Teaching Elementary Mathematics with Educational Robotics

Current education reforms call for engaging students in learning science, technology, engineering, and mathematics (STEM) in an integrative way. This critical case study of one fourth grade teacher investigated the use of educational robots (ER) not only for teaching coding, but as an instructional support in teaching mathematical concepts. To support teachers in teaching coding in an integrative and logical manner, our team developed the Collective Argumentation Learning and Coding (CALC) approach. The CALC approach consists of three elements: choice of task, coding content, and teacher support for argumentation. After a cohort of elementary teachers completed a professional development course, we followed them into their classrooms to support and document implementation of the CALC approach. Data for this case consisted of video recordings of two lessons, a Pre-interview, and Post-interview after each lesson. Research questions included: How does an elementary teacher use the CALC approach (integrative STEM approach) to teach mathematics concepts with ER? What are the teacher’s perspectives towards teaching mathematics with ER using an integrative STEM approach? Results from this critical case provide evidence that teachers can successfully integrate ER into the mathematics curriculum without losing coherence of mathematics topics and while remaining sensitive to students’ needs

Conceptions of Proof – In Research and Teaching

This chapter first analyses and compares mathematicians' and mathematics educators' different conceptualisations of proof and shows how these are formed by different professional backgrounds and research interests. This diversity of views makes it difficult to precisely explain what a proof is, especially to a novice at proving. In the second section, we examine teachers', student teachers' and pupils' proof conceptions and beliefs as revealed by empirical research. We find that the teachers' beliefs clearly revolve around the questions of what counts as proof in the classroom and whether the teaching of proof should focus on the product or on the process. The third section discusses which type of metaknowledge about proof educators should provide to teachers and thus to students, how they can do this and what the intrinsic difficulties of developing adequate metaknowledge are

An application of Habermas' rationality to the teacher's actions: Analysis of argumentation in two classrooms

International audienceIn this paper, I argue that Habermas' components of epistemic, teleologic, and communicative rationality provide insight into the differences in teachers' support for collective argumentation. I examine the teacher's supportive actions in two different classrooms. In their interactions with students, the teachers emphasize different components of rationality. I suggest that teachers may act in ways to support students' development of components of rationality by asking different kinds of questions and raise the question of whether it is useful to consider the components separately

An application of Habermas' rationality to the teacher's actions: Analysis of argumentation in two classrooms

International audienceIn this paper, I argue that Habermas' components of epistemic, teleologic, and communicative rationality provide insight into the differences in teachers' support for collective argumentation. I examine the teacher's supportive actions in two different classrooms. In their interactions with students, the teachers emphasize different components of rationality. I suggest that teachers may act in ways to support students' development of components of rationality by asking different kinds of questions and raise the question of whether it is useful to consider the components separately

The genus Lycianthes (Solanaceae, Capsiceae) in Mexico and Guatemala

Lycianthes, the third most species-rich genus in the Solanaceae, is distributed in both the New and Old Worlds and is especially diverse in Mexico. Here we provide an identification key, taxonomic descriptions, distribution maps, and illustrations of specimens, trichomes, flowers, and fruits for the 53 known Lycianthes taxa of Mexico and Guatemala. The new combination Lycianthes scandens (Mill.) M.Nee is made and replaces the name Lycianthes lenta (Cav.) Bitter, which is placed in synonymy. Within L. scandens, two varieties are recognized (Lycianthes scandens var. scandens and Lycianthes scandens var. flavicans (Bitter) J.Poore & E.Dean, comb. nov.). In addition, one new species (Lycianthes rafatorresii E.Dean, sp. nov.) is described from eastern Mexico, and 10 names (either recognized taxa or synonyms of recognized taxa) are lectotypified, including the names Solanum heteroclitum Sendtn., S. rantonnetii Carrière, and S. synantherum Sendtn. The species L. multiflora Bitter and L. synanthera (Sendtn.) Bitter are excluded from the treatment, as research indicates that they do not occur in Mexico and Guatemala, however full synonymy for both names is given

Impact of a Content and Methods Course Sequence on Prospective Secondary Mathematics Teachers\u27 Beliefs

In this article, we report on a study of beliefs about mathematics, teaching, and proof conducted with six prospective secondary mathematics teachers as they completed a two-semester sequence of a content course and a methods course. The initial beliefs of the participants were identified using interview and survey data, and potential shifts in beliefs were examined through further interview and survey data combined with classroom observations and written work. While their beliefs about mathematics and proof appeared to be relatively stable, their beliefs about teaching shifted from a more teacher-centered view to beliefs that foreground the activities and understandings of the students. These shifts are analyzed using the construct of belief structures, and activities and events from the courses that may have facilitated the shifts are identified. The results are consistent with the literature in some respects, such as the stability of the participants’ beliefs about mathematics. On the other hand, our results present new information about how prospective secondary mathematics teachers’ beliefs about teaching may be impacted