Teaching Mathematics With Technology: Using the Video Camera in Mathematical Problem Solving

1993 ◽  
Vol 41 (1) ◽  
pp. 41-43
Author(s):  
M. G. (Peggy) Kelly ◽  
James H. Wiebe
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematical Problem ◽  
Instructional Television ◽  
Video Camera ◽  
Video Technology ◽  
Evaluation Standards ◽  
Reasoning Abilities ◽  
Visual Element ◽  
Effective Use

In the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), technology, including the use of video, is discussed as a way to develop mathematical thinking and reasoning abilities, promote problem solving, and apply mathematics in the classroom. Effective use of the video camera and instructional television may help students construct meaning in mathematical situations. Video technology brings in the outside world and adds excitement to the classroom by contributing a visual element that is often lacking in class discussions.

The Interplay Between Mathematical and Computational Thinking in Primary School Students’ Mathematical Problem-Solving Within a Programming Environment

2021 ◽  
pp. 073563312097993
Author(s):  
Zhihao Cui ◽  
Oi-Lam Ng
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Computational Thinking ◽  
Programming Environment ◽  
Primary School Students ◽  
School Students ◽  
Mathematical Concepts ◽  
Block Based

In this paper, we explore the challenges experienced by a group of Primary 5 to 6 (age 12–14) students as they engaged in a series of problem-solving tasks through block-based programming. The challenges were analysed according to a taxonomy focusing on the presence of computational thinking (CT) elements in mathematics contexts: preparing problems, programming, create computational abstractions, as well as troubleshooting and debugging. Our results suggested that the challenges experienced by students were compounded by both having to learn the CT-based environment as well as to apply mathematical concepts and problem solving in that environment. Possible explanations for the observed challenges stemming from differences between CT and mathematical thinking are discussed in detail, along with suggestions towards improving the effectiveness of integrating CT into mathematics learning. This study provides evidence-based directions towards enriching mathematics education with computation.

Coordinate Geometry: A Powerful Tool for Solving Problems

1990 ◽  
Vol 83 (4) ◽  
pp. 264-268
Author(s):  
Stanley F. Taback
Keyword(s):  
Problem Solving ◽  
Teaching And Learning ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Mathematics Standards ◽  
Problem Situations ◽  
Coordinate Geometry

In calling for reform in the teaching and learning of mathematics, the Curriculum and Evaluation Standards for School Mathematics (Standards) developed by NCTM (1989) envisions mathematics study in which students reason and communicate about mathematical ideas that emerge from problem situations. A fundamental premise of the Standards, in fact, is the belief that “mathematical problem solving … is nearly synonymous with doing mathematics” (p. 137). And the ability to solve problems, we are told, is facilitated when students have opportunities to explore “connections” among different branches of mathematics.

Problem Solving: Is More Than Solving Problems

1998 ◽  
Vol 4 (1) ◽  
pp. 20-25
Author(s):  
Michael G. Mikusa
Keyword(s):  
Problem Solving ◽  
Correct Answer ◽  
Mathematical Problem ◽  
School Mathematics ◽  
Evaluation Standards ◽  
Students First ◽  
Mathematics Class ◽  
General Goals ◽  
Problem Solvers

The curriculum and evaluation Standards for School Mathematics (NCTM 1989) states that one of its five general goals is for all students to become mathematical problem solvers. It recommends that “to develop such abilities, students need to work on problems that may take hours, days, and even weeks to solve” (p. 6). Clearly the authors have not taught my students! When my students first encountered a mathematical problem, they believed that it could be solved simply because it was given to them in our mathematics class. They also “knew” that the technique or process for finding the solution to many problems was to apply a skill or procedure that had been recently taught in class. The goal for most of my students was simply to get an answer. If they ended up with the correct answer, great; if not, they knew that it was “my job” to show them the “proper” way to go about solving the problem.

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.

