Implementing the Standards: Incorporating Mathematical Modeling into the Curriculum

1991 ◽  
Vol 84 (5) ◽  
pp. 358-365
Author(s):  
Frank Swetz
Keyword(s):  
Mathematical Modeling ◽  
Problem Solving ◽  
Original Problem ◽  
Problem Situation ◽  
Multistage Process ◽  
Problem Solving Skills ◽  
Evaluation Standards ◽  
Problem Situations ◽  
Real World Problem ◽  
The Impact

In suggesting plans of action for the reform of mathematics education in North America, NCTM reports have focused strongly on the need to improve problem-solving skills and the need to “do” mathematics. Most recently, these goals have been reiterated and clarified in Curriculum and Evaluation Standards for School Mathematics (NCTM 1989). In discussing the impact of Standard 1: Mathematics as Problem Solving on students in grades 9-12, the report notes that students should be able to “apply the process of mathematical modeling to real-world problem situations” (p. 137). By using the phrase “apply the process of mathematical modeling,” the authors of this standard were most precise in their language. Mathematical modeling is a process and must be taught as a process. Certainly mathematical modeling involves problems, but it should not be considered as merely a collection of interesting problems and solution schemes. More important, modeling is a multistage process that evolves from the identification and mathematical articulation of a problem through its eventual solution and the testing of that solution in the original problem situation. The challenge for teachers is to understand this process of mathematical modeling and to apply it effectively in problem solving.

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.

Becoming Flexible with Functions: Investigating United States Population Growth

1996 ◽  
Vol 89 (5) ◽  
pp. 414-418
Author(s):  
Barry E. Shealy
Keyword(s):  
Mathematical Modeling ◽  
United States ◽  
Real World ◽  
Core Curriculum ◽  
National Council ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Problem Situations ◽  
United States Population ◽  
Real World Problem

Real-world contexts are appearing more often in international curricula, and the arguments for using modeling and applications are broadening (Blum and Niss 1991). The National Council of Teachers of Mathematics, in its Curriculum and Evaluation Standards for School Mathematics (1989), suggests that modeling is a great context for developing problem-solving and reasoning skills. These types of experiences promote communication and allow students to make connections among mathematical ideas and between mathematics and other disciplines. Modeling activities are also consistent with the concept of a core curriculum, offering contexts for a variety of types and depths of problems. It is not surprising that the Curriculum and Evaluation Standards points out that students should be able to “apply the process of mathematical modeling to real-world problem situations” (NCTM 1989, 137)

scholarly journals The Effect of Music Therapy on Problem-Solving Skills

2016 ◽  
Vol 6 (2) ◽  
pp. 169
Author(s):  
Zeinab Sirous Jahedi ◽  
Nasser Amini Khoi
Keyword(s):  
Problem Solving ◽  
Music Therapy ◽  
Sampling Method ◽  
Average Score ◽  
Control Group ◽  
Problem Solving Skills ◽  
Statistical Population ◽  
Quasi Experimental ◽  
And Control ◽  
The Impact

<p>The aim of the present research was study of the impact of music therapy on problem-solving skills of 4 to 6 years old children in Tehran. This research was a quasi-experimental study with pretest-posttest control group. The statistical population was all 4 to 6 years old children in region 2 of Tehran. Using the random sampling method, the study sample was chosen in two experiment (15 individuals) and control (15 individuals) groups.   The experiment group received 12 sessions of music therapy and the control group was waiting for treatment meanwhile. To evaluate the problem-solving skill in children, the three subscales of Wechsler’s Preschool and Primary Scale of Intelligence (WPPSI) were used, including: mazes, cubes and arithmetic.  Analysis of data obtained from the questionnaires was conducted in two parts of descriptive and inferential. The data analysis indicated the significant increase of problem-solving average score of the experiment group compared to the control group.</p>

The Effects of Grouping, Self Esteem, and Locus of Control on Microcomputer Performance and Help Seeking by Mildly Handicapped Students

1987 ◽  
Vol 3 (4) ◽  
pp. 443-460 ◽  
Author(s):  
Merith A. Cosden ◽  
Judy P. English
Keyword(s):  
Locus Of Control ◽  
Problem Solving ◽  
Help Seeking ◽  
Personal Characteristics ◽  
Self Esteem ◽  
Problem Solving Skills ◽  
Math Problem Solving ◽  
Performance Accuracy ◽  
Instructional Literature ◽  
The Impact

The impact of grouping, learning handicap, locus of control, and self esteem on students' performance on a math problem-solving program was assessed in two studies. Outcome measures included: 1) the level of difficulty at which students selected to work, 2) use of a program help command, and 3) response accuracy with and without help. Despite indication from the non-computer instructional literature that grouping would facilitate problem-solving skills for some students, neither problem selections nor performance accuracy varied as a function of group configuration. Personal characteristics influenced problem selections, help seeking, and accuracy in anticipated directions but not consistently. More consistent patterns were noted as a function of initial student competency in math.

scholarly journals Coping Strategies in Patients with Schizophrenia at Naimata Mental Hospital

2020 ◽  
Vol 2 (2) ◽  
pp. 97-109
Author(s):  
Generosus Magnum Marianus Haman ◽  
Tadeus A.L Regaletha ◽  
Dominirsep O Dodo
Keyword(s):  
Problem Solving ◽  
Coping Strategies ◽  
Mental Hospital ◽  
Healing Process ◽  
Cognitive Domain ◽  
Problem Solving Skills ◽  
Medical Diagnoses ◽  
Inpatient Ward ◽  
Motivational Support ◽  
The Impact

Schizophrenia is one of the most common medical diagnoses of mental disorders and is a severe mental disorder that is influenced by biological, psychological and environmental factors. Schizophrenics have cognitive and behavioral disorders, so they have difficulty in determining appropriate coping. Koping is meant a process in order to change the cognitive domain and or behavior constantly to regulate and control external and internal demands and pressures. The purpose of this study was to determine coping strategies in schizophrenia the maintenance stage patients in the inpatient ward of the Naimata Kupang mental hospital. This type of research is descriptive research with a quantitative approach. The population in this study were 70 patients with Schizophrenia. The sample in this study were 30 patients with schisophrenia. The results obtained are that there is no impact from physical health and education on the application of coping strategies to Schizophrenia patients. The impact of positive beliefs (Emotion Focused Coping), problem solving skills (Problem Focused Coping), social and occupational support or socioeconomic status on the application of coping strategies to schizophrenia patients. The type of Emotion Focused Coping used is the highest type of Distancing and the Escape-Avodiance type while for the type of use of Problem Focused Coping there are Confrontative-Coping, Planfull Problem Solving and Seeking Social Support. Hospitals and families are expected to always provide support to patients both in the form of verbal and non verbal, material, and motivational support to be able to support the healing process of schizophrenic patients.  

Developing Preservice Teachers’ Instructional Design Skills Through Case-Based Instruction: Examining the Impact of Discussion Format

2018 ◽  
Vol 70 (4) ◽  
pp. 319-334 ◽  
Author(s):  
Adrie A. Koehler ◽  
Peggy A. Ertmer ◽  
Timothy J. Newby
Keyword(s):  
Preservice Teachers ◽  
Problem Solving ◽  
Class Discussion ◽  
Problem Solving Skills ◽  
Cognitive Levels ◽  
Design Skills ◽  
Based Instruction ◽  
The Impact ◽  
Active Facilitator ◽  
Case Based

For more than 100 years, case-based instruction (CBI) has been an effective instructional method for building problem-solving skills in learners. While class discussion is often included as part of the CBI learning process, the impact on learning is unclear. Furthermore, little research has focused on how specific facilitation strategies influence the development of learners’ problem-solving skills. This study examined the impact of case discussion facilitation strategies on the development of preservice teachers’ problem-solving skills. Specifically, two discussion formats were compared: instructor-facilitated (class discussions guided by instructor-crafted prompts and an active facilitator) and instructor-supported (discussions guided by instructor-crafted prompts only). Results indicated that while preservice teachers’ problem-solving skills improved in both sections of the course, individuals in the instructor-facilitated section demonstrated significantly higher scores on course activities and designed instructional activities at higher cognitive levels compared with preservice teachers who participated in the instructor-supported discussions. Results underscore the importance of an active facilitator in CBI.

Effective Problem-Solving

2017 ◽  
pp. 103-112
Author(s):  
David J. Kolko ◽  
Eric M. Vernberg
Keyword(s):  
Problem Solving ◽  
Problem Situation ◽  
Problem Solving Skills ◽  
Step Process ◽  
Problem Solve ◽  
Effective Problem

This chapter introduces problem-solving skills to children. The content includes an overview of identifying problems, determining options, and making decisions based on goals. Emphasis is placed on reviewing materials from the previous chapter regarding the role of thoughts and interpretations. These skills are generalized to various areas of the child’s life before being applied to fire-related situations. A multi-step process is introduced to help the child learn to, first identify problems and goals, then problem-solve and consider consequences. These skills are then practiced by applying them to a recent problem situation that the child experienced. Worksheets provided in the appendix are used to facilitate the implementation of these activities.

In the classroom: Problem solving with number-picture problem situations

1962 ◽  
Vol 9 (3) ◽  
pp. 155-159
Author(s):  
Juliet Sharff
Keyword(s):  
Problem Solving ◽  
Grade Level ◽  
Problem Situation ◽  
Factual Information ◽  
Number Concepts ◽  
Problem Situations ◽  
Level Number

The class was inspired by the weather to develop its first picture problem situation. The teacher sketched at the chalk-board in response to children's suggestions and guided them so that basic grade-level number concepts were included. For example, the first cooperative class sketch featured a snowy hill and boys and girls with sleds. All data are not pictured; some are provided as factual information. The sketch (Fig. 1) and some of the resulting number problems were similiar to the following.

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.

Links to Literature: Using Representations to Explore Perimeter and Area

2001 ◽  
Vol 8 (1) ◽  
pp. 52-59
Author(s):  
Patricia S. Moyer
Keyword(s):  
Problem Solving ◽  
Word Problems ◽  
Mathematical Problem ◽  
Real Life ◽  
Problem Situation ◽  
Correct Operation ◽  
Problem Situations ◽  
Mathematical Problems ◽  
Mathematical Word Problems ◽  
Computational Processes

In an elementary school classroom, as in real life, the lines between the content areas should be blurred, particularly between mathematical problem solving and mathematical situations contextualized in good literature. For that reason, I always look for interesting books about mathematical situations. Why use children's literature to teach mathematics? A good story often places mathematical problems in the context of familiar situations and is similar to, yet a much more elaborate version of, mathematical word problems. Assertions that children's inability to solve word problems results from their inability to read or to compute effectively simply are not true. The problem is that children do not know how to choose the correct operation or sequence of operations to solve the problem. To solve a problem situation presented in words, children need to be able to connect computational processes with appropriate calculations. Their difficulties lie in the fact that children simply do not understand the mathematics well enough conceptually to make the connection with the problem- solving situation. Using books with authentic problem situations may help children see that learning computation serves a real-life purpose.

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