Daily Problem-Solving Warm-Ups: Harboring Mathematical Thinking In The Middle School Classroom

In this action research study of my classroom of 8th grade mathematics, I investigated the use of daily warm-ups written in problem-solving format. Data was collected to determine if use of such warm-ups would have an effect on students’ abilities to problem solve, their overall attitudes regarding problem solving and whether such an activity could also enhance their readiness each day to learn new mathematics concepts. It was also my hope that this practice would have some positive impact on maximizing the amount of time I have with my students for math instruction. I discovered that daily exposure to problem-solving practices did impact the students’ overall abilities and achievement (though sometimes not positively) and similarly the students’ attitudes showed slight changes as well. It certainly seemed to improve their readiness for the day’s lesson as class started in a more timely manner and students were more actively involved in learning mathematics (or perhaps working on mathematics) than other classes not involved in the research. As a result of this study, I plan to continue using daily warm-ups and problem-solving (perhaps on a less formal or regimented level) and continue gathering data to further determine if this methodology can be useful in improving students’ overall mathematical skills, abilities and achievement.

Learning generalization in problem solving by a blue-fronted parrot (Amazona aestiva)

Pepperberg (The Alex studies: cognitive and communicative abilities of gray parrots. Harvard University Press, Cambridge;1999) showed that some of the complex cognitive capabilities found in primates are also present in psittacine birds. Through the replication of an experiment performed with cotton-top tamarins (Saguinus oedipus oedipus) by Hauser et al. (Anim Behav 57:565-582; 1999), we examined a blue-fronted parrot`s (Amazona aestiva) ability to generalize the solution of a particular problem in new but similar cases. Our results show that, at least when it comes to solving this particular problem, our parrot subject exhibited learning generalization capabilities resembling the tamarins`.

The impact of the medical speciality in primary health-care problem solving in Belo Horizonte, Brazil: homeopaths versus family doctors: a preliminary quantitative study

Introduction: This research project examined influence of the doctors' speciality on primary health care (PHC) problem solving in Belo Horizonte (BH) Brazil, comparing homeopathic with family health doctors (FH), from the management's and the patients' viewpoint. In BH, both FH and homeopathic doctors work in PHC. The index of resolvability (IR) is used to compare resolution of problems by doctors. Methods: The present research compared IR, using official data from the Secretariat of Health and test requests made by the doctors and 482 structured interviews with patients. A total of 217,963 consultations by 14 homeopaths and 67 FH doctors between 1 July 2006 and 30 June 2007 were analysed. Results: The results show significant differences greater problem resolution by homeopaths compared to FH doctors. Conclusion: In BH, the medical speciality, homeopathy or FH, has an impact on problem solving, both from the managers' and the patients' point of view. Homeopaths request fewer tests and have better IR compared with FH doctors. Specialisation in homeopathy is an independent positive factor in problem solving at PHC level in BH, Brazil. Homeopathy (2012) 101, 44-50.

Decomposing intuitive components in a conceptual problem solving task

Research into intuitive problem solving has shown that objective closeness of participants' hypotheses were closer to the accurate solution than their subjective ratings of closeness. After separating conceptually intuitive problem solving from the solutions of rational incremental tasks and of sudden insight tasks, we replicated this finding by using more precise measures in a conceptual problem-solving task. In a second study, we distinguished performance level, processing style, implicit knowledge and subjective feeling of closeness to the solution within the problem-solving task and examined the relationships of these different components with measures of intelligence and personality. Verbal intelligence correlated with performance level in problem solving, but not with processing style and implicit knowledge. Faith in intuition, openness to experience, and conscientiousness correlated with processing style, but not with implicit knowledge. These findings suggest that one needs to decompose processing style and intuitive components in problem solving to make predictions on effects of intelligence and personality measures.

Exigencies for engaging undergraduates in rhetorical problem solving : insights from engineering managers and A3 report analyses

Undergraduate education has a historical tradition of preparing students to meet the problem-solving challenges they will encounter in work, civic, and personal contexts. This thesis research was conducted to study the role of rhetoric in engineering problem solving and decision making and to pose pedagogical strategies for preparing undergraduate students for workplace problem solving. Exploratory interviews with engineering managers as well as the heuristic analyses of engineering A3 project planning reports suggest that Aristotelian rhetorical principles are critical to the engineer's success: Engineers must ascertain the rhetorical situation surrounding engineering problems; apply and adapt invention heuristics to conduct inquiry; draw from their investigation to find innovative solutions; and influence decision making by navigating workplace decision-making systems and audiences using rhetorically constructed discourse. To prepare undergraduates for workplace problem solving, university educators are challenged to help undergraduates understand the exigence and realize the kairotic potential inherent in rhetorical problem solving. This thesis offers pedagogical strategies that focus on mentoring learning communities in problem-posing experiences that are situated in many disciplinary, work, and civic contexts. Undergraduates build a flexible rhetorical technê for problem solving as they navigate the nuances of relevant problem-solving systems through the lens of rhetorical practice.

Problem Solving Policing: Views of Citizens and Citizens Expectations in Germany

For the last two decades American police experts developed new police philosophies in order to tackle more successful the increasing crime problems. Community Policing tries to improve the cooperation between the population and the police and to increase the trust in the police. A crucial factor is a meaningful cooperation between the police and the citizens. Problem Oriented Policing aims at structural changes in the organisation and the procedures of the police in public. The police have to investigate the hidden problems and conflicts of an individual offence and to create proactive and long term concepts for the social area of conflicts beyond the specific case. It is doubtful whether these philosophies can be implemented in Germany since the legality principle prohibits meaningful, trustworthy relationships between citizens and police officers. However, if one examines the results of surveys on citizens views and expectations towards the police one finds that the majority of the German citizens favour the postulates of community and problem oriented policing. They expect through these measures an improvement of their life situation in the community and the feelings of safety. If one takes these results seriously one has to question if the legality principle is still appropriate. It seems to hamper new, more promising policing styles which seem to improve life of it's citizens and reflect what the citizens want and expect from their police force.

Effectiveness of an Online Social Constructivist Mathematical Problem Solving Course for Malaysian Pre-Service Teachers

This study assessed the effectiveness of an online mathematical problem solving course designed using a social constructivist approach for pre-service teachers. Thirty-seven pre-service teachers at the Batu Lintang Teacher Institute, Sarawak, Malaysia were randomly selected to participate in the study. The participants were required to complete the course online without the typical face-to-face classes and they were also required to solve authentic mathematical problems in small groups of 4-5 participants based on the Polya’s Problem Solving Model via asynchronous online discussions. Quantitative and qualitative methods such as questionnaires and interviews were used to evaluate the effects of the online learning course. Findings showed that a majority of the participants were satisfied with their learning experiences in the course. There were no significant changes in the participants’ attitudes toward mathematics, while the participants’ skills in problem solving for “understand the problem” and “devise a plan” steps based on the Polya’s Model were significantly enhanced, though no improvement was apparent for “carry out the plan” and “review”. The results also showed that there were significant improvements in the participants’ critical thinking skills. Furthermore, participants with higher initial computer skills were also found to show higher performance in mathematical problem solving as compared to those with lower computer skills. However, there were no significant differences in the participants’ achievements in the course based on gender. Generally, the online social constructivist mathematical problem solving course is beneficial to the participants and ought to be given the attention it deserves as an alternative to traditional classes. Nonetheless, careful considerations need to be made in the designing and implementing of online courses to minimize problems that participants might encounter while participating in such courses.

The Effect of Proximity, Explicitness, and Representation of Basic Science Information on Student Clinical Problem-Solving

Problem: Medical and veterinary students memorize facts but then have difficulty applying those facts in clinical problem solving. Cognitive engineering research suggests that the inability of medical and veterinary students to infer concepts from facts may be due in part to specific features of how information is represented and organized in educational materials. First, physical separation of pieces of information may increase the cognitive load on the student. Second, information that is necessary but not explicitly stated may also contribute to the student’s cognitive load. Finally, the types of representations – textual or graphical – may also support or hinder the student’s learning process. This may explain why students have difficulty applying biomedical facts in clinical problem solving. Purpose: To test the hypothesis that three specific aspects of expository text – the patial distance between the facts needed to infer a rule, the explicitness of information, and the format of representation – affected the ability of students to solve clinical problems. Setting: The study was conducted in the parasitology laboratory of a college of veterinary medicine in Texas. Sample: The study subjects were a convenience sample consisting of 132 second-year veterinary students who matriculated in 2007. The age of this class upon admission ranged from 20-52, and the gender makeup of this class consisted of approximately 75% females and 25% males. Results: No statistically significant difference in student ability to solve clinical problems was found when relevant facts were placed in proximity, nor when an explicit rule was stated. Further, no statistically significant difference in student ability to solve clinical problems was found when students were given different representations of material, including tables and concept maps. Findings: The findings from this study indicate that the three properties investigated – proximity, explicitness, and representation – had no statistically significant effect on student learning as it relates to clinical problem-solving ability. However, ad hoc observations as well as findings from other researchers suggest that the subjects were probably using rote learning techniques such as memorization, and therefore were not attempting to infer relationships from the factual material in the interventions, unless they were specifically prompted to look for patterns. A serendipitous finding unrelated to the study hypothesis was that those subjects who correctly answered questions regarding functional (non-morphologic) properties, such as mode of transmission and intermediate host, at the family taxonomic level were significantly more likely to correctly answer clinical case scenarios than were subjects who did not correctly answer questions regarding functional properties. These findings suggest a strong relationship (p < .001) between well-organized knowledge of taxonomic functional properties and clinical problem solving ability. Recommendations: Further study should be undertaken investigating the relationship between knowledge of functional taxonomic properties and clinical problem solving ability. In addition, the effect of prompting students to look for patterns in instructional material, followed by the effect of factors that affect cognitive load such as proximity, explicitness, and representation, should be explored.

A model for evaluation of generic competences in engineering: application to the problem. Solving competence at the technical University of Madrid.

The competence evaluation promoted by the European High Education Area entails a very important methodological change that requires guiding support to help teachers carry out this new and complex task. In this regard, the Technical University of Madrid (UPM, by its Spanish acronym) has financed a series of coordinated projects with a two-fold objective: a) To develop a model for teaching and evaluating core competences that is useful and easily applicable to its different degrees, and b) to provide support to teachers by creating an area within the Website for Educational Innovation where they can search for information on the model corresponding to each core competence approved by UPM. Information available on each competence includes its definition, the formulation of indicators providing evidence on the level of acquisition, the recommended teaching and evaluation methodology, examples of evaluation rules for the different levels of competence acquisition, and descriptions of best practices. These best practices correspond to pilot tests applied to several of the academic subjects conducted at UPM in order to validate the model. This work describes the general procedure that was used and presents the model developed specifically for the problem-solving competence. Some of the pilot experiences are also summarised and their results analysed

A model for evaluation of generic competences in engineering: application to the problem-solving competence at UPM.

The competence evaluation promoted by the European High Education Area entails a very important methodological change that requires guiding support to help teachers carry out this new and complex task. In this regard, the Technical University of Madrid (UPM, by its Spanish acronym) has financed a series of coordinated projects with a two-fold objective: a) To develop a model for teaching and evaluating core competences that is useful and easily applicable to its different degrees, and b) to provide support to teachers by creating an area within the Website for Educational Innovation where they can search for information on the model corresponding to each core competence approved by UPM. Information available on each competence includes its definition, the formulation of indicators providing evidence on the level of acquisition, the recommended teaching and evaluation methodology, examples of evaluation rules for the different levels of competence acquisition, and descriptions of best practices. These best practices correspond to pilot tests applied to several of the academic subjects conducted at UPM in order to validate the model. This work describes the general procedure that was used and presents the model developed specifically for the problem-solving competence. Some of the pilot experiences are also summarised and their results analysed