Principles for designing mathematical tasks that enhance imitative and creative reasoning

The design research programme Learning by Imitative and Creative Reasoning (LICR) studies whether, how and why tasks and teaching that enhance creative reasoning lead to a more productive struggle and more efficient learning than the common but inefficient task designs based on imitating given solution procedures. The purpose of this paper is to synthesise the research outcomes determined to date by providing the following: a conceptual framework for key concepts and relationships among teaching, tasks, student activities and learning; a theoretical basis for analyses of causal effects between task/teaching design and learning outcomes; a design research methodology for transforming initial design ideas, through cycles of evaluation and revision, into firmer design principles; and an application of this theory and methodology to empirical studies carried out to date, in order to propose task-design principles related to imitative and creative reasoning.Att lära matematik genom imitativa och kreativa resoneman

Mathematical problem solving in textbooks from twelve countries

A selection of secondary school mathematics textbooks from twelve countries on five continents was analysed to better understand the support they might be in teaching and learning mathematical problem solving. Over 5700 tasks were compared to the information provided earlier in each textbook to determine whether each task could be solved by mimicking available templates or whether a solution had to be constructed without guidance from the textbook.There were similarities between the twelve textbooks in the sense that most tasks could be solved using a template as guidance. A significantly lower proportion of the tasks required a solution to be constructed. This was especially striking in the initial sets of tasks.Textbook descriptions indicating problem solving did not guaranteethat a task solution had to be constructed without the support of anavailable template

Supporting teachers in supporting students’ mathematical problem solving

The purpose of this intervention study was to develop and evaluate a support model for teachers, designed to assist them in diagnosing students’ (age 16–19 years) difficulties and providing feedback to support students’ mathematical problem solving. Reporting on an iteration in a design research project, the results showed that the support helped the teachers to provide less procedural information and instead help students construct solutions for themselves. Constraints in achieving this included the nature of some tasks, difficulties in making reasonable diagnoses, and students’ inability to communicate their difficulties

Shifts in student attention on algorithmic and creative practice tasks

In mathematics classrooms, it is common practice to work through a series of comparable tasks provided in a textbook. A central question in mathematics education is if tasks should be accompanied with solution methods, or if students should construct the solutions themselves. To explore the impact of these two task designs on student behavior during repetitive practice, an eye-tracking study was conducted with 50 upper secondary and university students. Their eye movements were analyzed to study how the two groups shifted their gaze both within and across 10 task sets. The results show that when a solution method was present, the students reread this every time they solved the task, while only giving minute attention to the illustration that carried information supporting mathematical understanding. Students who practiced with tasks without a solution method seemed to construct a solution method by observing the illustration, which later could be retrieved from memory, making this method more efficient in the long run. We discuss the implications for teaching and how tasks without solution methods can increase student focus on important mathematical properties

Eye-tracking data and mathematical tasks with focus on mathematical reasoning

This data article contains eye-tracking data (i.e., dwell time and fixations), Z-transformed cognitive data (i.e., Raven's Advanced Progressive Matrices and Operation span), and practice and test scores from a study in mathematics education. This data is provided in a supplementary file. The method section describes the mathematics tasks used in the study. These mathematics tasks are of two kinds, with and without solution templates, to induce different types of mathematical reasoning

Upper Secondary Students’ Task Reasoning

Upper secondary students’ task solving reasoning was analysed, with a focus on grounds for different strategy choices and implementa- tions. The results indicate that mathematically well-founded considerations were rare. The dominating reasoning types were algorithmic reasoning, where students tried to remember a suitable algorithm, sometimes in a random way, and piloted reasoning, where progress was possible only when essentially all important strategy choices were made by the interviewer

Gaining Mathematical Understanding : The Effects of Creative Mathematical Reasoning and Cognitive Proficiency

