Classifying the Arithmetical Complexity of Teaching Models

This paper classifies the complexity of various teaching models by their position in the arithmetical hierarchy. In particular, we determine the arithmetical complexity of the index sets of the following classes: (1) the class of uniformly r.e. families with finite teaching dimension, and (2) the class of uniformly r.e. families with finite positive recursive teaching dimension witnessed by a uniformly r.e. teaching sequence. We also derive the arithmetical complexity of several other decision problems in teaching, such as the problem of deciding, given an effective coding $\{\mathcal L_0,\mathcal L_1,\mathcal L_2,\ldots\}$ of all uniformly r.e. families, any $e$ such that $\mathcal L_e = \{L^e_0,L^e_1,\ldots,\}$, any $i$ and $d$, whether or not the teaching dimension of $L^e_i$ with respect to $\mathcal L_e$ is upper bounded by $d$.Comment: 15 pages in International Conference on Algorithmic Learning Theory, 201

Many right answers: learning in mathematics through speaking and listening

Refresh your approach to teaching mathematics. Many Right Answers provides a focus on speaking and listening as an effective tool for learning mathematics. Many Right Answers: shows the reality of teaching and learning in some classrooms explores the complexity of teaching and learning, and of speaking and listening portrays and recognises that teachers are highly trained and reflective professionals encourages teachers to try out new things inspired by discussion with other practitioners. With additional comments from Professor Celia Hoyles OBE, this booklet and DVD provide support for trying out new ideas and building expertise over time, using the existing - and fine - practice currently out there. There are two free, downloadable accompanying resources - a learning journal, and questions and prompts

The Teaching Dimension of Kernel Perceptron

Algorithmic machine teaching has been studied under the linear setting where exact teaching is possible. However, little is known for teaching nonlinear learners. Here, we establish the sample complexity of teaching, aka teaching dimension, for kernelized perceptrons for different families of feature maps. As a warm-up, we show that the teaching complexity is $\Theta(d)$ for the exact teaching of linear perceptrons in $\mathbb{R}^d$, and $\Theta(d^k)$ for kernel perceptron with a polynomial kernel of order $k$. Furthermore, under certain smooth assumptions on the data distribution, we establish a rigorous bound on the complexity for approximately teaching a Gaussian kernel perceptron. We provide numerical examples of the optimal (approximate) teaching set under several canonical settings for linear, polynomial and Gaussian kernel perceptrons.Comment: AISTATS 202

Interpretative phenomenological analysis (IPA) : a qualitative methodology of choice in healthcare research

This paper focuses on the teaching of the qualitative method, Interpretative Phenomenological Analysis (IPA), to healthcare professionals (HCPs). It introduces briefly the philosophical background of IPA and how it has been used within healthcare research, and then discusses the teaching of IPA to HCPs within received educational theory. Lastly, the paper describes how IPA has been taught to students/trainees in some specific healthcare professions (clinical psychology, medicine, nursing and related disciplines). In doing this, the paper demonstrates the essential simplicity, paradoxical complexity, and methodological rigour that IPA can offer as a research tool in understanding healthcare and illness from the patient or service user perspective

The Sample Complexity of Teaching-by-Reinforcement on Q-Learning

We study the sample complexity of teaching, termed as "teaching dimension" (TDim) in the literature, for the teaching-by-reinforcement paradigm, where the teacher guides the student through rewards. This is distinct from the teaching-by-demonstration paradigm motivated by robotics applications, where the teacher teaches by providing demonstrations of state/action trajectories. The teaching-by-reinforcement paradigm applies to a wider range of real-world settings where a demonstration is inconvenient, but has not been studied systematically. In this paper, we focus on a specific family of reinforcement learning algorithms, Q-learning, and characterize the TDim under different teachers with varying control power over the environment, and present matching optimal teaching algorithms. Our TDim results provide the minimum number of samples needed for reinforcement learning, and we discuss their connections to standard PAC-style RL sample complexity and teaching-by-demonstration sample complexity results. Our teaching algorithms have the potential to speed up RL agent learning in applications where a helpful teacher is available

The Relationship between Task Complexity, Task Difficulty, and Speaking Performance: The Case of Chinese EFL Learners

