Technology Tips: Multiple Representations and Connections Using Technology

1998 ◽  
Vol 91 (1) ◽  
pp. 62-67
Author(s):  
Charles Vonder Embse ◽  
Vernon W. Yoder
Keyword(s):  
Problem Solving ◽  
Mathematics Teacher ◽  
Functional Relationship ◽  
Multiple Representations ◽  
Problem Situation ◽  
Dynamic Nature ◽  
Static Picture ◽  
Independent Variable ◽  
The Difference

George Polya's famous four-step problem-solving method begins with understanding the problem through various means, including identifying the unknown, establishing the conditions of the problem, separating the conditions into more convenient parts, and drawing a figure or picture (Polya 1945). As a mathematics teacher, the first question I often ask students when they seek help in doing a problem is “Did you draw a picture?” Many times, the answer to my questions is “Yes, but it didn't help.” The difficulty might be that the picture representing the problem, although correct, does not really represent the dynamic nature of the problem situation. Drawing a static picture representing one state of a functional relationship does not guarantee that students will “see” how changes in the independent variable produce corresponding changes in the dependent variable. A better situation would be to draw several pictures representing various stages of the problem. An even better situation would be to draw a dynamic picture in which the drawing changes as the independent variable changes. Like the difference between a videotape of a football play and a newspaper picture of the play, a dynamic picture can be used repeatedly as a tool to investigate in detail what really happens.

Anticipating Student Responses to Improve Problem Solving

2007 ◽  
Vol 12 (9) ◽  
pp. 504-511
Author(s):  
Ann H. Wallace
Keyword(s):  
Problem Solving ◽  
Mathematics Teacher ◽  
Careful Planning ◽  
Actual Problem ◽  
Student Responses ◽  
The Difference ◽  
Problem Solve ◽  
Teaching Problem ◽  
Or Task ◽  
The Way

I have been a Mathematics Teacher and Educator throughout all four publications of the Standards documents (NCTM 1991, 1995, 1989, and 2000). Over the years, while concentrating on improving various aspects of my teaching, specifically, improving my students' ability to problem solve, I have been perplexed to see students pick numbers out of a problem and perform an operation with no regard for the context. To address this issue by teaching problem-solving lessons made me realize that I did not know the difference between students solving a problem and actual problem solving. A lesson beginning with a problem or task does not make it a problem-solving lesson, especially when students would inevitably solve it the way I had intended. Instead of problem solving, my students were trying to figure out what I was thinking. To prevent the temptation of leading students in this way of thinking required careful planning of problem-solving lessons.

scholarly journals Effect of tennis education on problem solving skills in university studentsTenis eğitiminin üniversite öğrencilerinin problem çözme becerisi üzerine etkisi

2017 ◽  
Vol 14 (1) ◽  
pp. 1 ◽  
Author(s):  
Serife Vatansever ◽  
Güçlü Özen
Keyword(s):  
Problem Solving ◽  
University Students ◽  
Control Group ◽  
Problem Solving Skills ◽  
Significant Difference ◽  
Post Test ◽  
Independent Variable ◽  
The Difference ◽  
Turkish Language ◽  
And Control