A Visual Approach to Solving Mixture Problems

1996 ◽  
Vol 89 (2) ◽  
pp. 108-111
Author(s):  
Albert B. Bennett ◽  
Eugene Maier
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Mathematical Problem ◽  
Multiple Representations ◽  
School Mathematics ◽  
Mathematical Problem Solving ◽  
Evaluation Standards ◽  
Conceptual Understandings ◽  
Visual Approach

In the Curriculum and Evaluation Standards for School Mathematics (NCTM 1989), the 9–12 standards call for a shift from a curriculum dominated by memorization of isolated facts and procedures to one that emphasizes conceptual understandings, multiple representations and connections, mathematical modeling, and mathematical problem solving. One approach that affords opportunities for achieving these objectives is the use of diagrams and drawings. The familiar saying “A picture is worth a thousand words” could well be modified for mathematics to “A picture is worth a thousand numbers.” As an example of visual approaches in algebra, this article uses diagrams to solve mixture problems.

scholarly journals “I am part of the group, the others listen to me”: theorising productive listening in mathematical group work

2021 ◽  
Author(s):  
Marie Sjöblom ◽  
Tamsin Meaney
Keyword(s):  
Problem Solving ◽  
Group Work ◽  
Design Research ◽  
Mathematics Classroom ◽  
Mathematical Thinking ◽  
Mathematical Problem ◽  
Sufficient Information ◽  
Educational Design ◽  
Mathematical Problems ◽  
Communication Frameworks

AbstractAlthough group work is considered beneficial for problem solving, the listening that is needed for jointly solving mathematical problems is under-researched. In this article, the usefulness of two communication frameworks for understanding students’ listening is examined, using data from an educational design research study in an upper secondary mathematics classroom in Sweden. From the analysis, it was apparent that these frameworks did not provide sufficient information about the complexity of listening in this context. Consequently, a new framework, “productive listening,” is described which focuses on observable features connected to students’ ability to show willingness to listen and to request listening from others. This framework included the purpose for listening, connected to problem-solving stages, and social aspects to do with respecting the speaker’s contribution as being valuable and feeling that one’s own contribution would be listened to. These two aspects are linked to socio-mathematical norms about expecting to listen to others’ mathematical thinking and to ask clarifying questions about this thinking. By using this framework on the data from the earlier study, it was possible to better understand the complexity of listening in group work about mathematical problem solving.

scholarly journals MENINGKATKAN KEMAMPUAN PEMECAHAN MASALAH DAN PENALARAN MATEMATIS DENGAN LAPS-HEURISTIC DAN PENDEKATAN OPEN-ENDED

2017 ◽  
Vol 2 (1) ◽  
pp. 91-108
Author(s):  
Moch. Rasyid Ridha
Keyword(s):  
Problem Solving ◽  
Mathematical Reasoning ◽  
Mathematical Problem ◽  
Mathematical Problem Solving ◽  
Control Group ◽  
Microsoft Excel ◽  
Control Group Design ◽  
Reasoning Abilities ◽  
Reasoning Test ◽  
Medium Correlation

This article reports the findings from an experimental pretest-posttest control group design conducted by using open-ended approach with Logan avenue problem solving (LAPS)-Heuristic model to investigate students’ mathematical problem solving and reasoning abilities. The study involved 88 grade-10 students from SMA in Bandung. The instrumens of this study are mathematical problem solving test and mathematical reasoning test. By using SPSS 2.0.0 and Microsoft Excel 2013, the study found the open-ended approach with Logan avenue problem solving (LAPS)-Heuristic was able to improve students’ mathematical problem solving and reasoning abilities better than that of conventional approach. Students’ mathematical problem solving and reasoning abilities were classified as mediocore. Furthermore, the study found there was medium correlation between mathematical problem solving and reasoning abilities.

scholarly journals Teacher’s instruction in the reflection phase of the problem solving process

2015 ◽  
Vol 3 (1) ◽  
pp. 55-68
Author(s):  
Meira Koponen
Keyword(s):  
Problem Solving ◽  
Mathematical Thinking ◽  
Mathematical Problem ◽  
Fifth Grade ◽  
Mathematical Problem Solving ◽  
Classroom Discussions ◽  
Reflection Phase ◽  
Mathematical Discussions ◽  
Wrong Direction ◽  
Problem Solving Process

