Using Polya’s Problem Solving Process in the Mathematics Classroom to Prepare for Taks

2017 ◽  
pp. 233-235
Author(s):  
Sandra Nite
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Problem Solving Process

How Does Your Mathematical Garden Grow?

2007 ◽  
Vol 13 (2) ◽  
pp. 68-76
Author(s):  
Shari A. Beck ◽  
Vanessa E. Huse ◽  
Brenda R. Reed
Keyword(s):  
Problem Solving ◽  
Mathematics Classroom ◽  
Real Life ◽  
Middle School Mathematics ◽  
Content Standards ◽  
Mathematical Communication ◽  
Mathematical Ideas ◽  
Application Problem ◽  
Multiple Process ◽  
Problem Solving Process

Imagine a middle school mathematics classroom where students are actively engaged in a real-life application problem incorporating multiple Process and Content Standards as outlined by NCTM (2000). Sounds of mathematical communication arise as students use multiple representations to help connect mathematical ideas throughout the problem-solving process. Students apply various types of reasoning and explore alternate methods of proof while working attentively on applications that incorporate Number and Operations, Algebra, Geometry, and Measurement.

scholarly journals Analysis of Teacher-Student Interaction in the Joint Solving of Non-Routine Problems in Primary Education Classrooms

2020 ◽  
Vol 12 (24) ◽  
pp. 10428
Author(s):  
Beatriz Sánchez-Barbero ◽  
José María Chamoso ◽  
Santiago Vicente ◽  
Javier Rosales
Keyword(s):  
Problem Solving ◽  
Primary Education ◽  
Mathematics Classroom ◽  
Student Interaction ◽  
Process Selection ◽  
Teacher Student ◽  
Cognitive Difficulty ◽  
Teacher Student Interaction ◽  
Teachers And Students ◽  
Problem Solving Process

The analysis of teacher–student interaction when jointly solving routine problems in the primary education mathematics classroom has revealed that there is scarce reasoning and little participation on students’ part. To analyze whether this fact is due to the routine nature of the problems, a sample of teachers who solved, together with their students, a routine problem involving three questions with different cognitive difficulty levels (task 1) was analyzed, describing on which part of the problem-solving process (selection of information or reasoning) they focused their interaction. Results showed that they barely focused the interaction on reasoning, and participation of students was scarce, regardless of the cognitive difficulty of the question to be answered. To check whether these results could be due to the routine nature of the problem, a nonroutine problem (task 2) was solved by the same sample of teachers and students. The results revealed an increase in both reasoning and participation of students in processes that required complex reasoning. This being so, the main conclusion of the present study is that including nonroutine problem solving in the primary education classroom as a challenging task is a reasonable way to increase students’ ability to use their own reasoning to solve problems, and to promote greater teacher–student collaboration. These two aspects are relevant for students to become creative, critical, and reflective citizens.

Using Writing Strategies in Math to Increase Metacognitive Skills for the Gifted Learner

2017 ◽  
Vol 40 (1) ◽  
pp. 43-47 ◽  
Author(s):  
Heather Knox
Keyword(s):  
Academic Success ◽  
Problem Solving ◽  
Mathematics Classroom ◽  
Metacognitive Skills ◽  
Problem Solving Skills ◽  
Gifted Learners ◽  
Solution Strategies ◽  
Multiple Strategies ◽  
Problem Solving Process ◽  
Metacognitive Ability

Metacognition is vital for a student’s academic success. Gifted learners are no exception. By enhancing metacognition, gifted learners can identify multiple strategies to use in a situation, evaluate those strategies, and determine the most effective given the scenario. Increased metacognitive ability can prove useful for gifted learners in the mathematics classroom by improving their problem-solving skills and conceptual understanding of mathematical content. Implemented effectively, writing is one way to increase a student’s metacognitive ability. Journal writing in the mathematics classroom can help students by clarifying their thought process while further developing content knowledge. Implementing writing can lead to increased understanding of the problem, identification of additional strategies that can be used to solve the problem, and reflective thinking during the problem-solving process. Reflective writing in mathematics can help students evaluate solution strategies and identify strengths and areas of improvement in their mathematical understanding.

scholarly journals Learner metacognition and mathematics achievement during problem-solving in a mathematics classroom

2013 ◽  
Vol 9 (3) ◽  
Author(s):  
Stephan Du Toit ◽  
Gawie Du Toit
Keyword(s):  
Problem Solving ◽  
Mathematics Achievement ◽  
Mathematics Classroom ◽  
Metacognitive Awareness ◽  
Quantitative Methodology ◽  
Two Phase ◽  
Phase Approach ◽  
And Mathematics ◽  
Problem Solving Process ◽  
Metacognitive Awareness Inventory

In this investigation the level of learner metacognition as well as the level of mathematics achievement during problem-solving in a mathematics classroom was investigated. Learner metacognition plays a pivotal role during the problem-solving process and when the problem-solving is successful it can be viewed as evidence of high achievement in mathematics. Data were collected from one intact Grade 11 class of 25 girls. A word problem was given to the learners to solve individually. The learners recorded their thoughts relating to the problem as well as the calculations that corresponded to their thoughts. The level of achievement of the learners were analysed by noting calculation and conceptual errors in the solving of the problem. The learners’ level of metacognition was determined by analysing the written account of their thoughts and comparing it to the items on an adapted Metacognitive Awareness Inventory (MAI). Strong evidence was obtained from the recorded thoughts of learners that their metacognitive behaviours corresponded to the first three phases of Polya’s problem-solving model, but there was no evidence of metacognitive behaviours that corresponded with Polya’s fourth phase (Looking back) of problem-solving. It was further determined that the learners’ metacognitive awareness during the problem-solving session did not relate to the subscale Evaluation of the MAI. It was thus evident that the learners were not reflecting on the validity and correctness of their own solution. In this study a qualitative one- phase approach was used to examine the process of intervention, as well as a two-phase approach on the qualitative data which was also embedded in the quantitative methodology prior to and after the intervention phase (two-phase approach).