This study has been carried out with the aim of analyzing and comparing problem solving skills of the students taking or not taking tennis education.   Total 80 university students, 40 of whom taking tennis education and 40 of whom not taking these education have participated on the basis of volunteering. This research was conducted in an experimental model. In this study, Problem Solving Inventory adapted into Turkish language by Şahin, Şahin and Heppner (1993) and developed by Heppner and Peterson (1982) has been used. While the trail group participated in a tennis training program of 3 days a week, 2 hours a day and a total of 3 months, the control group continued their normal life without participating in any regular work.Statistical findings have been obtained by means of SPSS 20.0 packaged software.  The Independent-t test was applied to examine the difference between the experimental and control groups and the effect of the gender independent variable. And for calculating the difference of pre-test and posttest, Test of Paired Sample was applied  According to the parameter of problem solving skill, there was a significant difference between value of the pre-test and value of the post-test on experimental group (<0,05), pbut There was no significant difference between pre-test and post-test values depending on gender variable (>0,05). As a result, it is thought that exercises have a positive change on problem solving skills on the students who taking tennis education. ÖzetBu çalışma tenis eğitimi alan ve almayan öğrencilerin, problem çözme becerilerini inceleme ve karşılaştırma amacı ile yapılmıştır. Çalışmaya tenis eğitimi alan 40 öğrenci ile bu eğitimi almayan 40 öğrenci olmak üzere toplam 80 öğrenci gönüllü olarak katılmıştır.  Araştırma deneme modelinde tasarlanmıştır. Çalışmada, Hepner ve Peterson (1982) tarafından geliştirilen, Türkçe’ye uyarlaması ise Şahin, Şahin ve Heppner (1993) tarafından yapılan Problem Çözme Envanteri kullanılmıştır. Deneme grubu haftada 3 gün, günde 2 saat ve toplamda 3 aylık bir tenis eğitimi programına katılırken kontrol grubu herhangi bir düzenli çalışmaya katılmadan normal yaşamlarına devam etmiştir. Verilerin değerlendirilmesinde ve hesaplanmış değerlerin bulunmasında SPSS 20.0 istatistik paket program kullanılmıştır. Deneme ve kontrol grupları arasındaki fark ve cinsiyet bağımsız değişkeninin etkisinin incelenmesi için Bağımsız-t testi yapılmıştır. Ön test-son test arasındaki farklılığın tespiti için ise, Bağımlı-t testi yapılmıştır.  Araştırmada, problem çözme becerisi değişkenine göre, deney grubu ön test-son test değerleri arasında anlamlı farklılık bulunmuş (p<0,05), cinsiyet değişkenine bağlı olarak ön test-son test değerleri arasında anlamlı farklılık bulunamamıştır p>0,05). Sonuç olarak, tenis eğitimi alan öğrencilerde problem çözme becerileri egzersize bağlı olumlu yönde değişiklik gösterdiği düşünülmektedir.

PENINGKATAN KEMANDIRIAN BELAJAR SISWA SMP MELALUI PEMBELAJARAN BERBASIS MASALAH

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Tanti Jumaisyaroh Siregar
Keyword(s):  
Problem Based Learning ◽  
Mathematic Teacher ◽  
Self Regulated Learning ◽  
Regulated Learning ◽  
Quasi Experimental ◽  
Independent Variable ◽  
Direct Learning ◽  
The Difference ◽  
And Control ◽  
Learning Data

The purposes of this research were to know: the difference of improvement in self-regulated learning of students that given problem-based learning with students that given  direct learning. The type of this research is a quasi-experimental research by taking samples from the existing population. The variable of this research consist of independent variable that is problem based learning model while the dependent variable isself regulated learning of student.The population of this research is all students of SMP Swasta Ar-rahman Percut and the sample of this research is grade eight with taken sample two classes (experiment and control)  with total 60 students. The instrument of this research were: scale of self-regulated learning. Data that have been collected then analyzed and performed hypothesis testing by using T-test. Based of the results analysis, it showed that: improvment  of the students’ self-regulated learning that given problem-based learning was higher than the students’ ability that given direct learning His then, suggested that problem-based learning be used as an alternative for mathematic teacher to improved students’ ability in mathematical critical thinking and self-regulated learning.

scholarly journals Profile of the Change in Depression during Proton-Pump Inhibitor Therapy in Patients with Gastroesophageal Reflux Disease: Influence of the Mucosal Break

2021 ◽  
Vol 18 (11) ◽  
pp. 5964
Author(s):  
Chia-Liang Wu ◽  
Chien-Lin Chen ◽  
Shu-Hui Wen
Keyword(s):  
Gastroesophageal Reflux Disease ◽  
Gastroesophageal Reflux ◽  
Proton Pump ◽  
Reflux Disease ◽  
Proton Pump Inhibitor Therapy ◽  
Linear Regression Models ◽  
Independent Variable ◽  
The Difference ◽  
Mucosal Break ◽  
The Impact

Given the frequent concomitance between depression and gastroesophageal reflux disease (GERD), it is important to evaluate the change of depression in patients with GERD, especially considering the presence of esophageal mucosal breaks (MB). This study aimed to examine the change in the levels of depression in patients with GERD during proton-pump inhibitors (PPI) therapy. We designed a prospective cohort study to explore the profile of the alteration in depression with respect to the impact of esophageal MB. This study recruited 172 eligible patients with GERD between February 2016 and May 2018. The change in depression was defined as the difference between the respective Taiwanese Depression Questionnaire (TDQ) scores obtained at baseline and after PPI therapy. Multivariate linear regression models were used to estimate the factors associated with the change in depression. The results revealed statistically significant improvements in the TDQ score (mean score: baseline = 13.2, after PPI therapy = 10.9, p < 0.01, Cohen’s d = 0.30) during PPI therapy for GERD. Moreover, the MB was an independent variable associated with changes in the TDQ score [B = 3.31, 95% confidence interval (CI): (1.12, 5.51), p < 0.01] and the improvement in depression [odds ratio = 0.38, 95% CI: (0.17, 0.86), p = 0.02]. Our findings revealed that depressive symptoms improved slightly following PPI therapy. Moreover, MB was an unfavorable prognostic factor for the improvement in depression.

Ingestion rate and body size in phagotrophic organisms

1990 ◽  
Vol 68 (2) ◽  
pp. 313-317 ◽  
Author(s):  
Gerard M. Capriulo ◽  
David Lints ◽  
Martin Lewinter
Keyword(s):  
Body Weight ◽  
Functional Relationship ◽  
Ingestion Rate ◽  
Volume Ratio ◽  
Functional Design ◽  
Physiological Constraints ◽  
Unit Body Weight ◽  
The Difference ◽  
Log Linear ◽  
Physical Phenomena

A general functional relationship between body weight (10−11 to 108 g) and ingestion rate has been found to exist throughout the protistan and metazoan kingdoms. Results, based on a mathematical interpretation of standardized, quantitative data, indicate that ingestion rate is a log–log linear function (i.e., power function) of body weight (I = a W0.829 for cold-blooded forms and I = a W0.778 for warm-blooded forms, where I = ingestion rate and W = body weight). The slopes of the cold-blooded and warm-blooded regression lines are not significantly different from each other (i.e., they are parallel). This allows one to use the difference between the respective curves to estimate the weight-specific cost of warm-bloodedness. Such an analysis of the data indicates that a warm-blooded organism must ingest about ten times more food per unit body weight than cold-blooded forms. This functional relationship may be a manifestation of the physiological constraints placed on organisms by surface area to volume ratio phenomena, related to absorptive surfaces, mouth areas, and body volumes. The present analysis suggests that flexibility in functional design is limited by physical phenomena which affect phenotypic plasticity.

scholarly journals LOGICAL REASONING ANALYSIS BASED ON HIPPOCRATES PERSONALITY TYPES

Aksioma ◽  
2020 ◽  
Vol 9 (2) ◽  
pp. 57-73
Author(s):  
Nurdin Nurdin ◽  
Ita Sarmita Samad ◽  
Sardia Sardia
Keyword(s):  
Problem Solving ◽  
Mathematical Problem ◽  
Logical Reasoning ◽  
Personality Types ◽  
The Body ◽  
Mathematical Problem Solving ◽  
Different Types ◽  
Ways Of Thinking ◽  
The Difference ◽  
Descriptive Qualitative

Abstract: The theory distinguishes human based on four different personality types such as: sanguine, choleric, melancholic, and phlegmatic. Different types of personality caused by differences in the dominant fluid in the body. These differences will result in terms of behavior, ways of thinking and to get along. The type of this research that is descriptive qualitative which it is describing the logical reasoning based on Hippocrates personality types. The logical reasoning is analyzed through the four types of personality in relation to mathematical problem solving. The Analysis is done based on the logical reasoning indicator/ subindicator and the steps of problem solving stated by Polya. The result shows that there is a reasoning difference on each type of personalities. The difference can be terms of the strenght or the weakness. Sanguine is quicker in understanding problems and communicating results, choleric is more accelerated in work, melancholic is more perfect at work, and  phlegmatic is superior in terms of accuracy. Keywords: Logical reasoning, Hippocrates, sanguine, choleric, melancholic, phlegmatic

scholarly journals MEASURING STUDENTS’ PROBLEM-SOLVING SKILLS ON DIRECT CURRENT CIRCUITS WITH MULTIPLE REPRESENTATIONS

2020 ◽  
Vol 8 (3) ◽  
pp. 725-736
Author(s):  
Maria Dewati ◽  
A. Suparmi ◽  
Widha Sunarno ◽  
Sukarmin ◽  
C. Cari
Keyword(s):  
Problem Solving ◽  
Physics Education ◽  
Multiple Choice ◽  
Multiple Representations ◽  
Assessment Instruments ◽  
Multiple Choice Questions ◽  
Multiple Representation ◽  
Problem Solving Skills ◽  
Electrical Circuits ◽  
Physics Problems

