What’s the problem? Meaning making and learning to do mathematical word problems in the context of digital tools

The general background of this study is an interest in how digital tools contribute to structuring learning activities. The specific interest is to explore how such tools co-determine students’ reasoning when solving word problems in mathematics, and what kind of learning that follows. Theoretically the research takes its point of departure in a sociocultural perspective on the role of cultural tools in thinking, and in a complementary interest in the role of the communicative framing of cognitive activities. Data have been collected through video documentation of classroom activities in secondary schools where multimedia tools are integrated into mathematics teaching. The focus of the analysis is on cases where the students encounter some kind of difficulty. The results show how the tool to a significant degree co-determines the meaning making practices of students. Thus, it is not a passive element in the situation; rather it invites certain types of activities, for instance iterative computations that do not necessarily rely on an analysis of the problems to be solved. For long periods of time the students’ activities are framed within the context of the tool, and they do not engage in discussing mathematics at all when solving the problems. It is argued that both from a practical and theoretical point of view it is important to scrutinize what competences students develop when using tools of this kind.

What predicts injury from physical punishment? A test of the typologies of violence hypothesis

OBJECTIVE: This study examined the power of child, perpetrator, and socio-economic characteristics to predict injury in cases of reported child physical abuse. The study was designed to assess the validity of the assumption that physically injurious incidents of child physical abuse are qualitatively different from those that do not result in injury, that their generative factors are distinctive, and that the quality of caregiving in these two types of incidents is different. METHOD: A weighted, nationally representative sample of 8,164 substantiated punishment abuse cases in Canada was used. Various models were constructed and evaluated through logistic regression. RESULTS: Of six potential predictors - child age, perpetrator sex, child functioning, parent functioning, economic stress, and social stress - none predicted injury to the child. CONCLUSIONS: The findings suggest that injurious and non-injurious physical abuse cannot be distinguished on the basis of the personal characteristics or circumstances of the child or perpetrator. PRACTICE IMPLICATIONS: A common criterion for child welfare intervention into cases of suspected physical abuse is injury or risk of injury. This criterion assumes that injurious and non-injurious assaults are qualitatively different phenomena, predicted by different risk factors. In the present study an attempt was made to differentiate between injurious and non-injurious cases of punitive physical abuse on the basis of characteristics of the child, perpetrator, family, and social context. None of these factors explained the likelihood of injury, suggesting that the prediction of injury as an intervention criterion may be questionable.     

The effects of using drawings in developing young children’s mathematical word problem solving: A design experiment with third-grade Hungarian students

The present study aims to investigate the effects of a design experiment developed for third-grade students in the field of mathematics word problems. The main focus of the program was developing students?? knowledge about word problem solving strategies with an emphasis on the role of visual representations in mathematical modeling. The experiment involved five experimental and six control classes (N?=?106 and 138, respectively) of third-grade students. The experiment comprised 20 lessons with 73 word problems, providing a systematic overview of the basic word problem types. Teachers of the experimental classes received a booklet containing lesson plans and overhead transparencies with different types of visual representations attached to the word problems. Students themselves were invited to make drawings for each task, and group work and teacher-led discussion shaped their beliefs about the role of visual representations in word problem solving. The effect sizes of the experiment were calculated from the results of two tests: an arithmetic skill and a word problem test, and the unbiased estimates for Cohen??s d proved to be 0.20 and 0.62. There were significant changes also in experimental group students?? beliefs about mathematics. The experiment pointed to the possibility, feasibility, and importance of learning about visual representations in mathematical word problem solving as early as in grade?3 (around age 9?C10).     

Beyond phonology: What else is needed to describe the problems of below-average readers and spellers?

The difficulties experienced by below-average readers in phonological decoding tasks are well documented. Recent research has suggested that additional deficits in perceptual-motor fluency, handedness, and memory may also exist among below-average readers. To evaluate these claims, average and below-average readers and spellers were compared on a range of phonological processing, verbal short-term and working memory, rapid naming, handedness, and perceptual-motor fluency tasks. Average and below-average readers were sampled in a comparable manner and were also comparable on age, gender, nonverbal ability, socioeconomic status, and ethnicity. Below-average readers and spellers performed lower than average readers and spellers on rhyme detection, pseudoword decoding, and rapid digit (but not picture) naming tasks, but showed no differences in handedness tasks or on a range of other perceptual-motor tasks.     

Dynamic testing of gifted and average‐ability children's analogy problem solving: Does executive functioning play a role?

In this study, dynamic testing principles were applied to examine progression of analogy problem solving, the roles that cognitive flexibility and metacognition play in children's progression as well as training benefits, and instructional needs of 7‐ to 8‐year‐old gifted and average‐ability children. Utilizing a pretest training posttest control group design, participants were split in four subgroups: gifted dynamic testing (n = 22), gifted unguided practice (n = 23), average‐ability dynamic testing (n = 31), and average‐ability unguided practice (n = 37). Results revealed that dynamic testing led to more advanced progression than unguided practice, and that gifted and average‐ability children showed equivalent progression lines and instructional needs. For children in both ability categories, cognitive flexibility was not found to be related to progression in analogy problem solving or training benefits. In addition, metacognition was revealed to be associated with training benefits. Implications for educational practice were provided in the discussion.     

Is effort praise motivational? The role of beliefs in the effort–ability relationship

In two studies, we investigated how beliefs in the effort–ability relationship moderated the effects of effort praise on student motivation. Study 1 showed that the more the participants believed that effort and ability were related positively (the positive rule) versus related negatively (the inverse rule), the more they would have positive self-evaluation and intrinsic motivation after effort praise. Study 2, with participants’ beliefs manipulated by a priming procedure, showed that the participants in the positive rule condition had better self-evaluation and more intrinsic motivation after effort praise than their counterparts did in the inverse rule condition. The results of the two studies converged to indicate that the motivational effects of effort praise depend on beliefs in the effort–ability relationship.     

What is the responsibility of mathematics education to the Indigenous students that it serves?

Although refuted many times, the commonly accepted story about Indigenous communities in Australia is that they had few counting words and thus were lacking in ways to quantify amounts. In this paper, we use the case of quantifying to discuss how Indigenous mathematics can be used, not just to help Indigenous students transition into the classroom but also back into their home communities. We argue that mathematics education must take seriously its responsibility to support Indigenous students to gain school mathematics and also to help maintain the use of traditional mathematical ideas. If this does not occur, mathematics educators will contribute, intentionally or unintentionally to the loss of Indigenous knowledge that present and future generations of Indigenous people will hold them responsible for.     

What is the purpose of this experiment? Or can students learn something from doing experiments?

Historically there have been many claims made about the value of laboratory work in schools, yet research shows that it often achieves little meaningful learning by students. One reason, among many, for this failing is that students often do not know the “purposes” for these tasks. By purposes we mean the intentions the teacher has for the activity when she/he decides to use it with a particular class at a particular time. This we contrast with the “aims” of a laboratory activity, the often quite formalised statements about the intended endpoint of the activity that are too often the “opening lines” of a student laboratory report and are simply the “expected” specific science content knowledge outcomes—not necessarily learnt nor understood. This paper describes a unit of laboratory work which was unusual in that the teacher's purpose was to develop students' understanding about the way scientific facts are established with little expectation that they would understand the science content involved in the experiments. The unit was very successful from both a cognitive and affective perspective. An important feature was the way in which students gradually came to understand the teacher's purpose as they proceeded through the unit. © 2000 John Wiley & Sons, Inc. J Res Sci Teach 37: 655–675, 2000     

What’s the use of ethical philosophy? The role of ethical theory in special educational needs

This article examines the relevance of modern moral philosophy to education, with particular reference to special educational needs. Where moral philosophers explore the tension between utilitarian and deontological reasoning, they often consider the balance between the rights of the individual and the benefits or costs for the majority. I argue that the debate is predicated on a false dichotomy between minority and majority which is best overcome by a return to virtue ethics. In exploring this ethical debate, I draw on a case study from Australia of a student excluded from mainstream education on the basis that inclusion will not serve the greater good of the majority of students. My intention here is not to offer practical guidance in the complex day-to-day deliberations of educators dealing with issues of inclusion, but to elaborate the structure of the present thinking about inclusion. It is hoped that an appreciation of the deeper basis of ethical reasoning will itself lead to a greater recognition of the need for exploring the ethical grounds of teaching and learning. I will argue that any dichotomy between the utilitarian happiness of the many and the deontological commitment to the rights of the individual is based on a misconception of human identity. The false choice between the many and the one rests upon the assumption that morality is fundamentally about restricting personal preferences in favour of the good of the majority, that there exists a fundamental conflict between what is good for the individual and what is good for society as a whole. This will lead me to argue that we need to reinterpret human identity as constituted by its social relations and that this reorientation is best achieved by reference to virtue ethics.     

Arithmetic word problem solving. Are authentic word problems easier to solve than standard ones? / Resolución de problemas aritméticos verbales. ¿Se resuelven mejor si se presentan como problemas auténticos?

This study analysed the effectiveness of presenting mathematical problems as ‘authentic’, which simulated the main aspects of situations in which students are usually involved. To do so, four independent variables were considered: level of mathematical difficulty (easy or difficult); rewording: standard problems (similar to those presented in textbooks), authentic and containing irrelevant situational information; mathematical ability (measured by means of the BADyG test); and reading comprehension level (measured with the comprehension task from the PROLEC-R test). The dependent measure was the success rate of a sample of 156 primary education children (grades four, five and six) in solving each kind of word problem. The results showed that the authentic versions of difficult problems were solved more successfully than other versions by students with high levels of mathematical aptitude and reading comprehension. That means that authentic wording is useful when children are able to understand the added information and have the mathematical knowledge necessary to interpret it.     

What is the best way to achieve broader reach of improved practices in higher education?

This article examines a common problem in higher education – how to create more widespread use of improved practices, often commonly referred to as innovations. I argue that policy models of scale-up are often advocated in higher education but that they have a dubious history in community development and K-12 education and that higher education leaders should shirk policymakers’ push to use a scale-up model of change. These thoughts are conceptual and are based upon a critical review of literature in community development and K-12, but I also draw upon empirical data in reviewing examples of widespread use of innovations in higher education.