Moving to Solution

2013 ◽  
Vol 60 (6) ◽  
pp. 403-409 ◽  
Author(s):  
K. Werner ◽  
M. Raab
Keyword(s):  
Problem Solving ◽  
Embodied Cognition ◽  
Cognitive Functions ◽  
Problem Space ◽  
Arm Swing ◽  
String Problem ◽  
Problem Solving Process ◽  
Problem Solving Task ◽  
Bodily Movements

Embodied cognition theories suggest a link between bodily movements and cognitive functions. Given such a link, it is assumed that movement influences the two main stages of problem solving: creating a problem space and creating solutions. This study explores how specific the link between bodily movements and the problem-solving process is. Seventy-two participants were tested with variations of the two-string problem (Experiment 1) and the water-jar problem (Experiment 2), allowing for two possible solutions. In Experiment 1 participants were primed with arm-swing movements (swing group) and step movements on a chair (step group). In Experiment 2 participants sat in front of three jars with glass marbles and had to sort these marbles from the outer jars to the middle one (plus group) or vice versa (minus group). Results showed more swing-like solutions in the swing group and more step-like solutions in the step group, and more addition solutions in the plus group and more subtraction solutions in the minus group. This specificity of the connection between movement and problem-solving task will allow further experiments to investigate how bodily movements influence the stages of problem solving.

Proses Berpikir Logis Siswa Sekolah Dasar Bertipe Kecerdasan Logis Matematis dalam Memecahkan Masalah Matematika

2014 ◽  
Vol 2 (2) ◽  
Author(s):  
Liska Yanti Pane ◽  
Kamid Kamid ◽  
Asrial Asrial
Keyword(s):  
Problem Solving ◽  
Learning Process ◽  
Qualitative Method ◽  
Logical Thinking ◽  
Think Aloud ◽  
Process Data ◽  
Thinking Process ◽  
Problem Solving Process ◽  
Problem Solving Strategy ◽  
Solving Strategy

This research aims to describe logical thinking process of a logical-mathematical intelligence student. We employ qualitative method to disclose the subject’s learning process. Data are collected by interview and modified think aloud methods. The results show that subject has capability to find and organize problems and data correctly. Subject describes conditions that are needed to do the steps of problem solving strategy. The steps are done systematically until the end of problem solving process.

Proses Berpikir Kreatif Siswa Tipe Linguistik dalamPemecahan Masalah Biologi

2014 ◽  
Vol 2 (2) ◽  
Author(s):  
Imelda Aisah Sarip ◽  
Kamid Kamid ◽  
Bambang Hariyadi
Keyword(s):  
Problem Solving ◽  
Data Collection ◽  
Creative Thinking ◽  
Research Data ◽  
Think Aloud ◽  
The Subject ◽  
Thinking Process ◽  
Problem Solving Process ◽  
The Given

The aim of this research is to describe creative thinking process of linguistic type student in biology problem solving. This research is conducted to linguistic intelligence type of subject at SMPN 6 Kota Jambi. SL the subject was selected based on the aim of the research. Data collection is conducted by interview and a modified think aloud method. Data is analyzed based on creative thinking process purposed by Polya.The result of this research shows that SL could find and arrange the given problems and collect data correctly and appropriately. The problem solving steps is done systematically to the end of problem solving process. The last steps problem solving, SL does checking while doing scratching to make sure that the written answers meet her need.

Spoken Natural Language Dialog Systems

1995 ◽  
Author(s):  
Ronnie W. Smith ◽  
D. Richard Hipp
Keyword(s):  
Problem Solving ◽  
Natural Language ◽  
Error Correction ◽  
User Model ◽  
Dialog Systems ◽  
Problem Solving Process ◽  
Processing Architecture ◽  
Dialog Processing

As spoken natural language dialog systems technology continues to make great strides, numerous issues regarding dialog processing still need to be resolved. This book presents an exciting new dialog processing architecture that allows for a number of behaviors required for effective human-machine interactions, including: problem-solving to help the user carry out a task, coherent subdialog movement during the problem-solving process, user model usage, expectation usage for contextual interpretation and error correction, and variable initiative behavior for interacting with users of differing expertise. The book also details how different dialog problems in processing can be handled simultaneously, and provides instructions and in-depth result from pertinent experiments. Researchers and professionals in natural language systems will find this important new book an invaluable addition to their libraries.

Systems thinking, a consilience of values and logic

2005 ◽  
Vol 24 (4) ◽  
pp. 259-274
Author(s):  
Sameer Kumar ◽  
Thomas Ressler ◽  
Mark Ahrens
Keyword(s):  
Decision Making ◽  
Problem Solving ◽  
Systems Thinking ◽  
Qualitative Reasoning ◽  
Colleges And Universities ◽  
Decision Makers ◽  
Modern World ◽  
Problem Solving Process ◽  
Problem Solvers

This article is an appeal to incorporate qualitative reasoning into quantitative topics and courses, especially those devoted to decision-making offered in colleges and universities. Students, many of whom join professional workforce, must become more systems thinkers and decision-makers than merely problem-solvers. This will entail discussion of systems thinking, not just reaching “the answer”. Managers will need to formally and forcefully discuss objectives and values at each stage of the problem-solving process – at the start, during the problem-solving stage, and at the interpretation of the results stage – in order to move from problem solving to decision-making. The authors suggest some methods for doing this, and provide examples of why doing so is so important for decision-makers in the modern world.

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