Gerçekçi, Aritmetik/Cebirsel ve Geometrik Bağlamda Problem Çözme

In the last decades, voluminous research has been dedicated to the modeling process and students’ understanding of word problems (verbally set problems with realistic context). These problems were considered as a natural framework for the development of the meaning of mathematical relations and for linking mathematical knowledge and everyday situations. In this study we examine three different contexts of verbally set problems: realistic, arithmetic/algebraic and geometric. The research sample consists of 62 fourth-grade elementary school students (10 – 11 years old). The results show that there is a significant relationship between students’ achievement in problem solving in the three different contexts as well as a relationship between the choices of strategies in different contexts. It is shown that students solve problems without the use of visual-schematic representations. Surprisingly, not even in geometric context did student use visual representations. Therefore, a joint activity of students and teachers in constructing visual-schematic representations should be an important aspect not only of solving problems with realistic context, but also of solving geometry problems and problems posed in the mathematical language.Son yıllarda, modelleme sürecine ve öğrencilerin kelime problemlerini (gerçekçi bir bağlamı olan sözlü şekilde oluşturulmuş problemler) anlaması konusuna yönelik çok sayıda araştırma yapılmıştır. Bu problemler, matematiksel ilişkilerin anlamını geliştirmek ve matematiksel bilgi ile gündelik durumları birbirine bağlamak için doğal bir çerçeve olarak kabul edilmiştir. Bu çalışmada, sözlü şekilde oluşturulmuş problemlerin, gerçekçi, aritmetik/cebirsel ve geometrik olmak üzere üç farklı bağlamını inceliyoruz. Araştırmanın örneklemi, 62 ilkokul dördüncü sınıf öğrencisinden (10-11 yaş) oluşmaktadır. Sonuçlar, öğrencilerin üç farklı bağlamda problem çözmedeki başarıları arasında anlamlı bir ilişki olduğunu ve aynı zamanda, farklı bağlamlardaki strateji seçimleri arasında da bir ilişki olduğunu göstermektedir. Öğrencilerin problemleri görsel-şematik temsiller kullanmadan çözdükleri gösterilmiştir. Öğrenciler, şaşırtıcı bir biçimde, geometrik bağlamda bile görsel temsilleri kullanmamıştır. Dolayısıyla, öğrenci ve öğretmenlerin görsel-şematik temsiller oluşturma konusundaki ortak faaliyeti, yalnızca problemleri gerçekçi bağlamla çözmenin değil, aynı zamanda geometri problemlerini ve matematiksel dilde sorulan problemleri çözmenin de önemli bir unsuru olmalıdır

Knowledge-aware Complementary Product Representation Learning

Learning product representations that reflect complementary relationship plays a central role in e-commerce recommender system. In the absence of the product relationships graph, which existing methods rely on, there is a need to detect the complementary relationships directly from noisy and sparse customer purchase activities. Furthermore, unlike simple relationships such as similarity, complementariness is asymmetric and non-transitive. Standard usage of representation learning emphasizes on only one set of embedding, which is problematic for modelling such properties of complementariness. We propose using knowledge-aware learning with dual product embedding to solve the above challenges. We encode contextual knowledge into product representation by multi-task learning, to alleviate the sparsity issue. By explicitly modelling with user bias terms, we separate the noise of customer-specific preferences from the complementariness. Furthermore, we adopt the dual embedding framework to capture the intrinsic properties of complementariness and provide geometric interpretation motivated by the classic separating hyperplane theory. Finally, we propose a Bayesian network structure that unifies all the components, which also concludes several popular models as special cases. The proposed method compares favourably to state-of-art methods, in downstream classification and recommendation tasks. We also develop an implementation that scales efficiently to a dataset with millions of items and customers

