Over the past decades many teaching strategies have been proposed by various educators to improve education of all students including students with special needs. No single one of these proposed teaching strategies meets the needs of all students. The new Every Student Succeeds Act, successor to No Child Left behind Law, which transfers oversight from federal level back to states, could be a benefactor for constructivism and special education. Educators are also optimistic that the new Every Student Succeeds Act will be better for vulnerable students in special education because it will introduce more flexibility in how individual states carry out evaluation of students and teachers. In addition, it will provide more flexibility on testing and adapt the curriculum to student’s needs. It would further reduce time and energy for students preparing for standardized tests or statewide exams. It will also end “Adequate Yearly Progress” – a measure that required schools to show test score gains. Constructivist teaching philosophy is all about accepting student autonomy where student thinking drives the lessons, where dialogue, inquiry, and puzzlement are valued and assessing student learning is in the context of teaching. It helps teachers to draw on new ideas as they make decisions about which teaching techniques are most appropriate for all students to learn. Now is the time to revisit the great debate of constructivism versus teacher-centered instruction and special education. Time has come to effectively explore our educational system and examine the core unit of the whole enterprise, the textbook, the classroom, a setting that is often dominated by teacher talk and students listen.

Key words: constructivist teaching strategies, student with special needs, academic outcomes, students with learning disabilities, positive learning, policy makers, indirect instruction, every student succeeds act.

The major purpose of this study was to investigate factors and challenges that hindered effective teaching of mathematics for understanding in senior secondary schools in the Omusati Education Region in Namibia. The study investigated how the participants dealt with identified challenges in the mathematics classrooms in selected senior secondary schools. Further, the study attempted to establish necessary support and / or training opportunities that mathematics teachers might need to ensure effective application of teaching mathematics for understanding in their regular classrooms. The sample was made up of eight senior secondary schools out of the population of 12 senior secondary schools in the Omusati Education Region. The schools were selected from the school circuits using maximum variation and random sampling techniques. Twenty out of 32 mathematics teachers from eight selected senior secondary schools in the Omusati Education Region responded to the interviews and two lessons per participant were observed. Interviews and observations were used to collect data from the 20 senior secondary school mathematics teachers with respect to teaching mathematics for understanding. Frequency tables, pie charts and bar graphs were used to analyze the data collected. The results indicated that teaching for understanding was little observed in mathematics classrooms. Part of the challenges identified were, overcrowded classrooms, lack of teaching and learning resources, lack of support from advisory teachers, and automatic promotions, among others. Mathematics teachers needed induction programmes, in-service training opportunities, and advisory services amongst others in order to be able to teach mathematics effectively. The study recommended that teaching for understanding should be researched in all subjects in Namibian classrooms and should be made clearly understood by all teachers in order to be able to use and apply it during their teaching. New teachers should be provided with induction programmes to give them support and tools at the beginning of their teaching careers. Further research on teaching for understanding should be conducted in other school subjects in Namibia in order to ensure teaching for understanding across the curriculum.

Key words: teaching, understanding.

Although constructivism is a concept that has been embraced my many teachers over the past 1 5 years, the meanings that are attached to this term are varied and often inadequately understood. Teachers need to have a sound understanding of what constructivism means to evaluate its promise and to use it knowledgeably and effectively This paper explicates some of the theoretical background of constructivism and then presents a detailed example in which a traditional classroom lesson and a constructivist version of the same lesson are described and analyzed. Also discussed are pervasive myths and important instructional issues of this widely advocated and increasingly popular philosophical framework for teaching across the entire K-12 curriculum.

Open peer commentary on the article “From Problem Solving to Problem Posing, and from Strategies to Laying Down a Path in Solving: Taking Varela’s Ideas to Mathematics Education Research” by Jérôme Proulx & Jean-François Maheux. Upshot: The aim of this commentary is to extend the work of Proulx and Maheux to include consideration of the teacher-observer whose role (in part) in the mathematics classroom is to ensure that curriculum goals are being met.

This study describes an example of design-based research in which we make theoretical improvements in our understanding, in part based on empirical work, and use these to revise our curriculum and, simultaneously, our evolving theory of the relations between contexts and disciplinary formalisms. Prior to this study, we completed a first cycle of design revisions to a game-based ecological sciences curriculum to make more apparent specific domain concepts associated with targeted learning standards. Of particular interest was using gaming principles to embed standards-based science concepts in the curricular experience without undermining the situative embodiment central to our design philosophy. In Study One reported here, the same first-cycle elementary teacher used the refined second-cycle curriculum, again with high-ability fourth graders. We then analyzed qualitative and quantitative data on student participation and performance to further refine our theory and revise the curriculum. In Study Two, another teacher implemented a further refined second-cycle curriculum with lower achieving fourth graders, including several students labeled as having special needs. We use the design trajectory and results to illustrate and warrant the creation of a situationally embodied curriculum that supports the learning of specific disciplinary formalisms.

