Search results for: Problem solving
Page 1/4 34 items
Balancing competing demands: Enhancing the mathematical problem posing skills of prospective teachers through a mathematical letter writing initiative
Responding to mathematical problems is a core activity in classrooms. The problems that teachers select determine the mathematical content, processes and nature of mathematical inquiry occurring in classrooms and thereby contribute to the development of mathematical skills and dispositions. Selecting, designing or reformulating mathematical problems is a critical skill, then, for prospective and practising teachers. This study explores the influence of a mathematical letter writing initiative in developing the problem posing skills of 28 prospective primary teachers. We examine the characteristics of mathematical problems designed by prospective teachers, and their understandings of what constitutes a good mathematical problem, prior to and following completion of a 12-week letter writing initiative with 10–11-year-old children. Analysis of the data reveals the benefits of engaging in the initiative as evidenced in improvements in several problem characteristics. There was an increase in the number of multiple approach and multiple solution problems and in the level of cognitive demand of problems posed. The challenge of posing non-traditional problems, alongside the competing demands of building in opportunities for success, may have diminished participants’ ability to evaluate and attend to the cognitive demand of problems.
Updated: Aug. 02, 2022
In this study, the authors aimed investigated to identify elements that constitute the practical rationality of mathematics teaching. Specifically, they focused on the assumptions that participants made regarding what should constitute the launch of a problem-based lesson. The authors hypothesized that different assumptions may lead to tensions and dilemmas when launching a problem. The authors conclude that the manner in which teachers set up a problem can reduce the opportunities for high-level mathematical reasoning. Hence, they argue that the launch is important for teachers to maximize student engagement and mathematical reasoning. They also note that teachers’ decisions about launching a problem can enable students to exercise conceptual agency.
Updated: May. 24, 2018
Preparing Teacher-Students for Twenty-First-Century Learning Practices (PREP 21): A Framework for Enhancing Collaborative Problem-Solving and Strategic Learning Skills
The purpose of this paper is describe the authors' pedagogical framework for the twenty-first-century learning practices in teacher education. The authors argue that teacher education has been challenged by the need to enhance the new teachers’ ability to implement new pedagogical approaches and take advantage of ICT for teaching and learning. Since the current way of working in teacher education does not match well enough the needs of twenty-first-century learning environments, such as inquiry-based learning approaches that focus upon collaboration and social forms of learning, as well as the use of ICT. According to the authors' approach, pre-service teachers are educated in a way they are supposed to teach their future students.
Updated: Feb. 14, 2018
What Factors Support or Inhibit Secondary Mathematics Pre-service Teachers’ Implementation of Problem-Solving Tasks during Professional Experience?
This qualitative study examined the factors that support or inhibit secondary mathematics pre-service teachers’ implementation of problem-solving tasks during professional experience. The results showed that even though the majority of pre-service teachers reported having beliefs compatible with using problem-solving tasks, the secondary students’ ability, preparation time, and the cooperating teacher were key factors that inhibited pre-service teachers’ implementation of problem-solving tasks.
Updated: Jul. 09, 2017
Preparing Physical Education Preservice Teachers to Design Instructionally Aligned Lessons through Constructivist Pedagogical Practices
The purpose of this study was to explore the extent to which the constructivist pedagogies employed by teacher educators assisted preservice teachers (PSTs) in their understanding and construction of knowledge about instructional alignment. The findings revealed that PSTs varied in their articulation of the various elements of instructional alignment that were captured in the rich task. Furthermore, the results showed that through peer interaction in the form of discussion with critical friends, probing and challenging one another’s insights and interpretations, group problem solving and sharing of outcomes through various pedagogical strategies.
Updated: Nov. 01, 2016
By adopting a scenario-based approach, teacher educators and others designing online environments can help prepare students for the types of challenges they will face in communities and classrooms after graduation.. Solving complex problems inherent in a scenario-based approach affords students the opportunity to tackle ill-formed problems, integrate multiple perspectives, and use higher order thinking. These outcomes were among the goals of a redesign of online courses in an early childhood education degree program.
Updated: Aug. 31, 2016
The Shift From 'Learner/Doer of Mathematics' to 'Teacher of Mathematics': A Heuristic for Teacher Candidates
In this article, the authors present research on the implementation of a process for providing candidates learning experiences that help teacher candidates make the shift from 'student' to 'teacher.' Utilizing the Mathematics as Teacher Heuristic (MATH) process, prospective high school mathematics teachers explore rich problems by solving the task, analyzing samples of student work, designing a solution key, and modifying the task.
Updated: Jul. 04, 2016
Making Connections in Practice: How Prospective Elementary Teachers Connect to Children’s Mathematical Thinking and Community Funds of Knowledge in Mathematics Instruction
This research examines the ways prospective elementary teachers (PSTs) made connections to children’s mathematical thinking and children’s community funds of knowledge in mathematics lesson plans. The authors identified three distinct levels of connections to children’s mathematical thinking and their community funds of knowledge evidenced in PSTs’ work. Findings describe how these connections reflected different points on a learning trajectory.
Updated: Dec. 29, 2015
This study examined the problem-solving skills of preservice teachers through the use of an online video case with question prompts. This research was a three-level video presentation by two-grade-level between subjects factorial design. The findings indicate that, although the participants drew from at least one teaching knowledge component at any stage of the problem-solving process, they rarely used their content knowledge. The authors provided explanations for preservice teachers’ ability to use their teaching knowledge in video-based problem solving. In addition, the results reveal that the elementary education majors generated pedagogical and content solutions at a higher level than the secondary education counterparts.
Updated: Dec. 20, 2015
Based on findings from a semester-long study, this paper examines the development of Samoan prospective teachers’ mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The authors were also interested in assessing the impact of using the innovative tools, mental computations and creative authentic investigations on PPTs attitudes towards mathematics. The findings reveal that both the positive and negative variations suggested that learning experiences in the FYMM course influenced general perceptions about mathematics learning and therefore, one’s actions when confronted with problems to solve.
Updated: Dec. 09, 2015