In recent years, task-based language teaching (TBLT) has become a prevalent pedagogy in Chinese universities. Much research has focused on task complexity. Nevertheless, task difficulty, another crucial element of TBLT, has gained little attention from researchers. With twenty Chinese first-year undergraduates majoring in English participating in the present research, this study explored the relationship between task complexity, difficulty, and Chinese EFL learners’ English speaking performance, hoping to shed light on the design and implementation of tasks in L2 teaching. The results suggested that learners’ grammatical complexity, lexical sophistication, and accuracy varied significantly in the two tasks of different complexity. Only speaking speed was found to be positively correlated with task difficulty. When learners’ confidence to fulfill a task was bolstered, they would respond to the task at a faster speaking speed. Hence, teachers can design tasks of different complexity flexibly and fine-tune the complexity of the tasks to meet different teaching goals. Teachers can also strengthen the students’ confidence in accomplishing tasks to enhance their speaking fluency. Keywords: Chinese EFL learners, task-based language teaching, task difficulty, task complexity, linguistic complexity, accuracy, fluency DOI: 10.7176/JEP/13-20-08 Publication date:July 31st 202

The Revolving Door of Education: Teacher Turnover and Retention amongst the Graduates of a Liberal Arts Teacher Education Program

In the United States, elementary and secondary education teachers comprise 4% of the entire civilian workforce (Ingersoll, 2001). The composition of that 4% is changing because of teacher turnover. According to recent statistics, 46% of teachers leave the classroom within the first five years of teaching and 9.5% of teachers leave the classroom within their first year (Rinke, 2014; Riggs, 2013; Zheng & Zeller, 2016). This study is designed to examine the teaching experiences of graduates of one teacher education program and the potential differences between graduates who stay in teaching and those who leave. Throughout this study, the guiding questions were: How many Gettysburg College Teacher Education Program Alumni, 1985 - 2008, are still teaching in the classroom at a primary or secondary level? Why did some alumni leave the classroom at a primary or secondary level and why did some alumni never teach? How does the data from the Gettysburg College Teacher Education Program alumni correspond with the previous scholarship on teacher turnover and retention? When looked at from the perspective of an individual post-secondary institution, the individual stories of the alumni emerge and so does the complexity of teacher turnover and retention in America, which is not always reflected in studies conducting on a state or national level

Communicating about systems and complexity:from contingency to praxis

The chapter is part of a special Gedenkschrift publication honoring the work of Professsor Brenda Zimmerman in the field of complexity thinking. The term, Gedenkschrift, borrowed from German, can be translated as celebration publication. It is a memorial publication honoring a respected person, especially an academic, created and presented posthumously. The tribute tracks the influence of Brenda's work in formulating the heuristic developed by the author for teaching systems thinking in practice (STiP) as part of the postgraduate programme on STiP at the Open University

New teaching strategies in the teaching of the architectural project

Today we will observe the need to rethink the teaching and learning models at Schools of Architecture, reconsidering the ways of teaching and learning, attending not only to what we want to teach, but also to how we are going to teach with the objective of moving from the traditional model of transmission of knowledge from the teacher to the student, to a model based on the development of competences in the student. In this sense, the teaching of architectural design should step away from the attitude that is still prevalent in many schools, consisting of conveying predetermined teaching or a closed and complete architectural culture, which attempts to exhaust all the avenues of knowledge, showing a strict and infallible method. What is needed, though, is an active and plural education that considers the complexity of architecture, based on ongoing research and part of an open, flexible and dynamic disciplinary discourse. An education that allows students to develop skills and generate new knowledge from the creation of learning situations which stimulate independent learning, facilitate subsequent ongoing training and enable a more critical and profound intellectual development. Undoubtedly, students must acquire lots of knowledge and skills, and there are many learning processes which must be simultaneously present of their training. In this sense, this paper aims to define a series of teaching strategies that aim to establish a teaching of Architecture oriented more to show an attitude towards the project, to encourage, stimulate and involve students in their own process of learning, helping them to develop their capacity to learn to learn. A training oriented more than the pursuit of results to focus on the processes that lead to them.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech