The representation of geometric concepts in Grade 6 Mathematics textbooks: a socio-cultural analysis

In this study Vygotsky's theory of concept formation is used to gain insight into the representation of geometric concepts in grade six mathematics textbooks. According to Vygotsky, higher order mental functioning is developed when scientific and everyday concepts are dialecfoally linked. The textbook as a mediating artefact has an important role to play in the process of concept formation. To determine if the geometry of space and shape is presented as scientific concepts in the text, content analysis of three randomly sampled grade six mathematics textbooks were conducted. The analysis included an investigation of what misconceptions exist in the text and what level of cognitive demand is required by the textbook tasks and activities. The initial structure for the research was derived from Valverde et al. (2002)'s methodology after which frameworks for the content analysis were developed for the distinction between everyday and scientific concepts, the identification of misconceptions and the classification of levels of cognitive demand. The results not only showed a low prevalence of scientific concepts, but also high incidences of misconceptions put forward in the textbooks. There were few textbook tasks and activities that required problem-solving, thereby limiting the learner to lower order thinking

Math empowerment: a multidisciplinary example to engage primary school students in learning mathematics

This paper describes an educational project conducted in a primary school in Italy (Scuola Primaria Alessandro Manzoni at Mulazzano, near to Milan). The school requested our collaboration to help improve upon the results achieved on the National Tests for Mathematics, in which students, aged 7, registered performances lower than the national average the past year. From January to June, 2016, we supported teachers, providing them with information, tools and methods to increase their pupils’ curiosity and passion for mathematics. Mixing our different experiences and competences (instructional design and gamification, information technologies and psychology) we have tried to provide a broader spectrum of parameters, tools and keys to understand how to achieve an inclusive approach that is ‘personalised’ to each student. This collaboration with teachers and students allowed us to draw interesting observations about learning styles, pointing out the negative impact that standardized processes and instruments can have on the self‐esteem and, consequently, on student performance. The goal of this programme was to find the right learning levers to intrigue and excite students in mathematical concepts and their applications. Our hypothesis is that, by considering the learning of mathematics as a continuous process, in which students develop freely through their own experiments, observations, involvement and curiosity, students can achieve improved results on the National Tests (INVALSI). This paper includes results of a survey conducted by children ‐’About Me and Mathematics‘

Dialogical identities in students from cultural minorities or students categorised as presenting SEN: How do they shape learning, namely in mathematics?

Portuguese schools are multicultural. Diversity is their main characteristic. Portuguese policy documents assume inclusive principles (Ainscow & César, 2006). Students categorised as presenting Special Educational Needs (SEN) attend mainstream schools. Multiculturality and diversity are challenges to the educational system. We assume that teachers need to (re)construct the curricula, conceiving it as a mediating tool (César & Oliveira, 2005). Collaborative work facilitate students’ knowledge appropriation, the development of competencies (Elbers & de Haan, 2005), and the emergence of a learning community (Lave & Wenger, 1991). Students can be empowered and (re)construct their identities, including students whose voices are usually silenced. Identities are conceived as dialogical and conflictive (Hermans, 2001), particularly when the students’ cultures are far away from the school’s cultures, and transitions between them are difficult (César, 2003). These data are from the Interaction and Knowledge project whose main goal was to study and promote collaborative work in formal educational settings. It lasted 12 years, including classes all over the country (5th - 12th grades, 9/10 - 17/18 years old). It had two levels: (1) quasi experimental studies where different types of dyads were studied (César, 1994; Carvalho, 2001); (2) action-research studies based on interpretative/qualitative approaches, inspired in ethnographic methods; collaborative work was implemented during at least a school year (César & Santos, 2006). A ten years follow up was implemented. The cases in discussion were from two 9th grade classes, in two schools near Lisbon. Participant observation (different observers, including external evaluators; audio and/or videotaped), questionnaires, interviews, instruments inspired in projective tasks, students’ protocols and several documents were the data collecting instruments. The data analysis was a systematic and recurrent content analysis. The inductive categories and the interpretations that emerged were then discussed among the participants and by the project research group. The results illuminate that collaborative work and being part of a learning community can be powerful tools that allow students to (re)construct their identities, namely their identity as (mathematics) students. Collaborative work empowered students and had an impact in their life paths even many years after leaving the project. The participants’ accounts illuminate the role of teachers’ practices in their identities, as well as the conflicts these students had to face, namely the ones related to their cultures and to the experiences related to their categorisation as presenting SEN. Learning how to deal with these conflicts is an essential step to school achievement and to avoid exclusion

Developing Students’ Character Through Mathematics Teaching And Learning

The National Education System mandates that the national education serves to develop and shape the character and civilization of the nation. This confirms the quality of Indonesia's human to be developed by each educational unit. This normative national education goals need to be elaborated and implemented in the teaching and learning process, including mathematics teaching and learning. Mathematics teaching and learning should be well designed so that it can be used as a tool in developing positive character of students. Through the mathematics teaching and learning, implicitly or explicitly, can be developed variety of positive characteristics, such as critical thinking skills, logical thinking skills, analytical thinking skills, or meticulous. Such mathematics teaching and learning needs to be done consistently so will lead to habituation to the students that if beyond a certain limit, it belongs to the students' habits and entrenched in him. Key words: mathematics teaching and learning, characte

Building reflective practices in a pre-service math and science teacher education course that focuses on qualitative video analysis

The use of video for in-service and pre-service teacher development has been gaining acceptance, and yet video remains a challenging and understudied tool. Many projects have used video to help pre-service and in-service teachers reflect on their own teaching processes, examine teacher–student interactions, and develop their professional vision. But rarely has video been used in ways more akin to qualitative education research that is focused on student learning. Even more rarely has this focus occurred at the earliest stages of pre-service teaching when students have not yet decided to pursue teaching careers. Yet here we argue that there are benefits to our approach. We examine a course for prospective pre-service math and science teachers at the University of California, Berkeley, that engages participants in qualitative video analysis to foster their reflective practice. This course is unique in that the prospective pre-service teachers engage in qualitative video analysis at a level characteristic of professional educational research, in that their analysis focuses on student learning of math and science content. We describe classroom activities that provide opportunities for the preservice teacher participants to better observe, notice, and interpret their students’ sociocognitive activity. The course culmination project involves participants developing and teaching lessons in a high school classroom. The participants then videotape the lessons and conduct qualitative video analysis. Results include detailed examples of two selected prospective pre-service teachers demonstrating coherent and effective approaches to conceptualizing the learning and teaching of mathematical and science content along with some potential design principles for building reflective practices through qualitative video projects. © 2018 Association for Science Teacher Education

The visibility of models: using technology as a bridge between mathematics and engineering

Engineering mathematics is traditionally conceived as a set of unambiguous mathematical tools applied to solving engineering problems, and it would seem that modern mathematical software is making the toolbox metaphor ever more appropriate. We question the validity of this metaphor, and make the case that engineers do in fact use mathematics as more than a set of passive tools—that mathematical models for phenomena depend critically on the settings in which they are used, and the tools with which they are expressed. The perennial debate over whether mathematics should be taught by mathematicians or by engineers looks increasingly anachronistic in the light of technological change, and we think it is more instructive to examine the potential of technology for changing the relationships between mathematicians and engineers, and for connecting their respective knowledge domains in new ways