Engaging Students through Technology

2004 ◽  
Vol 9 (6) ◽  
pp. 300-305
Author(s):  
A. Kursat Erbas ◽  
Sarah Ledford ◽  
Drew Polly ◽  
Chandra H. Orrill
Keyword(s):  
Problem Solving ◽  
Mathematics Teaching ◽  
Mathematical Knowledge ◽  
Multiple Representations ◽  
Time Constraints ◽  
Mathematical Concepts ◽  
Problem Situations ◽  
Use Of Technology ◽  
And Mathematics ◽  
Support Students

The use of technology provides an effective way for promoting multiple representations in problem solving and mathematics. Multiple representations allow students to experience different ways of thinking, develop better insights and understandings of problem situations, and increase comprehension about mathematical concepts. Even with all the benefits of multiple representations, however, teachers find it difficult to incorporate open-ended problem solving that capitalizes on these representations because of time constraints and limitations of traditional mathematics teaching. Technology can become a vital and exciting tool in allowing students to explore multiple representations and mathematical situations and relationships (NCTM 2000). Technology empowers students who may have limited mathematical knowledge and limited symbolic and numeric manipulation skills to investigate problem situations. Technology not only frees the students from tedious and repetitive computations but actually encourages the use of multiple representations. Students can easily move from a spreadsheet to a graph or geometry software in their quest for solutions to a given problem. When supported by the teacher, these tools of technology provide students with opportunities to investigate and manipulate mathematical situations to observe, experiment with, and make conjectures about patterns, relationships, tendencies, and generalizations. Teachers should emphasize and encourage the use of multiple representations to support students' thinking and understanding of concepts and problem-solving situations in all areas of mathematics.

scholarly journals MERIA – Conflict Lines: Experience with Two Innovative Teaching Materials

2021 ◽  
Author(s):  
Željka Milin Šipuš ◽  
Matija Bašić ◽  
Michiel Doorman ◽  
Eva Špalj ◽  
Sanja Antoliš
Keyword(s):  
Mathematics Education ◽  
Mathematics Teaching ◽  
Field Trials ◽  
Teaching Materials ◽  
Mathematical Concepts ◽  
Innovative Teaching ◽  
Problem Situations ◽  
The Rich ◽  
Support Students ◽  
Curriculum Topics

The design of inquiry-based tasks and problem situations for daily mathematics teaching is still a challenge. In this article, we study the implementation of two tasks as part of didactic scenarios for inquiry-based mathematics teaching, examining teachers’ classroom orchestration supported by these scenarios. The context of the study is the Erasmus+ project MERIA – Mathematics Education: Relevant, Interesting and Applicable, which aims to encourage learning activities that are meaningful and inspiring for students by promoting the reinvention of target mathematical concepts. As innovative teaching materials for mathematics education in secondary schools, MERIA scenarios cover specific curriculum topics and were created based on two well-founded theories in mathematics education: realistic mathematics education and the theory of didactical situations. With the common name Conflict Lines (Conflict Lines – Introduction and Conflict Set – Parabola), the scenarios aim to support students’ inquiry about sets in the plane that are equidistant from given geometrical figures: a perpendicular bisector as a line equidistant from two points, and a parabola as a curve equidistant from a point and a line. We examine the results from field trials in the classroom regarding students’ formulation and validation of the new knowledge, and we describe the rich situations teachers may face that encourage them to proceed by building on students’ work. This is a crucial and creative moment for the teacher, creating opportunities and moving between students’ discoveries and the intended target knowledge.

Cultural Contexts in Science and Mathematics Teaching to Young Children

2019 ◽  
Vol 15 (2) ◽  
Author(s):  
Gina C. Obiakor ◽  
Kristen E. Obiakor ◽  
Charles C. Obiakor ◽  
Festus E. Obiakor
Keyword(s):  
Teacher Preparation ◽  
Mathematics Teaching ◽  
Mathematical Knowledge ◽  
Teaching Science ◽  
National Origin ◽  
Innovative Teaching ◽  
Cultural Contexts ◽  
Language And Gender ◽  
And Gender ◽  
And Mathematics

AbstractScience and mathematics have international and global origins and impacts that are intertwined with national origin, race, culture, religion, language, and gender, to mention a few. This means that scientific and mathematical knowledge goes beyond myopic narrow confines. Put another way, teaching science and mathematics without explicating their phenomenal foundations and influences is tantamount to “scotching the snake, but not killing it.” In this article, we use cases to discuss cultural contexts in teaching science and mathematics. Embedded in our discussion are issues of teacher preparation, innovative teaching, and disparities in public health and environmental health.

