Math-Towers: Promoting and supporting online collaborative mathematical exploration

Math-Towers (www.math-towers.ca) is a collaborative mathematics environment for pupils in grades 7 to 9. Using a fantasy adventure game context students are presented with a mathematical challenge, given online tools for working on the problem,and provided with a messaging system by which they may exchange ideas and partial solutions. This paper presents the philosophy behind the design of Math-Towers and work with students that indicates the extent to which we have been successful in meeting our aims. The technical and social problems encountered and revisions made to address these are also described.

Math-Towers: Online Interactive Collaborative Mathematics Explorations & Problem-Solving for Students Ages 11 to 15 years (Grades 6 to 10)

Math-Towers (www.math-towers.ca) is an online resource for students in grades 6 to 10 that supports collaborative problem-solving and investigations. This paper presents the philosophical position motivating the development of Math-Towers and describes how the site presents and motivates the mathematical challenges and supports participants' exploration and collaboration.

Measuring math anxiety in Italian college and high school students: Validity, reliability and gender invariance of the Abbreviated Math Anxiety Scale (AMAS)

Given that the ability to manage numbers is essential in a modern society, mathematics anxiety – which has been demonstrated to have unfortunate consequences in terms of mastery of math – has become a subject of increasing interest, and the need to accurately measure it has arisen. One of the widely employed scales to measure math anxiety is the Abbreviated Math Anxiety Scale (AMAS) (Hopko, Mahadevan, Bare & Hunt, 2003). The first aim of the present paper was to confirm the factor structure of the AMAS when administered to Italian high school and college students, and to test the invariance of the scale across educational levels. Additionally, we assessed the reliability and validity of the Italian version of the scale. Finally, we tested the invariance of the AMAS across genders. The overall findings provide evidence for the validity and reliability of the AMAS when administered to Italian students.

A review of behaviour change theories and techniques used in group based self-management programmes for chronic low back pain and arthritis

Background: Medical Research Council (MRC) guidelines recommend applying theory within complex interventions to explain how behaviour change occurs. Guidelines endorse self-management of chronic low back pain (CLBP) and osteoarthritis (OA), but evidence for its effectiveness is weak. Objective: This literature review aimed to determine the use of behaviour change theory and techniques within randomised controlled trials of group-based self-management programmes for chronic musculoskeletal pain, specifically CLBP and OA. Methods: A two-phase search strategy of electronic databases was used to identify systematic reviews and studies relevant to this area. Articles were coded for their use of behaviour change theory, and the number of behaviour change techniques (BCTs) was identified using a 93-item taxonomy, Taxonomy (v1). Results: 25 articles of 22 studies met the inclusion criteria, of which only three reported having based their intervention on theory, and all used Social Cognitive Theory. A total of 33 BCTs were coded across all articles with the most commonly identified techniques being '. instruction on how to perform the behaviour', '. demonstration of the behaviour', '. behavioural practice', '. credible source', '. graded tasks' and '. body changes'. Conclusion: Results demonstrate that theoretically driven research within group based self-management programmes for chronic musculoskeletal pain is lacking, or is poorly reported. Future research that follows recommended guidelines regarding the use of theory in study design and reporting is warranted.

Can I Count on Getting Better? Association between Math Anxiety and Poorer Understanding of Medical Risk Reductions

BACKGROUND: Lower numerical ability is associated with poorer understanding of health statistics, such as risk reductions of medical treatment. For many people, despite good numeracy skills, math provokes anxiety that impedes an ability to evaluate numerical information. Math-anxious individuals also report less confidence in their ability to perform math tasks. We hypothesized that, independent of objective numeracy, math anxiety would be associated with poorer responding and lower confidence when calculating risk reductions of medical treatments.

METHODS: Objective numeracy was assessed using an 11-item objective numeracy scale. A 13-item self-report scale was used to assess math anxiety. In experiment 1, participants were asked to interpret the baseline risk of disease and risk reductions associated with treatment options. Participants in experiment 2 were additionally provided a graphical display designed to facilitate the processing of math information and alleviate effects of math anxiety. Confidence ratings were provided on a 7-point scale.

RESULTS: Individuals of higher objective numeracy were more likely to respond correctly to baseline risks and risk reductions associated with treatment options and were more confident in their interpretations. Individuals who scored high in math anxiety were instead less likely to correctly interpret the baseline risks and risk reductions and were less confident in their risk calculations as well as in their assessments of the effectiveness of treatment options. Math anxiety predicted confidence levels but not correct responding when controlling for objective numeracy. The graphical display was most effective in increasing confidence among math-anxious individuals.

CONCLUSIONS: The findings suggest that math anxiety is associated with poorer medical risk interpretation but is more strongly related to confidence in interpretations.

How to feel "in love" with Math - a MOOC experience

In the past few years we have witnessed the fast development of distance learning tools such as Open Educational Resources (OER) and Massive Open Online Courses (MOOCs). This paper presents the “Mathematics without STRESS” MOOC Project, which is a cooperation between four schools from the Polytechnic Institute of Oporto (IPP). The concepts of MOOC and their quickly growing popularity are presented and complemented by a discussion of some MOOC definitions. The process of the project development is demonstrated by focusing on used MOOC structure, as well as the several types of course materials produced. At last, is presented a short discussion about problems and challenges met throughout the project. It is also our goal to contribute for a change in the way as teaching and learning Mathematics is seen and practiced nowadays.

Innovations in technology: a friendly math project and the learning analytics “challenge”

Currently the world around us "reboots" every minute and “staying at the forefront” seems to be a very arduous task. The continuous and “speeded” progress of society requires, from all the actors, a dynamic and efficient attitude both in terms progress monitoring and moving adaptation. With regard to education, no matter how updated we are in relation to the contents, the didactic strategies and technological resources, we are inevitably compelled to adapt to new paradigms and rethink the traditional teaching methods. It is in this context that the contribution of e-learning platforms arises. Here teachers and students have at their disposal new ways to enhance the teaching and learning process, and these platforms are seen, at the present time, as significant virtual teaching and learning supporting environments. This paper presents a Project and attempts to illustrate the potential that new technologies present as a “backing” tool in different stages of teaching and learning at different levels and areas of knowledge, particularly in Mathematics. We intend to promote a constructive discussion moment, exposing our actual perception - that the use of the Learning Management System Moodle, by Higher Education teachers, as supplementary teaching-learning environment for virtual classroom sessions can contribute for greater efficiency and effectiveness of teaching practice and to improve student achievement. Regarding the Learning analytics experience we will present a few results obtained with some assessment Learning Analytics tools, where we profoundly felt that the assessment of students’ performance in online learning environments is a challenging and demanding task.

Immediate effects of hip mobilization with movement in patients with hip osteoarthritis: A randomised controlled trial

Background Mobilization with movement (MWM) has been shown to reduce pain, increase range of motion (ROM) and physical function in a range of different musculoskeletal disorders. Despite this evidence, there is a lack of studies evaluating the effects of MWM for hip osteoarthritis (OA). Objectives To determine the immediate effects of MWM on pain, ROM and functional performance in patients with hip OA. Design Randomized controlled trial with immediate follow-up. Method Forty consenting patients (mean age 78 ± 6 years; 54% female) satisfied the eligibility criteria. All participants completed the study. Two forms of MWM techniques (n = 20) or a simulated MWM (sham) (n = 20) were applied. Primary outcomes: pain recorded by numerical rating scale (NRS). Secondary outcomes: hip flexion and internal rotation ROM, and physical performance (timed up and go, sit to stand, and 40 m self placed walk test) were assessed before and after the intervention. Results For the MWM group, pain decreased by 2 points on the NRS, hip flexion increased by 12.2°, internal rotation by 4.4°, and functional tests were also improved with clinically relevant effects following the MWM. There were no significant changes in the sham group for any outcome variable. Conclusions Pain, hip flexion ROM and physical performance immediately improved after the application of MWM in elderly patients suffering hip OA. The observed immediate changes were of clinical relevance. Future studies are required to determine the long-term effects of this intervention.

