discussed by Rubinstein (1975) and others.

The potential benefits of divergent thinking and metacognitive skills in STEAM learning: A discussion paper

In the wake of an almost decade long economic downturn and increasing competition from developing economies, a new agenda in the Australian Government for science, technology, engineering, and mathematics (STEM) education and research has emerged as a national priority. However, to art and design educators, the pervasiveness and apparent exclusivity of STEM can be viewed as another instance of art and design education being relegated to the margins of curriculum (Greene, 1995). In the spirit of interdisciplinarity, there have been some recent calls to expand STEM education to include the arts and design, transforming STEM into STEAM in education (Maeda, 2013). As with STEM, STEAM education emphasises the connections between previously disparate disciplines, meaning that education has been conceptualised in different ways, such as focusing on the creative design thinking process that is fundamental to engineering and art (Bequette & Bequette, 2012). In this article, we discuss divergent creative design thinking process and metacognitive skills, how, and why they may enhance learning in STEM and STEAM.