Purpose of study: This study aims to measure the level of students' problem-solving skills, using assessment instruments in the form of multiple-choice tests based on the multiple representation approach on DC electrical circuits. Methodology: This research is a quantitative descriptive involving 46 students of physics education. Students are asked to solve the problem of DC electrical circuits on 12 multiple choice questions with open reasons, involving verbal, mathematical, and picture representations. Data were analyzed by determining means and standard deviations. Main findings: The results of the study showed that there were 3 levels of students' problem-solving skills, namely 7 (15%) students in the high category, 22 (48%) students in the medium category and 17 (37%) students in the low category. Applications of this study: The implication of this research is to continuously develop assessment instruments based on multiple representations in the form of various types of tests, to help students improve their conceptual understanding, so students can solve physics problems correctly. The novelty of this study: Researchers explain the right way to solve physics problems, 1) students are trained to focus on identifying problems, 2) students are accustomed to planning solutions using a clear approach, to build an understanding of concepts, 3) students are directed to solve problems accordingly with understanding the concepts they have built.

scholarly journals Measuring the effectiveness of online problem solving for improving academic performance in a probability course

2022 ◽  
Author(s):  
José Antonio González ◽  
Mónica Giuliano ◽  
Silvia N. Pérez
Keyword(s):  
Problem Solving ◽  
Confidence Interval ◽  
Student Performance ◽  
Online Homework ◽  
Methodological Issues ◽  
Engineering Programs ◽  
Technological Diversity ◽  
The Subject ◽  
The Difference ◽  
Written Test

AbstractResearch on impact in student achievement of online homework systems compared to traditional methods is ambivalent. Methodological issues in the study design, besides of technological diversity, can account for this uncertainty. Hypothesis This study aims to estimate the effect size of homework practice with exercises automatically provided by the ‘e-status’ platform, in students from five Engineering programs. Instead of comparing students using the platform with others not using it, we distributed the subject topics into two blocks, and created nine probability problems for each block. After that, the students were randomly assigned to one block and could solve the related exercises through e-status. Teachers and evaluators were masked to the assignation. Five weeks after the assignment, all students answered a written test with questions regarding all topics. The study outcome was the difference between both blocks’ scores obtained from the test. The two groups comprised 163 and 166 students. Of these, 103 and 107 respectively attended the test, while the remainder were imputed with 0. Those assigned to the first block obtained an average outcome of −1.85, while the average in the second block was −3.29 (95% confidence interval of difference, −2.46 to −0.43). During the period in which they had access to the platform before the test, the average total time spent solving problems was less than three hours. Our findings provide evidence that a small amount of active online work can positively impact on student performance.

scholarly journals German Teacher Educators' Conceptions About Teaching Problem Solving in Mathematics Classroom - an Obstalce to a Large-Scale Dissemination?!

2018 ◽  
Vol 12 (2) ◽  
pp. 77-97
Author(s):  
Ana Kuzle
Keyword(s):  
Professional Development ◽  
Problem Solving ◽  
Mathematics Teacher ◽  
Large Scale ◽  
Teacher Educators ◽  
Mathematics Classroom ◽  
Research Report ◽  
Mathematics Teacher Educators ◽  
Set Up ◽  
Teaching Problem

Problem solving in Germany has roots in mathematics and psychology but it found its way to schools and classrooms, especially through German Kultusministerkonferenz, which represents all government departments of education. For the problem solving standard to get implemented in schools, a large scale dissemination through continuous professional development is very much needed, as the current mathematics teachers are not qualified to do so. As a consequence, one organ in Germany focuses on setting up courses for teacher educators who can “multiply” what they have learned and set up their own professional development courses for teachers. However, before attaining to this work, it is crucial to have an understanding what conceptions about teaching problem solving in mathematics classroom mathematics teacher educators hold. In this research report, I focus on mathematics teacher educators’ conceptions about problem solving standard and their effects regarding a large-scale dissemination.

Sign in / Sign up

Export Citation Format

Share Document