A Problem is Something You Don't Want to Have: Problem Solving by Kindergartners

2005 ◽  
Vol 12 (3) ◽  
pp. 146-154
Author(s):  
Lynne Outhred ◽  
Sarah Sardelich
Keyword(s):  
Problem Solving ◽  
Mathematics Teaching ◽  
Teaching And Learning ◽  
Social Process ◽  
Mathematical Concepts ◽  
Mathematics Teaching And Learning ◽  
Mental Actions

Although Adrian, when asked by his teacher what a problem is, was adamant that problems are to be avoided, educators believe problem solving is central to mathematics teaching and learning (NCTM 2000). Problem solving supports students as they apply their skills and their knowledge of mathematical concepts and processes to a range of different contexts and as they construct knowledge by reflecting on their own physical and mental actions. When children solve problems together, learning is a social process in which they learn not only from the teacher but also by discussing, arguing, and negotiating with their peers.

Investigations: Vehicles for Learning and Doing Mathematics

1996 ◽  
Vol 178 (2) ◽  
pp. 35-49 ◽  
Author(s):  
Carole Greenes
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Solution Method ◽  
Professional Organizations ◽  
Mathematical Concepts ◽  
Educational Benefits ◽  
Problem Situations ◽  
Mathematics Educators ◽  
Solution Methods ◽  
Problem Solving Strategies

Professional organizations of mathematics educators and mathematicians are calling for major reforms in the teaching and learning of mathematics. Among those reforms are a shift in emphasis in curriculum from mastery of lists of unrelated mathematical concepts and skills to exploration of rich mathematical topics and problem situations, and a shift in learning from memorizing and replicating algorithmic procedures to investigating and solving complex problems. To help students achieve proficiency in solving problems, the curriculum must focus on development of the major concepts of mathematics, the enhancement and enlargement of students' repertoires of problem-solving strategies and reasoning methods, and the refinement of communication and collaboration skills. Because they present intriguing problems whose solutions or solution methods are not immediately obvious, and require the application of concepts from different areas of mathematics, and, in some instances, knowledge from other content areas, investigations are powerful vehicles for helping students achieve expertise in solving problems. The nature of investigations and their educational benefits are described. Three types of investigations, whimsical, real, and mathematical, are defined and illustrated. For each investigation, the mathematical content and problem-solving strategies are identified, and a solution method is presented. The responsibilities of the teacher, before, during and after an investigation are described.

Supporting Online Collaborative Learning in Mathematics

2011 ◽  
pp. 1987-1993
Author(s):  
Rod Nason ◽  
Earl Woodruff
Keyword(s):  
Collaborative Learning ◽  
Mathematical Knowledge ◽  
Knowledge Building ◽  
Multiple Representations ◽  
Mathematical Concepts ◽  
Online Collaborative Learning ◽  
Building Activity ◽  
Multiple Cycles ◽  
Math Problems

Most school math problems do not require multiple cycles of designing, testing and refining (Lesh & Doerr, 2003), and therefore, do not elicit the collaboration between people with different repertoires of knowledge that most authentic math problems elicit (Nason & Woodruff, 2004). Another factor that limits the potential of most school math problems for eliciting knowledgebuilding discourse is that the answers generated from school math problems do not provide students with much worth discussing (Bereiter, 2002a). Another factor that has prevented most students from engaging in ongoing discourse and other mathematical knowledge-building activity within CSCL environments is the limitations inherent in most computerbased mathematical representational tools (Nason et al., 1996). Most of these tools are unable to carry out the crucial knowledge-building functions of: 1) generating multiple representations of mathematical concepts, 2) linking the different representations, and 3) transmitting meaning, sense and understanding.

Technology Tips: A Mathematical Look at a Free Throw Using Technology

1996 ◽  
Vol 89 (9) ◽  
pp. 774-779
Author(s):  
Charles Vonder Embse ◽  
Arne Engebretsen
Keyword(s):  
Problem Solving ◽  
Real World ◽  
Mathematics Curriculum ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Mathematical Concepts ◽  
Evaluation Standards ◽  
Free Throw ◽  
Problem Situations ◽  
Real World Problem

Technology can be used to promote students' understanding of mathematical concepts and problem-solving techniques. Its use also permits students' mathematical explorations prior to their formal development in the mathematics curriculum and in ways that can capture students' curiosity, imagination, and interest. The NCTM's Curriculum and Evaluation Standards for School Mathematics (1989) recommends that “[i]n grades 9–12, the mathematics curriculum should include the refinement and extension of methods of mathematical problem solving so that all students can … apply the process of mathematical modeling to real-world problem situations” (p. 137). Students empowered with technology have the opportunity to model real-world phenomena and visualize relationships found in the model while gaining ownership in the learning process.