Context: Public universities in South Africa are currently facing the challenge of decolonising knowledge. This change requires a review of curriculums, as well as teaching and learning with the goal of embracing the epistemology of the learners, addressing issues such as social justice and transformation. Problem: Human communication is subject to several perceptual errors in both listening and seeing, which challenges the success of the communication in the education system. The ability of the teacher and the learners to effectively communicate with one another is a factor for the success of each reaching their goals. The teacher imparts her knowledge in the classroom, but according to von Foerster, “[i]t is the listener, not the speaker, who determines the meaning of an utterance,” for the listener contextualises this information based on her own past lived experience. Thus, the student’s epistemology and her expression of her understanding is integral in the classroom context and should be actively included into the education system. Method: I present a cybernetic approach to the teacher-learner system, challenging traditional ideas about the role of each actor within the system, with special attention given to Pask’s conversation theory. Results: Early empirical findings suggest that a conversational contextual approach results in higher student involvement and better memory retention among the learners. Conversational approaches that are epistemologically inclusive diffuse social problems where the student groups require their individual worldviews to be reflected within the curriculum. This reduces the friction of competing epistemologies within the education system, moving toward a co-created contextually-driven knowledge system. Implications: Many educators would like deeper engagement from their learners but have not found a way to successfully engage the student group. A cybernetic approach is one method that can be adopted to remedy this. This is particularly useful in contexts where there is cultural diversity and impending social change. Constructivist content: I address von Glasersfeld’s points on human cognition, linking it to Austin’s speech acts.

Key words: Contextual approach, conversation theory, decolonisation of knowledge, education, epistemology, teaching and learning.

Context: South African public universities are currently undergoing a transitional period as they traverse the sensitive road of curriculum redesign that achieves an inclusive approach to education for the goal of the decolonisation of knowledge. Problem: Many classrooms have students from several cultural backgrounds yet in these spaces there is often a single dominant discourse on offer. An ethical question is raised in terms of what content should be addressed in the classroom. Method: An approach to curricula design as a conversation is presented. The philosophical aspects underlying shifts in epistemology are presented following an eclectic approach to curricula design that embraces second-order science in achieving the ongoing goal of decolonisation. The method used to achieve this goal is conversational heterarchical curriculum design assuming non quidem tabula rasa. Students can act as reference points (Nunataks) for curricula design, thus reducing the abstraction in the syllabus. Results: A heterarchical conversational approach offers a platform whereby social justice may be addressed in the classroom by providing a means by which the students’ own epistemology is embraced within the curriculum as the students provide the trajectory for the course content based on their own epistemology. A dynamic curriculum is then available that has immediate use in the communities that the students reside in. Students demonstrate understanding of the content as it is tied to their own way of knowing. Implications: The benefits of this approach include moving away from defining science according to a realist view. Educators may accept the idea that knowledge is not impartial and that method is tied to epistemology. When the observer is included in science, an awareness arises that theories (at least in the social sciences) affect what is studied, which in turn affects society. Constructivist content: The approach builds on von Foerster’s ideas on reflexivity. Pask’s conversation theory is a vehicle for the attainment of reflexive conversational teaching and learning.

Key words: Adaptation, curriculum design, conversation theory, cybernetics, decolonisation, ethics, heterarchy, nunatak, reflexivity, second-order science, ubuntuism.

Radical constructivism grows out of the belief that knowledge is constructed and legitimated by individuals as they make sense of their experiences in particular contexts and drawing on their own histories. Extending this understanding of learning and ways of knowing to girls as they work in the terrain of science, we argue that honoring student experience as the starting place for science instruction fundamentally alters the nature of science, the purpose of teaching and learning science, and the focus of relationships in science class. The implications for this position are extensive: they suggest that the dynamic relationships between language and cultural background of students and teachers alter the ways in which science education historically has enacted discipline, curriculum and pedagogy. We argue that this is particularly important to understand, for science and science education have historically operated within the masculine domain and working with girls in science in ways that respect their (gendered and cultural) construction of knowledge and their experiences, fundamentally alters the enterprise of science – an idea contradictory to most visions of the purposes of education and current reform efforts in science education, even the most liberal.

The merits of Empirical Modelling (EM) principles and tools as a constructivist approach to computer science education are illustrated with reference to ways in which they have been used in teaching topics related to the standard computer science curriculum. The products of EM are interactive models – construals – that serve a sense-making role. Model-building proceeds in an incremental fashion through the construction of networks of definitions that reflect the observables, dependencies and agents associated with a current situation. The three principal case studies discussed (teaching bubblesort, solving Sudoku puzzles, and recognising groups from their abstract multiplication tables) highlight respects in which EM accounts for aspects of computing that cannot be effectively addressed by thinking primarily in terms of abstractions, procedures and mechanisms. The discussion of EM as a constructivist approach to computer science education is set in the context of an analysis of constructivism in computer science published by Ben-Ari in 2001. Reconciling EM’s constructivist epistemology with this analysis involves recognising its pretensions to a broader view of computer science.

Excerpt: The evidence I have reviewed – showing the distributed, visual, and physical nature of mathematical understanding – seems particularly significant when considering that mathematics, for most students, is taught as a series of numbers and abstract concepts. It is probably not surprising that so many students feel that mathematics is inaccessible and uninteresting when they are plunged into a world of abstraction and numbers. Most curriculum standards and published textbooks do not invite visual thinking. Many textbooks provide pictures, but they do not invite students to think visually or to draw their own representations of ideas. When textbook and classroom approaches do encourage visual work, it is usually encouraged as a prelude to the development of abstract ideas rather than a tool for seeing and extending mathematical ideas and strengthening important brain networks.