In the field of mathematics education, one of the main questions remaining under debate is whether students’ development of mathematical reasoning and problem-solving is aided more by solving tasks with given instructions or by solving them without instructions. It has been argued, that providing little or no instruction for a mathematical task generates a mathematical struggle, which can facilitate learning. This view in contrast, tasks in which routine procedures can be applied can lead to mechanical repetition with little or no conceptual understanding. This study contrasts Creative Mathematical Reasoning (CMR), in which students must construct the mathematical method, with Algorithmic Reasoning (AR), in which predetermined methods and procedures on how to solve the task are given. Moreover, measures of fluid intelligence and working memory capacity are included in the analyses alongside the students’ math tracks. The results show that practicing with CMR tasks was superior to practicing with AR tasks in terms of students’ performance on practiced test tasks and transfer test tasks. Cognitive proficiency was shown to have an effect on students’ learning for both CMR and AR learning conditions. However, math tracks (advanced versus a more basic level) showed no significant effect. It is argued that going beyond step-by-step textbook solutions is essential and that students need to be presented with mathematical activities involving a struggle. In the CMR approach, students must focus on the relevant information in order to solve the task, and the characteristics of CMR tasks can guide students to the structural features that are critical for aiding comprehension

Myocarditis in childhood and young age

Εισαγωγή Η μυοκαρδίτιδα είναι μία φλεγμονώδης νόσος του μυοκαρδίου, κυρίως ιογενούς αιτιολογίας, με υψηλότερη συχνότητα εμφάνισης σε άρρενες βρεφικής και εφηβικής ηλικίας. Τα σημεία και τα συμπτώματα της μυοκαρδίτιδας ποικίλλουν από ήπια έως απειλητικά για τη ζωή. Χαρακτηρίζεται από υψηλά επίπεδα τροπονίνης και από συγκεκριμένα ευρήματα στο ηλεκτροκαρδιογράφημα και υπερηχοκαρδιογράφημα. Η μαγνητική καρδιάς και η ενδομυοκαρδιακή βιοψία θεωρούνται διαγνωστικές μέθοδοι εκλογής. Η πρόγνωση της μυοκαρδίτιδας είναι συνήθως καλή με μεγαλύτερη πιθανότητα εμφάνισης επιπλοκών σε νεογνά και βρέφη στα πρώιμα στάδια της νόσου. Το μειωμένο κλάσμα εξώθησης της αριστερής κοιλίας και τα υψηλά επίπεδα τροπονίνης θεωρούνται οι κυριότεροι κακοί προγνωστικοί παράγοντες. Σκοπός Σκοπός της μελέτης είναι να καταγράψει σχετικούς επιδημιολογικούς δείκτες της μυοκαρδίτιδας στην περιοχή της Κρήτης και να συσχετίσει δημογραφικά και κλινικοεργαστηριακά δεδομένα με επιπλοκές και δείκτες έκβασης της νόσου. Επίσης, ένας δεύτερος σκοπός της μελέτης είναι η διερεύνηση των σύγχρονων διαγνωστικών μεθόδων της παιδιατρικής και νεανικής μυοκαρδίτιδας και της συμβολής τους στη διάγνωση και πρόγνωση της νόσου. Μεθοδολογία Πρόκειται για αναδρομική μονοκεντρική μελέτη, της οποίας το δείγμα περιελάμβανε παιδιά, εφήβους και ενήλικες ως 32 ετών που νοσηλεύτηκαν στη Μονάδα Εντατικής Θεραπείας Παίδων (ΜΕΘΠ) και στην Καρδιολογική Κλινική του Πανεπιστημιακού Γενικού Νοσοκομείου Ηρακλείου από το 2008 ως και το 2020 με την τελική διάγνωση της μυοκαρδίτιδας. Η συλλογή των δεδομένων έγινε από ηλεκτρονικά και έντυπα αρχεία ασθενών και περιελάμβανε ποικιλία μεταβλητών για κάθε ασθενή. Η στατιστική μεθοδολογία