Learning to learn in mathematics: Two Fulbright distinguished awards in teaching fellows’ narratives

Two middle school educators earned a Fulbright Distinguished Award in Teaching fellowship. A Fulbright Finland Foundation inter-country travel grant provided the grantees with a unique opportunity to connect and collaborate at the University of Helsinki. Within this research, they described their inquiry experiences. The research included examining authentic student-centered learning continuums and phenomenon-based learning in Finland and teachers’ adaptability in relation to meeting the needs of linguistically and culturally diverse math classrooms in the Netherlands. This paper summarizes how cross-cultural dialogues, classroom observations, and informal interviews with educators, students, and thought leaders informed each grantee’s discovery of how student-centered learning is structured, delivered, and valued in Finland and the Netherlands. This article (1) describes how communication empowers middle school mathematics students, (2) analyzes the learning-to-learn framework, and (3) provides insights into how to utilize language diversity in a mathematics classroom.Peer reviewe

Development of learning to learn competence across secondary education and its association with attainment in Finnish/Swedish high-stake exit exam

The Finnish Learning to learn framework comprises cognitive competencies and motivational beliefs, which both have shown to be associated with academic success in different educational settings. However, studies of the stability and development of these constructs across six year long secondary education are scarce. In addition, this study investigates the predictive power of learning to learn constructs on achievement in the high-stakes Finnish matriculation examination. Following a sample of Finnish students (N = 2712, 55 % girls, aged 13-19) from lower secondary to general upper secondary education, this study found that Finnish the learning to learn construct and the relations between its components hold rather stable over the years. However, while cognitive competence improves and shows strong rank order stability during adolescence, learning-enhancing motivational beliefs show a downward trajectory and detrimental-to-learning beliefs somewhat opposite one, found in other studies. Gender differences were found in both students' motivational beliefs and in in their achievement in the matriculation examination. The role of motivational beliefs, especially effort belief, becomes stronger when adolescents grow older and advance on their educational path.Peer reviewe

Learning-to-Learn Stochastic Gradient Descent with Biased Regularization

We study the problem of learning-to-learn: inferring a learning algorithm that works well on tasks sampled from an unknown distribution. As class of algorithms we consider Stochastic Gradient Descent on the true risk regularized by the square euclidean distance to a bias vector. We present an average excess risk bound for such a learning algorithm. This result quantifies the potential benefit of using a bias vector with respect to the unbiased case. We then address the problem of estimating the bias from a sequence of tasks. We propose a meta-algorithm which incrementally updates the bias, as new tasks are observed. The low space and time complexity of this approach makes it appealing in practice. We provide guarantees on the learning ability of the meta-algorithm. A key feature of our results is that, when the number of tasks grows and their variance is relatively small, our learning-to-learn approach has a significant advantage over learning each task in isolation by Stochastic Gradient Descent without a bias term. We report on numerical experiments which demonstrate the effectiveness of our approach.Comment: 37 pages, 8 figure

Learning to Learn, from Transfer Learning to Domain Adaptation: A Unifying Perspective

The transfer learning and domain adaptation problems originate from a distribution mismatch between the source and target data distribution. The causes of such mismatch are traditionally considered different. Thus, transfer learn-ing and domain adaptation algorithms are designed to ad-dress different issues, and cannot be used in both settings unless substantially modified. Still, one might argue that these problems are just different declinations of learning to learn, i.e. the ability to leverage over prior knowledge when attempting to solve a new task. We propose a learning to learn framework able to lever-age over source data regardless of the origin of the distri-bution mismatch. We consider prior models as experts, and use their output confidence value as features. We use them to build the new target model, combined with the features from the target data through a high-level cue integration scheme. This results in a class of algorithms usable in a plug-and-play fashion over any learning to learn scenario, from binary and multi-class transfer learning to single and multiple source domain adaptation settings. Experiments on several public datasets show that our approach consis-tently achieves the state of the art. 1

The Finnish Education as an Individualized Service System with a Reference to Students with Special Educational Needs

The paper deals with some educational aspects of going to school in Finland concerning students with special educational needs/services. We proceed from empirical observation. Then, the general context is given to interpret the data and extend the observed added value of individualized educational support. The latter, in its turn, requires the identification of a special need and the existence of suitable educational options. These two pieces of information need to match optimally: early birds get the biggest harvest, and even if special education is never too late, the service needs become more challenging and the solutions - more expensive. The core of this complicated dual process is the decision making with more or less complete information of both the needs and the available palette of educational actions. The fundamental dilemma is to navigate between two poles: if a pupil is left out by such educational measures which could have helped him/her to become a full member of society and economy, we have a moral problem. If the economical-educational complex is not providing the best research-supported educational tools, we also have a pedagogical problem. However, it is not universally proved that full integration is the best way; neither is it proved that we need an entire set of segregated and specialized schools for several different kinds of special needs.Peer reviewe

Learning to Reason in Round-based Games: Multi-task Sequence Generation for Purchasing Decision Making in First-person Shooters

Sequential reasoning is a complex human ability, with extensive previous research focusing on gaming AI in a single continuous game, round-based decision makings extending to a sequence of games remain less explored. Counter-Strike: Global Offensive (CS:GO), as a round-based game with abundant expert demonstrations, provides an excellent environment for multi-player round-based sequential reasoning. In this work, we propose a Sequence Reasoner with Round Attribute Encoder and Multi-Task Decoder to interpret the strategies behind the round-based purchasing decisions. We adopt few-shot learning to sample multiple rounds in a match, and modified model agnostic meta-learning algorithm Reptile for the meta-learning loop. We formulate each round as a multi-task sequence generation problem. Our state representations combine action encoder, team encoder, player features, round attribute encoder, and economy encoders to help our agent learn to reason under this specific multi-player round-based scenario. A complete ablation study and comparison with the greedy approach certify the effectiveness of our model. Our research will open doors for interpretable AI for understanding episodic and long-term purchasing strategies beyond the gaming community.Comment: 16th AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment (AIIDE-20