Mathematical problem solving has a key part in developing students’ mathematical thinking. Yet in the Finnish primary school classrooms mathematics lessons are very traditional and have little room for problem solving and mathematical discussions. Although problem solving has been a part of the Finnish curriculum for a few decades, it is the teachers who seem to choose not to include problem solving in the classroom on a regular basis. In this article I take a look at three Finnish fifth grade teachers who took part in a study on problem solving. They each incorporated problem solving in their mathematics lessons approximately once a month, and in this study I focused on one of the problems – an open problem called “The Labyrinth”. In each lesson I chose to focus on the teachers’ instruction in the reflection phase of the problem solving process. When instructing individual students in the reflection phase and during whole-classroom discussions, the teacher has an opportunity to point out the important parts of the problem solving process, help the students make connections and recall key moments of the process. In the reflection phase there is an opportunity to reflect, review and analyze one’s solutions and make generalizations. In the Labyrinth problem the teacher’s own understanding of the solution was an important factor during the instruction and the whole-classroom discussion. If the teacher’s instruction was purely led by the students’ own discoveries and insights, some important points were left unexplored. The teacher can even lead the students to the wrong direction, if he or she hasn’t carefully thought through the solution of the problem beforehand. The problem solving lesson is not just about finding a suitable problem and presenting it to the students, but guiding the students in the process.

Unraveling the Relationship Between Students’ Mathematics-Related Beliefs and the Classroom Culture

2008 ◽  
Vol 13 (1) ◽  
pp. 24-36 ◽  
Author(s):  
Erik De Corte ◽  
Lieven Verschaffel ◽  
Fien Depaepe
Keyword(s):  
Problem Solving ◽  
Learning Environment ◽  
Mathematical Thinking ◽  
Empirical Studies ◽  
Mathematics Learning ◽  
Mathematical Problem ◽  
Reciprocal Relationship ◽  
Classroom Culture ◽  
School Students ◽  
Beliefs About Mathematics

Over the past 2 decades the study of students’ (and teachers’) mathematics-related beliefs has gradually received more and more attention from researchers in the field of educational psychology as well as from scholars in the area of mathematics education. In this article positive beliefs about mathematics and mathematics learning are considered as a major component of competence in mathematics. Results of empirical studies are presented showing that primary school students often have negative and/or naive beliefs about mathematics learning, focused on the phenomenon of “suspension of sense-making” in mathematical problem solving. A design experiment is then described in which a learning environment was developed and implemented, which was intended to improve students’ performance in problem solving as well as their mathematics-related beliefs. This and related work support the hypothesis that changes in the classroom culture and practices can foster students’ mathematical thinking and learning as well as their beliefs, but they do not provide a more in-depth understanding of how the interaction processes and patterns in the classroom influence students’ math learning in general and their mathematics-related beliefs in particular. Using a socioconstructivist perspective as a theoretical framework, the article then discusses a recent investigation that precisely attempts to contribute to unraveling the reciprocal relationship and impact between students’ beliefs, on the one hand, and crucial components of the learning environment, especially teachers’ beliefs and the classroom culture, on the other hand. The article concludes with some critical reflections and suggestions for future inquiry.

scholarly journals Advanced Mathematical Thinking and Students’ Mathematical Learning: Reflection from Students’ Problem-Solving in Mathematics Classroom

2016 ◽  
Vol 5 (3) ◽  
pp. 72 ◽  
Author(s):  
Wasukree Sangpom ◽  
Nisara Suthisung ◽  
Yanin Kongthip ◽  
Maitree Inprasitha
Keyword(s):  
Problem Solving ◽  
Undergraduate Students ◽  
Tertiary Education ◽  
Mathematics Classroom ◽  
Mathematical Thinking ◽  
Mathematical Problem ◽  
Advanced Mathematical Thinking ◽  
Mathematical Learning ◽  
Teaching Concept ◽  
Calculus I

<p>Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students’ inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In order to overcome this learning deficit, it is necessary that the concept of “reflection” be implemented in the teaching of this subject. It is believed that the adoption of this teaching concept will allow students to learn mathematics by themselves. This article is aimed at presenting mathematical problem-solving of undergraduate students on Calculus I. Concrete problems were assigned to students to participate, to improve students’ way of mathematical thinking, and to encourage the students’ mathematical learning and advanced mathematical thinking. The study was a qualitative research project conducted with first-year undergraduate students of Rajamangala University of Technology Phra Nakhon who had enrolled for Calculus I. Data were collected from interviews and field notes, along with video recordings. Findings showed that students succeeded in solving mathematical problems from simple to complex levels and using the subject fundamentals to connect to several methods of higher levels of thinking. Students also created effective means of problem-solving and applied these concepts to solve new problems.</p>

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