περιελάμβανε καταγραφή συχνοτήτων και περιγραφικών στατιστικών χαρακτηριστικών, έλεγχο συσχέτισης κατά Pearson, έλεγχο χ2, ανάλυση διακύμανσης, παλινδρομήσει; και θ στατιστική ανάλυση έγινε με το πρόγραμμα SPSS 25. Αποτελέσματα Το 87% των 76 ασθενών που συμπεριελήφθησαν στη μελέτη ήταν άρρενες με μέση ηλικία τα 19 έτη και κύριο σύμπτωμα το θωρακικό άλγος με συνοδά συμπτώματα από το αναπνευστικό και γαστρεντερικό σύστημα. Καταγράφηκαν υψηλά επίπεδα τροπονίνης, ιδίως στους ασθενείς της ΜΕΘΠ και συσχετίστηκαν στατιστικά σημαντικά (p<0.001) με τις AST, LDH, CK-MB όχι όμως με τοΒΝΡ και με τη διάρκεια νοσηλείας. Aνεξάρτητα σχετίζονταν με τα επίπεδα Tn-I της ημέρας εισαγωγής τα επίπεδα AST (p=0.002) και CK-MB ( p=0.038). Το 82% του συνόλου των ασθενών είχε κάποιο παθολογικό εύρημα στο ΗΚΓ, με συχνότερες τις ανασπάσεις ST και τα αρνητικά Τ. Ανάσπαση ST (65%) και αρνητικά Τ (59%) παρουσίαζαν συχνότερα ασθενείς της ΜΕΘΠ σε σύγκριση με ασθενείς της καρδιολογικής κλινικής (p=0.015 και p=0.025, αντίστοιχα). Το 35% των ασθενών εμφάνισε διαταραχή συσταλτικότητας αριστερής κοιλίας στο υπερηχοκαρδιογράφημα και το κλάσμα εξώθησης αριστερής κοιλίας (LVEF)<40% σχετίστηκε με αύξηση λευκών (p<0.001), μειωμένη κινητικότητα του τοιχώματός της αριστερής κοιλίας (p=0.001) και αρνητική έκβαση νόσου. Στο 75% των ασθενών που έκαναν MRI καρδιάς, η εξέταση ήταν θετική για μυοκαρδίτιδα. Ο ιολογικός έλεγχος ανέδειξε ως συχνότερα αίτια μυοκαρδίτιδας τον ρινοϊό και τον εντεροϊό. Ασθενείς μικρότερης ηλικίας που νοσηλεύτηκαν στην ΜΕΘΠ είχαν συχνότερα EF<40% σε σύγκριση με ενήλικες της καρδιολογικής κλινικής (p=0.01). Μια αρνητική έκβαση (επιδείνωση ή θάνατο) καλύτερα προέβλεπαν ένα EF<40% (p=0.001) και αυξημένος αριθμός λευκών αιμοσφαιρίων (p=0.002) την ημέρα της εισαγωγής. Βελτίωση παρουσίασαν περισσότεροι ασθενείς της Καρδιολογικής κλινικής συγκριτικά με τους ασθενείς της ΜΕΘΠ (98% vs. 79%, p=0.012) όπως και μικρότερο ποσοστό επιπλοκών (3.6% vs. 21.1%, p=0.015). Συμπεράσματα Οι παιδιατρικοί ασθενείς της ΜΕΘ παρουσιάζουν βαρύτερη μορφή μυοκαρδίτιδας από τους νέους ενήλικες ασθενείς της Καρδιολογικής, με υψηλότερες τιμές τροπονίνης και υψηλότερα ποσοστά μειωμένης συσταλτικότητας και διαταραχής της κινητικότητας τοιχώματος της αριστερής κοιλίας, ανασπάσεων ST και αρνητικών Τ. Ο ρινοϊός και εντεροϊός αποτελούν τα συχνότερα ιογενή αίτια της μυοκαρδίτιδας ενώ υψηλής διαγνωστικής αξίας αποδεικνύεται η MRI καρδίας. Αν και αρνητικά επηρεάζουν την έκβαση της οξείας μυοκαρδίτιδας η μικρή ηλικία, ο αρχικά αυξημένος αριθμός λευκών και ποσοστό LVEF<40%, η πρόγνωση της παραμένει καλή στο μεγαλύτερο ποσοστό ασθενών.Background Myocarditis is an inflammatory disease of the myocardium, mainly of viral etiology, with a higher incidence in male infants and adolescents. Signs and symptoms of myocarditis vary from mild to life-threatening. It is characterized by high levels of troponin and and by specific findings on the electrocardiogram and echocardiogram. Cardiovascular magnetic resonance imaging and endomyocardial biopsy are considered diagnostic methods of choice. The prognosis of myocarditis is usually good with a higher probability of complications in newborns and infants in the early stages of the disease. Decreased left ventricular ejection fraction and high troponin levels are considered to be the main poor prognostic factors. Objective The aim of this study is to record relevant epidemiological indicators of myocarditis in the region of Crete and to associate demographic and clinical -laboratory data with complications and disease outcome indicators. Also, a second purpose of the study is to investigate the contemporary diagnostic methods of pediatric and juvenile myocarditis and their contribution to the diagnosis and prognosis of the disease. Methods This is a retrospective monocentric study, in which the sample included children, adolescents and adults up to 32 years of age who were treated in the Pediatric Intensive Care Unit (PICU) and the Cardiology Clinic of the University General Hospital of Heraklion from 2008 to 2020 with the final diagnosis of myocarditis. Data collection was done from electronic and printed patient files and included a variety of variables for each patient. The statistical method included frequencies, descriptive statistics, Pearson correlation, Chi-squared test, analysis of variance (ANOVA), regressions and statistical analysis was performed with the SPSS program. Results Eighty-seven percent of 76 patients were male with a mean age of 19 years and the main symptom was chest pain with concomitant symptoms from the respiratory and gastrointestinal systems. High levels of troponin were recorded, especially in PICU patients and were statistically significant correlated with (p< 0.001) AST, LDH, CKMB, but not with BNP and duration of hospitalization. The AST (p = 0.002) and CKMB (p = 0.038) levels were independently related to the Tn-I levels of the day of admission. Eighty-two percent of all patients had a pathological finding on the electrocardiogram, with the most common being ST segment elevations and negative T waves. ST segment elevation (65%) and negative T waves (59%) were more common in PICU patients compared with patients in Cardiology Clinic (p = 0.015 and p = 0.025, respectively). Thirty-five percent of patients showed left ventricular contractility disorder on ultrasound and the left ventricular ejection fraction (LVEF) <40% was associated with increased white blood cells (WBC)(p <0.001), decreased left ventricular wall mobility (p = 0.001) and negative disease outcome. In seventy-five percent of patients who had a CMR, the test was positive for myocarditis. Viral control showed that rhinovirus and enterovirus were the most common causes of myocarditis. Younger patients hospitalized in PICU, were more likely to have EF <40% compared with adults in the cardiology clinic (p = 0.01). A negative outcome (deterioration or death) was better predicted by an EF <40% (p = 0.001) and an increased number of white blood cells (p = 0.002) on the day of admission. More patients from the Cardiology Clinic improved compared to PICU patients (98% vs. 79%, p = 0.012) and they showed a lower complication rate (3.6% vs. 21.1%, p = 0.015). Conclusion Pediatric ICU patients have a more severe form of myocarditis than yound adult patients of Cardiology Clinic, with higher troponin values and higher rates of reduced contractility and left ventricular wall mobility disorder, ST segment elevations and negative T waves. Rhinovirus and enterovirus are the most common viral causes of myocarditis, and CMR is proved to be of high diagnostic value. Although acute myocarditis outcome is negatively affected by young age, initially increased number of white blood cells and LVEF < 40%, its prognosis remains good in the majority of patients