Prospective Teachers’ Semiotic Conflicts in Computing Probabilities from a Two-Way Table
Carmen Batanero, José M. Contreras, Carmen Díaz & Ernesto Sánchez
pp. 3-16 | Article Number: mathedu.2015.001
The aim of this research was to assess the common knowledge of elementary probability in a sample of 183 prospective primary school teachers using and open-ended task, where teachers had to compute simple, compound and conditional probability from data presented in a two-way table. We base on theoretical ideas from the onto-semiotic approach to perform a semiotic analysis, in which we describe the mathematical objects and processes involved in the solutions of the tasks. Participants in the sample showed a weak common knowledge to compute simple, compound and conditional probabilities from a two-way table: they confused simple, compound and conditional probability; exchanged condition and event in conditional probabilities; confused probability and frequency or the union of events with the intersection. The semiotic analysis is used to provide and explanation for these errors in terms of semiotic conflicts. This list of difficulties expands what was found in previous research and may be used to reinforcing the preparation of prospective teachers to teach probability.
Keywords: assessment, simple, compound and conditional probability, teacher knowledge, 2x2 tables
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Prospective Teachers’ Personal Mathematics Teacher Efficacy Beliefs and Mathematical Knowledge for Teaching
pp. 17-36 | Article Number: mathedu.2015.002
The purposes of this study were as follows: (1) To examine how K-8 prospective teachers’ personal mathematics teacher efficacy beliefs vary when they are measured in the context of four written mathematical teaching scenarios, and (2) To examine the extent to which K-8 prospective teachers’ personal mathematics teacher efficacy beliefs and mathematical knowledge for teaching are aligned. Forty-two prospective teachers participated in the study. Participants were first asked to respond to four written mathematical teaching scenarios that required responding, as a teacher, to student questions about fraction concepts. Prospective teachers then evaluated how effective they believed their responses would be for developing student understanding. Approximately two weeks later, participants were asked to write mathematical explanations for four written mathematical tasks that paralleled the teaching scenarios and were then asked to evaluate their own mathematical understanding of each task. Different patterns emerged based on whether prospective teachers exhibited high or low mathematical knowledge for teaching on a particular task. Additionally, reported self-evaluations of mathematical knowledge for teaching were helpful for understanding the nature of prospective teachers’ personal teacher efficacy beliefs.
Keywords: mathematical knowledge for teaching, prospective teacher education, efficacy beliefs
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Teaching and Assessing Higher Order Thinking in the Mathematics Classroom with Clickers
Jim Rubin & Manikya Rajakaruna
pp. 37-51 | Article Number: mathedu.2015.003
Many schools have invested in clicker technology, due to the capacity of the software to track formative assessment and the increased motivation that students show for incorporating technology in the classroom. As with any adoption of new software that demands amending pedagogy and learning applications, the extent to which clickers are living up to expectations has not yet become apparent. The present study sought to explore the potential of using clickers to teach the reasoning processes behind solving higher order thinking word problems in a mathematics class. A pilot study was conducted with a college algebra class to refine questions used in the coursework and field test a survey to measure student attitudes towards the teaching methodology. The main study took place over the fall semester with a college algebra class (N=21). Results showed increased student motivation and acumen for using the technology and higher test scores, but frustration on the part of both the teacher and students when trying to apply the pedagogy for the purpose of learning higher order thinking reasoning processes. The potential for the technology to offer an alternative for formative assessment was a strong positive element.
Keywords: clickers, college algebra, higher order thinking, mathematics
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