Strategies for Problem Solving, Critical Analysis, and Goal Setting

2021 ◽  
Vol 43 (1) ◽  
pp. 41-55
Author(s):  
Zoi A. Traga Philippakos ◽  
Hailey Mathison Wilson ◽  
Karen Picerno
Keyword(s):  
Problem Solving ◽  
Goal Setting ◽  
Oral Language ◽  
Critical Analysis ◽  
Thinking Skills ◽  
Transfer Of Knowledge ◽  
Knowledge And Skills ◽  
Challenging Tasks ◽  
And Mathematics ◽  
Support Students

Problem solving requires the application of critical reading and thinking skills and the use of relevant strategies to reach a solution. Independent learners are able to apply taught strategies across contexts and often complete challenging tasks unassisted. The purpose of this paper is to explain how a process of analysis of assignments and evaluation can be applied in reading, writing, and with modifications in mathematics. This work draws on genre-based strategies, on oral language and dialogic pedagogy, and demonstrates how they can be applied across the curriculum to support students’ transfer of knowledge and skills from writing instruction to responses to reading and mathematics aiding them in reflection and eventually independence. Further, the paper provides guidelines for teachers’ explanations to promote critical thinking, questioning, and goal setting.

Design and Implementation of Computational Modeling for Learning Mathematical Concepts

2013 ◽  
pp. 128-146
Author(s):  
Shelby P. Morge ◽  
Mahnaz Moallem ◽  
Chris Gordon ◽  
Gene Tagliarini ◽  
Sridhar Narayan
Keyword(s):  
Problem Solving ◽  
Computational Models ◽  
Web Search ◽  
Mathematics Teacher Education ◽  
Design Development ◽  
Mathematical Concepts ◽  
Mathematical Practices ◽  
Technology Project ◽  
Information Technology Project ◽  
Support Students

The Common Core State Standards (CCSS) call for a change in the way mathematics is taught. The mathematical practices outlined by the CCSS call for mathematics as a problem-solving endeavor, rather than routine exercises and practice. A quick Web search can provide mathematics teachers with an abundance of workshops and courses, examples, and videos of the different mathematical practices to help them understand what they mean and look like in practice. However, those examples do not go far in changing the current culture of mathematics instruction. In this chapter, the authors discuss current US mathematics instructional practices and how the CCSS are asking for distinctly different teaching practices. In addition, the authors share how the innovative Using Squeak to Infuse Information Technology Project (USeIT) sidestepped traditional mathematics instructional approaches and utilized problem-solving activities and the development of computational models to support students’ learning of STEM concepts. The authors illustrate how the design, development, and implementation of a Squeak Etoys and Problem-Based Learning (PBL) activity addresses the CCSS expectations for mathematics content, practice for learning, and assessment, and discuss what this means for mathematics teacher education and professional development.

Construction of Mathematical and Financial Concepts based on Realistic Mathematics Education

2020 ◽  
Vol 22 (5) ◽  
pp. 226-253
Author(s):  
Susana Machado Ferreira ◽  
Vanilde Bisognin
Keyword(s):  
Mathematics Education ◽  
Course Design ◽  
Financial Education ◽  
Realistic Mathematics Education ◽  
Mathematical Concepts ◽  
Problem Situations ◽  
Video Recordings ◽  
Realistic Mathematics ◽  
Data Collection And Analysis ◽  
And Mathematics

Context: This article presents the excerpt of a qualitative Doctorate in Science and Mathematics Teaching research. Objectives: To describe the results of a study carried out with students from an initial teacher training course. Design: From the development of a didactic sequence, a connection was sought between the ideas of Financial Education anchored by Realistic Mathematics Education (RME). Environment and participants: The study was conducted with 11 students from a Pedagogy course at a Brazilian university. Data collection and analysis: The data were collected through written records of the activities performed by the students, the observations of the classes, and the audio and video recordings. The methodology of analysis was defined considering the procedures of Content Analysis, using the modality of thematic analysis that occurs in three phases: pre-analysis, exploration of the material and treatment of the results. Results: The discussions of the problem situations developed according to the principles of RME, aroused in the students interest, curiosity, autonomy, cooperation and reflection on financial situations, showing that this approach contributed in a significant way, with the development of the didactic sequence. Conclusions: This study shows that by teaching mathematics from everyday contexts, several benefits can be achieved, such as motivation and interest to learn mathematics, and by understanding mathematical concepts, students will be able to use them for the organization of their financial life, and in a conscious, responsible and autonomous way, improve their quality of life.

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