Discovering information flow using a high dimensional conceptual space

This paper presents an informational inference mechanism realized via the use of a high dimensional conceptual space. More specifically, we claim to have operationalized important aspects of G?rdenforss recent three-level cognitive model. The connectionist level is primed with the Hyperspace Analogue to Language (HAL) algorithm which produces vector representations for use at the conceptual level. We show how inference at the symbolic level can be implemented by employing Barwise and Seligmans theory of information flow. This article also features heuristics for enhancing HAL-based representations via the use of quality properties, determining concept inclusion and computing concept composition. The worth of these heuristics in underpinning informational inference are demonstrated via a series of experiments. These experiments, though small in scale, show that informational inference proposed in this article has a very different character to the semantic associations produced by the Minkowski distance metric and concept similarity computed via the cosine coefficient. In short, informational inference generally uncovers concepts that are carried, or, in some cases, implied by another concept, (or combination of concepts)

The Expressive Power of Word Embeddings

We seek to better understand the difference in quality of the several publicly released embeddings. We propose several tasks that help to distinguish the characteristics of different embeddings. Our evaluation of sentiment polarity and synonym/antonym relations shows that embeddings are able to capture surprisingly nuanced semantics even in the absence of sentence structure. Moreover, benchmarking the embeddings shows great variance in quality and characteristics of the semantics captured by the tested embeddings. Finally, we show the impact of varying the number of dimensions and the resolution of each dimension on the effective useful features captured by the embedding space. Our contributions highlight the importance of embeddings for NLP tasks and the effect of their quality on the final results.Comment: submitted to ICML 2013, Deep Learning for Audio, Speech and Language Processing Workshop. 8 pages, 8 figure

Characterizing the impact of geometric properties of word embeddings on task performance

Analysis of word embedding properties to inform their use in downstream NLP tasks has largely been studied by assessing nearest neighbors. However, geometric properties of the continuous feature space contribute directly to the use of embedding features in downstream models, and are largely unexplored. We consider four properties of word embedding geometry, namely: position relative to the origin, distribution of features in the vector space, global pairwise distances, and local pairwise distances. We define a sequence of transformations to generate new embeddings that expose subsets of these properties to downstream models and evaluate change in task performance to understand the contribution of each property to NLP models. We transform publicly available pretrained embeddings from three popular toolkits (word2vec, GloVe, and FastText) and evaluate on a variety of intrinsic tasks, which model linguistic information in the vector space, and extrinsic tasks, which use vectors as input to machine learning models. We find that intrinsic evaluations are highly sensitive to absolute position, while extrinsic tasks rely primarily on local similarity. Our findings suggest that future embedding models and post-processing techniques should focus primarily on similarity to nearby points in vector space.Comment: Appearing in the Third Workshop on Evaluating Vector Space Representations for NLP (RepEval 2019). 7 pages + reference

Mobile learning: benefits of augmented reality in geometry teaching

As a consequence of the technological advances and the widespread use of mobile devices to access information and communication in the last decades, mobile learning has become a spontaneous learning model, providing a more flexible and collaborative technology-based learning. Thus, mobile technologies can create new opportunities for enhancing the pupils’ learning experiences. This paper presents the development of a game to assist teaching and learning, aiming to help students acquire knowledge in the field of geometry. The game was intended to develop the following competences in primary school learners (8-10 years): a better visualization of geometric objects on a plane and in space; understanding of the properties of geometric solids; and familiarization with the vocabulary of geometry. Findings show that by using the game, students have improved around 35% the hits of correct responses to the classification and differentiation between edge, vertex and face in 3D solids.This research was supported by the Arts and Humanities Research Council Design Star CDT (AH/L503770/1), the Portuguese Foundation for Science and Technology (FCT) projects LARSyS (UID/EEA/50009/2013) and CIAC-Research Centre for Arts and Communication.info:eu-repo/semantics/publishedVersio

SemAxis: A Lightweight Framework to Characterize Domain-Specific Word Semantics Beyond Sentiment

Because word semantics can substantially change across communities and contexts, capturing domain-specific word semantics is an important challenge. Here, we propose SEMAXIS, a simple yet powerful framework to characterize word semantics using many semantic axes in word- vector spaces beyond sentiment. We demonstrate that SEMAXIS can capture nuanced semantic representations in multiple online communities. We also show that, when the sentiment axis is examined, SEMAXIS outperforms the state-of-the-art approaches in building domain-specific sentiment lexicons.Comment: Accepted in ACL 2018 as a full pape