On Aspects of Mathematical Reasoning : Affect and Gender

This thesis explores two aspects of mathematical reasoning: affect and gender. I started by looking at the reasoning of upper secondary students when solving tasks. This work revealed that when not guided by an interviewer, algorithmic reasoning, based on memorising algorithms which may or may not be appropriate for the task, was predominant in the students reasoning. Given this lack of mathematical grounding in students reasoning I looked in a second study at what grounds they had for different strategy choices and conclusions. This qualitative study suggested that beliefs about safety, expectation and motivation were important in the central decisions made during task solving.  But are reasoning and beliefs gendered? The third study explored upper secondary school teachers conceptions about gender and students mathematical reasoning. In this study I found that upper secondary school teachers attributed gender symbols including insecurity, use of standard methods and imitative reasoning to girls and symbols such as multiple strategies especially on the calculator, guessing and chance-taking were assigned to boys. In the fourth and final study I found that students, both male and female, shared their teachers view of rather traditional feminities and masculinities. Remarkably however, this result did not repeat itself when students were asked to reflect on their own behaviour: there were some discrepancies between the traits the students ascribed as gender different and the traits they ascribed to themselves. Taken together the thesis suggests that, contrary to conceptions, girls and boys share many of the same core beliefs about mathematics, but much work is still needed if we should create learning environments that provide better opportunities for students to develop beliefs that guide them towards well-grounded mathematical reasoning. 

Teachers' conceptions about students' mathematical reasoning : Gendered or not?

This study looks at how upper secondary school teachers gender stereotype aspects of students' mathematical reasoning. Girls were attributed gender symbols including insecurity, use of standard methods and imitative reasoning. Boys were assigned the symbols such as multiple strategies especially on the calculator, guessing and chance-taking. 

PokerMapper: : mapping executive functions, poker playing ability and responsible gambling in online environments

Research objectives Poker and responsible gambling both entail the use of the executive functions (EF), which are higher-level cognitive abilities. The main objective of this work was to assess if online poker players of different ability show different performances in their EF and if so, which functions are the most discriminating ones. The secondary objective was to assess if the EF performance can predict the quality of gambling, according to the Gambling Related Cognition Scale (GRCS), the South Oaks Gambling Screen (SOGS) and the Problem Gambling Severity Index (PGSI). Sample and methods The study design consisted of two stages: 46 Italian active players (41m, 5f; age 32±7,1ys; education 14,8±3ys) fulfilled the PGSI in a secure IT web system and uploaded their own hand history files, which were anonymized and then evaluated by two poker experts. 36 of these players (31m, 5f; age 33±7,3ys; education 15±3ys) accepted to take part in the second stage: the administration of an extensive neuropsychological test battery by a blinded trained professional. To answer the main research question we collected all final and intermediate scores of the EF tests on each player together with the scoring on the playing ability. To answer the secondary research question, we referred to GRCS, PGSI and SOGS scores.  We determined which variables that are good predictors of the playing ability score using statistical techniques able to deal with many regressors and few observations (LASSO, best subset algorithms and CART). In this context information criteria and cross-validation errors play a key role for the selection of the relevant regressors, while significance testing and goodness-of-fit measures can lead to wrong conclusions.   Preliminary findings We found significant predictors of the poker ability score in various tests. In particular, there are good predictors 1) in some Wisconsin Card Sorting Test items that measure flexibility in choosing strategy of problem-solving, strategic planning, modulating impulsive responding, goal setting and self-monitoring, 2) in those Cognitive Estimates Test variables related to deductive reasoning, problem solving, development of an appropriate strategy and self-monitoring, 3) in the Emotional Quotient Inventory Short (EQ-i:S) Stress Management score, composed by the Stress Tolerance and Impulse Control scores, and in the Interpersonal score (Empathy, Social Responsibility, Interpersonal Relationship). As for the quality of gambling, some EQ-i:S scales scores provide the best predictors: General Mood for the PGSI; Intrapersonal (Self-Regard; Emotional Self-Awareness, Assertiveness, Independence, Self-Actualization) and Adaptability  (Reality Testing, Flexibility, Problem Solving) for the SOGS, Adaptability for the GRCS. Implications for the field Through PokerMapper we gathered knowledge and evaluated the feasibility of the construction of short tasks/card games in online poker environments for profiling users’ executive functions. These card games will be part of an IT system able to dynamically profile EF and provide players with a feedback on their expected performance and ability to gamble responsibly in that particular moment. The implementation of such system in existing gambling platforms could lead to an effective proactive tool for supporting responsible gambling.