The development and implementation of math projects in a HEI: expectations, objectives, experiences and analysis

An overwhelming problem in Math Curriculums in Higher Education Institutions (HEI), we are daily facing in the last decade, is the substantial differences in Math background of our students. When you try to transmit, engage and teach subjects/contents that your “audience” is unable to respond to and/or even understand what we are trying to convey, it is somehow frustrating. In this sense, the Math projects and other didactic strategies, developed through Learning Management System Moodle, which include an array of activities that combine higher order thinking skills with math subjects and technology, for students of HE, appear as remedial but important, proactive and innovative measures in order to face and try to overcome these considerable problems. In this paper we will present some of these strategies, developed in some organic units of the Polytechnic Institute of Porto (IPP). But, how “fruitful” are the endless number of hours teachers spent in developing and implementing these platforms? Do students react to them as we would expect? Do they embrace this opportunity to overcome their difficulties? How do they use/interact individually with LMS platforms? Can this environment that provides the teacher with many interesting tools to improve the teaching – learning process, encourages students to reinforce their abilities and knowledge? In what way do they use each available material – videos, interactive tasks, texts, among others? What is the best way to assess student’s performance in these online learning environments? Learning Analytics tools provides us a huge amount of data, but how can we extract “good” and helpful information from them? These and many other questions still remain unanswered but we look forward to get some help in, at least, “get some drafts” for them because we feel that this “learning analysis”, that tackles the path from the objectives to the actual results, is perhaps the only way we have to move forward in the “best” learning and teaching direction.

Viva@Matemática project: a different way to see math

Viva@Mat is a project developed by four Math teachers from the School of Industrial Studies and Management (ESEIG) that was born with the fundamental objective of engaging ESEIG students with different math backgrounds in Math challenging activities. Some of these activities were transformed into real palpable materials and others into small interactive ones, being the great majority of them proposed by ESEIG’ students themselves. This small project rapidly grew into something we didn’t expect – it did flow over the walls of our institution to the general involving community – specifically to pre-university schools through the Viva@Math Exhibits – Orange, Blue and Green (the fourth, the Purple one is still in development). Nowadays, Viva@Math Exhibits – the public face of the Project – are itinerant and have been travelling between several, and different institutions (pre-university schools, preparatory schools, libraries, among others), around ESEIG and IPP area of influence and having registered visitors/participants of all ages. In this article we will describe the Viva@Math Project, its different activities that are categorized in some “great groups” like Numerical Trivia, Logic Activities and Mental Calculation, Puzzles, Geometric Curiosities, Magic Tricks, among others, designed to challenge students to use the underlying logical-mathematical reasoning to any ordinary and everyday activity. We will give specific and concrete examples of some of the activities developed and, also, reproduce of the general stimulating feedback the Project receives from the enrolled “actors” (teachers, students and their relatives, institutions, among others). We feel that this Project has become a small “bridge” between the pre-university schools and Higher Education Institutions (HEI), in trying to shorten the “gap” between the institutions of different levels of education and bring them to work together.

Correlation Among Math Anxiety, Attitudes Toward Math, and Math Achievement in Grade 9 Students: Relationships Across Gender

This research evaluated (a) the correlation between math anxiety, math attitudes, and achievement in math and (b) comparison among these variables in terms of gender among grade 9 students in a high school located in southern Ontario. Data were compiled from participant responses to the Attitudes Toward Math Inventory (ATMI) and the Math Anxiety Rating Scale for Adolescents (MARS-A), and achievement data were gathered from participants’ grade 9 academic math course marks and the EQAO Grade 9 Assessment of Mathematics. Nonparametric tests were conducted to determine whether there were relationships between the variables and to explore whether gender differences in anxiety, attitudes, and achievement existed for this sample. Results indicated that math anxiety was not related to math achievement but was a strong correlate of attitudes toward math. A strong positive relationship was found between math attitudes and achievement in math. Specifically, self-confidence in math, enjoyment of math, value of math, and motivation were all positive correlates of achievement in math. Also, results for gender comparisons were nonsignificant, indicating that gender differences in math anxiety, math attitudes, and math achievement scores were not prevalent in this group of grade 9 students. Therefore, attitudes toward math were considered to be a stronger predictor of performance than math anxiety or gender for this group.

Using Effective Teaching Strategies and Personality Type to Enhance the Mathematics Classroom: A Handbook for Intermediate Math Teachers

This project addressed the need for more insightful, current, and applicable resources for intermediate math teachers in Canadian classrooms. A need for a handbook in this division seemed warranted by a lack of government resource support. Throughout an extensive review of the literature, themes and topics for the handbook emerged. The handbook was designed to not only provide educators with examples of effective teaching strategies within the mathematics classroom but to also inform them about the ways in which their personal characteristics and personality type could affect their students and their own pedagogical practices. Three teaching professionals who had each taught in an intermediate math class within the past year evaluated the handbook. The feedback received from these educators was directly applied to the first draft of the handbook in order to make it more accessible and applicable to other math teachers. Although the handbook was written with teachers in mind, the language and format used throughout the manual also make it accessible to parents, tutors, preservice education students, and educational administrators. Essentially, any individual who is hoping to inspire and educate intermediate math students could make use of the content within the handbook.

Rôle du récepteur REG/EXTL3 dans l’inflammation et son implication possible dans l’ostéoarthrose (OA)

L’ostéoarthrose (OA) est une maladie articulaire dont l’incidence augmente avec le vieillissement de la population. Elle se caractérise par une détérioration progressive du cartilage articulaire accompagnée du remodelage de l’os sous-chondral et du changement des tissus mous de l’articulation. La douleur et le dysfonctionnement de l’articulation affectée sont généralement attribués à l’inflammation et l’épanchement de la synovie. Plusieurs évidences indiquent que l’inflammation de la membrane synoviale contribue grandement à la pathogenèse de l’OA. En effet, la synthèse et l’expression des enzymes protéolytiques qui dégradent la matrice cartilagineuse sont régulées par de nombreuses cytokines retrouvées au sein de ce foyer inflammatoire. Deux d’entre elles, l’interleukine-1 beta (IL-1β) et le «tumor necrosis factor » alpha (TNF-α), jouent un rôle majeur dans le déclenchement de l’inflammation associée à l’OA. Ces cytokines pro-inflammatoires agissent notamment sur les synoviocytes et les chondrocytes en activant NF-κB qui, à son tour, active les gènes de cytokines. Cette boucle de régulation positive amplifie et perpétue la réponse inflammatoire. Récemment, il a été rapporté que l’activation de NF-κB par TNF-α peut être potentialisée par EXTL3, un récepteur transmembranaire ; mais le mécanisme sous-jacent de cet effet demeure inconnu. Toutefois, les niveaux important d’EXTL3 et de son ligand Reg1B chez les patients arthrosiques, laissent croire que ces protéines jouent un rôle dans le développement de l’OA. Notre objectif était d’étudier le mécanisme par lequel EXTL3 amplifie l’activation de NF-κB par TNF-α et d’examiner si ce phénomène se produit aussi avec l’IL-1β. Nous avons utilisé les cellules C28/I2, une lignée cellulaire de chondrocytes, comme modèle d’étude. Les transfections transitoires avec un vecteur d’expression, les techniques d’immunofluorescence (IF), d’immunoprécipitation (IP) et d’immunobuvardage de type Western (IB); ont été utilisées dans le cadre de diverses approches expérimentales. Les résultats obtenus par transfection ont révélé que la protéine EXTL3 potentialisait l’activation de NF-κB aussi bien par IL-1β que par TNF-α. Ce résultat signifie que la potentialisation de l’activité NF-κB par EXTL3 n’est pas spécifique à TNF-α. D’autre part, l’IP avec TNFRI et TRAF2 a révélé la présence d’EXTL3 dans le complexe TNF-α/TNFRI/TRAF2 qui se forme au niveau de la membrane plasmique. De plus, ceci a été confirmé in vivo par microscopie confocale montrant la co-localisation de TNFRI-TRAF2-EXTL3 dans la membrane nucléaire, suggérant ainsi la formation d’un complexe identique au niveau des membranes plasmique et nucléaires. Toutefois, la présence du ligand Reg1B et/ou de la glucosamine inhibait la formation de ce complexe au niveau de la membrane plasmique, tout comme ils abolissaient la potentialisation de l’activité NF-κB par EXTL3. Ces résultats suggèrent non seulement que le recrutement d’EXTL3 libre dans le complexe TNF-α/TNFR1 est requis pour amplifier l’activation de NF-κB par TNF-α, mais aussi la capacité du ligand Reg1B et de la glucosamine à moduler cette activation à travers la baisse ou l’inhibition de l’interaction EXTL3-TNFR1. Les données de cette étude constituent une avancée majeure dans la compréhension des événements moléculaires qui contrôlent l’activation de NF-κB par les cytokines pro-inflammatoires. Ces résultats pourraient conduire au développement de nouvelles approches thérapeutiques pour le traitement de l’inflammation associée à l’OA et impliquant une activation incessante de NF-κB.